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Leading the way: the effective implementation of reform strategies and best practices to improve student achievement in math

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Leading the way: the effective implementation of reform strategies and best practices to improve student achievement in math

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Content LEADING THE WAY:
THE EFFECTIVE IMPLEMENTATION OF REFORM STRATEGIES AND BEST
PRACTICES TO IMPROVE STUDENT ACHIEVEMENT IN MATH
by
Kyunghae Hong Schwartz
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
May 2007
Copyright 2007 Kyunghae Hong Schwartz
ii
ACKNOWLEDGEMENTS
Fight On
My three-years in the doctoral program at USC put my Trojan “Fight On”
spirit to the ultimate test—the accomplishment of my life-long goal of earning a
doctoral degree did not come easy. Many times things did not look promising, but
the goal of finishing up the program and especially this dissertation served as a light
to lead me through the darkness of uncertainty and absurdity of life. It often seemed
as if the odds were against me, but because of a group of people who shared my
three year journey I was able to achieve my goal. Without them, it would not have
been possible and so here I acknowledge their contributions.
I have been fortunate to have Dr. David Marsh as my advisor. He has
enlightened me with his insight and understanding of learning; modeled for me the
power of conceptualizations in learning as well as life; and supported me when my
life was challenged by the sudden, unexpected companion of cancer. His insightful
and methodical guidance helped me to accomplish the enormous task of completing
the dissertation by breaking it down into small steps. Along the way, Dr. Marsh was
our cohort’s cheerleader at every significant stage, always available for a comforting
pat on the shoulder. Throughout the journey, other faculty and staff also proved
invaluable: The feedback and support given by my two other committee members,
Dr. Sylvia Rousseau and Dr. Carlye Olsen, was critical to my success and much
iii
appreciated while a well-earned “hats off” goes to Tina Tsai for her friendly and
thorough assistance to me and my cohort throughout the process.
My gratitude is also extended to my Los Angeles weekend cohort as well as
the dissertation cohort. They provided me with the camaraderie that helped me
survive the three-year journey, with their laughter and friendship. Special thanks go
to two of those comrades —Roger Rice and Kim Tresvant—who shared the three-
year journey with me and helped me along the way. Roger always raised the bar with
his incredible focused mind; pushing me and motivating me to excel. Kim and I
established a special sisterhood; her laid-back style helped me not to be overly
compulsive and kept me laughing throughout the journey.
And finally I would like to thank my husband and daughter for their endless
support and love. Without my husband and companion, Yorami (appropriately,
“cradle” in Korean), I would not be who I am and what I am. Without his selfless
support, encouragement and care, I would not have been able to achieve any of my
goals in life. His dedication to my life as my “Palm Sea Companion” and his
phenomenal job as my editor and stylist was essential for completing this enormous
task. In addition, my daughter, “My Sunshine” Elie, in a heartwarming role reversal,
continually checked up on her mother to make sure I was on the right path. She also
provided tremendous help in sorting out the data, working at my bedside as my
research assistant.
iv
I thank all of you for encouraging me to Fight On. I feel so grateful for
having been able to share my journey with you . Each one of you enriched my life
and provided strength and courage for me to embrace the immeasurable experience
which the past three years of study at USC has been.
v
TABLE OF CONTENTS
ACKNOWLEDGEMENTS .........................................................................................ii
LIST OF TABLES .......................................................................................................x
LIST OF FIGURES ...................................................................................................xii
ABSTRACT..............................................................................................................xiii
CHAPTER ONE: OVERVIEW OF THE STUDY......................................................1
Introduction..............................................................................................................1
Statement of the Problem.......................................................................................15
Purpose of the Study ..............................................................................................17
Research Questions ................................................................................................18
Importance of the Study.........................................................................................18
Assumptions...........................................................................................................20
Limitations .............................................................................................................21
Delimitations..........................................................................................................21
Definition of Terms................................................................................................22
Organization of the Study ......................................................................................27
CHAPTER TWO: REVIEW OF THE LITERATURE .............................................28
Introduction: Executive Summary .........................................................................28
The Status of Student Achievement in Mathematics .............................................30
The Student Achievement Gap over the Years......................................................37
The Importance of Student Achievement in Mathematics.....................................41
Math Curriculum, College Education and Earnings ..............................................45
Social and National Implications of Student Achievement in Math......................48
State and National Reform Efforts to Improve Math Achievement ......................50
Access To and Experience With High-Quality Math Curricula ............................68
Access to Highly Qualified Mathematics Teachers...............................................69
Access to Teachers Who Engage in Culturally Relevant Pedagogy......................70
Access to Math-based Enculturation and Socialization Experiences ....................70
Other Considerations to Improve Mathematics Instruction...................................72
Summary ................................................................................................................81
CHAPTER THREE: RESEARCH METHODOLOGY ............................................83
Qualitative Method-Case Study .............................................................................84
Sampling Criteria and Process ...............................................................................86
Selected School Profile ..........................................................................................89
vi
Student Achievement .............................................................................................91
Certificated Staff Information................................................................................93
Selected Participants ..............................................................................................93
School Site Administrators ....................................................................................93
Key Leaders ...........................................................................................................94
Math Teachers........................................................................................................96
All Certificated Staff..............................................................................................96
Instrumentation ......................................................................................................96
Frameworks for Instrument Design .......................................................................97
Data Sources for RQ 1: School Profile of Student Performance Data...............98
Conceptual Framework for RQ 2: Effective Math Programs and
School Design ....................................................................................................98
Conceptual Framework for RQ 3: The Change Process ..................................101
Conceptual Framework for RQ 4: Instructional Leadership............................102
Conceptual Framework for RQ 5: How did instructional leaders respond
in academic areas in which they were not experts? .........................................104
Data Collection Instruments.................................................................................106
School Profile...................................................................................................107
Key Leader Interview Guide............................................................................108
Teacher Interview Guide..................................................................................109
Teacher Questionnaire .....................................................................................109
Data Collection.....................................................................................................110
Data Analysis .......................................................................................................113
Validity and Reliability........................................................................................114
Summary ..............................................................................................................114
CHAPTER FOUR: FINDINGS, ANALYSIS AND DISCUSSION .......................116
Introduction..........................................................................................................116
Data Findings .......................................................................................................117
Research Question One....................................................................................117
CAHSEE Results .........................................................................................118
Overall Student Achievement Pattern......................................................118
Achievement Pattern by Grade Levels (10
th
and 11
th
). ............................119
Achievement Pattern by Gender. .............................................................120
Achievement Pattern by Ethnicity. ..........................................................120
Achievement Pattern by Language Status................................................120
Achievement Pattern by Economic Status. ..............................................121
Achievement Pattern by Special Education Services...............................121
CST Algebra I Results .................................................................................121
Overall Student Achievement Pattern in CST Algebra I. ........................124
Achievement Pattern by Grade Levels (9
th
-11
th
). ....................................124
vii
Achievement Pattern by Gender. .............................................................124
Achievement Pattern by Ethnicity. ..........................................................124
Achievement Pattern by Language Status................................................125
Achievement Pattern by Economic Status. ..............................................126
Achievement Pattern by Special Education Services...............................126
Advanced Placement Examination Results in Math ....................................127
Research Question Two ...................................................................................128
Influence of Policy Initiatives ......................................................................129
Passage of the CAHSEE. .........................................................................131
No Child Left Behind Legislation............................................................131
Board Policies. .........................................................................................133
Practices and Related Conditions Positively Affecting Student
Achievement ................................................................................................133
Benchmark Assessments..........................................................................136
Data-Driven Decision Making in Areas of Curriculum and
Instruction. ...............................................................................................138
Standards-Based Instruction. ...................................................................139
Curriculum Design...................................................................................140
Student Learning in Computer Lab Using NCE Software.......................142
Interventions: After-School Tutoring, CAHSEE Pullout Sessions..........143
Research Question Three .................................................................................144
Background Information ..............................................................................145
Structural Frame...........................................................................................148
NCLB & CAHSEE. .................................................................................148
Alignment of Board, District and School Priorities.................................149
Edusoft: Access to Technology and Student Performance Data..............149
Physical Layout of Campus. ....................................................................150
Human Resources Frame .............................................................................151
Principal’s Leadership..............................................................................151
Teaching Assignments and Master Schedule...........................................152
Math Resource/Data person. ....................................................................153
Highly Qualified Teachers (HQT): Veteran Teachers and Strategic
New Teacher Selection Process. ..............................................................154
Political Frame .............................................................................................155
Symbolic Frame ...........................................................................................157
