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Secondary school reform in mathematics: a case study of a high school in southern California

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SECONDARY SCHOOL REFORM IN MATHEMATICS:
A CASE STUDY OF A HIGH SCHOOL IN SOUTHERN CALIFORNIA

by

Herbert Taylor Nichols, III

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
DOCTOR OF EDUCATION

August 2007

Copyright 2007 Herbert Taylor Nichols, III

ii
DEDICATION
This dissertation is dedicated to my wife. Your patience, words of
encouragement, and advice have been greatly appreciated and I hereby acknowledge
them. Words can never express how much your support has meant to me during this
doctoral journey, where we were two on a voyage of learning. Your companionship
and counsel have been essential to not only this accomplishment, but also the success
I have experienced in the Los Angeles Unified School District and the University of
Southern California Phi Delta Kappa chapter. I thank God for the blessing of you in
my life.

iii
ACKNOWLEDGMENTS
I would like to acknowledge and thank mother and father who have always
emphasized the importance of education. My mother who was an elementary school
teacher and my father who as an aerospace engineer helped to put Apollo 11 on the
moon always were proud and encouraging about my academic success. Thank you
so much for all the moments of kindness you showed.
I would like to give a special thank you to two of my undergraduate
professors. Dr. Clyde Greer and Dr. John Stead who lead, taught, and mentored me
in the Social Studies of History and Political Thought. Thanks to you I have an
informed view of what has come before, what is present in current American
society, and what is likely to occur in the future of our world.
I would like to thank Mr. Mike Oliver and Mr. Phil Medeiros who were
excellent mentors during my early years of teaching at my first school site. Mike
you are a caring educator who is always willing to assist with eager new teachers
like me. Good new teachers are eager, but need direction from veterans like you.
Phil I respect your no nonsense way about you. You are always willing to share
common sense, especially where stupidity abounds.
To Dr. David Marsh, my dissertation chair, I say thank you. Thank you for
the opportunity to learn from you. Thank you for all the organizational strategies
you shared to help all students in the dissertation group succeed. I would also like
to thank Dr. Russo and Dr. Olsen for the revision advice you gave me during this
process. It is always a pleasure to see you and learn from you.

iv
TABLE OF CONTENTS

DEDICATION……………………………………………………………………...ii

ACKNOWLEDGEMENTS…..…………………………………………………… iii

LIST OF TABLES ………………………………………………………………..viii

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

ABSTRACT………………………………………………………………………..xi
CHAPTER 1: INTRODUCTION TO THE STUDY ................................................ 1
Overview…………………………………………………………………...……1
Statement of the Problem ................................................................................... 11
Purpose of the Study .......................................................................................... 12
Research Questions ............................................................................................ 13
The Importance of the Study .............................................................................. 13
Assumptions ....................................................................................................... 15
Lim itations .......................................................................................................... 15
Delimitations ...................................................................................................... 16
Definition of Terms ........................................................................................... 16
Organization of the Study ................................................................................... 20
CHAPTER 2: REVIEW OF THE LITERATURE .................................................. 22
Status of Academic Performance ....................................................................... 22
National Objective Standards ....................................................................... 22
International Comparative Studies and the Persistent Achievement Gap .... 23
The Performance and Achievement Gap ...................................................... 25
Importance of Mathematics, Achievement in College, and Economic Future .. 27
Importance of Mathematics .......................................................................... 27
Achievement in College ............................................................................... 28
Economic Future .......................................................................................... 30
Standards, Curriculum, Teachers, Reform, New Designs, and School Features 31
State Standards as an Effort ......................................................................... 31
Improved Curriculum and Better Prepared Teachers ................................... 32
Related Reform Efforts ............................................................................... 34
New Policy and Initiatives .......................................................................... 35
School Features ............................................................................................ 39
Instructional Leadership General and Specific .................................................. 41
Features of Effective Instructional Leadership ............................................ 41
CHAPTER 3: RESEARCH METHODOLOGY ..................................................... 59
Sampling Criteria and Process ........................................................................... 61
Selected School Profile ...................................................................................... 62

v
Student Achievement ......................................................................................... 63
Participants in the Study ..................................................................................... 64
Site Administrators ....................................................................................... 64
Key Leaders .................................................................................................. 64
Classroom Teachers ..................................................................................... 64
Instrumentation ................................................................................................... 65
Intellectual Frameworks ..................................................................................... 66
Framework for Effective Mathematics Instruction ..................................... 68
Framework for Research Question 3: The Change Process ......................... 69
Data Collection Instruments ................................................................................ 73
Instrument 1: School Profile ........................................................................... 73
Instrument 2: Key Leader Interview Guide ................................................... 75
Instrument 3: Teacher Interview Guide ......................................................... 76
Instrument 4: Math Teacher Questionnaire and Teacher Questionnaire ...... 76
Data Collection .................................................................................................... 77
Data Analysis ........................................................................................................ 79
Validity and Reliability ......................................................................................... 81
Conclusion ............................................................................................................ 82

CHAPTER 4: DATA FINDINGS, ANALSYIS AND DISCUSSION ..................... 83
Data Findings ........................................................................................................ 84
Research Question 1: Student Achievement in Mathematics ........................ 84
California Standards Test (CST) Scores .................................................. 85
Increased Algebra I Enrollment ............................................................... 85
Advanced Placement Passing Rates ......................................................... 87
California High School Exit Exam (CAHSEE) Pass Rates ..................... 88
Summary of RQ1 Findings ...................................................................... 90
Research Question 2: Policy Initiatives and Improved Curriculum .............. 91
Policy ........................................................................................................ 91
Existing Policies and School Response ............................................ 91
School Design .......................................................................................... 92
Student Performance Assessments ................................................... 92
Curriculum ........................................................................................ 94
School Culture ................................................................................... 94
Learning Activities ............................................................................ 96
Math Program Design .............................................................................. 96
Summary of RQ2 Findings .................................................................... 100
Research Question 3: Change Process .......................................................... 101
Structural Frame ....................................................................................... 101
Human Resources Frame ......................................................................... 102
Political Frame .......................................................................................... 104
Symbolic Frame ........................................................................................ 105
Summary of RQ3 Findings ..................................................................... 107

vi
Research Question 4: Strong Instructional Leadership .................................... 107
Vision for Learning ................................................................................ 107
Supervision and Monitoring of Instruction ........................................... 110
Community of Reflection and Data Driven Decision-Making
Analysis .................................................................................................... 111
Culture of Teaching and Learning ......................................................... 114
Summary of RQ4 Findings ..................................................................... 115
Research Question 5: Leadership Strategies .................................................. 116
Summary of RQ5 Findings ..................................................................... 120
Analysis and Discussion ....................................................................................... 120
1
st
Topic: Increased Enrolment in Higher Level Classes ............................. 121
2
nd
Topic: Using Benchmark Assessments as School Design ..................... 123
3
rd
Topic: Math Program Design that Works ................................................ 124
4
th
Topic: Personnel Addition – Central to Change ...................................... 126
5
th
Topic: Strategies to Overcome a Lack of Subject Matter Competency. 127

CHAPTER 5: SUMMARY, CONCLUSIONS, AND IMPLICATIONS .............. 129
Summary of Study ................................................................................................. 129
Background of the Study ................................................................................. 129
Purpose of the Study ........................................................................................ 130
Methods of Study ............................................................................................ 131
Frameworks .............................................................................................. 131
Sampling ................................................................................................... 133
Instruments ............................................................................................... 133
Data Collection and Analysis ................................................................. 134
Summary of Findings ............................................................................................ 136
Key Findings ..................................................................................................... 136
Research Question 1: Student Achievement in Mathematics .............. 136
Research Question 2: Policy Initiatives and Improved Curriculum ... 136
Research Question 3: The Change Process ........................................... 138
Research Question 4: Strong Instructional Leadership ........................ 138
Research Question 5: Leadership Strategies ......................................... 139
Conclusions About Findings in Study ............................................................ 140
Implications for Practice ....................................................................................... 142
Future Research ................................................................................................ 142
District Boards and Key District Leaders ...................................................... 142
Site Administrators ........................................................................................... 143
Teachers ............................................................................................................ 145
School on behalf of Students ........................................................................... 146

REFERENCES ....................................................................................................... 147

vii
APPENDICES ....................................................................................................... 155
Appendix A: CST School Profile Detail .......................................................... 156
Appendix B: Key Leader Interview Guide ....................................................... 160
Appendix C: Teacher Interview Guide ............................................................ 164
Appendix D: Math Teacher Questionnaire ...................................................... 165
Appendix E: Teacher Questionnaire ................................................................ 171

viii
LIST OF TABLES
1. Relationships of Data Collection Instruments .................................................. 65
2. Bolman and Deal’s Four Frames ……………………………………………...69
3. Instructional Leadership Framework…………………………………………..71
4. Strategies to Overcome a Lack of Subject Matter Competency……………… 75
5. Number Correlation…………………………………………...………….…... 79
6. Questionnaire Mean Score Analysis………………………….………….……80
7. Departmental Questionnaire Mean Score Analysis………………………….. 80
8. Questions relating to NCLB………………………………………………….. 92
9. Questions relating to Common and Benchmark Assessments………………...93
10. Questions relating to School Culture………………………………………….95
11. Questions relating to Math Program Design…………………………………..99
12. Questions relating to Achievement Priorities and Strategic Planning……….102
13. Questions relating to the Math Coach and Hiring Practices…………………103
14. Questions relating to the Political Obstacles and Community Support……...104
15. Questions relating to the Expectations, Visions, and School Climate……….106
16. Questions relating to the Influence of Site Leaders………………………….109
17. Questions relating to the Political Obstacles and Community Support……...110
18. Questions relating to the Community and Data Driven Actions……………..112

ix
19. Questions relating to the Value of Professional Development……………….115
20. Strategies to Overcome a Lack of Subject Matter Competency……………...117
21. Questions relating to Dilemmas and the use of Shared Expertise……………119
22. Summary of Data Collection Instruments to Research Questions……………134
A-1. CST School Profile Detail………………………………………………….. 157

x
LIST OF FIGURES
9. Framework for Effective School Design ......................................................... 67
10. Effective Math Programs ................................................................................. 68
11. Assessment of Principal’s Expertise in Math…………..……………………..74
12. Enrollment in Algebra 1 over the last six school years………..……………...86
13. Increase of Students Taking Algebra 1………………………………………. 87
14. 12
th
Grade Advanced Placement Test Results………………………………...88
15. African American CAHSEE Passing Rate……………………………………89
16. Hispanic CAHSEE Passing Rate……………………………………………...90

xi
ABSTRACT
The purpose of this study is to find out how urban high schools that have
experienced significant gains in math performance in their students looking at two
areas of concern. First, to find out how urban high schools bring together policy
initiatives, coupled with how urban high schools increase school site best practices to
bring about improved math performance in their schools. Second, to find out how
instructional leadership, if effectively carried out, improves high school math
performance for students.
This dissertation begins in Chapter 1 with an introduction to 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 key terms. A review of the
relevant literature follows in Chapter 2. The literature review addresses the pattern of
mathematics achievement, policy initiatives, successful strategies or math program,
the effect of instructional leadership, and how that leadership resolved dilemmas it
encountered. Chapter 3 presents the methodology used in the study, including the
sampling and selection process of the participating school 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 located in Chapter 4. Chapter 5
summarizes the study and recommends possible implications for best practice.
References and Appendices follow this section.