Research Question Four ...................................................................................158
Shared Instructional Leadership...................................................................159
Components of Shared Leadership ..............................................................160
Vision for Learning..................................................................................160
Supervision and Monitoring of Instruction..............................................163
Culture of Teaching and Learning ...........................................................166
viii
Data-Driven Decision Making .................................................................168
Research Question Five....................................................................................170
Emphasis of High Expectations ...................................................................171
Emphasis of Quality Instruction...................................................................174
Empowerment of Department Chairpersons................................................174
Quality Interventions....................................................................................175
Analysis and Discussion ......................................................................................176
Pressure of External Accountabilities ..............................................................178
Importance of Leadership to Create Shared Vision and Purpose ....................180
The Inquiry Process for Building Common Ground and Empowering
Teachers ...........................................................................................................181
The Principal’s Competency Viewed through Bolman and Deal’s Frames ....182
Enhancement of Curriculum and Instruction Based on Student
Performance Data.............................................................................................184
Building a Professional Learning Community with a Culture of
Collaboration....................................................................................................187
CHAPTER FIVE: SUMMARY AND IMPLICATIONS........................................189
Summary ..............................................................................................................189
Purpose of the Study ............................................................................................191
Research Questions ..............................................................................................192
Research Method..................................................................................................192
Research Instrumentation.....................................................................................193
Summary of Findings...........................................................................................196
Research Question One....................................................................................197
Research Question Two ...................................................................................198
Research Question Three .................................................................................200
Research Question Four ...................................................................................202
Research Question Five....................................................................................203
Implications..........................................................................................................204
Recommendations for Future Research ...........................................................205
Implications for Practice ..................................................................................205
Implications for Policy Makers....................................................................206
Implications for District Leaders .................................................................207
Implications for Site Leaders .......................................................................207
Implications for Classroom Teachers ..........................................................208
REFERENCES......................................................................................................... 209
APPENDICES .........................................................................................................214
APPENDIX A: KEY LEADER INTERVIEW GUIDE ......................................215
ix
APPENDIX B: TEACHER INTERVIEW GUIDE .............................................219
APPENDIX C: MATH TEACHER QUESTIONNAIRE....................................220
APPENDIX D: NON-MATH TEACHER QUESTIONNAIRE..........................228
x
LIST OF TABLES
1. Comparison Chart for 12
th
graders NAEP Performance in Mathematics ......... 33
2. 2000 NAEP Results in Math for 12
th
graders by Race/Ethnicity...................... 38
3. National Scale Score Results of 12
th
Graders by Race/Ethnicity: 1990-2000 ............ 39
4. Highest Educational Attainment for Kindergarteners by Percentage ............... 47
5. 2003-2005 API & AYP Comparison Chart ...................................................... 87
6. CST Algebra I Student Performance Chart....................................................... 88
7. CAHSEE Results from 2003-2005 ................................................................... 88
8. Relationship of Data Collection Instruments to Research Questions ............... 92
9. Overview of Bolman and Deal’s Four-Frame Model ....................................... 97
10. Framework for Instructional Leadership........................................................... 98
11. Instructional Strategies to Overcome a Lack of Subject Matter Competency ..............99
12. Comparison of Passing Rates of Vineyard High School Students on the
CAHSEE Math Section from 2003-2005........................................................ 112
13. Comparison of Vineyard High School’s Student Performance Results of
CST Algebra I Competency from 2003-2005................................................. 117
14. Comparison of Vineyard High School’s Student Performance Results of AP
Math Exams ................................................................................................................121
15. Summative Survey Results for Policy Initiatives........................................................124
16. Summative Survey Results by Percentages for Effective Instructional and
Curriculum Practices and Conditions.............................................................. 129
xi
17. Summative Survey Results by Percentages for the Change Process...........................139
18. Summative Teacher Survey Results for the Vision for Learning
Component of Instructional Leadership.......................................................... 153
19. Summative Survey Results for the Supervision and Monitoring of
Instruction Component of Instructional Leadership ....................................... 156
20. Summative Survey Results for the Culture of Teaching and Learning
Component of Instructional Leadership.......................................................... 159
21. Summative Survey Results by Percentages for the Data Driven Decision
Making Component of Instructional Leadership ............................................ 161
22. Summative Survey Results by Percentages for School Leaders’ Coping
Strategies......................................................................................................... 165
xii
LIST OF FIGURES
1. Conceptual Framework for School Design....................................................... 94
2. Conceptual Framework for Effective Math Programs...................................... 95
3. Process of Assessment of Math Expertise............................................................ 100
xiii
ABSTRACT
The purpose of the study was to identify how urban high schools can
successfully bring together policy initiatives and local best practices to effectively
improve math performance in their schools. In addition, the study examined how
instructional leadership is effectively carried out in high schools in the context of
improving math performance for students. Several issues seemed to be particularly
relevant to instructional leadership in this setting. To begin with, school leaders
often don’t have strong pedagogical content knowledge in mathematics education
and yet need to motivate and guide those who do, as well as provide data analysis
and review of their efforts. Little, however, is known about how leaders work
effectively in this context. A qualitative, descriptive case study design was utilized
for this study. This research design was selected because the study requires an
examination of an exemplary school which implemented best practices and programs
to improve student achievement in math. The study was anchored with five research
questions to address these critical areas and established conceptual frameworks for
research questions in order to interpret collected data through a certain perspectives.
Based on findings from the case study of Vineyard High School, examining
the school’s efforts to improve their math program and the positive results, six
critical factors emerged: external accountabilities, establishment of a shared vision
and purpose, a culture of trust and instructional leadership through teacher
empowerment, a school leader’s competency in Bolman and Deal’s four frames,
xiv
enhancement of curriculum and instruction based on student performance data, and a
professional learning community with a culture of collaboration. At Vineyard High
School these factors came together to create the environment which led so
successfully to improved student achievement in math. As school leaders and district
leaders explore ways to improve student achievement, the findings and conclusions
from this study can provide insight and guidance.
The study presented two recommendations for future research: 1) to examine
the cause of the incongruity between results on state mandated exams such as
CAHSEE and CST and those for AP exams, and 2) to conduct a comparison study to
find out to what extent the findings from this particular case can be generalized to
other settings.
1
CHAPTER ONE: OVERVIEW OF THE STUDY
Introduction
Since the Sputnik scare in 1957, there have been continual national and local
efforts to address inadequate student performance in public education in the United
States compared to national objective standards and international comparative
studies. In spite of a number of well-publicized alarming national reports, a vast
array of urgent proclamations and policies and the decades of reform that followed,
current student performance data reveal that many of our students still fall short.
In 1983, A Nation at Risk, the outcome of 18 months of study through
testimony received by the commission, painted a grim picture of America’s public
education. The report provided statistics to demonstrate nation-wide educational
inadequacies: 23 million American adults unable to function in their daily lives due
to their inability to read, write, and comprehend; U.S. students lagging far behind
students from other countries in international comparisons of student literacy. The
report mandated excellence in education. It asserted that while our country was
deeply committed to educational excellence and necessary reform it also needed to
be equally committed to educational equity for diverse student populations. It
regarded equity and high-quality education as the twin goals both in principle and in
practice.
2
The data used in A Nation at Risk (1983) also revealed similar concerns over
student performance in math. Only one-third of 17-year-olds showed competency in
solving complex mathematics problems. At the same time, remedial math courses in
public colleges increased by 72 percent, and made up 25 percent of all math courses
available to students. Additional evidence of nationwide inadequate student
performance in math can be found in the results of the National Assessment of
Educational Progress (NAEP). It is oftentimes referred to as the Nation’s Report
Card, since it is the only official ongoing assessment of US academic achievement in
various subject areas (Lubienski & Lubienski, 2006).
In spite of some improvement in student performance on NAEP from 1992
through 1999, it is still quite disturbing to recognize that less than 15 percent of all
students were considered to be “Proficient” and close to one-third of 12
th
graders
“Below Basic.” Regardless of grade difference, more than 30 percent of US eighth
and twelfth graders perform at the “Below Basic” level, which is quite disconcerting.
Such a pattern of student achievement lagging in math was evident not only
in nationwide studies, but also in international comparison studies. The Third
International Mathematics and Science Study (TIMSS) conducted in 1995, the
largest international comparative study of student achievement, involving
approximately 15,000 students from 1,500 schools located in 21 countries, drives the
point home. The study was conducted by the International Association for the
Evaluation of Educational Achievement (IAEEA) to better understand the
3
characteristics of student achievement. The Center for Education Reform (CER)
stated that based on the 1997 TIMSS report, the students in the United States ranked
19
th
out of 21 countries in math and 16
th
in science and that the most advanced U.S.
students scored 21st, at the very bottom of the list, in physics. CER remarked that
our students lag severely in the most crucial academic areas which are vital to the
future of the country, and went on to characterize the results as shameful to the
nation.
Another international assessment pointing to inadequate high school student
achievement in public education is the Program for International Student Assessment
(PISA), a system of international assessment that measures fifteen year-old students’
abilities in reading literacy, mathematics literacy, and science literacy every three
years. It was administered during the 2000 school year for the first time and is
organized by the Organization for Economic Cooperation and Development
(OCED), an intergovernmental organization of industrialized countries. PISA 2003,
which 41 countries took part in, focused on mathematics literacy with a focus on
problem-solving (NCES, 2005). According to the 2005 NCES report on the 2003
PISA results, scores for the American students in mathematics and problem solving
were lower than the average performance of most OECD countries. Their
performance was also lower on each mathematics literacy subscale representing a
specific content area: space and shape, change and relationships, quantity, and
uncertainty.
4
In addition to the overall inadequate performance by American students in
mathematics, many studies point out that student achievement gaps in math also exist
among students of different ethnicities and races. A Nation at Risk (1983) also noted
a performance gaps among minority students in literacy: while approximately 13
percent of all 17 year-old American students could be identified as functional
illiterates, among minority students the percentage considered illiterate was, at 40%,
more than three times as high.
Two decades later, similar results of student achievement have been
observed. The Education Trust (2000) noted that the academic achievement gap
between white and minority students was increasing. African-American and
Hispanic 17 year-old high school student scores show their reading and math skills to
be equal to the average white eighth graders. The National Center for Education
Statistics (NCES) (2003) reported that almost 60 percent of Hispanic 8
th
graders
scored at the “Below Basic” level and fewer than 10 percent scored at the
“Proficient” or “Advanced” levels on the 2002 NAEP mathematics test.
The Center for Education Reform (1998) also added a dismal picture of
public education with its data. “In 1996, 13 percent of all black students aged 16 to
24 were not in school and did not have a diploma. Furthermore, 17 percent of first-
generation Hispanics had dropped out of high school, including a tragic 44 percent
Hispanic immigrants in this age group. This is another lost generation” (Center for
Education Reform, 1998, p.1).
5
There are serious implications of this level of performance and the
achievement gap for the future of the country. The Bill & Melinda Gates Foundation
has also expressed its view in its report on the impact of the level of performance and
student achievement gap due to the inadequacy of high school structure to produce
individuals with proper skills. The Gates Foundation underscored that while high
school graduates or even dropouts were able to support families in the past, today
such low education levels are not sufficient in a society which requires analytical
thinking, communication, and problem solving. The Foundation also pointed out that
a higher education would influence an individual’s earnings along with the well-
being of the democracy. Lara and Pande (2001) also warned that the economic well-
being of the United States is in jeopardy due to the undereducated workforce, and
recent changes in the workplace have led to increased demand for a labor force more
skilled than ever before. They noted that in order for students to be successful in the
present competitive economic environment, they need to possess both strong
communication skills and a mastery of mathematics (2001, p.1).
The Education Trust (2003) reported that African American students’ college
completion rates have not improved, and a gap in college education attainment still
remains. Their low education level and performance gap results in their weak
financial well-being along with inadequate participation as active members of a
democratic society due to their inadequate competency in necessary skills such as
reading, communication, and problem solving (Kendall & Williams, 2004; Gaining
6
Ground, 2001; The Gates Foundation). Consequences such as these jeopardize the
fundamental promises of democracy, equity, and equal access at not only the
national level but at every level of national life (A Nation at Risk, 1983).
The importance of mathematics as a crucial dimension of schooling,
especially for urban youth, cannot be overstated. As elucidated in Rose and Betts’s
study Math Matters: The Links between High School Curriculum, College
Graduation, and Earnings (2001), adequate achievement in math is a vital matter for
urban youth. The results of their study confirmed that there is a strong positive
relationship between the rigor of the math courses that students took in high school
and both the probability of college education attainment and their potential earnings
for 10 years following their graduation. The authors suggested that it is more likely
that students who take highly advanced math classes in high school will continue
with a post-secondary education and find a job with high earnings.
Lara and Pande (2001) emphasized that students must possess strong
communication and math skills in order to be successful in the current work
environment and also that the economic future of the nation is in danger due to its
production of an inadequately educated workforce. They imply, based on recent
studies, that high school students are not ready to pursue a college education or work
as highly skilled employees.
Hambrick (2005) referred to a statement made by the Southwest Consortium
for the Improvement of Mathematics and Science Teaching (SCIMAST) in her
7
article “Remembering the child: On equity and inclusion in mathematics and science
classrooms” that “ensuring equity and excellence lies at the core of systematic
reform efforts, especially in science and mathematics, the two academic areas that
historically have not been widely open to females, ethnic minorities, or students from
less affluent communities and families” (SCIMAST, n.d., p.4).
Greary and Hamson (2000) also noted that the special emphasis on student
achievement in math and science shows success in these academic areas affecting
economic productivity for individuals and society. Sound mathematics and science
competencies provide individuals with better employment opportunities and higher
paying jobs. Well-educated and productive individuals have more chances for
enjoying favorable conditions of life. The authors argued that poor mathematical
competencies restrict opportunities for college majors and career choices.
Success in math affects the economic future of the nation and its destiny in
the global market. Greary and Hamson (2000) warned us that the impact of poor
math and literacy skills of the workforce will cost the U.S. economy nearly 170
billion dollars by the year 2000. The Education Trust (2003) noted that far too often
we can observe some students being taught rigorous subject matter while others are
only offered unchallenging, low-level instruction which “is better aligned with the
assembly-line jobs that are disappearing than today’s job market or college entry
requirements” (p.2).
8
The Education Trust (2000) reported in “Youth at the crossroads: Facing high
school and beyond” that more than 40 percent of employers test literacy and
mathematics skills and that there has been a sharp increase in failure rates on these
tests from 18.9% in 1996 to 35.5% in 1998. This phenomenon can be a major
challenge to our nation since projections of the job market predict that about 70
percent of positions will require at least some postsecondary education.
Such a persistent achievement gap can lead to politically unsettling issues of
equity and equal access to college education attainment and financial well-being, and
the serious deficiencies in academic performance along with a prominent
performance gap among minorities, cries out for solutions.
In order to respond to these needs to improve student achievement and
produce a qualified and skillful workforce to compete with other countries in the
global market state and national efforts have been undertaken to improve math
achievement in high schools, especially with regard to state standards, improved
curriculum and instruction and better teacher preparation and selection, as well as
additional related efforts. These efforts focus on alignment with state content
standards, improvement of curriculum and instruction, development of teacher
training programs, and implementation of reforms. In fact, the state and national
efforts served as change agents and sources of external support and leverage.
The No child Left Behind (NCLB) Act, the latest revision of the 1965
Elementary and Secondary Education Act (ESEA)—arguably the most significant of
9
all federal education laws—was signed into law by the Bush administration in 2002.
NCLB changed the role of the federal government by expanding its control and
influence in K-12 public education throughout the U.S. with high stakes exams and
school accountability. The law forced states to require mandatory mathematics and
reading assessments based on state curriculum standards of all students in grades 3-
12 (Schiller & Muller, 2003).
The federal government was able to mandate this, along with other
expectations and requirements for states and schools to meet, by predicating
qualification for federal aid on compliance with the new mandates. It increased
accountability for states, districts, and schools in regard to student performance and
teacher qualifications, in addition to the mandated testing. At the same time, the
legislation made clear the determination of the U.S. as a nation to improve student
achievement in math and science and the government’s commitment to help schools
increase math and science excellence. Under NCLB, states must administer annual
assessments aligned to state standards and use the results of the assessments as the
principal source to evaluate district and school accountability. States are also
expected to develop a well-established statewide accountability system to measure
public school and charter school performance. Another mandate from the federal
government is for states to establish rigorous academic content and performance
standards for all students, in language arts, mathematics, and science at a minimum
(Learning First Alliance). Such demands to establish academic content standards had
10
the effect of strengthening curriculum. Under NCLB, teacher quality control also has
been under scrutiny in light of the law’s Highly Qualified Teacher (HQT) provision.
All districts are required to ensure their teachers are teaching core curriculum to meet
the HQT requirements by the end of the 2006 school year. The states have
put forth a great deal of effort to meet the requirements in response to this
unprecedented federal involvement in public education. The report Brief on
Educational Progress, 1992-2000, was published by the Executive Office of the
President under the Clinton administration in 2000. According to the report, a great
deal of educational progress was made in the U.S. from 1992 to 2000 in areas such
as state content standards, accountability systems, student performance, and attempts
to close the student achievement gap. The report shows that 49 states established
content standards and 48 states had state assessment systems to measure student
performance in 2000, compared to only 14 states which had such standards in 1992.
As an example of the scope of such efforts, the state of California established its own
accountability system for districts and schools to follow. Aiming High: High Schools
for the 21
st
Century, is a roadmap for the public schools in California in their attempt
to successfully bring about high school reform. The California Department of
Education suggests schools and districts use Aiming High as a resource in their
pursuit of standards-based education.
Out of these reform efforts have come new school designs that focus on
student achievement and related school features. With both federal and state
11
funding, schools have investigated reform designs that can influence the entire
school context: physical setting, school operations, curriculum and instruction,
school organization, professional development, and resource allocation, all in an
attempt at comprehensive school reform (CPRE, 1998). The article (1998) reported
that more than 2,100 schools have adopted either Bob Slavin’s Success for All
program, James Comer’s School Development Project, or Henry Levin’s Accelerated
Schools. Other popular school reforms are the America’s Choice school design and
various implementations of small learning communities (SLCs). A brief account of
these programs is provided here to show the range of strategies employed in these
efforts at reform.