xii
The focus of this study centered on identifying policies and practices that lead
to increased student achievement. Many specific policies and practices were found to
be the factors that contributed to the increased student achievement. Further studies
in other core subjects such as Science and English could confirm and add validity to
the value of policies and practices that were found to be of value in this study. Also
this study looked at a school with a closely nit content department. There existed in
the school prior to implementation of reform policies and practices a long history of
collaboration and departmental conformity. A further study of this area of research
could study a school that did not have a history of collaboration, nor conformity.
1
CHAPTER 1
INTRODUCTION TO THE STUDY
Overview
Results of research studies and state assessments show that a gross lack of
growth is being achieved by “at risk” students who attend urban schools. This “no
progress” situation is especially evident in math. In a recent Los Angeles Times
articles a study of Birmingham High School revealed that many students are
dropping out after failing Algebra 1 three times or more. In 1983 the National
Commission on Excellence in Education published A Nation at Risk: The Imperative
for Educational Reform. One of the major developments feared by this report was
the progress of other nations ahead of the United States in mathematics and science.
An example of this is where the report speaks of other industrialized nations’
spending three times as much time on mathematics and science during the high
school years. A possible reason for the lack of time spent on mathematics and
science may be seen in the fact that in “13 States, 50% or more of the units required
for high school graduation may be electives chosen by the student” (p. 16).
In California the need for reform was recognized by the 2002 publication of
Aiming High: High Schools for the Twenty-First Century by the California
Department of Education. This statewide guidebook for high schools emphasizes
three procedures for success. The first is the understanding and implementation state
standards. The second is the use of Assessment which produces the data. The third
2
is related to data, which is Accountability. This document serves as the California
blueprint for improving high school instruction.
At the federal level the need for high school reform is seen in the January 8,
2002, passing of No Child Left Behind (NCLB) act. This was the latest version of
the 1965 Elementary and Secondary Education Act (ESEA). This law had certain
requirements intended to ensure nationwide school reform. A few include: Annual
testing of all students against state standards. Verification of minimum test
participation at the school level. All students having highly qualified fully
credentialed teachers (Illinois State Board of Education 2006) is about measuring
the progress of all students and holding high schools accountable for graduation rates
(U.S. Department of Education 2006).
Case study methodology is the key to identifying what instructional elements
are instrumental in successful urban schools. Qualitative data will be used to
identify the varying values of the various instructional elements that successful urban
schools use. There are two state assessments that are of particular importance in
viewing how all California public schools are successfully or unsuccessfully meeting
the educational needs of their students. The first is the California Standards Tests
(CSTs) that shows to what degree students have mastered the math, language arts,
science, and social science standards that the state has adopted. These standards
have also been supported in the subject matter frameworks. The frameworks and
standards together constitute a roadmap for meaningful and “complete” student
learning.
3
The second state assessment that is of significance for informing as to
success is the California High School Exit Exam (CHSEE). Passing this test proves
that a student has mastered basic skills at least at an 8
th
grade level. Students are
only allowed to take the test so many times and failure to pass it results in not being
allowed to receive a diploma from California’s public high schools. The results of
both these tests will allow identification of successful urban schools.
Numerous math programs have sought to bridge the gap between the need for
reform and the high stakes exams, where the accountability comes from. Carnegie
Learning’s Cognitive Tutor is one such program. Some figures from a summary
report show that students who complete the three-course sequence of Algebra I,
Geometry, and Algebra II perform 30% better on the TIMSS assessment and real-
world problem solving by 227%. Furthermore students who have been enrolled in
Cognitive Tutor Algebra I are 69% more likely to pass traditional Geometry and
71% more likely to pass traditional Algebra II taught without computers (Koedinger
& Corbett, 2000). Another Math program which seems to be showing good results
with students is the John Hopkins Transition to Advanced Mathematics (or TAM).
TAM is successful through a research-based combining of traditional and innovative
teaching strategies. Central to the design is an emphasis on the National Research
Council’s Strands of Mathematical Proficiency, which include Conceptual
Understanding, Procedural Fluency, Strategic Competence, Adaptive Reasoning, and
Productive Disposition (John Hopkins University, 2005).
4
The main research question for this dissertation is what are the varying
values of the various instructional elements that are prominent as identifiable causes
for successful urban schools and how and to what degree can these instructional
elements would be helpful in assisting federally identified Program Improvement
(PI) schools. This study is qualitative by nature and yet the above two tests are
viewed and analyzed in a quantitative manner. The federal government determines
PI schools based on the above two state tests, coupled with attendance, that is the
primary way that quantitative plays a role in this dissertation.
Yet despite the efforts and concerns of government agencies the academic
performance of American high school students remains low for many types of
students when viewed by national objective standards and by international
comparative studies. Data collected by the College Board in 2005 regarding both the
SAT Results and in a separate report AP results show the varying levels of success
and achievement for various subgroups. A study about Hispanic students by the
Education Policy Institute in 2000 shows some delineation between high school and
college graduates. So as to identify the difference in Hispanics and Whites in both
cases of what is helping them to achieve, the indicators included High School
diploma, family income, and parent educational attainment. According to the The
Education Digest in 2006, overall student achievement in math has actually
improved over the last decade. But contrary to this apparent success the divide
between at risk students and middle and high-income students continues to grow
exponentially.
5
In Highlights from the Trend in International Mathematics and Science
Study (TIMSS) from 2003 published in 2004, it is clear that not only are students
failing to perform at a national proficiency, but they are as well failing behind in
international comparisons. According to Education Leadership (2004) there is an
“Arithmetic Gap.” There is a widespread computation “Deficiency” that stops
students from being proficient or even moderately successful in learning algebra and
geometry. In the High School Graduation Rates in the United States (2002) a study
shows how startling the amount of dropouts are. It would be even more curious to
find out what percent of those left school as a result of trouble in Mathematics. In
Making the Grade: A Report of the Nation’s SAT 1 Results in the Nation’s Urban
Schools 2001 the math achievement gap is delineated by ethnicity, gender, economic
indicators, and the number of test takers. Studies like Locating the Dropout Crisis:
Which High Schools Produce the Nation’s Dropouts? Where Are They Located?
Who Attends Them? (2004) shows more than an achievement gap--it may be an
opportunity gap also. This study considers the consequences of attending schools
that have what it calls low “promoting power.” The good news is that according to
the Education Week (2006) the lowest students are in some cases making the greatest
gains. The bad news is that according to African-American Issues In Higher
Education (2004) students end up in this situation at an early age perhaps due to low
birth weight, single-parent households, and young mothers all lead to a delay in low
Socioeconomic Success (SES) in students. In Review of Educational Research
(2005) SES is linked to be moderately to strongly related to academic achievement.
6
The performance gap in mathematics represents an especially important
problem in many respects. Mathematics proficiency is especially important for urban
youth because it only takes the one significant roadblock to stop a student from
succeeding and bring them to a point where they give up on school and, generally
speaking, go into low paying jobs or the streets. For many it can be the difference
between life and death, considering the dangers that plague our youth. Math
achievement is related directly to the dropout rates of Hispanic and African
American students. In No Excuses: Closing the Racial Gap in Learning it is
considered why minority students are being provided inadequacy in their education,
which frequently leads them to drop out, be less likely to graduate from high school,
be less likely to be accepted into colleges, and graduate from colleges less than Asian
and White students (Thernstrom, 2003). It might be called the Mathematics
achievement gap and in Coursetaking and Achievement in Mathematics and Science
statistics on student achievement are broken up into subcategories of student groups
(Oakes, 2000). A great source for viewing how significant the differences in
Mathematics achievement is a careful look at the NCES, The Nation’s Report Card:
Mathematics 2005 which presents the results of the National Assessment of
Educational Progress (NAEP), shows specific statistical breakup by gender,
race/ethnicity, and students’ eligibility for free/reduced-price lunch (NAEP, 2005).
It is useful to look at NAEP as it identifies and compares Mathematical achievement
gap with those specific criteria (Lee, 2002). One cause for the lack of student
achievement in Mathematics is that the American Mathematics curriculum and
7
classroom instruction are not as challenging as many other countries, as shown in
TIMSS (Silver, 1998).
In response to these concerns, State and National efforts to increase math
achievement in high schools have focused on state standards, improved curriculum
and instruction, better prepared teachers and related reform efforts. The State of
State Math Standards (2005) evaluates the state of state mathematics standards. This
work traces and notes the “standard weaknesses,” as well as a brief history of the
development of various state standards and links them to how federal and state
policy influenced their creation and development (Klein). According to Kathryn
Schiller who found that in cases where test performance really mattered, there is less
of an achievement gap between racial and ethnic groups (2003). In this way a higher
demand on performance relates to improved curriculum instruction.
There is a clear link between better curriculum and student success (Rose,
N.D.). In Relationship between Professional Development, Teacher’s Instructional
Practices, and the Achievement of Students in Science and Mathematics, Douglas
Huffman examines numerous types of professional development including
immersion, examining practice, curriculum development, and collaborative work.
Of these, Huffman and his co-authors found that of those mentioned only curriculum
development significantly increased student achievement (2003). Last, Ann Taylor
also found that curriculum development was the key. She found that Lesson Study
did two things; it increased the mathematical knowledge of teachers, and brought
into practice-improved methods of teaching mathematics. The Center for Teaching
8
and Learning concluded that “America’s math teachers are under-prepared to teach
mathematics in all high school mathematics subject areas (2002).” That is to say
there is not only problem with Geometry, there is a problem with Algebra 1 and 2,
Trigonometry, and Calculus. As a whole, there is no subgroup of subjects that is on
track.
According to Sandra Bryan current reform movement stresses standards and
accountability in the form of high-stakes test. She says it is also about designing
schools and doing some restructuring (2004). Some reform efforts have been less
than successful. In one report by the Education Evaluation and Policy Analysis the
reform of increasing the number of credits students have to earn in mathematics and
science to graduate from high school by itself does not improve student proficiency
in these subjects (Teitelbaum, 2003). It makes sense that taking more of a subject
would not necessarily help, if students are hopelessly behind to begin with. Some
reform efforts have more to do with redesign, than reform. For example Johanthan
Plucker speaks of how to better prepare students for their future, by using
reorganizing high schools into small learning communities or academies and
instituting a rigorous curriculum, while offering college preparatory courses (2004).
The Southern Regional Education Board did an excellent case study that shows how
small learning communities can turn schools around completely (2003). In High
Challenge, High Support Tom Vander Ark laments the high turnover in leadership as
it affects reform and how crucial it is that school districts define high expectations
and offer an array of options (2006).
9
Out of this effort have come new school designs that focus on student
achievement and related school features. When it comes to the hands on design
approach value has been found in relating Mathematics to real-life experiences and
situations (Burnett, 1997). Unique designs like PASS allowed students to take
students to take their curriculum with them (Conger, 1997). Brian Bottage identified
the value and effect of contextualized math instruction (1999).
One school feature that is very helpful is self-efficacy. It is useful when
practicing teachers believed they could plan a math lesson and felt competent in their
achievements (Sottile, 2002). Another school feature that has showed promise for
both results, when it comes to instructors and students, is the use of computer
technology (Willner, 2002). An additional integration of math with technology has
been found to be particular helpful by some communities (Blume, 2001). Integrated
mathematics has been shown to promote critical thinking and led to improving
student comprehension and performance (Lee, 1997).
Building local capacity for improvement must be joined with new policy
initiatives and designs. According to Amanda Datnow leadership is the key element
in comprehensive school reform. She has written a work which chronicles the
development of school reform and new school leadership design (2003). Some
leadership design has focused wisely on helping urban school leaders (Houle, 2006).
It is a new day in public school administration that requires greater innovativeness.
It is about being perceived by others as innovative, perceiving others as innovative,
and mutually perceiving each other as innovative (Baugh, 2006). One initiative that
10
insight can be gained from is Project IMPACT (Increasing the Mathematical
Power of All Children and Teachers), which was concerned with equitable and
successful mathematics reform (Bamberger, N.D.). According to the North Central
Regional Educational Lab in order to sustain active reform, effective leadership is
needed. This has a good summary about what is known about how good leaders
influence schools and students (2000). One new design used in Chicago elementary
schools was to increase the relational trust amongst teachers, students, parents, and
administrators, and were found to be very beneficial to accomplishing school-reform
efforts (Educational Leadership, 2003). New and better designs or best practices in
mathematics are being chronicled and share now, more than ever (Grouws, 2000).
Fortunately, a considerable amount of quality work has been done in
identifying the features of instructional leadership in this new context. The quality
of the instructional leader is the determinant of how successful a school will be. K.
Leithwood wrote a comprehensive article about How Leadership Influences Student
Learning. In this work of particle interest was how he describes the instructional
leader “Setting Directions,” or making visions move forward. The successful
instructional leader is also concerned with “Developing People,” a worthwhile and
crucial investment. Of great value is his insight on how to successfully go about
“Redesigning the Organization,” or changing the school culture (2005). The Center
for Collaborative Education has found that it is crucial that society builds up,
prepares, and trains their principals especially in urban communities with students
who are at risk (2005). Another study devoted to developing successful principals
11
found four key concepts which were the essential elements of good leadership,
effective program design, multiple pathways to high quality leadership development,
and policy reform and finances (Davis, 2005). Furthermore, part of the path to
success is prioritizing the activities the activities that need to be done so that student
achievement is gained (Waters, 2004). This prioritization is especially necessary as
there are identifiable problems that threaten successful instructional Principal
leadership (Institute for Educational Leadership, 2001). Some authors like Tim
Waters have tried to qualify these priorities as he did identifying 21 leadership
responsibilities that lead to student achievement (N.D.). In Preparing and
Supporting Diverse, Culturally Competent Leaders: Practice and Policy
Considerations it is shown that fulfilling outward responsibilities are not enough,
inward motivations and cultural understanding play a key role in the big picture
(2005). According to H.M. Marks one needs to add transformational leadership to
the mix to accomplish the task (Marks, 2003). An interesting study was done that
asked teachers what principal actions they most appreciated. The teachers identified
two features that most supported them. First, that principals talked with teachers in
order to promote reflection. Second, that principals spoke with them so as to
promote professional growth (Blasé, 2000).
Statement of the Problem
But what is still not known for urban high schools that have experienced
significant gains in math performance in their students are two areas of concern.
First, how do urban high schools bring together policy initiatives? Also, how do
12
urban high schools increase school site best practices to bring about improved
math performance in their schools? Second, how does instructional leadership if
effectively carried out, improve high school math performance for students? Two
issues seem to be especially relevant to this second concern of instructional
leadership. The apparent situation that leaders often don’t have strong pedagogical
content knowledge in mathematics education, and this is compounded by the need to
carry out functions related to fiscal, personnel, organizational leadership, data
analysis and review. Little is known about how leaders work effectively in this
context of balancing all these issues and concerns.
Purpose of the Study
The purpose of this study is to find out how urban high schools that have
experienced significant gains in math performance in their students looking at two
areas of concern. First, to find out how urban high schools bring together policy
initiatives, coupled with how urban high schools increase school site best practices to
bring about improved math performance in their schools. Second, to find out how
instructional leadership, if effectively carried out, improves high school math
performance for students. In the pursuit of effective instructional leadership there is
a need to discover how to help leaders who do not have a strong pedagogical content
knowledge be successful as instructional leaders. Second, there is a need to discover
how instructional leadership can be successfully completed while Two issues seem
to be especially relevant to this second concern of instructional leadership while
fulfilling the need to carry out functions related to fiscal, personnel, organizational
13
leadership, data analysis and review. The purpose of this study is two-fold to find
a guide at bringing together policy initiatives with best practices. And second to
determine some guiding examples of best practices for the instructional leader who is
successful about pedagogical and organizational leadership.
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 seem to be related to improved math achievement in the
school?
3. What change process did the school use to enhance its math program and
strategies to assist students in math?
4. To what extent was strong instructional leadership important in improving
(a) the math programs/strategies, and (b) math achievement among
students?
5. How did instructional leaders respond in academic areas in which they
were not experts?
Importance of the Study
Responding to the need for improved student proficiency is imperative to the
health and competitiveness of the American education system. State and federal
accountability systems ensure that schools teach adopted content standards and
14
expect all students to achieve proficiency. The idea behind state standards is to
decrease and then eliminate the achievement gap. Students with low SES are in
particular educational trouble as compared to more affluent American students. By
examining how successful public high schools bring standards, curriculum, and best
practice together increase student proficiency in mathematics. This study has
importance as it will provide resources for educators, researches, and policymakers.
Teachers strive to increase student proficiency meeting the tribulation
caused by an incomplete understanding of how policy governs curriculum. This
study provides detailed information about the design and implementation of one
school’s successful mathematics program. The significance of this study relies on
the interaction of the internal and external environment, providing insight into
effective mathematics practices and programs that may be replicated at other similar
schools.
Site administrators are in a position to stay in tune to district policy and
initiatives. They are in a dynamic position to affect the values and climate of their
school, and also implement mathematics reform strategies. This study explores how
instructional leaders act as a catalyst for positive change in the values and climate of
a particular school, which will let other administrators gain a picture of what has
worked for others.
District level administrators can utilize this study to inform their strategy for
district wide progress. This study will add to the base of knowledge related to
increasing student proficiency district wide. Additionally, researchers will have a
15
conceptual framework to evaluate district or individual school reform efforts.
Policymakers at both the state and federal level want to find mathematics reform
strategies that work. A deeper understanding of how schools reach success will
allow legislation that encourages strategies that work. This is done especially
through what content standards are adopted by the state.
Assumptions
This study assumes that student progress in mathematics was in part a result of
a successful instructional program. It also assumes that instructional leadership is a
key component in increasing student success in mathematics. The data
instrumentations used in this study were based on accepted methodology and were
considered reliable instruments for the collection of data. The respondents were
assumed to be forthright with their answers and information obtained from them was
assumed to be accurate. Lastly, this study assumed that the California Standards
Test (CST) and the California High School Exit Exam (CAHSEE) are able to
accurately gage a student’s specific level of proficiency.
Limitations
This study was limited, because for one it was not longitudinal in regards to
how long it occurred. It was also limited by the investigation of mathematics in one
public high school in Southern California. Data collection occurred over a ___ week
period in the Fall of 2006. These constraints limit the ability to generalize specific
results to other schools and/or content areas. Although efforts were taken to prevent
16
bias, the researcher did not have control over any bias already held by the
participants. The analysis of the data relied on researcher interpretation.
Delimitations
The parameters of the study were confined to an exploration of one public high
school’s success in increasing mathematics proficiency. The field of inquiry was
limited to considering the critical factors associated with increased proficiency. In
respect to these circumstances this descriptive, analytical case study gathered data
from one public high school in Southern California. The limited sample size and
qualitative direction of this study limit the ability to generalize specifically to other
situations. The school studied was purposefully selected based on the following
criteria:
1. Improved Proficiency in Mathematics Achievement
2. Urban and Diverse Socio-Economic Status (SES)
3. 9-12 Comprehensive Public High School
4. Same Principal for at Least Three Years
Definition of Terms
For the purpose of this study, the following terms were operationally defined
below.
The Academic Performance Index (API): The API is the cornerstone of the
Public Schools Accountability Act (PSAA). The API ranks school performance, sets
growth targets, and provides similar-school comparisons. The API is a single
17
number on a scale of 200 to 1,000, indicating how well a school has performed
academically the previous school year (California Department of Education, 2001).
Adequate Yearly Progress (AYP): AYP is an individual state's measure of
yearly progress toward achieving state academic standards. "Adequate Yearly
Progress" is the minimum level of improvement that states, school districts and
schools must achieve each year.
Achievement gap: denotes differences in the academic achievement in of a
particular group of students.
Assessment: The processes used to collect information about student progress
toward educational goals. The form varies with what is being assessed and the
purposes for which the results will be used. Secondary Periodic Assessments
measure student proficiency toward California Content Standards for the explicit
purpose of improving teaching and learning (LAUSD, 2005).
Benchmark: Formative uniform measure of student progress relative to
standards. Standards-aligned assessments and assignments provide information
about progress toward the end target (California Department of Education, 2001).
Best Practices: Practices that have been implemented and statistically shown
to be effective in bringing about significant gains in student achievement, which can
be replicated in generalized school settings.
California High School Exit Examination (CAHSEE): A graduation
requirement, authorized by state law in 1999, that requires California public students,
18
beginning with the graduating class of 2004, to pass the CAHSEE in order to
receive a high school diploma. The CAHSEE will cover the curricular areas of
reading, writing, and mathematics and will be aligned with the state content
standards adopted by the State Board of Education (California Department of
Education, 2001).
California Standards Test (CST): Pupil achievement by grade level, as
measured by the Standards Testing and Reporting (STAR).
Content Standards: Stated expectations of what students should know and be
able to do in particular subjects and grade levels. They define not only what is
expected of students, but also what schools should teach (LAUSD, 2005).
Cultural Capital: The term cultural capital represents the collection of non-
economic forces such as family background, social class, varying investments in and
commitments to education, different resources, etc. which influence academic
success.
Data-driven Decision-making: The process of making decisions about
curriculum and instruction based on the analysis of classroom data and standardized
test data. Data-driven decision-making used data on operational functions, the
quantity and quality of inputs, and how students learn to suggest educational
solutions (Massell, 2000).
Deficit Theory: Assumes that some student cannot achieve at thigh levels
because of deficits inherent in their race, ethnicity, language, or culture.
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CSD Highly Qualified Teacher: The definition of "highly qualified" in the law
requires that public elementary and secondary school teachers have obtained full
state certification or passed the state teacher licensing examination; hold a license to
teach in the state; and not have had a certificate or license requirement waived under
emergency, temporary or provisional.
Instructional Leadership: An influence that guided the activities designed to
impart knowledge or skills to students (Olsen, 2005).
Leadership: Leadership is a process of influence leading to the achievement of
desired purposes. Successful leaders develop a vision for their schools based on their
personal and professional values [and goals]. They articulate this vision at every
opportunity and influence their staff and other stakeholders to share the vision. The
philosophy, structures and activities of the school are geared towards the
achievement of this shared vision.
Master Schedule: This is a construct that reflects the format of the school day.
The following elements are included in and are specified by the master schedule; the
length of each instructional period, when and how frequently courses are offered,
which teachers are assigned to teach specific courses and grouping of students.
National Assessment of Educational Progress (NAEP): The NAEP is an
ongoing, national assessment of what America’s students in grades four, eight, and
twelve know and can do in various academic subject areas. NAEP is administered
by the National Center for Education Statistics of the U.S. Department of Education.
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One NAEP component provides states with a measure of their students’ academic
performance over time and a comparison to the results of other states and students
nationwide (California Department of Education, 2001).
Pedagogical Content Knowledge: Identifies the distinctive bodies of
knowledge for teaching. It represents the blending of content and pedagogy into an
understanding of how particular topics, problems or issues are organized,
represented, and adapted to the diverse interests and abilities of learners, and
presented for instruction (Shulman, 1987).
Performance Bands: Bands that identify levels of student achievement based
on a demonstrated degree of mastery of specified content standards. California has
identified five performance levels for its statewide standards based assessments:
Advanced, Proficient, Basic, Below Basic, and Far Below Basic (California
Department of Education, 2001).
Organization of Study
This dissertation begins in Chapter 1 with an introduction to 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 key terms. A review of the
relevant literature follows in Chapter 2. The literature review addresses the pattern of
mathematics achievement, policy initiatives, successful strategies or math program,
the effect of instructional leadership, and how that leadership resolved dilemmas it
encountered. Chapter 3 presents the methodology used in the study, including the
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sampling and selection process of the participating school 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 located in Chapter 4. Chapter 5
summarizes the study and recommends possible implications for best practice.
References and Appendices follow this section.
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CHAPTER 2
LITERATURE REVIEW
Status of Academic Performance
National Objective Standards
Yet despite the efforts and concerns of government agencies the academic
performance of American high school students remains low for many types of
students when viewed by national objective standards and by international
comparative studies. Data collected by the College Board regarding both the SAT
Results and in a separate report AP results show the varying levels of success and
achievement for various subgroups. The AP exam is meant to be equivalent in rigor
and difficulty from year to year. Since AP exams are not graded on a curve, low-
performing AP exam takers cannot water down the scoring scale. This is in part why
these results can indicate how on track America’s students are. The AP exams are
setting a standard that is driving schools towards proficiency. The data suggests that
at least in the arena of AP classes national standards are being met. Furthermore a
significant portion of key states’ students are achieving a passing score of 3 by the
time they are graduating high school. New York, Maryland, and Utah have over
20% of the graduating students passing at least one AP exam by graduating.
California, Virginia, Connecticut, Massachusetts, and Florida are all within arms
reach of passing the 20% milestone (2005). It is significant that at least to some
extent huge segments of the student populations are achieving at a national level.
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It would be even more curios to find out what percent of those left school as
a result of trouble in Mathematics. In Making the Grade: A Report of the Nation’s
SAT 1 Results in the Nation’s Urban Schools the math achievement gap is delineated
by ethnicity, gender, economic indicators, and the number of test takers. The report
does a lot to compare urban with non-urban schools by comparing the Great City
Schools (GCS) with the national SAT results. Fifty-eight major urban school
districts make up the GCS that is used to compare urban students to the national
average. Comparisons of note are made about the mean scores and achievement
gaps in relation to four criteria; academic preparation, gender, race/ethnicity, and
household income. Population wise the 10% of all test-takers were from the GCS. In
all the comparisons one of the most key findings was that “White students taking the
SAT nationally and in the GCS were more likely to have taken core or more
academic coursework than students from other racial groups.” Furthermore it is of
importance to note that GCS schools’ test takers are more likely to be African-
American and Hispanic (College Board, 2001).
International Comparative Studies and the Persistent Achievement Gap
In Highlights from the Trend in International Mathematics and Science
Study (TIMSS) from 2003 published in 2004, it is clear that not only are students
failing to perform at a national proficiency, but they are as well failing behind in
international comparisons. In 2003, U.S. eighth grade boys and girls both showed
improvement in mathematics compared to 1995. The 2003 results showed U.S.
eighth grade boys’ average score in mathematics being a 507. This is 12 score
24
points higher than in 1995, when U.S. boys scored 495. The U.S. girls’ average
mathematics score reached was 502 in 2003. This is also 12 score points higher
than in 1995, when U.S. girls scored 490 (Gonzales, 2004).
The United States is one of four countries in which both eighth-grade boys
and girls improved their average mathematics performance in 2003 over previous
assessment years. In addition to the United States, both eighth grade boys and girls
improved their average mathematics performance in Israel, Lithuania, and the
Philippines. Although this is good, the concern comes when the scores of other
countries are looked at. Four countries scored 80 or more points more than the
United States (504) on the 8
th
mathematics average scaled scores. These countries
were the Republic of Korea (589), Singapore (605), Chinese Taipei (585), and
Hong Kong SAR (586) (Gonzales, 2004). The problem is even if the U.S.
continues to increase and these four Asian countries do not increase, the gap is
significant and requires a specific and well-laid plan for success.
One cause for the lack of student achievement in mathematics is that the
American Mathematics curriculum and classroom instruction are not as challenging
as many other countries as shown in TIMSS. Edward A. Silver was instrumental at
synthesizing the lessons from TIMSS. By looking at TIMSS, he found that the
United States was deficient in three ways, when it comes to Curriculum Content.
First, the U.S. school mathematics curriculum is unfocused. More topics are
included in the U.S. curriculum at each grade level than are found in the curricula of
most other countries considered by the study. The second problem is that the U.S.
25
mathematics curriculum is excessively repetitive. Numerous topics appear in the
U.S. curriculum at more grades than in the curricula of most other countries. Lastly,
Silver explains that the U.S. school mathematics curriculum is not demanding
enough. Compared to many other countries, the math content taught at grade 8 in the
United States is similar to the math content taught at grade 7 elsewhere. Also, there
is a lower expectation of how students need to perform on that curriculum (Silver,
1998).
Silver finds evidence in TIMSS of two problems with how teachers go about
their teaching. U.S. mathematics instruction is oriented neither toward
understanding, nor toward intellectual challenge. That is they tend “to state ideas
rather than develop them.” Also they tend to use “tasks that engage students with
low-level cognitive activity, such as memorizing and recalling, rather than high-level
thinking.” The second problem is more than in many other countries whose students
are performing better, teachers in the United States lack structured, sustained
opportunities to improve their practice (Silver, 1998).
The Performance and Achievement Gap
The performance gap in mathematics represents an especially important
problem in many respects. A great source for viewing how significant the differences
in mathematics achievement is a careful look at the NCES, The Nation’s Report
Card: Mathematics 2005 which presents the results of the National Assessment of
Educational Progress (NAEP) shows specific statistical break up by gender,
race/ethnicity, and students’ eligibility for free/reduced-price lunch. The average
26
scaled scores and achievement-level results in mathematics, by race/ethnicity,
grade 8 show the achievement gap. In 2003 80% of white students were at or above
basic level, whereas 39% of African-American students and 48% of Hispanic
students were at or above the basic level. This gives a achievement gap of 41%
between African-American and White students, and an achievement gap of 32%
between Hispanic and White students. In 2005 the gap narrowed a bit with still 80%
of White students were at or above basic level, whereas 42% of African-American
students and 52% of Hispanic students were at or above the basic level. This
amounts to an achievement gap of 38% between African-American and White
students. And an achievement gap of 28% between Hispanic and white students
exists (NAEP 2005). That amounts to 4% decrease in both the achievement gap of
both groups as compared with white students.
Studies like Locating the Dropout Crisis: Which High Schools Produce the
Nation’s Dropouts? Where Are They Located? Who Attends Them? This shows that
more than an achievement gap it may be an opportunity gap also. Consider the fact
that nearly 50% of our nation’s African-American students, 40% of Hispanic
students, and only 11% of White students attend high schools, where more than 50%
of students do not graduate from high school. Specifically there are around 1,000
high schools in the country where students have a 50/50 chance of graduating. A
majority minority high school is five times more likely to have weak promoting
power where fewer than 50% of freshmen reach senior status than a majority White
27
school. In the 100 largest cities, 50% or more students attend schools where weak
promoting power exist (Balfanz & Legters, 2004).
Going back to the 2003 TIMSS there is in some small, yet significant way the
achievement gap is being closed a little. As a result of the improvement in the
average mathematics achievement of African-American eighth-grade students
between 1995 and 2003, the gap in average scores between White and African-
American eighth-grade students narrowed, from 97 score points in 1995 to 77 score
points in 2003 (Gonzales, 2004). This amounts to a 21% decrease in the difference
of achievement between eighth-grade White and African-American students.
Importance of Mathematics, Achievement in College, and Economic Future
Importance of Mathematics
The importance of Mathematics cannot be understated. According to Silver In
grades K-8, mathematics receives more instructional attention than any other school
subject, second only to reading. Mathematical competence is often used to
determine and limit access to educational opportunities at the postsecondary level.
Though it is so important, there is a double standard when you compare it to literacy.
Whereas there appears a “core belief” that everyone can learn to read and write in
English, in mathematics it is culturally acceptable to say he/she is “just not very good
at math.” This expectation affects low-level students hard. That is, TIMSS has
found that lower-track mathematics classes receive less instruction than regular or
higher-track classes and, even worse, the little instruction they do receive relates
almost exclusively to basic knowledge and skills. That is why Silver suggests three
28
recommendations to help raise the importance of mathematics in the school
culture. The first recommendation is to choose to have a serious national
commitment to improve mathematics learning by all students. Second, the
mathematics curriculum and instructional practices practiced in the middle grades
need to be enhanced with research proven practice. Last, Silver calls for a substantial
financial and time investment needs to be made in teacher professional development
so that a more ambitious curriculum and more intellectually challenging mathematics
instruction can take place leading to student success (Silver, 1998).
There is a widespread “computation deficiency” that stops students from being
proficient or even moderately successful in learning algebra and geometry. In the
High School Graduation Rates in the United States a study shows how startling the
amount of dropouts are. This goes to the desperateness of the situation and how
truly important mathematics is when it comes to the curriculum pie. The graduation
rate in 1998 was 71% overall. White students graduated at a rate of 78%, while 56%
of African-American students and 54% of Hispanic students graduated. Out of the
fifty largest school districts in the country, Cleveland City had the lowest graduation
rate of 28%. They also had the lowest African-American graduation rate (Greene,
2002). This discrepancy could be called the “graduation gap,” and to suggest that
the importance of Mathematics cannot be understated.
Achievement in College
A study about Hispanic students by the Education Policy Institute in 2000
shows some delineation between high school and college graduates. So as to
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identify the difference between Hispanics and Whites as to what is helping them to
achieve. The indicators included High School diploma, family income, and parent
educational attainment. First when it comes to High School diploma the gender
results for who graduates are almost exactly reversed. That as where 55% of White
males graduated and 45% of White females, 57% of Hispanic females graduated as
compared with 43% of Hispanic males. Parental education is an indicator of college
success 90% of White college graduates had parents who had completed some
college, where as only 73% of Hispanic graduates had complete some college or
higher. Family income is also affected student success. Whereas 88% of White
graduates came from families of middle to high income, only 68% of Hispanic
students came from such financially successful families. Coming from an urban
community seems to be an indicator of college success. Whereas only 18% of White
graduates came from an urban area, a significant 42% of Hispanic graduates came
from an urban area. Educational aspirations are one key to increasing Hispanic
success in college. The study looked at a group of eighth graders, more than 99% of
the Hispanic graduates when interviewed back in eighth grade had committed to
going to college. Lastly part of the reason for the low success of Hispanic students
may be a “preparation gap.” Whereas 80% of White students were found qualified
to start college, only 65% of Hispanic students were found ready to start college
(Watson, 2000).
Math achievement is related directly to the dropout rates of Hispanic and
African-American students. In No Excuses: Closing the Racial Gap in Learning it is
30
considered why minority students are being provided inadequacy in their
education, which frequently leads them to drop out, be less likely to graduate from
high school, be accepted into colleges less, and graduate from colleges less than
Asian and White students. The authors suggest that building academic skills is the
key to increasing minority success in college. “Real learning” they say is not what is
typical before college. The days and year are too short, instructional time is wasted,
the classrooms are out of control, the teachers have low expectations, basic skills are
not taught to mastery, and sophisticated and stimulating material is not offered. That
description is characteristic of poor urban schools. Teachers need help to understand
and help their students grow in personal responsibility for their own future. Teachers
need to communicate the “excitement and importance of learning” if students are to
value education properly and be successful in college (Thernstrom & Thernstrom,
2003).
Economic Future
When the same Hispanic study is considered that followed eighth graders from
eighth grade through eighth years after high school, an “economic gap” appears.
There is a difference in pay and kind of work. The largest occupational choice for
both White and Hispanic students was the service industry, where 35% of Hispanics
and 30% of White students were involved. Approximately 75% of both groups are
working full-time and the rest part-time. At a margin of two to one, Whites were
more likely to be in engineering and computer technology careers. Whites were also
33% more likely to be in the health and medical field. Lastly, Whites were five
31
times more likely to be in the military. Eight years after graduation Hispanic
students earn an average of $20,074 a year, while White students earn an average of
$24,225 a year. This amounts to a significant difference of 21% in average income
(Watson, 2000).
Standards, Curriculum, Teachers, Reform, New Designs, and School Features
State Standards as an Effort
In response to these concerns, State and National efforts to increase math
achievement in high schools have focused on state standards, improved curriculum
and instruction, better prepared teachers and related reform efforts. The State of
State Math Standards (2005) evaluates the state of state mathematics standards. This
work traces and notes the “standard weaknesses,” as well as a brief history of the
development of various state standards and links them to how federal and state
policy influenced their creation and development. Only three states received A’s on
the 2005 results; namely California, Indiana, and Massachusetts. Also only three
states received B’s, namely Alabama, New Mexico, and Georgia. Of the remaining
44 states, 29 received D’s or Fails and only 15 scraped by average C’s (Klein, 2005).
Twenty-nine states equals 58% of the states failing. The six states receiving A’s or
B’s equals only 12% of the states really being on track for their students.
According to Kathryn Schiller and Chandra Muller, cases where test
performance really mattered, there is less of an achievement gap between racial and
ethnic groups. Specifically that states linking test performance to a greater number
of consequences for schools tended to have all students enroll in similar freshman
32
mathematics courses aimed at graduation and college. In these situations minority
students where much closer to their White peers who were taking the advanced
courses, towards a college track. It was the authors who suggested a situation where
“school accountability focused students and teachers on a common goal of academic
excellence, with those students who showed potential being particularly encouraged
to progress further in” mathematics (2003). In this way a higher demand on
performance relates to improved curriculum instruction, especially when standards
raise expectations on how well students can do and what they can achieve.
Improved Curriculum and Better Prepared Teachers
In Relationship between Professional Development, Teacher’s Instructional
Practices, and the Achievement of Students in Science and Mathematics, Douglas
Huffman examines numerous types of professional development including
immersion, examining practice, curriculum development, and collaborative work.
Of these Huffman and his co-authors found that of those mentioned only curriculum
development significantly increased student achievement. This study defines
“curriculum development involves having teachers help create new instructional
materials to better meet the needs of students.” For both science and mathematic
teachers the study found that curriculum development was a significant predictor of
teachers’ use of a standards-based curriculum and instruction. The kind of
curriculum development was local in the sense that it was teachers working together
within a school (2003).
33
Ann Taylor and her coauthors also found that curriculum development was
the key. She found that Lesson Study did two things, it increased the mathematical
knowledge of teachers, and brought into practice improved methods of teaching
mathematics. The Center for Teaching and Learning concluded that “America’s
math teachers are under-prepared to teach mathematics in all high school
mathematics subject areas.” There are five steps to lesson study. The first step is
“defining the problem” where a general goal is chosen. The second step is “planning
the lesson” where a group of teachers plan a lesson to teach in their respective
classes. The third step is “teaching and evaluating the lesson” where practice is put
into observation. The fourth step is “reflecting on its effects” were teachers meet and
discuss their observations of the lesson. The fifth step is “revising the lesson” where
the teachers meet and revise the lesson for the next year. The sixth step is that the
following year they “teach the revised lesson.” The final step is to “reflect on the
lesson” that was revised and taught (2002).
In Marzano’s chapter called A Guaranteed and Viable Curriculum from What
Works in Schools he sets out steps needed to better communicate instruction. The
first step is to identify and communicate essential content for all students. The
separation of essential data from supplemental data is a paramount concern. The
second step is to make sure that the essential content can be addressed in the amount
of time allocated for it. The third step is to sequence and organize the essential
content so that students have a good opportunity to learn it. That is that logically
organizing topics into various related units. The fourth step is to check that teachers
34
go through the essential content. The fifth step is to protect the instructional time
from being used for other things (2003).