When, in 1986, the Baltimore school superintendent needed a new school
design to turn around his failing schools, he called on the assistance of Bob Slavin, a
researcher from John Hopkins. The model they eventually adopted, a research driven
program with a philosophy of “all students can be successful in learning,” became
the Success for All program (Smith, n.d.).
The Comer School Development Program, a school model commonly known
as the Development Program, focuses on a holistic child development model. It
connects student academic performance with their emotional well-being and social
and moral development in a positive, caring school culture conducive to learning.
The Comer Process takes the view that schools are responsible for bringing their
12
stakeholders—teachers, administrators, and parents—together to create an action
plan to help students academically and socio-emotionally.
The primary goal of Accelerated Schools Plus, a school design created by
Henry Levin at Stanford University in 1986, is to provide all students with a rigorous
and enriched curriculum based on the entire school community’s vision of learning.
The model emphasizes “gifted-and-talented” instruction—normally available only to
students formally identified as gifted-and talented—for all students through a process
known as “powerful learning.”
The purpose of small learning community (SLC) programs is to reorganize
comprehensive high schools into smaller learning units so students are able to build
connections with their school community while at the same time the schools can
provide students with personalized support. Some of the common strategies utilized
in creating smaller learning units are creating schools within schools and career
academies, restructuring the school day, instituting personal adult advocates, and
developing advisory systems.
The America’s Choice school design refers to a K-12 comprehensive school
reform (CSR) model which was created by the National Center on Education and the
Economy (NCEE). The design, as described by Supovitz and Poglinco (2001),
pursues high student achievement through rigorous curriculum and stresses the
importance of providing a safety net for all students. It focuses on high expectations,
13
literacy, common core curriculum, standards-based assessments, distributed
leadership, safety nets, and commitment to teacher professionalism.
Fortunately, a considerable amount of good work has been done in
identifying the features of instructional leadership in this new context. Supovitz and
Poglinco (2001) note that the recent focus of educational leadership is on
instructional leadership itself. They quote Cuban’s theory (1998) that traditionally
the three main roles of school principals are: 1) first and foremost, managerial
responsibilities, 2) a political role as negotiator and mediator with stakeholders, and
3) an instructional role as a supervisor of teachers. However, under the recent
accountability system, this last role has expanded so that school principals are now
expected to be instructional leaders who possess sound understanding and
knowledge of curriculum and instruction, know how to collect and analyze student
assessment data and how to create a professional learning community. The main
focus of all this is focused on improving student achievement (Supovitz & Poglinco,
2001).
As new research-supported school reform models are increasingly
implemented by schools in their attempts to positively impact student achievement, it
becomes crucial for schools to maximize teaching success and optimize student
learning in order to improve student math achievement.
In their attempt to create the most effective learning environment, it is crucial
for school leaders to realize the importance of their role as instructional leaders by
14
focusing on the essential components of successful schools. Marzano (2003) put
forward and ranked five school-level factors that he believes are needed in order to
bring about the changes necessary to improve student achievement: a guaranteed and
viable curriculum, challenging goals and effective feedback, parental and community
involvement, a safe and orderly environment, and collegiality and professionalism.
But learning factors such as these can only be effective in so far as a school is able to
bring them about. For example, in order for schools to provide a “guaranteed and
viable curriculum,” Marzano (2003) asserted that they must maximize opportunities
for students to learn and protect instructional time.
Thus it is important for school leaders to find out how they can ensure, in
order to improve student achievement, a guaranteed and viable curriculum,
challenging goals, and effective feedback. Johnson (2002) offers sound strategies to
improve student achievement based on student performance data. The author
emphasizes (2002) that any school reform leadership team has to be at the forefront
in initiating and maintaining on-going communication with the school community
and of bringing about consensus regarding the change process based on the
meaningful use of data.
In addition to school principals’ adoption of this new type of instructional
leadership, many studies suggest it is even more powerful and effective for them to
create shared instructional leadership with teachers in order to improve student
achievement by creating a professional learning community. Such shared
15
instructional leadership has been noted as a significant factor in curriculum (Darling-
Hammond, 1995). Marks and Printy (2003) state that shared instructional leadership
encourages the on-going collaboration of principals and teachers on student learning
factors such as curriculum, instruction, and assessment. They suggest that the
integrated style of shared instructional leadership and transformational leadership
lead to the best outcomes of all. As a transformational leader, the principal
establishes among the stakeholders a set of goals of the highest commitment and
maximizes the organizational ability for student achievement. Simultaneously, as an
instructional leader, the principal collaborates with teachers so as to improve student
achievement and achieve the school’s goals.
Statement of the Problem
We live in the age of information and it is more crucial than ever in the
nation’s history to have a highly qualified and skillful workforce to compete with
other countries in the global market. This urgent need calls for national and local
attention to the outcome of public education, especially mathematics due to its
inordinate role as the primary gateway to college education, technology, and
advanced science. Student achievement at the high school level is progressing only
marginally, especially in the critical area of math. Such inadequate student
achievement in math has been a national concern for the last few decades, in spite of
the great deal of attention at the national and state level that has been placed on
schools and districts to make them accountable for student achievement. As a result,
16
a national urgency has come about to establish effective policy initiatives in order to
improve student achievement in math.
In addition, there is a potential socio-political crisis in the nation due to the
student achievement gap in math. As Rose and Betts’s study (2001) shows, the rigor
of math classes that students take in high school affects their success in their career
and their financial well-being over the ten years following their high school
graduation. Such a finding implies that high school math placement is closely related
to economic status and social status. According to the results of numerous high
stakes examinations such as NAEP, the California Standards Test (CST), and
CAHSEE, Latino and African-American students perform at a significantly lower
level than Caucasian and Asian students nationwide. This makes it crucial to narrow
the current gap between ethnic groups in academic performance in math in order to
prevent the resultant economic disparities.
Math education has been bombarded with constant public criticism, a stream
of new initiatives, and a variety of external accountabilities. But as they address the
criticism and respond to the new mandates, it is important for policymakers,
educational leaders, and practitioners to know which policy initiatives can be shown
to be related to improved math achievement at the school. Under the increased
scrutiny, there has been a quest for the best practices and the most effective
curriculum and instruction to improve student achievement in math. Therefore, it is
crucial to identify what factors comprise these best practices; what curriculum,
17
instruction and related conditions are most likely to actually promote improvement
of math achievement.
Moreover, in order to enhance math programs and instructional strategies,
just as for any attempt at organizational improvement, schools cannot avoid going
through a change process. It is thus worthwhile to examine effective change
processes that have been implemented at the school level to improve student
achievement in math. Successful change processes, for the purpose of enhancing
math programs and strategies and improving student achievement in math, require
effective leadership at the site, especially strong instructional leadership, in spite of
the many challenges and dilemmas that are inevitable in the change process.
Purpose of the Study
The purpose of the study is to identify how urban high schools successfully
bring together policy initiatives and local best practices to effectively improve math
performance in their schools. In addition, the study examines how instructional
leadership is effectively carried out in high schools in the context of improving math
performance for students. Several issues seem to be particularly relevant to
instructional leadership in this setting: leaders often don’t have strong pedagogical
content knowledge in mathematics education yet need to carry out functions related
to fiscal, personnel, and organizational leadership, as well as data analysis and
review. Little, however, is known about how leaders work effectively in this context.
18
Research Questions
The research questions addressed by this study are:
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—were shown to be related to improved math achievement at the
school?
3. What change process did the school use to enhance its math program and
strategies to assist students in math?
4. 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
This study is important because of the current challenges and pressures that
schools are faced with at the national and state levels, such as the NCLB Act on
which continued federal aid is predicated, or the CAHSEE requirement which
students must pass in order to receive a high school diploma. These external
accountabilities have enhanced schools’ interest and eagerness in learning more
about successful models to improve their own current practice, especially their math
curriculum and instruction.
19
It is especially important for districts, school-site administrators, school
leadership teams, and classroom teachers to know about successful models and what
their roles should be in order to replicate the successful model at their schools in
efforts to improve student performance. It is the intention of this study to provide
schools with the following set of tools needed to accomplish the difficult work of
effective reform.
School-site administrators will gain knowledge of effective curriculum and
instruction that have produced successful outcomes in math performance. They will
also better understand various components of the necessary change process in order
to implement reforms that improve student performance in math. Based on such
understanding and new knowledge, school-site administrators will be able to utilize
and restructure their leadership team and resources throughout the change process.
They will assist their schools in experiencing a successful transition in becoming an
improved school which efficiently and effectively introduces new practices based on
the replication of successful best practices. The study will also help school
administrators understand effective leadership styles and frames in their efforts to
become effective instructional leaders.
School leadership teams will understand the various components of successful
models to improve math instruction. They will also understand the dichotomies
inherent in the components, which then will help them map out strategies to replicate
the successful model at their own site. Based on their sound understanding of the
20
successful model and the necessary change process, they will be able to organize
their resources and strategize their efforts to bring about the necessary changes.
School leadership teams will also be better able to enhance instructional
leadership among themselves and at the school site, identify organizational goals
related to math program improvement, and plan professional development
opportunities in order to bring their staff to an appropriate level of instructional
knowledge and competence.
Math teachers will also benefit from this study findings. They will gain the
understanding of the current research findings through the literature review and
acquire hands-on knowledge of best practices and furthermore, based on such
understanding, they will be able to modify and strengthen their instruction to
improve student achievement in math.
Assumptions
This study assumes that student achievement in math is the outcome of a
concerted school effort to bring about necessary school reform and to utilize the best
practices that are focused on student learning. It also assumes that instructional
leadership is the backbone of school efforts to improve student achievement and in
closing student achievement gaps. The Interview Guide and Teacher Questionnaire
questions were organized on the basis of sound conceptual frameworks and are
regarded as valid tools for the collection of data needed for the study. It is assumed
21
that respondents’ statements are truthful and therefore the information obtained from
them are further assumed to be reliable and true.
Limitations
This study employed a qualitative case study to identify various components
of a successful math program model and school practice and the data was based on
the findings from a study of a single public high school in Southern California. This
limits its generalizability to different school settings or different subject matters.
Although efforts were made to eliminate as much bias as possible, the researcher did
not have control over any biases that participants brought to their responses. Finally,
the analysis of the data in the study was subject to researcher interpretation.
Delimitations
The collected data is delimited to a high school located in an urban area in
Southern California. The intention of the study is to identify various components
of a successful math program which shows improvement of student achievement
in math over a period of several years. As a result, the study mainly provides
insights into math curriculum and instruction. The school site and program are
purposely selected because of size, ethnicity, and student performance results in
math. In addition, the size of the sample and the nature of the qualitative method
employed in this study limit the ability to generalize the findings of the study to
other situations. The school was purposefully selected based on the following
criteria:
22
1. Comprehensive public high school in southern California serving grades 9-12
with at least 1200 students
2. Student demographic information showing at least 50% of its students from
traditionally ethnic minority groups
3. API (Academic Performance Index) score of at least 600
4. Statewide rank of 5 or higher
5. improvement of student performance in math as evidenced by results on the
California Standards Test (CST) in Algebra I over a three year period
6. No participation in special grant programs such as IIUSP.
7. Leadership stability defined by at least three years of service at the school site
by the principal during the time the improvement was made.
Definition of Terms
For the purpose of this study, the following terms were defined as follows:
Academic performance index (API): California’s numerical indicator of
student achievement, used as a basis for a comparative ranking of schools statewide
(California Department of Education [CDE], 2002).
Achievement gap: denotes differences in the academic achievement of a
particular group of students.
NCREL: Bridging the Great Divide (2002): Broadening Perspectives on
Closing the Achievement. North Central Regional Educational Laboratory
http://www.ncrel.org/policy/pubs/pdfs/bridging.pdf
23
Accountability: A designed effort or system that holds districts, schools
and/or students responsible for student performance. Accountability systems
typically consisted of assessments, public reporting of results, and rewards or
sanctions based upon student performance over time (Elmore, 2002).
Assessment: A measurement of a student’s particular skill or knowledge that
may be written, oral, or performance in nature. Standardized assessments were
administered and scored in exactly the same way for all students to measure specific
skills and knowledge.
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.
Benchmark: An articulated expectation of student performance at specific
grades, ages, or developmental levels.
Best Practices: A best practice is a technique or methodology that, through
experience and research, has proven to reliably lead to a desired result. Target Teach,
SearchVB.com, Needham, MA
http://searchvb.techtarget.com/sDefinition/0,,sid8_gci498678,00.html
California High School Exit Examination (CAHSEE): A graduation
requirement, authorized by state law in 1999, that requires California public students,
beginning with the graduating class of 2004, to pass the CAHSEE in order to receive
24
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). California Department of
Education http://www.cde.ca.gov/ta/ac/sa/def05cstall.asp
Conceptual framework: A consistent and comprehensive integration of
research literature, theories, and other pertinent information that was the basis for the
collection of data and analysis of findings within the study.
Constructivism: The learning theory asserting that children construct new
information themselves based on a foundation of preexisting beliefs. Within this
process, their ideas became more complex and they needed to verify new
information in a social context. This position advocated that students needed to
create their own knowledge and it could not be transferred to them through listening
to lectures or engaging in rote practice.
Content standards: As the foundation of a standards-based system, content
standards described what content knowledge and skills students were required to
master (American Federation of Teachers, 2001).
Data-driven decision making: The process of making decisions about
curriculum and instruction based on the analysis of classroom data and standardized
25
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).
Design: A plan intended to affect change which may be school wide, specific
to a certain level or population, or specific to individual schools.
Equity: Educational impartiality that ensured all student fair treatment and
access to the services they needed in order to receive a high-quality education.
Highly Qualified Teacher: A Highly Qualified Teacher (HQT) is one who has
an appropriate credential to teach in the area(s) assigned and who has demonstrated
subject matter competency through various acceptable most often through passing
rigorous state exams or through a highly objective uniform state standard of
evaluation (HOUSSE). Source = Under NCLB, Title IX, section 9101-
Leadership: Instructional leadership: Instructional leadership: an individual
who influencing, motivating and directing activities to improve student learning
http://www.ncsl.org.uk/media/F7A/88/bush-school-leadership-full.pdf.
Implementation: The translating of an idea into action in order to accomplish
the specified goal.
Instructional improvement: A change in the structures or opportunities that
enabled quality teaching, thus resulting in improved learning (Gilbert et al., 2003).
Instructional leadership: An influence that guided the activities designed to
impart knowledge or skills to students. (Olson, 2005)
26
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.
Performance Standards: The level of performance that students were
expected to demonstrate in relation to the content standards; such as, basic,
proficient, or advanced levels of performance (Hambleton, 1999).
Reform: A change effort that was undertaken to improve the educational
system.
Sanctions: The consequences imposed for not meeting expected performance
outcomes in accountability systems. (Olson, 2005)
Stakeholder: Any person with interest in the operation and outcomes of a
specific educational system, including administrators, teachers, parents, students and
community members.
Standards-based reform: The change to an educational system that utilized
subject-matter benchmarks to monitor student achievement, assessments aligned
with standards to measure student performance, and accountability systems that
provided rewards or sanctions to district, schools, and students based on student
performance. Implementation of all three components—standards, assessment, and
accountability—was termed standards-based accountability. (Olson, 2005)
27
Systemic reform: Change that occurs in all aspects and levels of the
educational process that impacted all stakeholders with implications for multiple
components, including policies, curriculum, assessment, professional development,
instruction, and budgeting. The goal of systemic reform was more clarity, coherence,
and economy throughout the system (Schmoker, 2003).
Teaching and learning: Based on the premise that effective instruction
resulted in strong student performance, improving teaching and learning referred to
the demonstration of improved instruction, even in the absence of precise student
outcome measurements. (Olson, 2005)
Organization of the Study
Chapter One of this study presents an introduction to the importance of
conducting a case study of a high school’s successful practices in improving student
achievement in mathematics. Chapter Two provides an in-depth review of the
current literature, including trends and issues in student achievement in math, school
reform, mathematics reform, and instructional leadership. Chapter Three describes
the research methodology used for the study as well as the rationale for the selection
of the study sample and the instrumentation employed for data collection. Chapter
Four presents the findings of all data collected and a summary of the findings of the
study. Chapter Five concludes the study by summarizing the findings and drawing
conclusions regarding the five research questions and also includes implications of
the study and recommendations for future research.
28
CHAPTER TWO: REVIEW OF THE LITERATURE
Introduction: Executive Summary
In comparison with national objective standards and international
comparative studies, inadequate performance of American high school students has
garnered much attention at the national and state level. In 1983, A Nation at Risk was
published by the National Commission of Excellence in Education, sounding an
alarm for U.S. citizens about the status of student performance in public education.
The compelling data in the report depicted a grim picture of public education: an
increase in illiteracy, math incompetence, and a glaring student performance gap
among ethnic groups. Ultimately, the commission’s report explicitly challenged the
nation to bring about fundamental changes in public education.