Related Reform Efforts
The Buly and Valencia’s framework is concerned with “Five Potential Policy
Levers,” including Instruction as the first one. The instruction component is
concerned about how state and district policies mandate specific instructional
strategies. The research piece recommends that when it comes to instruction,
“Instead of mandating particular types of instruction from outside the classroom …
we suggest that policies should support educators’ efforts to probe beneath the
surface of test scores (2003).”
The next consideration is multiple indicators. This work recommends that a
range of assessments or indicators be used in order to gauge where students are
really at. The third component is concerned with alignment among standards,
assessment and instruction. In this concern there is a balance to be achieved between
assignments being grade level appropriate and the usefulness depending on the group
of students of using under or above grade level materials. The fourth, allocation of
resources, is limited by state allocation for state purposes when it comes to
textbooks. When it comes to professional development there may be more freedom
the article suggests to break out of the mold. The last part of the framework is
evaluating reform in a very consciousness manner. That is to warn against jumping
35
to unfounded conclusions or letting the surface do the talking (Buly & Valencia,
2003).

New Policy and Initiatives
Building local capacity for improvement must be joined with new policy
initiatives and designs. According to Amanda Datnow and Joseph Murphy
leadership is the key element in comprehensive school reform. They have written a
work which chronicles the development of school reform and new school leadership
design. Three national comprehensive school reform designs, including “Success for
All: District and School Leadership,” “The Coalition of Essential Schools,” and “The
Comer School Development Process.” The first “Success for All: District and
School Leadership” calls for the principal to move from being managers of the status
quo to facilitators of reform. Skills of collaboration and learning to share power with
teachers involves learning to balance when to be directive and when to step back and
allow teachers to lead reform efforts. Sometimes they note that master teachers are
designated to help in direct school improvement acting as teacher leaders. A specific
way this program utilizes teacher leaders is how it normally has a SFA Facilitator
whose responsibilities are three fold. The first responsibility is to know the progress
of each teacher in implementing the program and to provide support accordingly.
The second responsibility is to know the progress of each student and ensure that no
student falls through the cracks. The last responsibility is to manage assessments
36
and regrouping efficiently. Keeping that in mind the facilitator manual states “the
facilitator must be a mentor, and not an evaluator” characterized as a “respectful and
supportive” relationship (2003).
The second program design to aid building local capacity is “The Coalition of
Essential Schools.” This program is difficult to define as a reform model or program
due to how it centers around by the people. Specifically how six “common
principles” influence the actions of educators when it comes to practice. The first
common principle is “use minds well” where value is found in helping young people
learn to use their minds well. The second is “less is more” when you have students
master a limited number of essential skills and areas of knowledge, but with
intellectual and imaginative competencies. The third is “all students” which directs
the application of goals to all students. The fourth is “personalization” where
learning is personalized by teachers not having responsibility for more than 80
students at the high school or middle school and no more than 20 in elementary
schools. The fifth is seeing the “student-as-worker” where students are provoked to
learn and teach themselves. The last is “authentic assessment” in which learning is
documented and assessed with tools based on student performance of real tasks
(Datnow & Murphy, 2003).
The third design program that can build local capacity is “The Comer School
Development Process” which aims to develop leadership in urban schools. Central
to this frame is exercising a certain kind of leadership where collaborative, non-
blaming, and power-sharing occurs. This method is rightly called a “school
37
development process.” Most principals they found were killing themselves by
doing a disproportionate amount of the work. When these principals were
interviewed they shared how their assistant principals and coordinators had let them
down before. So this program is a good place to go to see some ways one can help
principals develop their leadership team (Datnow & Murphy, 2003).
According to the North Central Regional Educational Lab in order to sustain
reform active and effective leadership is needed. This has a good summary about
what is needed for good leaders to influence schools and build local capacity. Here
there are four skills that will allow a leader to be effective and put through new
initiatives. The first is instructional leadership, which is examined in depth in the
next section. The second is management where proper decisions will allow a
leaders’ staff to avoid unnecessary stress and anxiety. The third is threefold
communication, collaboration, and community building. The fourth also has three
parts that are vision development, risk taking, and change management (2000). The
last two should not be overlooked as they form an intricate picture of what is needed
for instituting new designs or initiatives.
In Marzano’s Chapter 4, What Works in Schools, challenging goals and
effective feedback, he made some insightful assertions about the good that can come
as a result of setting academic goals. There are three steps to implementing
challenging goals and effective feedback. Step one is an assessment system that
provides timely feedback on specific knowledge and skills for specific students.
Step two is to establish specific and challenging achievement goals for the school as
38
a whole. Step three is to establish specific goals or expectations for individual
students (2003).
The Resnik literature establishes effort-based education into eight components.
Three are of particular interest in regards to expectations that transmitted to the
student. The first is clear expectations, being clear with students what is requested
and required of them to know and learn. The second is recognition of
accomplishment which leads to students gaining self-efficacy. The third is
administering fair and credible evaluations (1999).
Marzano emphasizes three principles that recognize the importance of how
data has changed how we dialogue. The first principle states that, “The new era of
school reform is based on the realization that reform is a highly contextualized
phenomenon.” The second principle states that, “The new era of school reform is
characterized by a heavy emphasis on data.” The third principle states that, “In the
new era of school reform, change is approached on an incremental basis (2003).”
Marzano emphasizes three principles that recognize the importance of how
data has changed how we dialogue. The first principle states that, “The new era of
school reform is based on the realization that reform is a highly contextualized
phenomenon.” The second principle states that, “The new era of school reform is
characterized by a heavy emphasis on data.” The third principle states that, “In the
new era of school reform, change is approached on an incremental basis (2003).”
In Data Can Drive Development by Barbara Bray there are five components
that are important in order to let data have meaning and impact. The first is teacher
39
research which in part has teachers working and reflecting together. The second is
patterns and themes, which allows a value to be given for student scores, student
work, class participation, and interviews. The third is data collection tools which
allows the data to be laid out in a useable manner. The fourth is classroom
observations an analysis of teacher/student progress. The fifth is using the tools to
improve teaching practice (2003).
In Learning Points 11 components of a comprehensive school reform program
are shared that help to emphasize the importance in four ways that “Practitioners
[can] put scientifically based research to work.” The first of the four key
components is analyzing school data. The second is generating a hypothesis. This is
in response to the data, trying to figure out why or what was involved in students not
succeeding . The third is creating an action plan, which is central to change. After
identifying a problem this is the only right action, to do something about it. The
fourth and final key is evaluating research in light of the theoretical framework,
research design, research methodology, implementation and replication, evidence of
results, and approved research (2004).
School Features
One new school feature found in Chicago elementary schools was to increase
the relational trust among teachers, students, parents, and administrators and was
found to be very beneficial to accomplishing school-reform efforts. Four
components make up relational trust. The first is “respect” as it relates social
discourse across the school community. The second is “personal regard” which
40
comes from the willingness of participants to extend themselves beyond the formal
requirements of their union contract. The third is “competence in core role
responsibilities” where school community members also want their interactions with
others to produce desired outcomes. The final one is “personal integrity” which ask
the question whether we can trust others to keep their word (Bryk & Schneider,
2003).
A comprehensive design full of school features is set forth in the book The
New American High School where four components. The first component is
“learning activities” which has the three subcomponents of challenging students to
think, solving problems, and collaboration. The second component is “student
performance assessments” which includes capturing conceptual understanding,
problem-solving, and communication. The third component is “curriculum
foundations” which includes subcomponents of school-to-career applications,
student outcomes, and constructivist knowledge. The fourth component is “school
cultures” which consists of enhanced learning, meaningful staff-student interactions,
and ongoing professional development (Marsh & Codding, 1998).
Ten school features in Mathematics are being suggested in Improving Student
Achievement in Mathematics, Part 2: Recommendations for the Classroom. The
first school feature should be present is a direct relationship between mathematics
content and the mathematics achievement of students. The second is focusing
instruction of meaningful development of mathematical reasoning. The third is
reaching the point where students can learn both concepts and skills by solving
41
problems. The fourth feature is giving students the opportunity to discover and
invent new knowledge. The fifth is teaching that appreciates students’ intuitive
solution methods. The sixth is the proper use of small groups, which focus around
concepts. The seventh is the use of whole-class discussion followed by individual
and group work. The eighth is teaching mathematics with an emphasis on number
sense which effects the acquisition of other concepts. The ninth is that teachers use
math manipulatives often. Last, calculators can be used as a tool for “exploration
and discovery.” It is not the school features that matter, but also the features of a
school’s mathematics program (Grouws & Cebulla, 2000).
Instructional Leadership General and Specific
Features of Effective Instructional Leadership
When it comes to features of effective instructional leadership a place to begin
is with the work of Kenneth Leithwood. The quality of the instructional leader is the
determinant of how successful a school will be. Leithwood wrote a comprehensive
article about How leadership influences student learning. In this work when
considering what effect leadership has on student learning he reaches two
conclusions. First “leadership is second only to classroom instruction among all
school-related factors that contribute to what students learn at school.” And second
that “leadership effects are usually largest where and when they are needed most.”
He also describes the instructional leader “Setting Directions,” or making visions
move forward. The successful instructional leader is also concerned with
“Developing People,” a worthwhile and crucial investment. Of great value is his
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insight on how to successfully go about “Redesigning the Organization,” or
changing the school culture. In the end, he and his coauthors reach three conclusions
about how successful leadership influences student achievement. The first is
“mostly leaders contribute to student learning indirectly, through their influence on
other people or features of their organization.” The second conclusion is “the
evidence provides very good clues about who or what educational leaders should pay
the most attention to within their organizations.” The last conclusion is that “we
need to know much more about what leaders do to further develop those high-
priority parts of their organizations.” District and school leadership are the critical
bridge between educational reform and reform making a difference in the lives of
students (2004).
The Center for Collaborative Education has found that it is crucial that society
builds up, prepares, and trains their principals especially in urban communities with
students who are at risk. They identify three basics of successful leadership. The
first is “Setting Direction” which involves principals investing time to develop a
shared understanding of what the school should look like and what needs to be done
to get it there. The second of the basics is “Developing People” where a leader’s
“emotional intelligence” comes into play as his or her ability and willingness to be
“tuned in” to employees as people. The third basic is “Redesigning the
Organization” which involves principals strengthening school culture when they
“clearly and consistently articulate high expectations for all students, including
subgroups that are too often marginalized and blamed for schools not making
43
adequate yearly progress.” The article concludes with four leadership practices
that will lead to the achievement of students. The first is to “create and sustain
schools that can compete with private, charter and magnet schools.” The second is to
“empower others to make significant decisions.” The third is to “provide
instructional guidance” for the staff. The fourth is to “develop and implement
strategic and school improvement plans” that will bring research based instructional
strategies into practice at their school sites (2005).
In the Fall 2003 Conversations: Turning Points – Transforming Middle
schools author Amy Mednick speaks of “The Principal’s New Role: Creating a
Community of Leaders.” “Sharing real decision-making power with staff and
faculty” is the first step in creating this community. Here the principal shares
authority by providing meaningful opportunities for teachers to contribute to
major school decisions. He or she works with the faculty to establish “academic
teams, discipline-based teams, study groups, and the leadership team.” The
principal makes clear that every team’s success is of paramount importance and
that he or she will support them for the duration of the process. The second step
is “Providing support for effective functioning of teams,” which is where the
principal ensures that teachers have the skills and understanding to contribute
effectively in teams. These skills include “defining a purpose, setting measurable
goals, creating norms for operating, setting agendas, and assigning tasks.” The
principal also gives ongoing feedback to teams that supports and encourages
their work. The third step is “being an instructional leader who prompts others to
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continuously learn and improve their practice.” This is where as an
instructional leader, the principal often visits classrooms to work with teachers
and students or attends academic team meetings to contribute to the development
of effective teaching and learning strategies. In this role, the principal also
obtains instructional resources and professional development opportunities that
“improve learning, teaching, and assessment practices.” The fourth step is
“developing collaborative accountability” which occurs when the principal
works with the leadership team to hold individuals and teams accountable for
reaching the goals they have chosen for themselves. By asking teacher teams to
document their progress, the “principal and leadership team make it clear that
every team’s results matter, and that when a team reaches its goals, the whole
school moves forward.” The final step is “managing and monitoring the change
process to make sure it is always moving forward.” This is where the principal
and the leadership team ensure that all members of the school community fully
understand the components of the change process and are committed to the shared
vision (2003).
Another study devoted to developing successful principals found four key
concepts which were the essential elements of good leadership, effective program
design, multiple pathways to high quality leadership development, and policy reform
and finances. The first key concept is “good leadership” which shows through upon
student achievement through two “important pathways – the support and
development of effective teachers and the implementation of effective organizational
45
processes.” The second key concept is “effective program design” where principal
preparation programs imply that certain program features are essential in the
development of effective school leaders. Specific evidence indicates that effective
programs are “research-based, have curricular coherence, provide experience in
authentic contexts, use cohort groupings and mentors, and are structured to enable
collaborative activity between the program and area schools.” The third key concept is
“multiple pathways to high quality leadership development” which is seen as the
focus on principal preparation and development has intensified, innovations in both
leadership development programs and program structures have exponentially
increased. Here leadership and management skills over academic proficiency have
come to the forefront. The fourth key concept is “policy reform and finances” where
effective policy reform is aligned with knowledge of program components and the
systems that support their implementation and sustainability. Additional research is
needed to examine how various programs are implemented, governed, and financed
(Davis & Darling-Hammond, 2005).
Furthermore part of the path to success is prioritizing the activities the
activities that need to be done so that student achievement is gained. The
development of principal standards produced an wide range of various
responsibilities without distinction between important and essential responsibilities.
Furthermore an example of this is the 184 indicators developed within the six
Standards for School Leaders in 1996 by the Interstate School Leaders Licensure
Council. Waters points out that not only are they “overwhelming in scope, the
46
standards offer no guidance on which responsibilities and practices should take
primacy.” The article then focuses on “Distinguishing what is essential.” In the end
this article was concerned with “Knowing the essential.” They found 21 areas of
leadership responsibility and 66 associated practices that correlate with student
achievement. Professional development for principals needs to focus on Contextual
Knowledge and Experiential Knowledge, rather than Declarative Knowledge and
Procedural Knowledge (Waters & Sally, 2004).
Tim Waters, Robert Marzano, and Brian McNulty have worked to qualify
these priorities as he did identifying 21 leadership responsibilities that lead to student
achievement. The first leadership responsibility is “culture” that fosters shared
beliefs and a sense of community. The second is “order” which is about establishing
a set of standard operating procedures and routines. The third is “discipline” which
protects teachers from issues and influences that are disruptive to the educational
environment. The fourth is “resources” needed for providing teachers with materials
and the professional development that they need. The fifth is “curriculum,
instruction, and assessment” that form the bedrock of any reform movement or
program. The sixth “focus” is needed to establish goals and keep the goals at the
center of decision-making. The seventh is “knowledge of curriculum, instruction
assessment” where individuals are up to date on cutting edge research based practice.
The eighth is “visibility” that the leader has meaningful contact and interactions with
the teachers and students. The ninth is “contingent rewards” which recognizes and
rewards individual accomplishments. The tenth is “communication” where school
47
leaders establish strong lines of communication with teachers, parents, and
students. The eleventh is “outreach” where a leader is vocal advocate and
spokesperson for the school.
The twelfth is “input” which involves teachers influencing the design and
implementation of crucial decisions and policies. The thirteenth is “affirmation”
where a leader recognizes and celebrates school accomplishments. The fourteenth is
“relationship” which demonstrates an awareness of the personal aspects of teachers
and staff. The fifteenth is “change agent” where the leader is willing to and actively
challenging the status quo. The sixteenth is being an “optimizer” who inspires and
leads new and challenging innovations. The seventeenth is “ideals/beliefs” where a
leader communicates and operates from strong ideals and beliefs about schooling.
The eighteenth is when a leader “monitors/evaluates” the effectiveness of school
practices and their impact on student learning. The nineteenth is “flexibility” where
the dynamic leader adapts his or her leadership behavior to the needs of the current
situation and is comfortable with dissent. The twentieth is “situational awareness”
makes a leader aware of the details and undercurrents in the running of the school
and uses that insight to address problems as they come up. The last “intellectual
stimulation” helps a leader ensure that faculty and staff are aware of the most current
theories and practices for discussion and implementation (2003). These 21
leadership responsibilities serve an important role of prioritizing what should be
done and what should be given first.
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In Preparing and Supporting Diverse, Culturally Competent Leaders:
Practice and Policy Considerations the Institute for Educational Leadership shares
that fulfilling outward responsibilities are not enough, inward motivations and
cultural understanding play a key role in the big picture. This article has five themes
to emphasize the need for this inward direction. The first theme is that educational
leaders need to be culturally competent or they cannot be fully effective. The second
theme is that “culturally competent leaders work to understand their own biases as
well as patterns of discrimination.” The third theme is that culturally competent
leaders must know and be able to apply what is learned in relationships with their
own families and communities. The fourth theme is where “culturally competent
leadership develops over time and needs to be supported from preparation through
practice.” The final theme relates to how state and local policies need to be built
upon a sense of urgency about the need for culturally competent leaders (2005). It is
not enough for leaders to do the right things, they need to do the right things for the
right reasons. Teachers appreciate an environment like this. In one study they asked
teachers what principal actions they most appreciated. The teachers identified two
features that most supported them. First, that principals talked with teachers in order
to promote reflection. Second, that principals spoke with them so as to promote
professional growth (Blasé & Blasé, 2000).
This prioritization is especially necessary as there are identifiable problems
that threaten successful instructional principal leadership is seen in Leadership for
Student Learning: Reinventing the Principalship. Communities are looking for
49
principals to act as strong leaders for student learning. The absence of strong
leadership at the school level could undermine the success of education reforms.
Instructional leading principals can make the difference. These school leaders
“exercise a measurable, though indirect, effect on school effectiveness and
student achievement.” Instructional leading principals influence school
performance by “shaping school goals, direction, structure, and organizational
and social networks.” Successful instructional leading principals guide the
school policies, procedures and practices that lead directly to student learning
(Institute for Educational Leadership, 2001).
The characteristics that the leaders need to have are described by Michael
Fullan as five core competencies. The first is “Broader moral purpose.” Leaders
must have the capacity to inspire and motivate people to accomplish the challenges
inherent in urban school reform. They must have the skills to work with a broad
group of contingencies in a consistent, fair and equitable manner when implementing
the reform. In the second “Keeping up with and understanding the change process”
the leader must be familiar with and comprehend the change process and dynamics
of change; approaching challenges with creative processes. Through the change
process the leader must have the capacity to re-culture the community in a safe
environment in an effort to keep moving forward with change. The third is
“Cultivating relationships” where leaders must have the capacity to establish and
support good relationships across all of the unique and diverse groups of the school
environment; fostering a community spirit. The fourth “Sharing of knowledge” must
50
be a core value of the leader; sharing of knowledge and information creates a more
inclusive effort where people are informed, engaged and active participants. The
leader must establish protocols and procedures to facilitate this. The fifth “Creating
coherence” is a common challenge for the urban school leader which offers so much
diversity is bringing everyone together as a collaborative group that can work as a
group with a coherent vision and action plan (2001).
Robert Marzano has a lot to say about research-based strategies that concern
being an instructional leadership in Chapter 9 of What Works in Schools. He begins
with Bennett’s strategy list of 40 including:

• use of experiments
• teacher estimation strategies
• teacher expectations
• effort reinforcement
• classroom time management
• direct instruction
• memorization
• questioning
• homework
• classroom assessment
Marzano mentions other lists, including Creemers from 1994. There are nine
categories of instructional strategies that affect student achievement. The first is
51
“identifying similarities and differences” by assigning assignments that involve
comparison, classification, metaphors, and analogies. The second is “summarizing
and note taking” by having students generate and revise notes about the lesson. The
third is “reinforcing effort and providing recognition” by recognizing and celebrating
progress towards learning goals. The fourth is “homework and practice” for the
purpose of students practicing skills and procedures that have been the focus of
instruction. The fifth is “nonlinguistic representations” which centers around having
students construct graphic organizers or physical models of content. The sixth is
“cooperative learning” which includes organizing students in cooperative and ability
groups when appropriate. The seventh is “setting objectives and providing
feedback” which occurs during and at the end of the instructional unit. The eighth is
“generating and testing hypotheses” which entails engaging students in projects that
involve generating and testing hypotheses. The final is “questions, cues, and
advance organizers” prior to presenting new content and providing ways for students
to connect to what they have studied previously. He then moves onto an action step
which may lead to success. The step is to provide teachers with an instructional
framework that utilizes and recommends sound research-based strategies (2003).
In Marzano’s Chapters 17 and 18 of What Works in Schools, he speaks of some
necessary steps for a school leader to pursue. In Chapter 17 named “Using the
Model,” this is broken into four phases. The first phase is to take the pulse of your
school. This is done by thoroughly asking three questions. First, to what extent do
we engage in this behavior or address this issue? Second, how much will a change in
52
our practices on this item increase the academic achievement of our students? And
lastly, how much effort will it take to significantly change our practices regarding
this issue (2003)?
Marzano’s phase two of the administrative steps is to identify and implement
an intervention. Identifying the specific intervention is very important. Follow-
through is more important, as Marzano says, “it must be thoroughly implemented if a
school is to expect it to impact student achievement.” The third phase is to examine
the effect on achievement. Marzano here emphasizes the need not only for
collecting data, but also for choosing the type of achievement data which will act as
the best evidence. In phase four a school should address the next issue. This
concept, the restarting of the correction cycle, will allow continued progress to be
made (2003).
Marzano also speaks of “Leadership for Change” which is composed of three
principles leading to effectiveness. First, leadership for change is most effective
when carried out by a small group of educators with the principal functioning as a
strong cohesive force. Second, the leadership team must operated in such a way as
to provide strong guidance while demonstrating respect for those not on the team.
The third principle states, effective leadership for change is characterized by specific
behaviors that enhance interpersonal relationships. An emphasis is also placed on
the specific behaviors of optimism, honesty, and consideration (2003).
This leads to a work called Balanced Leadership by Waters and Marzano
which practices towards accomplishing desired progress. The first promotes
53
cooperation among staff. The second is to promote a sense of well being. The
third is to promote cohesion among the staff. The fourth is to develop shared
understanding of purpose. The fifth is to develop a shared vision of what the school
could be like (2003).
Marzano speaks about Collegiality and Professionalism in Chapter 7 of What
Works in Schools. First he is concerned with collegiality which includes (a) openly
sharing failures and mistakes, (b) demonstrating respect for each other, and (c)
constructively analyzing and criticizing practices and procedures. Another aspect of
collegiality is the kind and level of dialogue that occurs between teachers. Marzano
states that Friendship has a negative correlation of -0.252, Advice has a positive
correlation of 0.222, and Discussion has a very positive correlation of 0.326 (2003).
Professionalism is also a key to Marzano as 43% of variance in student success
can be attributed to teacher qualifications or lack there of. He speaks of the “three-
legged stool” which recognizes the need for teachers to experience a good teacher
education program, careful teacher licensing, and advanced professional
certification. Key to teacher preparation is a development of pedagogical
knowledge. Marzano points out that “The amount of courses teachers took in
instructional techniques accounted for four times the variance in teacher performance
than did subject-matter knowledge (2003).
Marzano recommends three action steps to accomplish the above objectives.
The first action step is to “Establish norms of conduct and behavior that engender
collegiality and professionalism.” The second action step is to “Establish
54
governance structures that allow for teacher involvement in decisions and policies
for the school.” The third action step is to “Engage teachers in meaningful staff
development activities (2003).”
In Blasé and Blasé’s book five key attributes of professional learning
communities. The first attribute is “Supportive and shared leadership” where
principals shared power, authority, and decision-making with teachers. The second
attribute is “Shared values and vision” in which principals and teachers developed an
inspiring and pragmatic picture of a school that holds common educational values
(2004).
The third attribute “Collective learning and application of learning” is where
principals and teachers learn together, used data together, and fostered teaching
strategies on student needs. The fourth attribute “Supportive conditions” exists
where teachers were provided time to talk, plan, and solve problems, influence
decisions, and developed collaborative roles and responsibilities. The fifth attribute
is “Sharing of personal practices” where teachers hold frequent reviews of each
others’ instructional practice (2004).
Blasé in his book has 12 tips to direct leaders into having successful
professional development. The first step is to build an atmosphere of democracy
with shared decision-making and collective responsibility and culture of learning
among teachers and administrators. The second step is to cultivate learning in the
faculty and parents as to the importance of school improvement and staff
55
development. The third step is to provide training in action research, which is
when enlightenment may occur that leads to true change (2004).
The fourth step is to collectively assess the effects of instruction and the
climate of the school. The fifth step is to organize a staff development committee to
coordinate activities. The sixth step is to focus staff development programs on the
areas of curriculum, instruction, and technology, as they are more likely to have
effects on student learning. The seventh step is concerned with organizing study
groups and supporting their activities (2004). All these steps have been taken by
NHHS in the form of the collaboration and decisions made by the SCDC as it sought
to accomplish the achievement of a creating a professional learning community. The
first seven steps are important as they are foundational blocks and constitute what
has been a ceiling as far as what level many schools have been able to achieve.
The eighth step is to develop peer coaching relationships and support their
activities (2004). In The Evolution of Peer Coaching by Beverly Showers and Bruce
Joyce, four key principles are identified. The first key principle is when peer
coaches work with entire faculties, all teachers must agree to be members of peer
coaching study teams. The second key principle is to omit the verbal feedback
which is so commonly found. The third key principle is to redefine as to who is the
coach, that is the when being observed is the coach and the observer is the
“coached.” The fourth principle is the collaborative work of peer coaching teams is
much broader than observations, specifically planning and watching one another
with students (1996).
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The ninth step that Blasé and Blasé recommend is that principals provide
time for collaboration for the purpose of studying teaching and learning. The tenth
step is a commitment to spend time studying outcomes, curriculum, and teaching
practice; which are more key in increasing achievement. The eleventh step is to
provide time for teachers to study the implementation of new innovations in
curriculum, teaching, and instruction. The last step is to encourage individual
teachers to develop instructional goals and objectives and to meet for the purpose of
discussing progress (2004).
In Blasé and Blasé Chapter 8, called the “successful instructional leader”
direction is given as to what should be done and how it should be done to lead a
school in the right instructional direction. There are nine emerging trends in
supervisory practice. The first is training for administrators and teachers in
supervision, mentoring, and coaching. The second is sensitivity to the processes of
professional growth and continuous improvement. The third is training in
observation and reflection on practice in teacher preparation programs. The fourth is
integration of supervision with staff development, curriculum development, and
school improvement systems. The fifth is improved professional practice both in and
outside the classroom. The sixth is continuous improvement as life-time learners.
The seventh is to have a focus on group processes in classrooms rather than a one-
on-one supervisory experience. The eighth is collegial assistance among educators,
parents, and students. The final one is the use of terms such as colleague
57
consultation and coaching to describe collaboration among professionals helping
each other to improve practice (2004).
Also in that chapter is list of nine ministerial roles that are identified for
principals and other administrators. The first is Purposing which is bringing together
shared visions into a covenant that speaks compelling to all stakeholders with a
moral voice. The second is Maintaining Harmony which is about building a
consensual understanding of school purposes and how the school should function,
while respecting individual conscience and individual style differences. The third is
Institutionalizing Values about translating the school’s covenant into a workable set
of procedures and structures. The fourth is Motivating involves providing for the
basic psychological needs of members, on one hand, and for the basic cultural needs
of members to experience sensible and meaningful school lives. The fifth is
Managing about ensuring the necessary day-to-day support that keeps the school
running effectively and efficiently. The sixth is Explaining concerned with giving
reasons for asking members to do certain things and giving explanations that lead to
an understanding of the larger picture. The seventh is Enabling where actively
actions are taken to removing obstacles that prevent members from meeting their
commitments on one hand and providing resources and support that help members to
meet their commitments on the other. The eighth is Modeling concerned with
accepting responsibility as head follower of the school’s covenant by modeling
purposes and values in thought, word, and action. The ninth is Supervising about
providing the necessary oversight to ensure that the school is meeting its
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commitments and, when it is not, to find out why and help everyone to do
something about it (2004).
Lastly in Chapter 8, Blasé and Blasé identify five tips for principals. The
first tip is to “Talk openly and frequently with teachers about instruction” recognizes
the varying skills, knowledge, attitudes, and personal characteristics from those
routinely taught and developed in educational leadership programs. The second tip
is to “Provide time and peer connections for teachers” realizing that mutuality of a
collaborative process. The third tip is to “Empower teachers” by creating a free,
mutual, and critical dialogue, not in judgment and evaluation. The fourth tip is
“Understand and embrace the challenges of change” remembering that change is a
journey, not a blue print. The fifth is to “Lead,” seeing the teacher as an intellectual
rather than the teacher as technician (2004).
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CHAPTER 3
RESEARCH METHODOLOGY
This chapter outlines the methodology used in this case study and includes a
detailed description of the research design, sampling criterion and process, and
methodology used for data collection and analysis. The purpose of this study is to
learn about how urban high school leaders successfully bring together policy
initiatives and local best practice to improve math performance in their schools, and
because individual school leaders often do not have strong content knowledge in
mathematics, this study examines how they marshaled resources and carried out
functions related to organizational leadership, and data analysis to successfully
influence their school’s success in mathematics. This case study examines the
following research questions:
1. What was the pattern of math achievement for various students at the
school?
2. What policy initiatives as well as curriculum, instruction and related
conditions seem to be related to improved math achievement in the
school?
3. What change process did the school use to enhance its math program and
strategies to assist students in math?
4. To what extent was strong 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?
In light of the stated purpose of the study, a case study approach was used to
provide a deep consideration of the school being studied. Mixed methods were used
to gather data and evidence in support of this case study. Such efforts included
gathering quantitative data used to support the descriptions presented in the study.
Factual case studies are of great value due to their “wealth of detail, give credibility
to situations and problems, and, most important, provide real outcomes.” They are
excellent in “describing current organizational problems,” while furnishing concrete,
not theoretical solutions.” Case studies are limited in the sense that “factual cases
tend to become outdated as organizations, strategies, problems, and people change
over time” (Warner, 2006).
The unit of analysis for this case study is one public high school. All of the
instruments used in this study were common to current educational research and
were intended to bring forth relevant responses to the research questions being
examined above. Conceptual frameworks were used to support the analytical style
used in this study and to provide a context for the reader. Triangulation was used to
verify and support findings. Document analysis evidence was cross referenced with
interview and questionnaire findings where possible. This process is intended to
increase the reliability of the findings made. 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
consider deeply the processes related to the research questions of this study. The
school selected for the study was chosen consistent with the following criteria:
1. Improvement in math achievement for three consecutive years as evidenced
by results on the California Standards Test (CST) in Algebra I.
2. Diverse as defined by a student population of at least 1200 students with more
than 50% from ethnic minority groups.
3. Public comprehensive high school in Southern California.
4. Leadership stability as defined by a principal being at the school for at least
three years during the time the improvement was made.
5. School has an API of 600 or above and a state rank of 5 or better out of all
schools.
The 11 members in the cohort research group led by Dr. David Marsh
worked together to develop the sampling criteria, and then to identify schools in
southern California that met those criteria. Qualifying high schools were identified
by analyzing data available on the California Department of Education’s web site.
Some criteria were dropped due to the criteria limiting the sample of schools to too
few sites. Specifically two criteria were altered or dropped to achieve a greater
sample of sites to choose from. The criteria of how many minority students was
lowered from 65% to the final 50%. Additionally the criteria of free and reduced
lunch was dropped completely. An excel spreadsheet was created that detailed
62
schools fitting the profile in terms of their CST scores in Algebra I (see Appendix
A). A geographic map plotting the selected schools was also created to help cohort
members select a qualifying school for their study based on proximity and other
relevant factors. The group also worked to identify what population would
participate in the study and included site administrators, key teacher leaders, and
classroom teachers. Site administrators and key teacher leaders were interviewed
using the interview guide attached as Appendix B. Teachers who were not leaders
were interviewed with the teacher interview guide, which is attached as Appendix C.
All math teachers at the site were then asked to complete a 48-item teacher
questionnaire (see Appendix D) whose results provided the researcher with data
about teacher perceptions about issues related to the research questions being
studied. All core subject teachers at the site who were not math teachers completed a
shorter questionnaire (see Appendix E) 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 due efforts would be made to ensure
confidentiality and anonymity. Those to be interviewed were scheduled for at least
one thorough discussion. All interviews were held on campus and in an environment
that ensured confidentiality and comfort.
Selected School Profile
The school selected for this study is West Valley High School in the San
Fernando Valley Unified School District. The school is located approximately 10
miles north west of Los Angeles in the west San Fernando Valley. The district is the
63
second largest district in the country with nearly 800,000 students. The school
district educates students in grades kindergarten through 12, along with primary and
adult services. The stated mission of the district is, “The teachers, administrators
and staff of the Camelot Unified School District (CUSD) believe in the equal worth
and dignity of all students and are committed to educate all students to their
maximum potential.” The district is comprised of 472 elementary schools, 84
middle schools, 79 comprehensive high schools and 43 continuation high schools.
At 3597 students, West Valley High School is a large school with a
significant cultural diversity from the community and from outside the community as
over a 1/3 of the students are bussed in. The two largest ethnic groups in the school
are Hispanic and White at 38% and 36% respectively. The remainder of the school
is comprised of 17% African American, 5.4% Asian and 3% Filipino. More than
15% of the school’s students are English Language Learners (ELL). Native Spanish
speakers represent 12.1% of the school’s population, Farsi 1.1%, Hebrew 0.5%,
Korean 0.4%, Filipino 0.2%, and 0.8% other languages. Nearly 40% of the students
at West Valley High School qualify for the free or reduced price lunch program.
Student Achievement
Key to the success of the school is its commitment that all students can
achieve and learn. The results are encouraging as West Valley has increased steadily
their API since 2001 from 649 to 676. During this same period the school’s
statewide rank has gone up from 4 to where it is currently a 5. In the area of Algebra
64
achievement, it made an increase of 11%. The school has showed great progress
in achievement across all sub groups.
Participants in the Study
The following educational stakeholders participated in the study and provided
vital information and keen insight towards answering the research questions being
examined in this study.
Site Administrators. The principal and the assistant principal over mathematics
played a very key role in this study. Even as the principal is the primary
instructional leader of the school, of near equal importance is the role of the assistant
principal running the day-to-day responsibilities of ensuring good mathematics
instruction. The assistant principal is also a key figure in translating the instructional
direction of the principal towards the teachers.
Key Leaders. Teacher and other leaders is perhaps the most important element
to fulfilling good instructional principal into practice, especially in achieving long
term change. Teacher leaders who participated including department chairs, site-
council members, and mathematics coaches. These front line instructional leaders
are the key to buy in and implementation with fidelity. Other leaders included
counselors among others. Counselors were of a particular interest as they are in a
unique position to observe student improvement.
Classroom Teachers. Classroom teachers are the ground troops in the war
against ignorance, and last line of defense to protect students from the likely
limitations of a life with no high school diploma. To the degree classroom teachers
65
are successful at implementing, is to the degree to which any program will have
fidelity.
Instrumentation
The instrumentation used in this study was developed collaboratively by 11
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 led by Dr. David Marsh, Associate Dean of Academic Programs and
professor at the University. The collaboration included 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 so as to answer the research questions. Work was
done to identify the relationship between the research questions and the data
collection instruments to ensure maximum effectiveness in the data collecting
process. Table 1 depicts the relationships between the different data collection
instruments used in the study and the research questions examined.
Table 1: Relationship of Data Collection Instruments to Research Questions

Research Question
Instrument 2 3 4 5
School Profile X
Key Leader Interview X X X X
Teacher Interview X X X X
Teacher Questionnaire X X X X
66

Intellectual Frameworks
Following the development of the chart depicted in Table 1, the members of
the cohort developed the actual instruments through a process grounded in
conceptual frameworks such as working collaboratively. Four frameworks were
developed so as to lead the process of creating data collection instruments. The
frameworks were key in proper utilization of instruments 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 acts 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.
Frameworks for Research Question 2: Effective Math Programs and School Design
Research Question 2 asked about the policy initiatives, curriculum and
instruction that relate to improved math achievement in the school. Two frameworks
were developed to assist in the analysis of this research question. The first is a
framework describing effective school design. The elements of this framework
come from Marsh and Codding’s model of school design. The basic elements are
reflected in Figure 1. The first framework emphasizes curriculum foundations built
on student-centered approaches and outcomes. The second framework, School
Cultures, is about having meaningful interactions between students and staff,
67
including professional development and learning opportunities. The third is
Learning Activities that strive to have students use higher order thinking skills, solve
problems and collaborate. The last framework is called Student Performance
Assessments which emphasizes effective communications, problem solving and
conceptual understanding.
Figure 1 – Framework for Effective School Design
School
Design
Curriculum Learning
Activities
Challenge
Students to
Think
Students
Solve
Problems
School
Culture
Based on
Enhanced
Learning
Meaningful
Staff-Student
Interactions
Ongoing
Professional
Development
Collaborative
School-to-Career
Applications
Constructivist
Knowledge
Based on
Student
Outcomes
Student Performance
Assessments
Capture
Conceptual
Understanding
Capture
Problem
Solving
Capture
Communication
Skills

Framework for Effective Mathematics Instruction
The second framework deals with the important elements of effective math
programs and is depicted in Figure 2. The first elements include a student-centered
curriculum that emphasizes conceptual understanding seeking mastery of
68
computations and manipulations of mathematical symbols and procedures as tools
in the problem-solving process. The second element is to incorporate rigorous,
standards-based practices that rely on content standards and assessments that are
related to data-driven decision-making. The last element is an effective and coherent
classroom pedagogy that is benchmarked by sound lesson design, makes use of prior
knowledge, and using culturally relevance that promotes high levels of student
engagement.
Figure 2 – Effective Math Programs

Effective
Math
Programs
Classroom Practices
ο Effective and
coherent lesson
design
ο Promotes high levels
of student
engagement
ο Makes use of prior
knowledge
ο Cultural relevance
Curriculum Design
• Student-centered
curriculum
• Driven by learner
outcomes
• Emphasizes Conceptual
• Focuses on problem-
solving
• Incorporates current
learning theory
Standards Based
Instruction
ο Assessments aligned
to standards
ο Student achievement
data drives
instruction and
decision
ο Common
performance
rubrics through
69
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.
Bolman and Deal’s Reframing Organizations (2003) provides leaders with a
framework for addressing the diverse aspects of complex organizations as they
manage the change process and is detailed in Table 2. In this work four frames
helped the researchers to view the operation of their organization; that is structural,
human resources, political, and symbolic. The four frames helped the researchers to
understand and categorize the site’s actions that brought student success.
Table 2 – Bolman and Deal’s Four Frames
Structural Human Resources Political Symbolic
Top Down
Hierarchies
Employees as
Partners & Family
Power Vision
Rules,
Policies,
Procedures
People of the
Organization
Bargaining Belief and Faith
Specialized
Tasks
Productivity through
Group Effort
Compete for
Limited
Resources
Stories
Goals &
Objectives
Self-actualization Negotiations Culture

As seen above the four frames have intricate parts. The Structural deals with
top down hierarchies, specialized tasks, goals/objectives and rules, policies, and
procedures. The Human Resources frame relates to employees as partners,
productivity through group effort, and self-actualization. The third frame Political is
70
characterized by power, bargaining, and negotiations. The last frame Symbolic is
known for relating to vision, belief, faith, stories, and organizational culture.
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. Table 3 depicts the instructional leadership framework used in this study.
The below framework is taken from two places. First the work of Ruth Johnson
Using data to close the Achievement Gap: How to measure equity in our schools
(2002), and the second work of Karen Hessel and John Holloway is called A
Framework for School Leaders: Linking the ISLLC Standards to Practice (2002).
The five frames as it where are Vision for Learning, Supervision and Monitoring of
Instruction, Community and Political, Culture of Teaching and Learning, and Data
Driven Decision Making.
The first frame Vision for Learning is facilitating the development, articulation,
implementation, and stewardship of a vision of learning that is shared and supported
by the school community. This includes developing a vision, communicating that
vision, implementing that vision, and monitoring and evaluating how that vision
addresses obstacles that impeded implementation. The second frame Supervision
and Monitoring of Instruction is about observing and monitoring the instructional
program. This is where constructive feedback and guidance is given regularly to
teachers. This can be accomplished through weekly classroom observations,
allocation of resources, supervisions of personnel, and hiring personal that supports
71
this goal. The third frame the Community and Political is concerned with the goals
of putting a value on diversity, knowing the communities’ needs, and involving the
community in the school.
Table 3 – 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- Communic
ating the
vision
C- Implement
the vision
D- Monitor
and
evaluate
the vision
E- Addresses
obstacles
to vision
implement
ation and
realization