A decade after the publication of A Nation at Risk, the dismal state of public
education had gotten no better. In 1995, the Third International Mathematics and
Science Study (TIMSS) was conducted by the International Association for the
Evaluation of Educational Achievement (IEA). According to the findings of the
study, American 12
th
graders scored near the very bottom, ranking 19
th
out of 21
nations in math and 16
th
in science. U.S. advanced students scored last in physics. In
addition, the study corroborated the student achievement gap based on ethnicity that
had been noted in the earlier study. (The Center for Education Reform, 1998)
In response, a wide range of federal and state efforts have addressed the
inadequacy of student achievement and the disparity between different racial and
29
ethnic student populations. The No Child Left Behind (NCLB) Act is the most
prominent example of such efforts at the federal level. Under Congressional
mandate, including provision for punitive consequences, state and local education
agencies are required to provide rigorous standards-based instruction and ensure
equity in student performance and learning opportunities for all students regardless
of their ethnicity or race.
This mandated legal requirement for equity in public education becomes
most crucial when applied to mathematics—at a national scale in both an economic
and socio-political sense. We live in an age of information and highly advanced
technology embedded in a global market system; as a result, the society we live in
demands workers with advanced math and science skills. It is not coincidental that
current studies indicate that student achievement in math is one of the strongest
predictors of student career success and financial well-being. In order to ensure
equity in financial security and career opportunities, schools must be sure that all
students have access to advanced math classes and the necessary support for their
success in completing them.
Under current external pressures such as NCLB, schools are now exerting
desperate efforts to improve student achievement and narrow the achievement gap.
A few schools have been quite successful in bringing about these reforms. Their
school site leaders and instructional leaders have shown themselves to be
knowledgeable about the required change process and competent in maximizing
30
instructional leadership. As a result, these schools have established what has come to
be known as “best practice” those instructional and organizational practices shown to
have led to higher student achievement.
The Status of Student Achievement in Mathematics
A Nation at Risk, the nation-wide report published in 1983 by the National
Commission on Excellence, brought national concern and attention to public
education. It warned the nation about how American students were not being
adequately educated and how far they lagged behind in comparison with other
industrialized nations. Even more than two decades later, its outcry over the alarming
effects of inadequate academic achievement on the economic prospects of the nation
still sound relevant in light of the current status of and concerns about student
achievement in public education.
Our nation is at risk. Our once unchallenged prominence in commerce,
industry, science, and technological innovation is being overtaken by
competitors throughout the world. This report is concerned with only one of
the many causes and dimensions of the problem, but it is the one that
undergirds American prosperity, security, and civility. We report to the
American people that while we can take justifiable pride in what our schools
and colleges have historically accomplished and contributed to the United
States and the well-being of its people, the educational foundations of our
society are presently being eroded by a rising tide of mediocrity that threatens
our very future as a nation and a people. What was unimaginable a generation
ago has begun to occur—others are matching and surpassing our educational
attainments (National Commission on Excellence, p.1).
The national report enlisted indicators of such risk based on their eighteen-
month study. It referred to the findings of an international comparison study:
31
American students ranked last in seven out of 19 academic tests and never first or
second. Close to 23 million American adults were functionally illiterate and about 13
percent of seventeen-year-olds could be considered functional illiterates. The
College Board’s Scholastic Aptitude Test (SAT) showed 50 points of decline in
average verbal skill scores and 40 points in average math scores. Many seventeen-
year-olds did not have the expected level of critical thinking skills and about 40
percent of them did not possess the necessary inferential skills in their reading tasks
and only one-third could figure out a math problem requiring multiple steps.
Another important study addressing similar concerns related to inadequacy of
student achievement is the 1997 TIMSS (Third International Mathematics and
Science Study) report, conducted by the International Association for the Evaluation
of Educational Achievement (IAEEA). The TIMSS study, the largest international
comparative study of student achievement, involved 1,500 schools and 15,000
students from 21 countries during the 1995 school year and tested mathematics and
science knowledge. The National Center for Education Statistics explained that the
student participants in the study were randomly selected to represent all students in
their own nations and that the entire assessment process was examined by
international technical review committees to ensure its adherence to established
standards. The Center for Education Reform (CER) stated (1998) that the students
from the United States ranked 19
th
out of 21 countries in math and 16
th
in science and
that most advanced U.S. students scored 21
st
, at the very bottom of the list, in
32
physics. CER remarked (1998) that our students lagged severely in these most
crucial academic areas which are vital to the future of the country, and went on to
characterize the results as shameful to the nation.
Following the 1995 study, additional studies were conducted in 1999 and
2003. According to the 1999 TIMSS-R results (The Third International Mathematics
and Science Study Repeat), U.S. eighth-graders ranked at 17
th
of the 37 other
TIMSS-R nations, performing similarly to students in six nations, and performing
lower than students in 14 countries. The average score of American students was 502
while other nations’ average math scores ranged from 604 for Singapore to 275 for
South Africa (NCES, 2000). According to the report on the 2003 TIMSS results,
which was released in 2004 by the Education Department’s National Center for
Education Statistics (NCES), 46 countries participated and U.S. students ranked 12
th
in their math scores with an average score of 504 while other nations’ average scores
varied from 605 for Singapore to 264 for South Africa. U.S. eighth graders improved
their average mathematics and science performances compared to 1995 but no
measurable changes were seen in the average mathematics and science achievements
of U.S. fourth graders between 1995 and 2003 and their performance in both math
and science was lower in 2003 than in 1995.
Other international assessment data pointing to high school students’
inadequate achievement in public education can be found in the Program for
International Student Assessment (PISA), a system of international assessment that
33
measures fifteen-year-old students’ abilities in reading literacy, mathematics literacy,
and science literacy every three years. It was administered during the 2000 school
year for the first time and is organized by the Organization for Economic
Cooperation and Development (OCED), an inter-governmental organization of
industrialized countries. PISA 2003, which 41 countries took part in, focused on
mathematics literacy with a concentration on problem-solving (NCES, 2005).
According to the 2005 NCES report on the 2003 PISA results, the performance of
American students in mathematics and problem solving was lower than the average
for most OECD countries. Their performance was also lower on each mathematics
literacy subscale representing a specific content area: space and shape, change and
relationships, quantity, and uncertainty. The OECD provided seven performance
levels ranging from “Below Level 1,” indicating the lowest competence, and “Level
6,” representing the highest mastery of content literacy. Greater percentages of U.S.
students were placed below level 1 and at levels 1 and 2 than the OECD average.
They also had a lower representation at levels 4, 5, and 6.
Additional evidence of nationwide inadequate student performance in math
can be found in the results of the National Assessment of Educational Progress
(NAEP). It is oftentimes referred to as “The Nation’s Report Card” since it is the
only official ongoing assessment of US academic achievement in various subject
areas (Lubienski & Lubienski, 2006). It is “a congressionally mandated survey to
measure what students know and can do. The goal of NAEP is to estimate
34
educational achievement and changes in that achievement over time for American
students of specified grades as well as for subpopulations defined by demographic
characteristics and by specific background characteristics and experiences” (NCES,
1998). It is also “a reference for the American public, especially educators, parents,
students, and policymakers” (U.S. Department of Education, 2004, p.1). NAEP
results provide a wide range of valuable information regarding American students’
knowledge and skills in various subject areas at grades 4, 8, and 12. For the NAEP
mathematics assessment five content standards are identified: 1) number sense,
properties, and operations, 2) measurement, 3)geometry and spatial sense, 4) data
analysis, statistics, and probability, and 5) algebra and functions. The comparison of
the NAEP math results from 1990, 1992, and 1996 among 12
th
graders indicate the
following changes over time:
Table 1: Comparison Chart for 12
th
graders NAEP Performance in Mathematics
1990 1992 1996
Advanced 1.4% 1.6% 1.9%
Proficient 10.5% 13.1% 14.4%
Basic 46.2% 49% 52.9%
Below Basic 41.9% 36.3% 30.8%
Source: NAEP Achievement Levels* 1992-1998 for Mathematics, US Department of Education
*The National Assessment Governing Board (NAGB) defined four achievement levels as follow: 1)
advanced –exhibiting superior performance, 2) proficient: solid academic performance, 3) basic—
partial mastery, and 4) below basic—less than partial mastery.
In spite of some improvement in student performance, it is still quite
disturbing to recognize that less than 15 percent of these students were considered to
35
be “Proficient” and nearly a third of 12
th
graders were “Below Basic.” While the
2005 NAEP results for 12
th
graders in mathematics are not available at the present
time to be included in this study, the 2005 NAEP results in math for eighth graders
indicate that to some extent similar concerns and phenomena exist for eighth graders:
The average scores for 1996, 2000, 2003, and 2005 were respectively 270, 273, 278,
and 279. In 2003, the percentage of eighth graders performing at or above
“Proficient” level was 29% and those performing at “Below Basic” were 32% while
in 2005, 30% were at or above “Proficient” and 31% at the “Below Basic” level.
Regardless of grade difference, more than 30 percent of US eighth and twelfth
graders perform at the “Below Basic” level, which is quite disconcerting.
The Center for Education Reform (1998) also noted, “Since 1983, over 10
million Americans had reached the 12
th
grade not even having learned to read at a
basic level. Over 20 million have reached the senior year unable to do basic math.
Almost 25 million have reached the 12grade not knowing the essentials of U.S.
history” (p.1).
The National Center for Education Statistics (NCES) report of 2006, “A
Profile of the American High School Senior in 2004: A First Look” also provides an
illustration of inadequate math performance in U.S. high schools, in this case among
high school seniors. The report, referred to as E.D. TAB, was the first follow-up of
the longitudinal study of 2002. The study, which states that it provided national data
on 2004 high school seniors, scrutinized math achievement of twelfth-grade senior
36
cohorts along with their expected educational attainment, and their life goals and
values. The longitudinal E.D. TAB study relates to this research in regard to its data
on senior math performance. The E.D. TAB included multiple levels of mathematics
in its assessment: 1) simple arithmetical operations with whole numbers, 2) simple
operations with decimals, fractions, powers and roots, 3) simple problem-solving
requiring low level mathematical concepts, 4) understanding of intermediate-level
mathematical concepts and/or multiple-step solutions to word problems and 5)
complex multi-step word problems. It found that approximately 96 percent of the
2004 senior cohorts were capable of performing simple arithmetical problems with
whole numbers but this dropped to 79 percent of them who could perform these
same operations when they involved decimals, fractions and roots. While 62 percent
of them were able to perform simple problem solving, only about 35 percent
displayed competency in intermediate level mathematical concepts and this declined
to four percent who showed highly advanced competence in solving complex math
problems and utilizing advanced mathematical concepts and skills in problem
solving.
The Council of Chief State School Officers (2001) quoted the 2000
Education Trust report, stating that seventeen-year-old high school students in the
U.S. are showing less progress in reading, math, and science than students in the
past. Almost 30 percent of high school graduates needed to take a remedial course in
English or mathematics.
37
The Student Achievement Gap over the Years
The status of student achievement in the U.S. has an additional layer of
complexity lying below the surface of the inadequate student performance revealed
by state and national standards and measured by international comparative studies:
that undercurrent is the hold of consistent gaps in student academic achievement
between students from different groups based on diversity in socioeconomic
condition, race or ethnicity, language, and disability. The first national study to
describe ethnic differences and bring attention to racial and ethnic inequities in
academic achievement among children of various ages was conducted by James
Coleman in 1966 (Phillips, 2000). Phillips noted that since then, we have made
significant progress in survey design, cognitive assessment, and data analysis; yet we
seem not to have acquired much understanding of the causes of the academic
achievement gap.
Almost two decades later the 1983 National Commission on Excellence
remarked in their famous report, A Nation at Risk, with its profound analysis of
equity in public education:
Part of what is at risk is the promise first made on this continent: All,
regardless of race or class or economic status, are entitled to a fair chance and
to the tools for developing their individual powers of mind and spirit to the
utmost. This promise means that all children by virtue of their own efforts,
competently guided, can hope to attain the mature and informed judgment
needed to secure gainful employment, and to manage their own lives, thereby
serving not only their own interests but also progress of society itself (The
National Commission on Excellence, 1983, p.2).
38
In its list of indicators of the national risk, the Commission pointed to one that
showed an achievement gap among minority students: while about 13 percent of all
seventeen-year-olds in the U.S. can be regarded as functionally illiterate, functional
illiteracy among minority students may be as high as 40 percent.
The Center for Education Reform (1998) also added to the dismal picture of
public education with its data showing that, “In 1996, 13 percent of all black students
aged 16 to 24 were not in school and did not have a diploma. Furthermore, 17
percent of first-generation Latinos had dropped out of high school, including a tragic
44 percent of Latino immigrants in this age group. This is another lost generation”
(Center for Education Reform, 1998, p.1).
Jaekyung Lee (2002) examined the trends in Black-White and Hispanic-
White achievement gaps over the last three decades by studying NAEP and SAT
results. In her article, “Racial and Ethnic Achievement Gap Trends: Reversing the
Progress toward Equity?” Lee found that there had been moderate achievement gains
for all students during the last thirty years: Reading improved between 1971 and
1999 and mathematics between 1973 and 1999. The author also noted that there was
significant academic improvement for Latino and African American students during
the 1970s and the first half of the 1980s based on the NAEP results. During that
time, Lee noted (2002) a substantial narrowing of the African American-White and
Latino-White academic achievement gaps took place. Nevertheless, there had been a
setback during the 1990s. While it appeared that during the period 1971-1999 the
39
African American-White student gaps declined by 20 to 40 percent, through a closer
study of the phenomenon Lee found that there was actually a two-fold trend: the
achievement gap narrowed through the late 1980s and thereafter remained the same
or rose a little. However, during the period between 1986 and 1999, the gap actually
increased; white students improved their achievement while African American
students in comparison did not experience much growth. In her study, Lee also noted
(2002) that the Latino-American achievement gaps in NAEP fell a little, with rather
inconsistent gains and losses during the period of 1973-1999. Lee suggested that the
Latino-White student achievement gap was narrowed most by 1982. She noted that
similar trends were also observed in her examination of SAT (Scholastic Aptitude -
Testing) results: a narrowing of the African American-White and Latino–White
student achievement gaps in SAT scores halted in the late 1980s and through the
early 1990s, the scores remained stable or widened.
As a National Center for Education Statistics (NCES) report showed (2001),
the 2000 NAEP results demonstrated that considerable gaps in student achievement
still remain among different racial or ethnic groups. Hambrick and Svedkauskaite
(2004) remarked that the 2000 NAEP results disclosed the fact that the academic
achievement gap continues to remain in public education. In spite of small gains in
mathematics since 1990, stark gaps were evident as can be seen in the following
table:
Table 2: 2000 NAEP Results in Math for 12
th
graders by Race/Ethnicity
40
White African
American
Latino Asian-
Pacific
American
Indian
Advanced
or
Proficient
20% 3% 4% 34% 10%
Basic 54% 28% 39% 46% 47%
Below
Basic
26% 69% 46% 20% 43%
Source: 2001 NCES Report
The chart clearly shows that White and Asian-Pacific students perform much
higher than their peers. According to the data, the African American students
severely lagged, with 69% of them scoring at the “Below Basic” level.
Similar trends can be observed in the comparison chart of the national scale score of
the 2000 NAEP by race and ethnicity as shown below:
Table 3: National Scale Score Results of 12
th
Graders by Race/Ethnicity: 1990-2000
White African
American
Latino Asian-
Pacific
American-
Indian
1990 301 268 276 311 N.A.
1992 306 276 284 316 N.A.
1996 311 280 287 319 279
2000 308 274 283 319 293
Source: 2001 NCES Report
The Education Commission of the States (ECS) noted (2004) that persistent
educational underachievement of Latino students, the fastest growing minority
student group in the nation, is one of the most vital issues in public education.
41
Although there has been improvement over the past twenty years in Latino students’
performance on national high-stakes exams, significant achievement gaps still exist.
They are more likely to be unprepared for learning starting in kindergarten, to be
retained, and to drop out of school. The 1998 NAEP mathematics test results show
that about six percent of Latino 12
th
graders scored at the “Proficient” level; on the
other hand, 18 percent of their white peers scored at that level. Four years later, the
achievement gap was still evident in the 2002 NAEP math test results.
NCES (2003) reports that almost 60 percent of Latino 8
th
graders scored at
the “Below Basic” level while fewer than 10 percent scored at the “Proficient” or
“Advanced” levels on the 2002 NAEP mathematics test. The Education Trust (2000)
underscored that the academic achievement gap between white and minority students
was increasing. African American and Latino seventeen-year-old high school
students, the age group of seniors, show reading and math skills equivalent to the
average white 8th grader.
The Importance of Student Achievement in Mathematics
There are serious implications stemming from this level of performance and
from the accompanying achievement gap for the future of the country. This is not a
new educational issue, a similar concern was raised by the NCEE in its report, A
Nation at Risk (1983), addressing the American people:
Learning is the indispensable investment required for success in the
“information age” we are entering. Our concern, however, goes well beyond
matters such as industry and commerce. It also includes the intellectual,
42
moral, and spiritual strengths of our people which knit together the very
fabric of our society. The people of the United States need to know that
individuals in our society who do not possess the levels of skill, literacy, and
training essential to this new era will be effectively disenfranchised, not
simply from the material rewards that accompany in our national life. A high
level of shared education is essential to a free, democratic society and to the
fostering of a common culture, especially in a country that prides itself on
pluralism and individual freedom (p.2).
In the report, the Commission mentions multiple layers of impact: financial well-
being at the personal level, danger to the establishment of democratic society at the
societal level, and a threat to the constitution of common ground for the nation at a
socio-political level.