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

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

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

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

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

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

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

A- Utilizes
assessment
data to place
students
appropriately
B- Formative
benchmark
school site
assessments
C- Summative
standardized
assessment
D- Disaggregate
data by
students,
classes and
cohorts
E- Use data to
guide and
improve
teachers
instructional
program
F- Use data to
create master
schedule
G- Using data to
inform and
improve
pacing
instructional
plans

72
The fourth frame Culture of Teaching and Learning concerns advocating,
nurturing, and sustaining a school culture and instructional program. The valuing of
students is paramount while using staff development to sustain the culture that is
inclusive of and respectful of diversity. Practices need to be implemented for
culturally relevant teaching and learning that celebrates the efforts and achievements
of students, teachers and staff. The fifth frame is Data Driven Decision Making
Analysis which uses data as a tool for informing instruction and supporting student
learning. This is done most notably though using assessment data to appropriately
place students, school site benchmark assessments, summative standardized
assessments, disaggregating the gained data by students and classes, using data to
guide and improve the instructional program, and using data to create a responsive
master schedule.
Framework for Research Question 5: Assessment of Individual Leader’s expertise in
math and Leadership Strategies to Improve Student Achievement.
Research Question 5 asked about how instructional leaders responded in
academic areas in which they were not experts. The framework developed by the
cohort 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 assessment was developed from the
guidelines of what is a highly qualified teacher as seen in NCLB (NCLB, N.D.). The
assessment resulted in one of three levels of expertise being assigned to the leader
that is high, medium, or low. This is seen in Figure 3. Second, a range of strategies
73
based on the literature around school improvement was devised to help the
researcher identify broad categories of efforts associated with which to view each of
the school’s efforts to improve student achievement in math. This second part of the
framework is detailed in Table 4.
Data Collection Instruments
Instrument 1 - School Profile: The School profile instrument was designed to
provide a framework for better understanding the characteristics that make up the
particular school community. A comprehensive picture was sought through data
collected in two areas--specifically in the areas of demographics and student
performance. Demographic data looked both at the student and teacher demographic
traits. Teacher data included credentialing and years of experience. Student data
included special consideration of English Language Learners (ELLs). Student

74
Figure 3 - Assessment of Principal’s Expertise in Math

Assessment of Principal’s Expertise in Math
Step 1
Is the Principal
HQT Compliant?
Yes No
High
Expertise
Step 2
Does the
Principal have a
credential or
major in math?
Yes No
Medium
Expertise
Does the Principal
have a minor or
taught math?
Yes No
Medium
Expertise
Low
Expertise
75
Table 4 – Strategies to Overcome a Lack of Subject Matter Competency

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

Performance data was important as it relates to the academic achievement pattern.
Performance data was gained from the Academic Performance Index, CAHSEE pass
rates, and district benchmark assessments.
Instrument 2 – Key Leader Interview Guide: The Key Leader Interview
Guide was developed to facilitate the collection of data relevant to research questions
numbers 2 through 5. The goal of the key leader interview guide is to discover what
the key leader observed lead to the improvement in mathematics. The key leader
76
answered questions related to a specific research question. This is included as
Appendix B.
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 with the goal of
discovering what the teacher observed lead to the improvement in mathematics. The
Teacher answered questions related to a specific research question. This is included
as Appendix C.
Instrument 4 – Math Teacher Questionnaire and Teacher Questionnaire:
The Math Teacher Questionnaire and Teacher Questionnaire were developed to
facilitate the collection of data relevant to research questions numbers 2 through 5.
Both questionnaires used a five point scale ranging from Strongly Agree to Strongly
Disagree, so as to allow teachers to express what they observed to have lead to the
progress in mathematics achievement. All questions in both questionnaires relate to
a specific research question. Of the 30 questions on the Non-Math Teacher
Questionnaire and the 50 questions on the Math Teacher Questionnaire there are
seventeen questions that are on both questionnaires. Of the questions The Math
Teacher Questionnaire and Teacher Questionnaires are included as Appendices D
and E respectively.

77
Data Collection
This study collected data over a three-month period from September 2006
through November 2006. The data was collected in three distinct rounds in order to
ensure two things--an inaccurate snap shot was taken and to give interviewees a
chance to review notes from their interview to ensure accuracy. Having multiple
rounds also allowed latter rounds to be informed and deliberate, rather than random
as themes emerge to the surface.
Central to data collection was obtaining the approval of the Institutional
Review Board (IRB) prior to the collection of any data. The IRB process is
government mandated in order to ensure study participants are respected during the
data collection process, whether it be in doing questionnaires or interviews. For
approval IRB considers whether the data collection approach is appropriate. Their
consideration of appropriateness required the submission of several documents to the
IRB by the researcher. The main document submitted was the Request of Claim of
Exemption for Non-Medical Research, in which three topics described the purpose
of the study, the population to be studied, and the methodology used in the study.
For this study, Dr. David Marsh submitted one IRB proposal for the 11 related case
studies being done by members of the thematic cohort earlier described. By having
the same data collection instruments and methodology a greater body of research
knowledge is achieved.
Once the IRB gave final approval for the study to begin, the cohort members
returned to their list of qualified schools and approached the school they had selected
78
to study. The individual cohort members contacted the principals of their
respective schools and informed them about the study and gauged their level of
interest, then approval. Approved dates were then arranged with the assistant
principal over mathematics as to when to do data collection including questionnaires
and interviews. Participants were informed that all participation was voluntary and
that they could choose to end participation at any time. The questionnaire was
voluntary and the teachers were given ample time to turn in their questionnaires, so
that they would have every opportunity for their voice to count in the data collection
process.
The first round of data collection sought to gain an overview of the school.
An interviewer with the principal was hard to find out how the school has worked to
make such progress. In this round the researcher also spent time in classrooms,
ascertained a copy of the school master schedule, and distributed both Teacher
Questionnaires. The second round of data collection served as an opportunity to
follow up in a deeper investigative way. The researcher during this period
interviewed assistant principals, department chairs and teacher leaders. Also the
questionnaires were collected and compiled into a database of information. The last
round of data collection sought the collection of any missing questionnaires still at
the school site. This was also an opportunity to have further interviews with follow-
up questions that arose due to the teacher questionnaire and interview results.

79

Data Analysis
Questionnaire data was ascertained from two questionnaires--the
Mathematics Teacher questionnaire and the Non-Mathematics questionnaire. A inter
questionnaire correlation was compiled, shown below in Table 5.
Table 5: Number Correlation

This Number Correlation, as it is titled, was created to allow direct comparisons of
mathematics teachers and non-mathematics teachers responses. All data was
compiled into an excel database. Built into the excel database were automatic
calculations that gave the mean for every question. These mean scores for individual
questions showed to what degree affirmative answers were chosen as to the
particular reasons for success. Shown next are the question number, their research
question group, and a mean score in the form of Table 6.
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Table 6: Questionnaire Mean Score Analysis

A mean score of 2.75-3.25 would be considered in the neutral area. A score of 3.25-
3.75 would be considered an affirmative response, while a score above 3.75 would
be considered a strong affirmation. A score of 2.25-2.75 would be considered a
negative response, while a score of less than 2.25 would be considered a strong
negative response.
Greater depth of data was gathered from the non-math teacher questionnaires
by printing each department on a different color of paper. This allowed for the
ascertaining of departmental data, rather than just the limitation of all non-math
teachers. Here below see in Table 7 an excerpt showing the department scores.
Table 7: Departmental Questionnaire Mean Score Analysis

Seventeen questions correlate between the two questionnaires and special interest
was given to the difference between how math and non-math teachers answered
them.
81
Interview notes were taken manually and transcribed to be reviewed by the
participants. Following a verification of accuracy trends and tendencies were sought
after. Similar concepts, patterns, and frequencies were looked at to inform pointed
final questions in the third round of data collection. The answers to these pointed,
more informed questions lead to a clearer understanding of how effective
instructional leadership helped to produce significant math achievement. One key to
analyzing the data of the interviews was to type them up and color coat what answers
related to what research question. Although a participant may be asked about the
change process (research question 3), they may in their response speak about how
the instructional leader responded in academic areas (research question 5). Freedom
was given to the individual to the answer, so that the researcher could ascertain the
fullest answer that relates to all research questions.
Validity and Reliability
This study used multiple sources of data to ensure internal validity as best as
possible. Triangulation of data included interviews with leaders, teachers, and with
teacher questionnaires as well as direct classroom observation. In the third round of
data collection the researcher was allowed the opportunity to follow-up on
unanswered and additional questions. In addition, interviewees were given the
opportunity to review notes from their interview to check for accuracy of intent and
phrasing. Though the findings in this study are reasonable, as a single case study
they are not necessarily generalizable to other settings.

82
Conclusion
The purpose of this chapter was to describe the methodologies used in this
study. Included was a detailed description of the sampling criteria, the data
collection instruments, data collection process and data analysis methodology. The
procedures used for this study were collectively developed by the students in the
cohort led by Dr. David Marsh and were approved by the IRB of the University of
Southern California. Data collection was mainly comprised of teacher and key
leader interviews and two teacher questionnaires. Direct classroom observations
were made to triangulate data whenever possible. The findings discussed in the next
chapter are based on a thorough analysis of the data collected.
83
CHAPTER 4
DATA FINDINGS, ANALYSIS, AND DISCUSSION
This chapter shares the findings of a case study of one high school’s
successful attempt to improve mathematics achievement. The purpose of this study is
to find out how urban high schools that have experienced significant gains in math
performance in their students looking at two areas of concern. First, to find out how
urban high schools bring together policy initiatives, coupled with how urban high
schools increase school site best practices to bring about improved math performance
in their schools. Second, to find out how instructional leadership, if effectively
carried out, improves high school math performance for students. In the pursuit of
effective instructional leadership there is a need to discover how to help leaders who
do not have a strong pedagogical content knowledge be successful as instructional
leaders. Two issues seem to be especially relevant to this second concern of
instructional leadership while fulfilling the need to carry out functions related to
fiscal, personnel, organizational leadership, data analysis and review. The purpose
of this study is two-fold to find a guide at bringing together policy initiatives with
best practices. And second to determine some guiding examples of best practices for
the instructional leader who is successful about pedagogical and organizational
leadership.
The case study’s five research questions guided the discourse of the findings:
1. What was the pattern of Math achievement for various students at the
school?
84
2. What Policy initiatives as well as curriculum, instruction and related
conditions seem to be related to improved math achievement in the
school?
3. What change process did the school use to enhance its math program and
strategies to assist students in math?
4. To what extent was strong instructional leadership important in improving
(a) the math programs/strategies and (b) math achievement among
students?
5. How did instructional leaders respond in academic areas in which they
were not experts?
The following remainder of this chapter consists of Data Findings for the five
Research Questions. Within consideration is given to numerous data developments
in methodical order guided by the five Research Questions. Following this Analysis
and Discussion follows where five topics of interest are considered that show some
of the most notable phenomena. The data instruments included school profile, key
leader and teacher interviews, math and non-math department surveys. The surveys
were entered into excel to provide averages that showed the degree of agreement and
disagreement on topics and issues.
Data Findings
Research Question 1: Student Achievement in Mathematics
The first research questions asked, “What was the pattern of Math achievement
for various students at the school?” This school demonstrated improvement in math
85
achievement as evidenced by California Standards Test scores, increased Algebra I
enrollment, Advanced Placement pass rates, and CAHSEE pass rates.
California Standards Test (CST) Scores
The first is the progress in results shown through the California Standards Test
(CST) in Algebra I. The California Standards Test is the state benchmark exam that
helps to determine passage on the API and AYP index. The key to the success of the
school, is its’ commitment that all students can achieve and learn. The results are
encouraging as West Valley has increased steadily their API since 2001 from 649 to
676. During this same period the school’s statewide rank has gone up from 4 to
where it is currently a 5. In the area of Algebra achievement it has made an overall
increase of 11%. The school has showed great progress in achievement across all
sub groups.
Increased Algebra I Enrollment
Algebra 1 enrolment is an indicator of to what degree schools are structuring
education so that students are prepared to meet college admission requirements. In
Figure 4 an increase in Algebra 1 enrolment is progressive and striking. For example
in the 2002-2003 school year, there were only 324 Algebra 1 students and more than
half of them were in 10-12
th
graders. Compare this to 853 students a year later in the
2003-2004 school year of which 83% were 9
th
graders.

86

Figure 4: Enrolment in Algebra 1 over the last six school years.
417
324
853
1021
1083
973
254
149
705
811 811
832
163
175
148
210
272
141
0
200
400
600
800
1000
1200
2001-2002 2002-2003 2003-2004 2004-2005 2005-2006 2006-2007
Number of Students Enrolled
All Students
9th Graders
10-12th Graders

This represents a clear change not only practice, but also in philosophy.
Furthermore the 2006-2007 school year shows an apparent decrease in overall
Algebra 1 enrolment falling from 1083 (2005-2006) to 973. This drop of enrolment
is further proof of significant growth, as the drop occurred in the 10-12
th
Graders
who had to remediate nearly half as much as the previous year.
The difference in priority and philosophy is even clearer when students who
took Algebra 1 are compared directly as a proportion to the students taking the 6
th

and 7
th
grade standard course “General Mathematics.” In figure 5 over a four
transition a total reversal in priority is apparent. While just over 20% of students are
in Algebra 1 in the 2002-2003 school year, just under 90% are enrolled in Algebra 1
by the 2005-2006 school year. This constitutes a 70% increase in students taking
classes that are more challenging and also necessary for college admission.
87
627
289
239
89
201
458
536
715
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
2002-2003 2003-2004 2004-2005 2005-2006
Number of 9th Grade Students Tested
Algebra 1
General Mathematics
Figure 5: Increase of Students Taking Algebra 1
Advanced Placement Passing Rates
Advanced Placement test results are also an indicator of how a school’s
students perform especially in comparison to other students. Advanced Placement
tests are used by high school students to earn college credit for such classes as
Calculus or U.S. History. The passing rates of 12
th
grade students with 3 or above
are shown in Figure 6. Of the three years there is data for West Valley HS out
performs the state as a whole with a high percentage of difference. In 2004 there is
53.l percent difference in the favor of West Valley’s student success at receiving 3 or
above. Although in the next two years the state narrows the gap in 2006 West Valley
still out performs by 22.7%.

88
96
62
79
42.9
45
56.3
0
20
40
60
80
100
120
2004 2005 2006
Percentage of Scores 3 or Higher
West Valley HS
Statewide
Figure 6: 12
th
Grade Advanced Placement Test Results
California High School Exit Exam (CAHSEE) Pass Rates
Results on the California High School Exit Exam also serves of an indicator of
how a school prepares to the state as a whole. The California High School Exit
Exam is the mandated state test that must be passed prior to a student receiving a
high school diploma. Figures 7 and 8 show the pass rates for African American and
Hispanic students respectfully. In the 2001-2002 year West Valley African
Americans have a pass rate of 38%, compared with the state percentage of 20%. By
the 2005-2006 school year West Valley African Americans have a pass rate of 55%,
compared with the state percentage of 40%. In those four years West Valley African
Americans rose by 17%, while the statewide African Americans rose by 20%.
Though the statewide increase is a little larger than West Valley they still hold have
15% greater number of African American students passing the CAHSEE.

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Figure 7: African American CAHSEE Passing Rate
0
10
20
30
40
50
60
70
2001-2002 2002-2003 2003-2004 2004-2005 2005-2006
Percentage of Students Passing
West Valley HS
Statewide

In the 2001-2002 year West Valley Hispanics have a pass rate of 26%,
compared with the state percentage of 22%. By the 2005-2006 school year West
Valley Hispanics have a pass rate of 52%, compared with the state percentage of
49%. In those four years West Valley Hispanics rose by 26%, while the statewide
African Americans rose by 27%. Though the statewide increase is a little larger than
West Valley they still hold have 3% greater number of Hispanics students passing
the CAHSEE.

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Figure 8: Hispanic CAHSEE Passing Rate
These two groups are of particular interest as they often given key
consideration in relation to the Achievement Gap. In those four years the percentage
of African Americans passing nearly doubled. Also percentage of Hispanic students
passing did double. This is further indication that the students are on the right path.
When looking at the Achievement Gap progress is also evident. The pass rates for
White students were 80% and 82% for Asians for the 2002-2003 school year. In the
2005-2006 school year White students rose to 88% passing rate and 98% for Asians.
This constitutes a 20% increase of success for Asians and 10% increase for White
students. This is compared with a 100% increase for Hispanics and nearly 100%
increase for African Americans. It is an indicator of something dynamic that West
Valley’s Achievement Gap is being eliminated by such leaps and bounds.
Summary of RQ1 Findings
In all the progress made by West Valley is not only viewable by multiple
measures, but is also seems to be statistically sound in how it originates from
0
10
20
30
40
50
60
70
2001-2002 2002-2003 2003-2004 2004-2005 2005-2006
Percentage of Students Passing
West Valley HS
Statewide
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multiple sources. The above four indicators clearly show how West Valley has a
diverse body of success, when it comes to areas of achievement.
Research Question 2: Policy Initiatives and Improved Curriculum
Research Question 2 is “What Policy Initiatives as well as curriculum,
instruction and related conditions seem to be related to improved math achievement
in the school?” Improved math achievement at West Valley High School is related
to three areas of policy initiatives. First federal policy in NCLB providing better
prepared teachers. Also in the school design aspect as seen in utilizing of periodic or
benchmark assessments. And lastly Math Program Design which is characterized by
five school level initiatives.
Policy
Existing Policies and School Response. The policy initiative that most
impacted West Valley High School was the federal No Child Left Behind Act
(NCLB). Three of the four key leaders and one of the four teachers sited NCLB as
influential in ensuring that qualified, prepared, and credentialed teachers were hired.
The math and non-math teacher questionnaires show that is the limit of their
favorable view of NCLB. In Table 8 the results of the two questionnaires are shown
relating to NCLB:

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Table 8: Questions relating to NCLB

Above non-math teachers felt more strongly against the notion that NCLB had
promoted increased student achievement. Both groups response fell into the
Negative Response range. When the math teachers were asked if NCLB acted as a
main external pressure, they had an average that could be described as in the Neutral
Area. Both math and non-math teachers do not feel board policies have contributed
to improved math achievement in their school. In all teachers at West Valley High
School do not feel that NCLB, nor board policies improve achievement, but rather
NCLB may only help to ensure better prepared teachers.
School Design
Student Performance Assessments. Performance Assessments are very central
to the daily life of the West Valley High School teacher. One of the school
mathematics leaders is the math coach who said, “We try to align curriculum to
benchmark assessments, which are good practice for the CSTs.” Another
Question Average Result
MQ 1 - The NCLB Legislation has promoted
increased student achievement at our school.
2.69
Negative
Response
NM 1 – The NCLB Legislation has promoted
increased student achievement at our school.
2.38
Negative
Response
MQ 10 – The NCLB Act has been one of the
main external pressures for improved math
achievement at this school.
2.88 Neutral Area
MQ 3 – Board Policies in our district have
contributed to improved math achievement in
our school.
2.44
Negative
Response
NM 3 – Board Policies in our district have
contributed to improved math achievement in
our school.
2.75
Negative
Response
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mathematics leader is the Math department chair who described the periodic
assessments as helpful. One of the teachers like the organizational structure created
by the periodic assessment of knowing what to be teaching when. Another teacher
like the math coach sees CST value in the benchmark periodic assessments as, “They
are a really good indicator of how students are going to do on the May CSTs.” In
table 9 the results of the two questionnaires are shown in relation to common and
benchmark assessments.
Table 9: Questions relating to Common and Benchmark Assessments

The math department answered both questions with strong agreement saying
that common assessments have been implemented and produced useful data that
helps to drive instruction. Conversely non-math teachers on average were neutral
about implementation and the value of data. Consideration of departmental
differences among non-math teachers shows a divide. Departments show a large
Question Average Result
MQ 4 – Our school has successfully
implemented common assessments that support
increased student achievement.
3.50
Agreeable
Response
NM 4 – Our school has successfully
implemented common assessments that support
increased student achievement.
3.11 Neutral Area
MQ 8 – Periodic benchmark assessments
provide useful data that our teachers use to
drive instruction.
3.31
Agreeable
Response
NM 8 – Periodic benchmark assessments
provide useful data that our teachers use to
drive instruction.
3.13 Neutral Area
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range of response as seen with the agreeable response departments, including Art
(3.60), Foreign Language (3.60), and ESL (3.57) and departments with a negative
response including Social Science (2.33) and Special Education (2.73). In all it is
apparent that the Mathematics department has used and finds value in common
benchmark assessments. It is also clear that different departments have a diverse
degree of appreciation for such assessments, most likely in accordance with how as a
department they have used them.
Curriculum. Curriculum was very important to the success of the school. The
specifics about that curriculum are discussed shortly under Math Program Design.
The school’s curriculum is centered by the integration of rigorous programs. The
math department chair says that the curriculum is informed by the desire for students
to succeed. Philosophically the move to have all students take Algebra and other A-
G requirements, is an accomplishment that one teachers was proud of. In all the
West Valley is successful as its curriculum is not independent from sound pedagogy
and rigor.
School Culture. School culture was greatly influenced by standardized tests,
especially the CAHSEE. There exists on the campus a spirit of “no slacking”
according to the Assistant Principal in charge of mathematics. In response to a
question as to the effect of the CAHSEE that same Assistant Principal said,
“Students are choosing to work hard, because [graduation] matters to them.” The
principal summarized it as “High stakes tests motivate the student, when it matters to
95
them.” In Table 10 the results of the two questionnaires are shown in relation to
common and benchmark assessments.
Table 10: Questions relating to School Culture

As seen above both Math and non-math teachers agree strongly that CAHSEE
requirement for a high school diploma has contributed to the school’s effort to
improve student achievement. Math teachers in question 9 agree strongly that as a
matter of school culture student need is a major consideration. Teachers are willing
to take students who are not their first choice, because as a department they value
each other’s strengths. Consistent with earlier mentioned NCLB questions math
question 12 did not get a favorable response. In all the school culture is
characterized by prudence and a keen emphasis on student need.
Question Average Result
MQ 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.
4.00 Strong Agreement
NM 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.
3.84 Strong Agreement
MQ 9 – Student need is a major consideration
when making teacher assignments in math at
our school.
3.75 Strong Agreement
MQ 12 – Our school’s effort to improve
achievement in math instruction had nothing
to do with external accountability such as
NCLB regulations and the CAHSEE
requirement.
2.94 Neutral Area
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Learning Activities. West Valley has many specific learning activities that
are considered in depth below under Math Program Design. One learning activity of
significance is test preparation. They are practicing, according to the Math
Department chair, “to be ready for standardized tests.” Warm ups are integrated into
the curriculum, to according the Math Coach, “help students learn strategies to help
them pass and do better in Mathematics.” In all learning activities like test
preparation strategies are a smart way to help students understand the phrasing of
standardized tests.
Math Program Design
Math program design has been dynamic and has influenced classroom
practices, curriculum acceptance, and the implementation of standards based
instructional practices. There are five aspects of their reform to be considered under
Math Program Design. The first the Mathematics Diagnostic Testing Project
(MDTP) testing project, Star Academy Program, John Hopkins Academy Program
(TAMS), Twilight Model, and District CAHSEE Boot Camp.
The first of the five school level reform initiatives is the University of
California at Los Angles (UCLA) Mathematics Diagnostic Testing Project (MDTP)
testing project is key to the proper placement of students. MDTP is a statewide
project by the CSU and UC system that develops, distributes, scores, and reports the
results of tests that measure student readiness for mathematics courses. At West
Valley administering the Algebra Readiness Test assesses preparation for first-year
Algebra. Printed results are sent to school showing item analysis by number and
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percentage of students and individual results and letters. The student letter tells
students their score and shares what topics are done well and which need review (see
Appendix F). West Valley uses this test to confirm that students need to be the
intervention programs mentioned next and also to convince reluctant parents of the
need for special intervention. The Department Chair expressed how this diagnostic
test is so key at the beginning of the year. She said it is very helpful in convincing
parents of their student’s need for practice. Many parents like to come in and
demand that their student be put in Geometry I as ninth graders, because they want
the m to take Calculus as seniors. The test serves as a “red flag” saying the student is
not ready for that.
The Star Academy Program and the John Hopkins Academy Program (TAMS)
are the two during the day special interventions that students belong to. The Star
Academy is aimed at Below Basic students and John Hopkins is aimed at Far Below
Basic Students. Every teacher and key leader shared about these two programs as
the key to progress made over the past three years.
The John Hopkins Academy is more recently founded a year and a half ago. It
is structured as two hours of mathematics. Student group work is central to the
activities under the John Hopkins Academy Program. In the first semester of ninth
grade Pre-Algebra is completed. Algebra I is completed over the course of the
Spring semester. The second year Carnegie Geometry is used. The effect of the
John Hopkins Academy is already felt in the progress made by students in general.
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The Star Academy Program which was put in place four years ago has had a
significant impact. These students are characterized by low grades and averaged test
scores in 8
th
grade, before entering the program as 9
th
graders. During the first year
the students have two hours of English and two hours of Mathematics. During the
first hour of 9
th
grade Algebra I, Carnegie Algebra I is used, while the second hour
Prentice Hall is used. During the second year the students are kept together as a
cohort so to speak, but are ready to take one hour of mathematics like all at grade
level students. As a cohort regular teacher collaboration with each other and the
students helps reach the program goal of becoming self-initiated learners and critical
thinkers who have the desire and necessary tools to function successfully at the
college level and in life. The program goal is being realized in two ways. First the
CAHSEE passing rate for Star Academy students is 99%. Second 100% of Star
Academy graduates go onto higher education after high school. An amazing 93% of
students go to colleges and universities and the remaining 7% enter trade or
professional schools after graduation.
Another intervention strategy is the implementation of the Twilight Model.
This for students who have a semester in which they earn all fails. After that
semester occurs, they enter the Twilight Model where they come to school from 3:30
p.m. to 6:30 p.m. and take only English and Mathematics during that time. Only
after earning five credits for each are they allowed to come back to school during the
regular school day. This levees quite a bit of pressure on students socially. If they
want to be at school with their friends again, they need to be studious and achieve.
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A last way they help struggling students relates to passing the CAHSEE.
The district has designed what is referred to as a CAHSEE Boot Camp. This was
created for a certain level of student, who failed the CAHSEE the previous year. The
Boot Camp occurred for four hours a day for two weeks prior to a certain Spring
CAHSEE administration. This was a useful curriculum for reviewing a great body
of skills needed for passing the CAHSEE. In Table 11 the results of the two
questionnaires are shown relating to Math Program Design:
Table 11: Questions relating to Math Program Design

Question Average Result
NM 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.
3.40 Agreeable Response
MQ 6 – The master schedule at our school is built based
on student need.
3.69 Agreeable Response
MQ 13 – Support classes have been included in our
master schedule to improve student achievement in
math.
4.38 Strong Agreement
MQ 25 – Our school has implemented effective
intervention strategies for students having difficulty in
math.
3.63 Agreeable Response
MQ 48 – Quality interventions in math have been
implemented on our site to help students at risk of
failing academically.
3.69 Agreeable Response
NM 28 – Quality interventions have been implemented
on our site to help students at risk of failing
academically.
3.50 Agreeable Response
MQ 7 – Teachers at our school use researched-based
instructional strategies to increase student achievement.
3.19 Neutral Area
NM 7 – Teachers at our school use research-based
instructional strategies to increase student achievement.
3.55 Agreeable Response
MQ 5 – Teachers at our school teach standards-based
lessons.
3.88 Strong Agreement
NM 5 – Teachers at our school teach standards-based
lessons.
3.93 Strong Agreement
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According to non-math (9) and math teachers (6) respectively there is
agreement that structures and policies that student achievement are in place and that
the master schedule of their school is built based on student need. There is strong
agreement among math teachers (number 13) that support classes have been included
in the master schedule to improve student achievement. Math teachers (number 25)
agree that effective intervention strategies have been implemented. Both math and
non-math teachers agree (MQ 48 and NM 28) that quality interventions have been
implemented to support students at risk of failing academically. When asked if
teachers use research-based instructional strategies, non-math teachers agreed, while
math teachers’ responses fell into the neutral area (MQ 7 and NM 7). Lastly in math
teacher question 5 and non-math teacher question 5, there is strong agreement that
teachers at their school teach standards-based lessons. This was also expressed in
interviews, when teachers stated that the district benchmark assessments where good
practice for the standards-based CST. They found that although some of the
phrasing could be made more similar, the concepts where aligned and useful for
practice. In all there is strong agreement from the faculty that there are on the right
track, for the right reasons. There is a clear sense of fulfillment that there are making
the necessary accommodations to help as many students succeed as possible.
Summary of RQ2 Findings
The three areas of initiatives whether it is federal, general, or school site by
themselves might not be enough to have created so much progress. But when they
are viewed as Partners in Progress a picture emerges of how multiple initiatives
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from multiple levels of an operational structure, can work together to produce
great success. Certain policy initiatives and dynamic programs were brought
together to directly influence the progress the school made. The success of the
school appears to be directly related to how the policy and program acted as husband
and wife in a happy marriage.
Research Question 3: The Change Process
Research Question 3 is “What change process did the school use to enhance its
math program and strategies to assist students in math?” The change process is
considered through four frames. The strategic plans of the school were analyzed
through the Structural Frame. The hiring and responsibility actions were considered
in light of the Human Resources Frame. Precise decision-making was evident
through the lens of the Political Frame. The fruit of high expectations were analyzed
through the Symbolic Frame.
Structural Frame
Structurally West Valley High School had to make numerous foundational
changes in order to carry out its Math Program Design. The school had to juggle the
matrix to allow for the block schedules for special programs. It would have meetings
for staff to decide on the direction and nature of Small Leaning Communities. A
commitment to professional development was necessary before starting the change
process. Computers had to be purchased and personnel had to be trained to maintain
the equipment used with the Carnegie Math. The matrix changed so that all students
were taking their A-G required classes. In Table 12 the results of the two
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questionnaires are shown in relation to achievement priorities and having a
strategic plan.
Table 12: Questions relating to Achievement Priorities and Strategic Planning

Both math and non-math teachers feel unsure about whether the school made
an achievement as it allocated its resources. That being said, both math and non-
math teachers agree that the school had a clear strategic plan to improve student
achievement. In consideration of all the things identified in Math Program Design
above, it is not surprising that teachers would recognize that the many actions came
out of a strategic plan. It is interesting that they would unsure or neutral about the
possibility that financial resources were allocated as a priority towards student
achievement.
Human Resources Frame
Several personnel changes have been instrumental in the success witnessed at
West Valley High School. The most important personnel change according to all the
school leaders interviewed was the addition of a Math Coach. She is a half time
Question Average Result
MQ 20 – Student achievement in math was
made a priority as the school allocated its
financial resources.
2.94 Neutral Area
NM 15 – Student achievement in math was
made a priority as the school allocated its
financial resources.
3.11 Neutral Area
MQ 21 – Our school had a clear strategic plan
to improve student achievement in math.
3.38
Agreeable
Response
NM 14 – Our school had a clear strategic plan
to improve student achievement.
3.25
Agreeable
Response
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coach who, teachers half day and coaches the other half. They way she
coordinates and shares good pedagogy is by all accounts central to the success they
have experienced. In addition to this key leaders shared that replacing long-term
subs with regular teachers has helped. The department chair also found it helpful
that there were finding teachers with a greater background in technology. The
teachers interviewed found great value in working together under the direction of the
Math Coach. In Table 13 the results of the two questionnaires are shown in relation
to the Math Coach and hiring practices.
Table 13: Questions relating to the Math Coach and Hiring Practices

The math department overwhelmingly agrees, with a 4.38 average out of 5.0
possible that the Math Coach was added to assist in the effort of improving student
achievement in math. According to the non-math question number 10, there is
school wide agreement that there has school emphasis on hiring quality teachers and
fostering a positive working environment on campus between individuals.

Question Average Result
MQ 15 – Our school has added the use of math
coaches or experts to assist in the effort to
improve student achievement in math.
4.38 Strong Agreement
NM 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.
3.48
Agreeable
Response
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Political Frame
When campus leaders were asked about their experience negotiating the
political aspects of the change process their responses varied. The department chair
emphasized the importance of getting teachers and parents to buy in. She found it
easier to achieve consistent teacher buy in from the Math Department, due to a long
history of departmental collaboration and agreement. The Math Coach experienced
acceptance and respect from the teachers, because of her 10 years there, the fact that
she is a part time coach, and her willingness to teach at least one group of the lowest
students. The Principal dealt with the political situation by not being shy of making
decisions. The teachers interviewed found great value in working together under the
direction of the Math Coach. In Table 14 the results of the two questionnaires are
shown in relation to the political obstacles and community support.
Table 14: Questions relating to the Political Obstacles and Community Support

As indicated in non-math teacher question number 11, the school is neutral
about whether a clear focus has been set on overcoming political obstacles. There
this is however strong agreement that the principal continually works to gain the
Question Average Result
NM 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.
3.00 Neutral Area
NM 17 – The principal works to gain the
support of the community for the school’s
academic efforts.
4.25 Strong Agreement
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support of the community towards fulfilling the school’s academic efforts. In all
the political situation is helped by careful and precise decision-making by the key
leaders.
Symbolic Frame
School mathematics leaders are doing numerous vision based actions in order
to build the right student climate. The assistant principal emphasized that “everyone
likes to be recognized for their achievement.” She went on to describe how they
have built a “culture of open communication and high expectations” for the West
Valley student body. A math teacher echoed this sentiment, calling it “clear
expectations of high results.” She also shared that they revise the school vision
periodically. The Math Coach shared how Senior and Mathematics Department
Awards are used to celebrate student achievement. The principal is using creative
intervention strategies to fulfill the school vision as described under Math Program
Design where the “Twilight Model” is described. According to another math
teacher, the principal emphasizes it is a good school that has the potential to produce
good results. In Table 15 the results of the two questionnaires are shown in relation
to the expectations, vision, and school climate.

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Table 15: Questions relating to the Expectations, Vision, & School Climate

Math teachers according to math question number 41 are neutral about the
notion that district personal, school leaders and teachers are all on the same page.
The math teachers overwhelmingly feel (question 47) that West Valley’s leaders
emphasize high expectations for student achievement in math. Non-math teachers in
their corresponding question 27 feel very strongly about the school leaders’ high
expectations. Non-math questions 12 and 13 together show that there has been a
shared vision that has focused on motivating students and staff as well as celebrating
successes. Non-math question 18 shows how cultural diversity is a priority. Lastly
non-math question 19 emphasizes how there is a culture of appreciation. From the
Question Average Result
MQ 41 – The district personnel, school leaders
and teachers all have a shared vision for
increased math achievement.
3.19 Neutral Area
MQ 47 – Site leaders emphasize having high
expectations for student achievement in math.
3.63 Strong Agreement
NM 27 – Site leaders emphasize having high
expectations for student achievement.
3.78 Strong Agreement
NM 12 – In an effort to improve instruction on
our campus, our school has focused on
motivating students and staff as well as
celebrating successes.
3.36
Agreeable
Response
NM 13 – There is a shared vision for increased
student achievement at our school.
3.43
Agreeable
Response
NM 18 – The school leadership works to
establish and maintain a respect for cultural
diversity.
3.82 Strong Agreement
NM 19 – Students and staff are valued and
their successes celebrated.
3.31
Agreeable
Response
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interviews and questionnaires a strong body of evidence suggests that the school
is characterized by a high expectation filled vision, which influences many positive
practices through out all content areas.
Summary of RQ3 Findings
The change process that occurred to effect change at the school was observable
and fell nicely under the four frames. The Structural Frame shows the effects of the
strategic plan were realized. The Human Resources Frame showed how school
decisions about hiring and responsibility are effective. The Political Frame showed
careful and precise decision-making. The Symbolic Frame emphasized the benefits
of genuine high expectations.
Research Question 4: Strong Instructional Leadership
Research Question 4 is “To what extent was strong instructional leadership
important in improving (a) the math programs/strategies and (b) math achievement
among students?” Strong instructional leadership was seen in five areas including
the vision for learning, the supervision and monitoring of instruction, community of
reflection, data driven decision-making analysis, and culture of teaching and
learning.
Vision for Learning
There is consensus among all school leaders that two school leaders under the
direction of the principal are responsible for the shared vision of the mathematics
department. That is the Department Chair and especially the Math Coach together.
The Assistant Principal describes them as doing “a great job and [that they] are well
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respected by the staff.” The Math Department chair celebrated how the Math
Coach with “excellence” brings back useful concepts and methods from district
coach meetings, including strategies from other schools. The Math Coach was
exuberant about the impact of teachers going in other teachers’ rooms and observing
lessons.
The teachers felt strongly about the influence of site leaders as well. One
teacher shared the value of spending time speaking as a department about the
direction of learning and how to implement that direction. Another teacher was
excited about the shared vision describing the department as “very supportive, she
always gets what she needs.” Not just material needs, but educational as good
communication and mentoring occurs. Another teacher was grateful to the principal
due to “good grasp of the sequence of math” and her ability of “getting students in
the right place.” In Table 16 the results of the two questionnaires are shown in
relation to the influence of site leaders.

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Table 16: Questions relating to the Influence of Site Leaders

The above questions were all asked of math teachers have two results either an
Agreeable Response (questions 30, 31, and 32) or Neutral Area (questions 28, 37,
39, and 42). The math teachers feel neutral as to whether teachers learn by watching
each other, have regular support from proven instructional leaders, have received
coaching and mentoring, and whether district/school leaders seem knowledge about
effective math practices. They do however have significant agreement that the math
coach has helped them to become more reflective with instruction, they have gained
valuable resources from the mathematics coach, and that the professional
development resources instructional leaders provide are used in their mathematics
Question Average Result
MQ 28 – Teachers learn by watching each
other teach and discussing best practices.
2.63 Neutral Area
MQ 30 – Our school used math coaches to help
teachers become more reflective with their
math instruction.
3.38
Agreeable
Response
MQ 31 – I have gained valuable resources
from math coaches/ instructional leaders that
have improved the quality of my math
instruction.
3.50
Agreeable
Response
MQ 32 – My school’s instructional leader
provides professional development resources
that I use in my mathematics instruction.
3.31
Agreeable
Response
MQ 37 – I have regular support from proven
instructional leaders in math instruction.
3.19 Neutral Area
MQ 39 – I received coaching and mentoring
from instructional leaders or peer coaches.
2.94 Neutral Area
MQ 42 – My district and school leaders seem
knowledgeable about instructionally effective
math practices and assessment strategies.
2.81 Neutral Area
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instruction. It seems sure that a clear vision for learning exists through out the
math department, even if how they got there is a mystery to some of the math faculty
members. Perhaps a better explanation of why they were taking certain actions
when, would have prevented this confusion.
Supervision and Monitoring of Instruction
It is important to the site leaders that proper supervision and monitoring of
instruction occurs. Site leaders have attempted to make the focus on student learning
and results by meeting at the site council, sharing data and reports with all
department chairs. Weekly meetings are held with school leaders from all areas or
responsibility. One way the principal found to monitor instruction is to meet with
groups of students and give them the straight truth about their poor performance and
benefit from the staff being honest with them. In Table 17 the results of the two
questionnaires are shown in relation to the political obstacles and community
support.
Table 17: Questions relating to the Political Obstacles and Community Support

Question Average Result
MQ 33 – The school leader is aware of the mathematics
instruction and academic progress of the students in my
class.
3.31 Agreeable Response
MQ 50 – Teacher assignments in the math department
are made strategically and with student need in mind.
3.56 Agreeable Response
NM 30 – Teacher assignments are made strategically
and with student need in mind.
3.43 Agreeable Response
NM 21 – The principal works hard to monitor and
supervise instruction in the classroom.
3.27 Agreeable Response
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There is agreement among math teachers that the school leader is aware of
the mathematics instruction and academic progress of the students in their classes.
That is to say supervision and monitoring of instruction are present. Both math and
non-math teachers agree that teacher assignments are made strategically and with
student need in mind. So students are being evaluated and placed appropriately by
site leaders who are supervising and monitoring the needs of instruction.
Furthermore, results of non-math question 21 indicate that there is agreement that the
principal works hard to monitor and supervise instruction.
Community of Reflection and Data Driven Decision-Making Analysis
When key leaders were asked to what degree teacher collaboration and
reflection were fostered and encouraged they gave particular responses. The
Assistant Principal shared how when departments meet they discuss what is working,
what is not working. Also she shared that having the coach do demonstration lessons
is of great value. The Department Chair was that the more time given the better for
spending together. This time was so precious, because they used it for “sharing best
practices.” The Math Coach expressed how they “love meeting as a department,
working together as a group.” The Principal said it was her goal to give plenty of
time to collaborate and reflect. One teacher praised the principal for having shared
data numbers, that helped the coach and department chair lead conversations aimed
at raising scores on the CST. Another teacher was pleased, due to the supportive
chair and coach and the “clear expectations of high results.” In Table 18 the results
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of the two questionnaires are shown in relation to the community and data driven
decision-making.
Table 18: Questions relating to the Community and Data Driven Actions

Question Average Result
MQ 16 – Teachers collaborate to develop common
assessments and rubrics.
2.88 Neutral Area
MQ 18 – Teachers have helped develop strategies used at
our school to improve instructional practice in math.
3.44 Agreeable Response
MQ 23 – Teacher collaboration has played a key role in
increasing student achievement in math.
2.75 Neutral Area
MQ 27 – My principal actively supports opportunities for
staff member to collaborate and plan Mathematics
lessons and units.
2.94 Neutral Area
MQ 19 – The principal has served as a “change agent”
for improved student achievement in math.
3.06 Neutral Area
MQ 34 – The school leader provides opportunities for
faculty members to discuss mathematics instruction.
3.19 Neutral Area
MQ 35 – The school instructional leader encourages
faculty members to discuss effective math instructional
strategies.
3.25 Neutral Area
MQ 49 – Our site leaders emphasize a culture of
collaboration as a means of improving instruction at our
site.
3.00 Neutral Area
NM 25 – Site leadership fosters a culture of inquiry and
collaborative problem solving.
3.02 Neutral Area
MQ 17 – Professional development offerings at our site
are based on student achievement data.
2.88 Neutral Area
NM 16 – Professional development offerings at our site
are based on student achievement data.
2.77 Neutral Area
MQ 25 – Site leadership fosters a culture of inquiry and
collaborative problem solving.
3.02 Neutral Area
MQ 38 – The math achievement goals and measures
from my school were clearly articulated and east to
understand.
3.50 Agreeable Response
NM 20 – The school leaders used data-driven
information to address problems/issues related to student
achievement.
3.41 Agreeable Response
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The teachers’ responses fall into the neutral area in relation to eight of the
11 questions above. This includes the following topics (question number):
- Teachers develop common assessments (MQ 16)
- Teacher collaboration being key to increasing student achievement (MQ 23)
- Principal actively supporting collaborative opportunities (MQ 27)
- Principal as “change agent” (MQ 19)
- Time provided for faculty member discussion (MQ 34)
- Encouragement of discussion of effective math instructional strategies (MQ
35)
- Culture of collaboration as a means to improving instruction (MQ 49)
- Site leadership fosters a culture of inquiry and collaborative problem-solving.
(MQ 25)
- Leaders foster a culture of inquiry and group problem solving (NM 25)
- Professional development offerings at our site are based on student
achievement data. (MQ 17)
- Professional development offerings at our site are based on student
achievement data. (NM 16)
On the three in this area received agreeable responses. Math teachers agree
(question 18) that teachers have helped develop strategies used at our school to
improve instructional practice in math. The math teachers also agree that the
achievement goals and measures from their school were clearly articulated. The
non-math teachers lastly agree that school leaders use data-driven information to
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address problems/issues related to student achievement. In all there seems to be a
strong community of reflection and data based direction, though all teachers may not
recognize it as such.
Culture of Teaching and Learning
Staff development was not the most significant contribution to a culture of
teaching and learning. The assistant principal shared that there are staff
developments every month. Often these focus on concept lessons and evolving all
teachers. The department chair would gladly forgo some of the district mandated
staff development Tuesdays in exchange for more department meeting opportunities.
The coach echoed this sentiment by emphasizing her love for meeting as a
department and working together as a group. The teachers shared what was working
for them in developing a culture of teaching and learning. One teacher expressed
how over the course of the past few years he worked closer and closer with the other
teachers as a collaborative relationship developed. Another teacher emphasized the
value of the kind of math teachers who make up the group. They are in her words
“very thorough math teachers.” In Table 19 the results of the two questionnaires are
shown in relation to the value of professional development as contributing to a
culture of teaching and learning.

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Table 19: Questions Relating to the Value of Professional Development

All four questions above show negative responses overall. According to these
questions neither the district, nor their mandated professional developments were
useful towards the development of school culture and success. The positive
comments under this topic all relate to teachers working together under the direction
of the coach and department chair, rather than an official regiment of professional
development.
Summary of RQ4 Findings
In all strong instructional leadership was key in the direction of the school on
the road to success. It is as though there was an Achievement Highway and the white
lines on the side of the road was instructional leadership, keeping the vehicle of
progress on the road in order to reach the destination of success. Perhaps this
analogy is best seen in how the above teachers believed their leaders were informed
Question Average Result
MQ 22 – Professional development has played
a key role in increasing student achievement in
math.
2.50
Negative
Response
MQ 26 – My district supports teachers with
effective staff development in Mathematics
Instruction.
2.38
Negative
Response
MQ 46 – Professional development in math
has been a key tool used by site leaders in our
effort to improve instruction on our campus.
2.63
Negative
Response
NM 29 – Professional development has been a
key tool used by site leaders in our effort to
improve instruction on our campus.
2.72
Negative
Response
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and involved. There are many school leaders who are informed, but are not
necessarily recognized by their staffs.
Research Question 5: Leadership Strategies
Research Question 5 is “How did leaders in the school resolve dilemmas
about instructional leadership?” The strategies to overcome a lack of subject matter
competency is linked with the action of utilizing shared expertise to overcome this
dilemma. In this particular case the principal did not come from a mathematical
background and so this utilization of shared expertise was central to the progress that
was made. In the coming first section general obstacles and solutions are considered.
The framework for use of strategies is then considered and which ones the principal
utilize as found during the study. Lastly, the results of the surveys and interview
guide understanding of how the principal used shared expertise to accomplish school
growth.
Key leaders instituted dynamic strategies to overcome obstacles. One obstacle
was that the principal was not an expert in the area of Mathematics. Another obstacle
that occurred was a lack of money. This impacted the ability to offer tutoring after
school, buy manipulative, and help students below grade level. Some teachers had
trouble keep up with the pace of a demanding curriculum. Other teachers needed
help building their instructional practices. Also some technology issues occurred,
which hampered progress. Some of the solutions that helped remedy are as follows.
For now they are still getting Title 1 money which now assists with the lack of funds.
“Good communication and careful over site” according to the assistant principal
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helps teachers deal with the pace of the curriculum. When it comes to building
instructional strategies two strategies came in handy. Every year they rotate
department supervisors, so every assistant principal gets to supervise different
departments. The principal shared that the school site council meeting every other
Tuesday and the weekly Monday meeting with the Leadership Team made of
Department Chairs helped in all these areas. The Assistant Principal stated that as
she was an English person overseeing the Mathematics department she found
“relying and trusting the expertise of the math coach is essential.”
In Table 20 an altered list of the Strategies to Overcome a Lack of Subject
Matter Competency is shared showing whether the strategy was used or not in the
third column.
Table 20 – Strategies to Overcome a Lack of Subject Matter Competency

Item Strategy Strategy
Used
1 Delegate Leadership to Assistant with greater expertise YES
2 Empower Department Chair YES
3 Bring in Outside Expertise NO
4 Emphasize inquiry and problem solving NO
5 Emphasize quality instruction YES
6
Emphasize strategies to engage students in the learning
process
YES
7 Emphasize articulation with feeder schools YES
8 Emphasize raised expectations YES
9 Emphasize Strategic Teacher Assignments YES
10
Emphasize Revised Course Cope and Sequence and/ or
Curriculum
YES
11 Emphasize Interventions for lower performing students YES
12 Emphasize Professional Development YES
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The principal used 10 of the 12 strategies this study identified as useful to
overcome a lack of subject matter competency. The only two that evidence was not
observed for was the following. First the act of brining in outside experts was not
done. And second an emphasis on inquiry and problem solving was not observable.
In all outside experts are not useful for accomplishing progress at West Valley High
School, but empowered department chairs and content coaches are essential. It is
true to the body of evidence to say the principal has relied and built up a strong
understanding and knowledge in those key leaders and teachers who continue to
excel under her leadership.
Specifically the ten strategies were used and observable were the following.
First, the principal delegated leadership to the Assistant Principal and Math Coach.
Second, the principal empowered the Department Chair and Math Coach with
responsibility and leadership. Third, the principal emphasized the importance of
quality instruction. Fourth, she also emphasized articulation with feeder schools for
proper programming and transition. Fifth, she raised expectations of what teachers
were accustomed to expect out of their students achievement wise. Sixth, she
worked with the Math Coach to make strategic teacher assignments that gave
struggling students special consideration. Seventh, she revised course sequence and
curriculum to meet the needs of all levels of students. Eighth, she introduces
strategies to engage students in taking their education seriously. Ninth, she budgeted
and directed financial resources to provide interventions for struggling or lower
performing students. Tenth, she emphasized the importance of professional
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development, while respecting her own delegation to the Assistant Principal,
Department Chair, and Math Coach of how to use that time.
In Table 21 the results of the two questionnaires are shown in relation to
dilemmas and the use of shared expertise. This table has in it some of the evidence
that supports the above assertions that the principal used 10 of the 12 strategies.
Some of the evidence supporting the observation of the 10 strategies is not evidence
mentioned in this discussion of Research Question 5, but rather was evidence
presented with in the preceding pages that discussed findings of Research Questions
1-4.
Table 21: Questions relating to Dilemmas and the use of Shared Expertise

Math teachers feel very strongly that outside experts have not been used to
produce the progress made in instruction (number 44). Non-math teachers feel the
same, even if not as strongly that outside experts were not the key (number 24). The
Question Average Result
MQ 44 – Outside experts have been used to promote
greater capacity in the area of instruction.
2.13 Strong Negative
NM 24 – Outside experts have been used to promote
greater capacity in the area of instruction.
2.65 Negative Response
MQ 45 – The school’s leaders emphasize the importance
of quality instruction as a primary mission of the school.
3.94 Strong Agreement
NM 26 – The school’s leaders emphasize the importance
of quality instruction as a primary mission of the school.
3.73 Agreeable Response
MQ 43 – The Math Department Chair has been
entrusted with and is empowered to make important
curricular decisions.
3.63 Agreeable Response
NM 23 – The principal has delegated some curricular
authority to an assistant principal with greater expertise
in curriculum and instruction.
3.34 Agreeable Response
NM 22 – The principal makes effective use of the
department chairs and relies on their expertise when
making important curricular decisions.
3.60 Agreeable Response
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Math teachers feel strongly that the school’s leaders emphasize the importance of
quality instruction as a primary mission of the school (number 45). Non-math
teachers agree with the same notion as to the driving mission of the school (number
26). Math teachers in question 43 agree that the Math Department Chair has been
entrusted with and is empowered to make important curricular decisions. Non-math
teachers in questions 22 and 23 agree with the notion that the principal delegated
curricular authority to assistant principals and makes effective use of the department
chairs, relying on their expertise when making curricular decisions.
Summary of RQ5 Findings
In all the results of this case study, show that the use of dynamic strategies can
overcome a lack of content matter expertise. That is that strategic and deliberate
actions of trust and empowerment are key to achieving far reaching success, when
presented with similar circumstances.
Analysis and Discussion
The findings mean many things and have many implications. The implications
are considered in Chapter 5. What the findings mean is considered here, starting
with the first topic of how increased enrolment is an important act of high
expectations and predecessor to success. The second topic considers how using
benchmark assessments can be central to the important progress that can be made by
good school design. Third topic dissects the anatomy of Math Program Design that
works. The fourth topic cannot be ignored as to the importance key personal
addition and use made. The last topic recognizes the meaning behind the successful
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use of shared expertise as a key development in overcoming lack of subject
matter competency.
1
st
Topic: Increased Enrolment in Higher Level Classes
Algebra 1 enrolment is an indicator of to what degree schools are structuring
education so that students are prepared to meet college admission requirements. The
increase in Algebra 1 enrolment at West Valley High School is progressive and
striking. For example in the 2002-2003 school year, there were only 324 Algebra 1
students and more than half of them were in 10-12
th
graders. Compare this to 853
students a year later in the 2003-2004 school year of which 83% were 9
th
graders.
This represents a clear change not only practice, but also in philosophy. Furthermore
the 2006-2007 school year shows an apparent decrease in overall Algebra 1
enrolment falling from 1083 (2005-2006) to 973. This drop of enrolment is further
proof of significant growth, as the drop occurred in the 10-12
th
Graders who had to
remediate nearly half as much as the previous year. Going from 272 10-12
th
graders
(2005-2006) to 141 10-12
th
graders (2006-2007).
The difference in priority and philosophy is even more clear when students
who took Algebra 1 are compared directly as a proportion to the students taking the
6
th
and 7
th
grade standard course “General Mathematics.” Over a four-year transition
a total reversal in priority is apparent. While just over 20% of students are in
Algebra 1 (201 versus 625) in the 2002-2003 school year, as compared with just
under 90% are enrolled in Algebra 1 (715 versus 89) by the 2005-2006 school year.
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This constitutes a 70% increase in students taking classes that are more
challenging and also necessary for college admission.
There are four reasons that explain the drastic increased enrollment in higher
level classes. The first reason is district directive. That is the major scheduling
movement coincides with what the central district instructed school sites to do. That
is there was a district directive that students take Algebra I in ninth grade, so that all
students would be on track towards college enrolment requirements. A second
reason is school choice. It may have been a district directive that got the idea out
there, but it took action at the school level to accomplish such a feet. Often schools
drag their feet about instituting district directives/initiatives. In this case the school
administrators and Mathematics department worked hard to change the school course
that would allow all students to be on a college ready path. A third reason for how
increased enrolment has been so successful, is the drop of repeat takers by 50%.
This indicates not only a change of course, but an increase in fidelity and
accountability. The fourth and final reason for the development is a fundamental
change in philosophy. It is clear before student achievement was changed fully a
change in teacher hearts occurred, which is central to increase in higher level class
enrollment. This means in terms of the study, movement towards higher level
classes and the higher expectations that underlie it were important factors in
accomplishing the great progress this school made.

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2
nd
Topic: Using Benchmark Assessments as School Design
The school design aspect especially seen in utilizing of periodic or benchmark
assessments. Performance Assessments are very central to the daily life of the West
Valley High School teacher. The Math Coach and Math department chair see the
periodic or benchmark assessments as good practice. There was agreement among
the teachers interviewed as to these assessments being good practice for the state
standards tested by the CSTs. When asked about benchmark assessments the math
department answered questionnaires with strong agreement saying that common
assessments have been implemented and produced useful data that helps to drive
instruction. The Mathematics department has used and finds value in common
benchmark assessments.
There are three reasons for why benchmark/periodic assessments have been
useful elements for school design. The first reason for their usefulness is district
mandate. Due to the district mandate to administer the assessments, it forced all
teachers to administer them. They would have had less value, if only enthusiastic
teachers administered them, if for no other reason then it would have skewed
assessment results. A second reason for the usefulness of the assessments is school
value. The math department as a group believes that the assessments are good
practice and useful in preparation for the CSTs. This positive view of the tests,
effects how teachers administrator them in their individual classes. A teacher can be
made to give test, but making them care is another matter and quite an
accomplishment in this case. The third and final reason for why these benchmark
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assessments stand as so useful form of school design is the useful data created
that helps drive instruction. The first two reasons are part of the reason that the data
is useful, as they impact the validity and completeness of the created data. The
department wisely then reflects and learns from the results. This means in terms of
the study, utilization of benchmark assessments was an important factor in
accomplishing the great progress this school made.
3
rd
Topic: Math Program Design that Works
Math program design has been dynamic and has influenced classroom
practices, curriculum design, and standards based instruction. There are five aspects
of their reform to be considered under Math Program Design. The first the
Mathematics Diagnostic Testing Project (MDTP) testing project, Star Academy
Program, John Hopkins Academy Program (TAMS), Twilight Model, and District
CAHSEE Boot Camp.
The first of those the University of California at Los Angles (UCLA)
Mathematics Diagnostic Testing Project (MDTP) testing project, which is a
statewide project by the CSU and UC system that develops, distributes, scores, and
reports the results of tests that measure student readiness for mathematics courses.
At West Valley administering the Algebra Readiness Test assesses preparation for
first-year Algebra. The Star Academy Program and the John Hopkins Academy
Program (TAMS) are the two during the day special interventions that students
belong to. The Star Academy is aimed at Below Basic students and John Hopkins is
aimed at Far Below Basic Students. Every teacher and key leader shared about these
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two programs as the key to progress made over the past three years. Both
programs are being utilized successfully. And 99% of Star students are passing the
CAHSEE, coupled with 100% going onto higher education.
The fourth intervention strategy is the implementation of the Twilight Model.
This for students who have a semester in which they earn all fails. After that
semester occurs, they enter the Twilight Model where they come to school from 3:30
p.m. to 6:30 p.m. and take only English and Mathematics during that time. The fifth
intervention program strategy is built to help struggling students pass the CAHSEE.
The district has designed what is referred to as a CAHSEE Boot Camp. The Boot
Camp occurred for four hours a day for two weeks prior to a certain Spring CAHSEE
administration. This was a useful curriculum for reviewing a great body of skills
needed for passing the CAHSEE.
There are three reasons why the math program design works so well. The first
is the use of pre-testing in the act of making informed placement decisions. Because
the pre-testing and subsequent scheduling occurs at the beginning of the year, it is
successful at helping to ensure that students are placed correctly. The second reason
for the impact of the math program is the use of two special academy programs. The
Star Academy Program and John Hopkins Academy Program are designed to help
the two lowest performing groups of math students (Far Below Basic & Below
Basic). These programs have their intended effect on student success, by being
thorough and meeting the specific needs of students that they are designed for. The
third and last reason the math program design is successful is the use of multiple
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interventions to meet the multiple and diverse needs of students. In the form of
the Twilight Model and CAHSEE Boot Camp the school is able to help students in
different ways, even as students are very different. This means in terms of the study,
varying methods, programs, and interventions was an important factor in
accomplishing the great progress this school made.
4
th
Topic: Personnel Addition – Central to Change
The most important personnel change according to all the school leaders
interviewed was the addition of a Math Coach. She is a half time coach who,
teachers half day and coaches the other half. They way she coordinates and shares
good pedagogy is by all accounts central to the success they have experienced. The
teachers interviewed found great value in working together under the direction of the
Math Coach. The math department overwhelmingly agrees (question 15), with a
4.38 average out of 5.0 possible that “Our school has added the used of math coaches
to assist in the effort to improve student achievement in math.”
There are three reasons why the addition of a Math Coach not only successful,
but central to departmental progress and change. The first reason that coach
experiences great influence is that she is a homegrown hero. She is not an outsider
picked by the district or authoritarian school administrator, but rather she has been
teaching in that department for just over a decade. The second reason her actions are
found to be full of effectiveness is that she is a half-day coach. As she still teaches
half the day, the other math teachers view her as one of them, as opposed to “out of
touch.” The third and final reason for her success is her ability to be a good mediator
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between district directives and math teacher practice. She goes to district
meetings and brings directives, lessons, and methods back to the department. How
she successfully communicates this information and gathers departmental buy in is
perhaps the most important thing she does bringing about the personnel effect that
was central to change. This means in terms of the study, the addition of a Math
Coach was a factor in accomplishing the great progress this school made.
5
th
Topic: Strategies to Overcome a Lack of Subject Matter Competency
According to key leaders obstacles could be approached with dynamic
strategies. Some obstacles that occurred were lack of money. This impacted the
ability to offer tutoring after school, buy manipulative, and help students below
grade level. Some teachers had trouble keep up with the pace of a demanding
curriculum. Other teachers needed help building their instructional practices. Also
some technology issues occurred, which hampered progress. Solutions were found
falling into specific strategies. The principal used 10 of the 12 strategies this study
identified as useful to overcome a lack of subject matter competency. The only two
that evidence was not observed for was the following. First the act of brining in
outside experts was not done. And second an emphasis on inquiry and problem
solving was not observable. In all outside experts are not useful for accomplishing
progress at West Valley High School, but empowered department chairs and content
coaches are essential. The 10 strategies that were observable included the following
documentable statements. The principal delegates leadership to an assistant with
greater expertise. The principal empowers the department chair. The principal
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emphasizes quality instruction, raised expectations, articulation with feeder
schools, and strategies to engage students in the learning process. The principal also
emphasizes professional development, strategic teacher assignments, revised course
scope and sequence, and lastly specific interventions for lower performing students.
There are five reasons for why a lack of subject matter competency was not an
issue for this school. The first reason is the principal delegates leadership to an
assistant principal. The second reason for success is how the principal empowers the
department chair. The third reason is what the principal emphasizes. The principal
emphasizes quality instruction, raised expectations, articulation with feeder schools,
and strategies to engage students in the learning process. The fourth reason for
success is the courage to make strategic teacher assignments. The fifth and final
reason is that she did put limits on creating new programs and ways to help
struggling students. This means in terms of the study, use of shared expertise as a
strategy was an important factor in accomplishing the great progress this school
made.
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CHAPTER 5
SUMMARY, CONCLUSIONS AND IMPLICATIONS
Summary of Study
Background of the Study
The need for reform has been recognized by many studies. In California the
need for reform was recognized by the 2002 publication of Aiming High: High
Schools for the Twenty-First Century by the California Department of Education.
This statewide guidebook for high schools emphasizes three procedures for success.
This document shared how to implement standards, use assessment data, and
institute accountability. This situation lead to the first topic sentence: The
academic performance of American high school students is low for many types of
students when viewed by national objectives standards and by international
comparative studies. The achievement gap persists and represents a serious national
challenge for us all. The second topic sentence relates to the Achievement Gap: The
performance gap in math and represents an especially important problem in many
respects. The third topic sentence central to the preceding research of Chapter 2
was: State and national efforts to improve math achievement in high schools have
focused on state standards, improved curriculum and instruction, better prepared
teachers and related reform efforts. The fourth topic sentence was: Out of these
reform efforts have come new school designs that focus on student achievement and
related school features. The fifth topic sentence is: Building local capacity for
improvement must be joined with new policy, initiatives and designs. The last topic
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sentence was: More specifically, considerable research has been done to identify
features of effective instructional leadership in this context. These topic sentences
guided the research behind the study which showed a great need for research.
Purpose of the Study
The purpose of this study is to find out how urban high schools that have
experienced significant gains in math performance in their students looking at two
areas of concern. First, to find out how urban high schools bring together policy
initiatives, coupled with how urban high schools increase school site best practices to
bring about improved math performance in their schools. Second, to find out how
instructional leadership is instrumental in improving high school math performance
for students. The purpose of this study is two-fold to find a guide at bringing
together policy initiatives with best practices. And second to determine some
guiding examples of best practices for the instructional leader who is successful
about pedagogical and organizational leadership.
The research questions that guided this study were:
1. What was the pattern of math achievement for various students at the
school?
2. What policy initiatives as well as curriculum, instruction and related
conditions seem to be related to improved math achievement 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. To what extent was strong instructional leadership important in
improving (a) the math programs/strategies, and (b) math achievement
among students?
5. How did instructional leaders respond in academic areas in which they
were not experts? Following the development of the chart depicted in
Methods of Study
Frameworks
There were four frameworks that fall under methods of study. The first of the
four frameworks discusses effective school design. It has four parts, the first
emphasizes curriculum foundations built on student-centered approaches and
outcomes. The second part, School Cultures, is about having meaningful
interactions between students and staff, including professional development and
learning opportunities. The third is Learning Activities that strive to have students
use higher order thinking skills, solve problems and collaborate. The last part is
called Student Performance Assessments which emphasizes effective
communications, problem solving and conceptual understanding.
The second framework deals with the important elements of effective math
programs and is depicted in Figure 2. The first elements include a student-centered
curriculum that emphasizes conceptual understanding seeking mastery of
computations and manipulations of mathematical symbols and procedures as tools in
the problem-solving process. The second element is to incorporate rigorous,
standards-based practices that rely on content standards and assessments that are
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related to data-driven decision-making. The last element is an effective and
coherent classroom pedagogy that is benchmarked by sound lesson design, makes
use of prior knowledge, and using culturally relevance that promotes high levels of
student engagement.
The third framework concerns the change process used by the school to
enhance its math program and about strategies used to assist students in math.
Bolman and Deal’s Reframing Organizations (2003) provides leaders with a
framework with four frames for addressing the diverse aspects of complex
organizations as they manage the change process. The Structural deals with top
down hierarchies, specialized tasks, goals/objectives and rules, policies, and
procedures. The Human Resources frame relates to employees as partners,
productivity through group effort, and self-actualization. The third frame Political is
characterized by power, bargaining, and negotiations. The last frame Symbolic is
known for relating to vision, belief, faith, stories, and organizational culture.
The fourth framework is an instructional leadership framework. It consists of
a Vision for Learning, Supervision and Monitoring of Instruction, the Community
and Political, Culture of Teaching and Learning, and Data Driven Decision Making
Analysis. The fifth framework is the assessment of Individual Leader’s expertise in
math and leadership. The framework developed by the cohort 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 assessment was developed from the guidelines of what is a highly
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qualified teacher as seen in NCLB (NCLB, N.D.). The assessment resulted in one
of three levels of expertise being assigned to the leader that is high, medium, or low.
Sampling
A purposeful sampling process was used in order to provide an opportunity to
consider deeply the processes related to the research questions of this study. The
school selected for the study was chosen consistent with the following criteria:
1. Improvement in math achievement for three consecutive years as evidenced
by results on the California Standards Test (CST) in Algebra I.
2. Diverse as defined by a student population of at least 1200 students with more
than 50% from ethnic minority groups.
3. Public comprehensive high school in Southern California.
4. Leadership stability as defined by a principal being at the school for at least
three years during the time the improvement was made.
5. School has an API of 600 or above and a state rank of 5 or better out of all
schools.
Qualifying high schools were identified by analyzing data available on the
California Department of Education’s web site. Some criteria were dropped due to
the criteria limiting the sample of schools to too few sites.
Instruments
The instrumentation used in this study was developed collaboratively by 11
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
134
seminar led by Dr. David Marsh, Associate Dean of Academic Programs and
professor at the University. The collaboration included 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 so as to answer the research questions. Work was
done to identify the relationship between the research questions and the data
collection instruments to ensure maximum effectiveness in the data collecting
process. Table 22 depicts a summary of the data collection instruments used in the
study and the research questions the instruments examined.
Table 22: Summary of Data Collection Instruments to Research Questions

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

Data Collection and Analysis
This study collected data over a three-month period from September 2006
through November 2006. The data was collected in three distinct rounds in order to
ensure two things--an inaccurate snap shot was taken and to give interviewees a
chance to review notes from their interview to ensure accuracy.
135
The first round of data collection sought to gain an overview of the school.
The second round of data collection served as an opportunity to follow up in a deeper
investigative way. The last round of data collection sought the collection of any
missing questionnaires still at the school site. This was also an opportunity to have
further interviews with follow- up questions that arose due to the teacher
questionnaire and interview results.
All data was compiled into an excel database. Built into the excel database
were automatic calculations that gave the mean for every question. These mean
scores for individual questions showed to what degree affirmative answers were
chosen as to the particular reasons for success. A mean score of 2.75-3.25 would be
considered in the neutral area. A score of 3.25-3.75 would be considered an
affirmative response, while a score above 3.75 would be considered a strong
affirmation. A score of 2.25-2.75 would be considered a negative response, while a
score of less than 2.25 would be considered a strong negative response.
Summary of Findings
Key Findings
Research Question 1: Student Achievement in Mathematics
The first research question asked, “What was the pattern of Math achievement
for various students at the school?” Four key findings relate to this question and are
listed here:
136
1. West Valley High School demonstrated improvement in math achievement
for three consecutive years as shown through the California Standards Test
(CST) in Algebra I.
2. Algebra I enrollment of over the course of six years has gone from just over
20% of students in 2002-2003 to just under 90% by the 2005-2006 school
year, constituting a 70% increase.
3. In passage of Advanced Placement exams, West Valley High School every
year has out performed state results by 22-55%.
4. West Valley High School out performs the state average in the passing of the
California High School Exit Exam.
5. According to the CAHSEE results, West Valley has narrowed the achievement
gap greatly, as both Hispanic and African American students have increased
their passing rates by 100%.
Research Question 2: Policy Initiatives and Improved Curriculum
The second research question asked, “What Policy Initiatives as well as
curriculum instruction and related conditions seem to be related to improved math
achievement in the school?” Nine key findings relate to this question and are listed
here:
1. The federal policy of No Child Left Behind had the positive influence of
ensuring that qualified, prepared, and credentialed teachers were hired.
2. Student Performance and Benchmark assessments are useful in pacing and
practice for California State Tests.
137
3. School culture was greatly influenced by the CAHSEE, as the high stake
test motivated students, because graduation mattered to them.
4. The Mathematics Diagnostic Testing Project (MDTP) has gauged student
Algebra readiness and allowed for the most beneficial student placement.
5. The John Hopkins Academy Program has successfully helped struggling
students in the Far Below Basic Band.
6. The Star Academy Program has triumphantly helped struggling students in the
Below Basic Band and a hundred percent of them pass the CAHSEE and go
onto higher education institutions.
7. The Twilight Model is helping students who are easily districted or have a lack
of motivation to be motivated.
8. The CAHSEE Boot Camp is a successful crash course which has successfully
refreshed student knowledge and practice for the state Exit Exam
administration.
9. The staff feels overwhelming that good interventions have been put in place to
help struggling students succeed.
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?” Four key
findings relate to this question and are listed here:
1. In regards to the structural frame block schedules, meetings, professional
development planning, and computer purchases had to be accomplished.
138
2. The most important human resource frame related development was the
addition of a Math Coach who has been central to the positive developments
in the Mathematics Department.
3. There is strong agreement among the staff that in regards to the political frame,
the principal has not been shy from making decisions and yet works to gain
support from the community about the school’s academic efforts.
4. The symbolic frame is reach in the shared vision experienced by staff who
foster a “culture of open communication and high expectations” for all
students.
Research Question 4: Strong Instructional Leadership
The fourth research question asked, “To what extent was strong instructional
leadership important in improving (a) the math programs/strategies and (b) math
achievement among students?” Four key findings relate to this question and are
listed here:
1. A Vision for Learning is present through out the situation as the Department
Chair and Math Coach work together and the principal is seen by staff as
having a good grasp of the sequence of math and a keen ability to place
students in the right place.
2. Supervision and monitoring of instruction occurs as the teachers
overwhelmingly observe that the school leaders are aware of mathematics
instruction and academic progress of the students in their classes.
139
3. A community of reflection and data driven decision making is seen in the
teachers helping to develop the strategies used at the school to improve
instructional practice in math and how data-driven information is used to
address problems and issues related to student achievement.
4. There exists a culture of teaching and learning as seen in the love of math
department members for meeting together and the fact that they have build
that department into one described as “very thorough math teachers.”
Research Question 5: Leadership Strategies
The fifth research question asked, “How did leaders in the school resolve
dilemmas about instructional leadership?” Three key findings relate to this question
and are listed here:
1. The principal delegated to an assistant principal and empowered the
department chair and Math Coach.
2. The principal emphasized quality instruction, engaging strategies, feeder
school articulation, raised expectations, and dynamic interventions for
struggling students.
3. The Principal in regards to teachers emphasized strategic teacher assignments,
a revised course cope and sequence, and professional development.
Conclusion About Findings in Study
Relevant data related to Research Question 1 showed that there was a change
in philosophy that effected a change in results. This change in philosophy was seen
most vividly in the increase of upper level course enrolment going from a mere 20%
140
to just under 90% in four years. West Valley superior results on the CST,
Advanced Placement Exams, and CAHSEE showed it surpassing state averages.
Further proof of this philosophy change is seen in the narrowing of the achievement
gap at the school among Hispanics and African Americans as these to groups
increased their passing rates by 100% while their White and Asian counterparts only
increased slightly.
Data collected pertaining to Research Question 2 showed many initiatives and
curriculum implementations that brought about the great progress of West Valley
High School. No Child Left Behind was helpful in ensuring the hiring of qualified
teachers. Benchmark assessments were shown to be good practice for CSTs. High
stakes tests like the CAHSEE influenced how students valued school. Special
interventions and methods were proven to properly program and assist students many
who would perhaps fallen between the cracks. And lastly the staff could feel in
touch with the success of students, who were responding to their teacher’s high
expectations.
In regards to the Change Process the four frames were all central and fulfilled
specific purposes. Schedules and resources were changed to accomplish the
curriculum and initiatives instituted above. The addition of a math coach was the
most important human resource change as it allowed for the development of a new
department professionalism. The principal effectively explained to the community
the school’s educational direction. And very pertinent to the success of students is
141
symbolic environment created were open communication and high expectations is
seen department wide.
The strong instructional leadership described in Research Question 4 was seen
through the evidence presented. The Department Chair and Math Coach working
together and having a good grasp as to the sequence of math proved were most of the
leadership came from. School leaders including the principal are aware of academic
progress of the students in their classes. How the department meets and works on
the same page is evidence as to why a universal success in Mathematics is observed.
The principal used specific leadership strategies (Research Question 5) in order
to lead her school in this progress. First the principal delegated to an assistant
principal and empowered the Department Chair and Math Coach. Second progress
was proved through the principal raising expectation and instituting dynamic
interventions for struggling students. Last the principal helped to cause all the
progress by the observed strategic teacher assignments and emphasis on
collaborative professional development.

Implications for Practice
Future Research
1. The focus of this study centered on identifying policies and practices that lead
to increased student achievement. Many specific policies and practices were
found to be the factors that contributed to the increased student achievement.
142
Further studies in other core subjects such as Science and English could
confirm and add validity to the value of policies and practices that were
found to be of value in this study.
2. This study looked at a school with a closely nit content department. There
existed in the school prior to implementation of reform policies and practices
a long history of collaboration and departmental conformity. A further study
of this area of research could study a school that did not have a history of
collaboration, nor conformity.
District Boards and Key District Leaders
1. One of the key findings of this study was how upper level math class
enrollment increased by 70%, due in part to a district initiative that all
students take classes that would lead meet college entrance requirements.
Board policies that emphasis the notion that all students can succeed and
achieve college entrance were factors that were found to be important
contributors. Districts should mandate high expectations at schools by
insisting on master schedules that provide broad-based college readiness.
2. Of great value to the schools was the district emphasis on Periodic or
Benchmark Assessments. These assessments were produced and mandated
by the District office. Two factors surrounding Benchmark Assessments to
be important contributors to how implement with the greatest return. First
they are mandated, so as to have all students take them. And second they are
standards based, so they act as good practice for the California State Tests.
143
Districts should create and mandate the use of standards-based benchmark
assessments and strongly encourage their use for informing instruction.
3. Perhaps the most crucial decision by the district in this case was the funding of
a Math Coach position. The findings showed this individual often bridged
district initiative and school site reform. Districts should consider the
usefulness of funding positions within schools that aid in the implementation
of district initiatives. As with West Valley High School it may build a very
useful bridge between initiative and practice.
Site Administrators
1. Findings show that Periodic and Benchmark Assessments have value when site
administrators take an active role in using the data created by them. The
findings showed that the principal spent time pondering and learning from the
assessments at the school site leadership meetings. This filtered down as
good practice to the various departments sifting through the data. Site
Administrators should show good leadership with the benchmark assessments
data by demonstrating to the departments hot to use data to inform
instruction.
2. The findings show that school benefits when site administrators institute some
sort of diagnostic tool to aid with placement. Choosing to use a system like
the Mathematics Diagnostic Testing Project gives real insight so as to avoid
students being misplaced for inappropriate amounts of time. Site
144
Administrators should use placement/diagnostic indicators in order to
accomplish careful and appropriate placement of students.
3. Instituting specific programs to meet the needs of specific groups of students
was found beneficial according to the findings. After properly identifying the
needs of students, the findings show that much of student improvement can
be accomplished through the design of specific programs. Site
Administrators should institute a diverse set of interventions during the day,
after school, and for a specified concentrated time as need to meet the
complex needs of struggling students.
4. Perhaps the most important site administrator implication is how to use a
district funded Math Coach. Though they may be paid by the district, to
accomplish district initiatives they report to site administrators at least to
some extent. According to the findings Site Administrators should utilize a
Math Coach as an essential element to great progress. It is especially
recommended that they are empowered and that the respect of teachers is
cultivated towards them.
5. The findings show that the site administrators made strategic teacher
assignments and were aware of mathematics instruction and academic
progress of the students in their classes. The perception of site administrator
awareness came out strongly in the findings, so it cannot be understated how
it is helpful that teachers believe that the site administrators know how
students are progressing in their respective classrooms. Because a site
145
administrator knows what is going on, he or she then can make strategic
teacher assignments and be respected for the decision. Site Administrators
should work with their teachers to create understanding and knowledge of a
shared period-by-period view of progress and achievement for every teacher
they supervise.
Teachers
1. The findings show that the staff feels overwhelming that good interventions
have been put in place to help struggling students succeed. This finding
represents how the teachers are on the same page and have bought into the
school initiatives. From these results, teachers having a common
understanding seems likely to allow for a common understanding about
curriculum, so they can work together helping students through consistency.
2. According to the findings there is benefit in cultivating a community of
reflection and a culture of teaching and learning. By fostering a community
of reflection among teachers, it may increase the chance of improved
instructional practice. A culture of teaching and learning should be
developed by cultivating an environment where department members love to
meet as a group.
School on behalf of Students
1. Findings show that students make great progress when a culture of open
communication and high expectations exists. A school needs to listen to its’
students and have high expectations towards them. It is easy enough to get
146
bogged down thinking about poverty or other issues, so a conscious
decision must be made to have high expectations. Supporting high
expectations by good practice follows, prior to student improved achievement
according to the findings. The school on behalf of students should foster
such an environment of high expectations.
2. Findings show that giving the students the extra attention and specific help
they need helps them to succeed. One development in the findings was how
the special academies gave accountability to the students. To help struggling
students, schools need to identify and meet specific needs, while providing a
special connection that helps students to keep on the academic road. The
school, on behalf of students, should provide them with specific activities
and/or groups they can be connected with and are able to relate to.
147
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APPENDICES

156
Appendix A

Table A-1: CST School Profile Detail

Algebra 1
School
Increase in
Top two
Quintiles
Decrease in
Bottom Two
Quintiles
Algebra I
Total Gains District
Schurr High 4% -67% 71% Montebello Unified
Mark Keppel High 22% -28% 50% Alhambra Unified
Escondido High 15% -32% 47% Escondido Union High
Western High 21% -26% 47% Anaheim Union High
Brawley High 9% -31% 40% Brawley Union High
Oxnard High 13% -17% 30% Oxnard Union High
San Gabriel High 11% -17% 28% Alhambra Unified
El Rancho High 4% -22% 26% El Rancho Unified
Palm Springs High 9% -17% 26% Palm Springs Unified
Townsend (Robert O.) 17% -7% 24% Chino Valley Unified
Loara High 11% -13% 24% Anaheim Union High
Gabrielino High 6% -17% 23% San Gabriel Unified
Whittier High 4% -16% 20% Whittier Union High
Serra Senior High 4% -15% 19% San Diego Unified
Los Angeles Center 7% -11% 18% Los Angeles Unified
Alhambra High 6% -11% 17% Alhambra Unified
University High 10% -7% 17% Irvine Unified
Point Loma Senior 4% -13% 17% San Diego Unified
Mira Mesa High 2% -13% 15% San Diego Unified
Central High 4% -11% 15% Central Union High
Arcadia High 3% -12% 15% Arcadia Unified
San Diego Creative 9% -6% 15% San Diego Unified
Southwest High 4% -11% 15% Central Union High
Arlington High 2% -12% 14% Riverside Unified
Monte Vista High 5% -8% 13% Grossmont Union
La Serna High 5% -8% 13% Whittier Union High
Diamond Bar High 10% -2% 12% Walnut Valley Unified
North High 2% -10% 12% Torrance Unified
El Camino High 2% -10% 12% Oceanside Unified
Taft (William Howard) 6% -5% 11% Los Angeles Unified
John F. Kennedy High 0% -11% 11% Anaheim Union High
Hilltop Senior High 4% -7% 11% Sweetwater Union
Charter Oak High 0% -10% 10% FALSE
Tustin High -1% -10% 9% Tustin Unified
157
Bonita Vista Senior 4% -5% 9% Sweetwater Union
Burroughs High 7% -2% 9% Burbank Unified
Eastlake High 3% -6% 9% Sweetwater Union
King/Drew Med. Mag. 2% -6% 8% Los Angeles Unified
Polytechnic High 4% -4% 8% Long Beach Unified
Bravo Medical Magnet 3% -5% 8% Los Angeles Unified
Valencia High 2% -6% 8% Placentia-Yorba Linda
Polytechnic High -1% -8% 7% Riverside Unified
Millikan Senior High 2% -5% 7% Long Beach Unified
Hamilton (Alexander) 0% -6% 6% Los Angeles Unified
Gahr (Richard) High 1% -5% 6% ABC Unified
University City High 1% -5% 6% San Diego Unified
Westminster High 0% -6% 6% Huntington Beach
Ramona High 0% -4% 4% Riverside Unified
Diamond Ranch High 1% -2% 3% Pomona Unified
Santiago High 1% -1% 2% Corona-Norco Unified
West High -10% -12% 2% Torrance Unified
Pasadena High -2% -4% 2% Pasadena Unified
North (John W.) High -1% -3% 2% Riverside Unified
Rancho Verde High -2% -3% 1% Val Verde Unified
Morse Senior High -1% -2% 1% San Diego Unified
Henry Senior High -1% -2% 1% San Diego Unified
Walnut High 1% 0% 1% Walnut Valley Unified
Ayala (Ruben S.) High -3% -3% 0% Chino Valley Unified
Culver City Senior -1% -1% 0% Culver City Unified
Wilson (Glen A.) High -2% -1% -1% Hacienda la Puente
Fallbrook High -2% -1% -1% Fallbrook Union High
Warren High -1% 0% -1% Downey Unified
Rio Mesa High -3% -2% -1% Oxnard Union High
Torrance High -3% -1% -2% Torrance Unified
Rowland (John A.) -2% 0% -2% Rowland Unified
West Covina High -1% 1% -2% West Covina Unified
La Mirada High 1% 3% -2% Norwalk-La Mirada
Marshall Fundamental -1% 3% -4% Pasadena Unified
Corona Senior High -3% 2% -5% Corona-Norco Unified
Orange Glen High -2% 4% -6% Escondido Union High
Costa Mesa High -2% 4% -6% Newport-Mesa Unified
Vista High -1% 5% -6% Vista Unified
Centennial High 0% 7% -7% Corona-Norco Unified
Irvine High -2% 5% -7% Irvine Unified
Eagle Rock High -4% 4% -8% Los Angeles Unified
Otay Ranch Senior -8% 0% -8% Sweetwater Union
Orange High -5% 4% -9% Orange Unified
Lakewood High -6% 4% -10% Long Beach Unified
Sunny Hills High -5% 5% -10% Fullerton Joint Union
Rancho Cucamonga -2% 8% -10% Chaffey Joint Union
158
Wilson High -5% 7% -12% Long Beach Unified
La Sierra High -6% 7% -13% Alvord Unified
Temple City High -8% 5% -13% Temple City Unified
Highland High -6% 10% -16% Antelope Valley Union
Redlands Senior High -6% 12% -18% Redlands Unified
La Habra High -12% 9% -21% Fullerton Joint Union
Chino Hills High -10% 11% -21% Chino Valley Unified
Chatsworth High -9% 12% -21% Los Angeles Unified
La Quinta High -5% 16% -21% Desert Sands Unified
Colony High -5% 16% -21% Chaffey Joint Union
Fountain Valley High -21% 1% -22% Huntington Beach
Mayfair High -9% 13% -22% Bellflower Unified
Alta Loma High -6% 17% -23% Chaffey Joint Union
Upland High -13% 11% -24% Upland Unified
Monrovia High -8% 17% -25% Monrovia Unified
Santa Barbara High -9% 17% -26% Santa Barbara High
Sonora High -10% 18% -28% Fullerton Joint Union
Rancho Alamitos High -14% 14% -28% Garden Grove Unified
West Valley High -12% 17% -29% Hemet Unified
South Hills High -15% 19% -34% Covina-Valley Unified
Cerritos High -20% 16% -36% ABC Unified
La Quinta High -20% 16% -36% Garden Grove Unified
Sherman Oaks Ctr. -21% 17% -38% Los Angeles Unified
Fullerton High -10% 28% -38% Fullerton Joint Union
Los Altos High -18% 21% -39% Hacienda la Puente
Etiwanda High -17% 23% -40% Chaffey Joint Union
Cleveland High -17% 24% -41% Los Angeles Unified
Garden Grove High -30% 12% -42% Garden Grove Unified
Troy High -17% 30% -47% Fullerton Joint Union
Los Amigos High -33% 27% -60% Garden Grove Unified
California High -60% 51% -111% Whittier Union High

Avg Growth/Decline -2.36% -0.46% -1.90%
159
Appendix B

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?

160
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, as well as the Concerns Based Adoption Model (CBAM).
In case you are not familiar with either of these models, Here is a copy of the
frameworks for your reference and clarification. (give the frameworks 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
CBAM
o Ask to describe where their staff is and how they got there

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
161

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

5. Where do you view your staff on the CBAM continuum (Concerns Based
Adoption Model)? And, how did they get there?

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?

162
Leadership Questionnaire RQ5

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

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

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

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

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

163
Appendix C

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.

164
Appendix D

Math Teacher Questionnaire

Thank you for taking the time to complete this survey. It is hoped that the results
will serve as a rich source of data that may serve to better inform schools seeking to
improve in math achievement. Please return the survey to your department chair
at the end of your department meeting today. 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

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

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

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

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

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

5. Student need is a major consideration when making teacher assignments in math
at our school.
1 2 3 4 5
165

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

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

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

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

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

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

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

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

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

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

166
15. Teacher collaborate to develop common assessments and rubrics.
1 2 3 4 5

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

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

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

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

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

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

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

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

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

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

167
26. My principal actively supports opportunities for staff members to collaborate
and plan Mathematics lessons and units.
1 2 3 4 5

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

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

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

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

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

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

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

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

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

168
36. I have regular support from proven instructional leaders in math instruction.
1 2 3 4 5

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

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

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

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

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

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

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

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

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

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

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

169
47. The school leaders and teachers worked collaboratively to solve math
performance problems and dilemmas.
1 2 3 4 5

48. The school leaders have regular and quality interactions with math teachers.
1 2 3 4 5
170
Appendix E

Teacher Questionnaire

Thank you for taking the time to complete this survey. It is hoped that the results
will serve as a rich source of data that may serve to better inform schools seeking to
improve in math achievement. Please return the survey to your department chair
at the end of your department meeting today. 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

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

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

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

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

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

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

171
6. The master schedule at our school is built based on student need.
1 2 3 4 5

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

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

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

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

10. Professional development has played a key role in increasing student
achievement.
1 2 3 4 5

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

12. Student achievement is a priority when the school allocates its financial
resources.
1 2 3 4 5

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

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

15. Our school has implemented effective intervention strategies for students having
difficulty in core academic courses.
1 2 3 4 5

172
16. My principal actively supports opportunities for staff members to collaborate
and plan lessons and units.
1 2 3 4 5

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

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

18. The school leader is knowledgeable about instruction and of the academic
progress of the students in our school.
1 2 3 4 5

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

20. There is a shared vision for increased student achievement at our school.
1 2 3 4 5

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

21. The school leaders used data-driven information to address problems/issues
related to student achievement.
1 2 3 4 5

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

23. The leadership behaviors of the school administrators contributed to growth in
student achievement.
1 2 3 4 5

173
24. The school leaders and teachers worked collaboratively to solve student
achievement problems and dilemmas.
1 2 3 4 5

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

Abstract (if available)

Abstract The purpose of this study is to find out how urban high schools that have experienced significant gains in math performance in their students looking at two areas of concern. First, to find out how urban high schools bring together policy initiatives, coupled with how urban high schools increase school site best practices to bring about improved math performance in their schools. Second, to find out how instructional leadership, if effectively carried out, improves high school math performance for students.

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Asset Metadata

Creator Nichols, Herbert Taylor, III (author)

Core Title Secondary school reform in mathematics: a case study of a high school in southern California

School Rossier School of Education

Degree Doctor of Education

Degree Program Education (Leadership)

Publication Date 07/26/2007

Defense Date 06/28/2007

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

Tag mathematics,OAI-PMH Harvest,reform,Secondary

Place Name California (states), USA (countries)

Language English

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

Creator Email NICK.NICHOLS@LAUSD.NET

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m680

Unique identifier UC1213753

Identifier etd-Nichols-20070726 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-523561 (legacy record id),usctheses-m680 (legacy record id)

Legacy Identifier etd-Nichols-20070726.pdf

Dmrecord 523561

Document Type Dissertation

Rights Nichols, Herbert Taylor, III

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