The Bill & Melinda Gates Foundation expressed a similar view in its report
describing the inadequacy of the high school structure to produce individuals with
the necessary skills and how this is compounded by low performance and
achievement gaps. The Gates Foundation pointed out that the structure of current
high schools was created at the beginning of the 20
th
century to help students prepare
for work in an industrial economy very different from that of the 21
st
century. It went
on to explain that low-performing students paradoxically tend to receive watered-
down curriculum with no individualized support in response to their lack of
achievement, and thus fail to acquire the higher level skills such as reading, writing
and problem solving needed to be successful in this new work environment. It
accused public high schools of accepting mediocrity and ignoring the needs of
average students to be successful in their pursuit of education. The Gates Foundation
43
underscored that while high school graduates or even dropouts were able to support
families in the past, such basic educational levels are not acceptable today in a
society which requires analytical thinking, high-level communication skills, and
problem solving. The Foundation also pointed out the influence that higher education
would have on individual earnings as well as the well-being of the democracy.
Lara and Pande (2001) also warned that the economic well-being of the
United States is in jeopardy due to the undereducated workforce and recent changes
in the workplace that have led to an increased demand for a better skilled labor force
than ever before. They noted that in order for students to be successful in the present
competitive economic environment, they need to possess strong communication
skills and a mastery of mathematics (2001, p.1).
Kendall and Williams (2004) also noted that the number of factory jobs being
held by people with some college education has tripled. They also agreed with
Immerwhar (cited in Kendall & Williams, 2004) that a college education is essential
to become part of the middle class, adding that individuals who are not prepared to
continue with postsecondary education would lose out on a brighter economic future.
Carnevale and Desrocher’s study (cited in Kendall & Williams, 2004) also asserts
that increased international competitiveness and the economic strength of America
depends upon a structure that prepares college-educated workers.
In addition to financial well-being at both the personal and national levels,
and the health of the democracy, the achievement gap and the generally low level of
44
performance among Latino and African American students reveal that there is a
serious equity issue that violates the spirit if not the letter of the Constitution of the
United States of America. As noted previously, the national report stated in part that,
“Part of what is at risk is the promise [that all]… regardless of race or class or
economic status, are entitled to a fair chance and to the tools for developing their
individual powers of mind and spirit to the utmost” (A Nation at Risk, 1983, p.2).
However, numerous studies and assessment results indicate that Latino and African
American students do not perform at a comparable level with their peers. As we saw,
the Education Trust (2000) noted that African American and Latino students are
much more likely to drop out of high school. In 1998, the dropout rate for white
students was eight percent, in comparison to 14 percent for African American
students and 30 percent for Latino students. The Education Trust (2003) reported that
African American college completion rates have not improved, and a gap in college
education attainment still remains. Their generally low education level, inadequate
competency in the necessary skills of reading, communication, and problem solving,
along with the pernicious effects of the performance gap, undermine their financial
well-being and do not allow them to adequately participate as active members of a
democratic society (Kendall & Williams 2004, Gaining Ground 2001, The Gates
Foundation). Such consequences jeopardize the fundamental philosophy of
democracy, equity, and equal access at the national level (A Nation at Risk, 1983).
Perhaps noting a response to these concerns, Martin (2004) stated that there have
45
been an increasing number of studies on mathematics education and achievement
among minority students, especially African American and Latino students, as well
as a growing number of studies focusing on mathematics education with a
perspective toward social justice and power relations (Martin, 2004).
Math Curriculum, College Education and Earnings
The importance of mathematics as an especially important dimension of
schooling, especially for urban youth, cannot be overstated. In 1997, Robert Moses,
political activist, teacher, and designer of the Algebra Project” asserted, “ I can’t
make you take algebra, but this is why you want to. Algebra opens the door to
college preparation. You may not go to college but if you don’t go it shouldn’t be
because you haven’t prepared yourself to go” (The Algebra Project Today, p.1.
retrieved from www.learntoquestion.com on 7/4/06). Moses saw that it was crucial
that students get the best education as their right, especially in math.
The Education Trust (2000) reported that the society’s needs at the present
time are very different from the past. It shared its view that our new high school
graduates, who are interested in entering the job market whether it requires a college
education or technical certificates, should have met the prerequisites for algebra,
geometry, and lab sciences, and have strong communication skills.
The 2000 revision of the National Council of Teachers of Mathematics
(NCTM) standards stated that those “Who understand and do mathematics will have
significantly enhanced opportunities and options for shaping their futures…All
46
students should have the opportunity and the support necessary to learn significant
mathematics with depth and understanding” (p.5).
In Math Matters: The Links Between High School Curriculum, College
Graduation, and Earnings, Rose and Betts (2001) studied the relationship between
mathematics in high school and both the probability of college education and
potential earnings of high school students 10 years after they graduate high school.
Their study found that there is a strong direct relationship between high school math
curriculum and future earnings. Rose and Betts found that what really matters is not
simply the number of math courses a student takes in high school but the rigor of the
math curriculum, such as course in advanced algebra or calculus.
Rose and Betts’s study also indicated a strong positive relationship between
the rigor of the math curriculum and the rate of completion of college education.
Students who took vocational math as their most rigorous math course work had only
a 3 percent chance of completing a college education compared with 6 percent with
pre-algebra, 19 percent of those taking algebra class, 34 percent with intermediate
algebra, 55 percent with advanced algebra, all the way up to 79 percent for those
taking calculus.
In their examination of the relationship between the rigor of the math
curriculum and future earnings, the median income for students who took vocational
math as their most rigorous course was $17,000 while that for students with pre-
algebra was $20,000, for students with advanced algebra $26,000, and for students
47
who took calculus the median income was $28,000. Such findings demonstrate a
strong positive relationship between the rigor of math classes students took and their
earnings. Rose and Betts also looked at math class levels taken by different ethnic
groups. While only two percent of Latino and African American students took
calculus in high school, 4 percent of whites and 12 percent of Asian students did so.
When we look at the percentage of different ethnic student groups taking advanced
algebra, the disparity becomes more evident: 7 percent of Latino students and 9
percent of African American students took such courses as opposed to 19 percent for
white students and 31 percent of Asian students. Such a disparity raises issues again
in regard to equity and equal access to academic opportunities and future financial
well-being, especially for Latino and African American students. Hambrick (2005)
referred to a statement made by the Southwest Consortium for the Improvement of
Mathematics and Science Teaching (SCIMAST), in her article “Remembering the
child: On equity and inclusion in mathematics and science classrooms”, which noted
that “ensuring equity and excellence lies at the core of systematic reform efforts,
especially in science and mathematics, the two academic areas that historically have
not been widely open to females, ethnic minorities, or students from less affluent
communities and families” (SCIMAST, n.d., p.4)
Greary and Hamson (2000) also noted that the special emphasis on student
achievement in math and science shows success in these academic areas affecting
economic productivity for individuals and society. Sound mathematics and science
48
competencies provide individuals with better employment opportunities and higher
paying jobs. Well-educated and productive individuals have more chances for
enjoying favorable conditions of life. The authors argue that poor mathematical
competencies restrict opportunities in college majors and career choices.
Social and National Implications of Student Achievement in Math
Success in math affects not only individual success in college education
attainment and higher earnings as Rose and Betts found in their 2001 study, but also
the success of the nation in its economic future and its destiny in the global market.
No Child Left Behind stated in its report “The facts about math achievement”,
America’s schools are not producing the math excellence required for global
economic leadership and homeland security in the 21
st
century….Math is
critical in the information age. We must improve achievement to maintain
our economic leadership. While technology advances with lightening speed,
stagnant math performance in schools shortchanges our students’ future. That
endangers our prosperity and our nation’s security”
(www.NoChildLeftBehind.gov).
Greary and Hamson (2000) warned that the impact of the workforce’s poor
math and literacy skills would cost the U.S. economy nearly 170 billion dollars by
the year 2000. The Education Trust (2003) noted that all too often we can observe
some students being taught rigorous subject matter, while others are only offered
unchallenging, low-level instruction which “is better aligned with the assembly-line
jobs that are disappearing than today’s job market or college entry requirements”
(p.2).
49
The Education Trust (2000) reported in “Youth at the crossroads: Facing high
school and beyond” that more than 40 percent of employers test for literacy and
mathematics skills and that there has been a sharp increase in failure rates on these
tests from 18.9% in 1996 to 35.5% in 1998. The report also pointed out that it was
interesting to note that while employees’ skills have declined, job requirements have
been going up. This phenomenon is likely to become a major challenge to our nation
since the projection for the job market is that about 70 percent of future positions
will require at least some postsecondary education.
In addition to falling math competency across the general student population,
there is a great deal of evidence that an academic achievement gap in math, such as
that seen in the NAEP results and Rose and Betts’s findings, still exists among
different ethnic student populations. Such a persistent achievement gap can lead to
politically unsettling issues of equity and equal access to college education
attainment and financial well-being. The chart below makes clear the unequal
representation of student achievement across race and ethnicity.
Table 4: Highest Educational Attainment for Kindergarteners by Percentage
African Americans Asians Latinos Whites
Graduate from high
school
88 90 63 88
Complete at least
some college
50 74 33 59
Obtain at least a
bachelor’s degree
16 51 10 28
Source: US Census Bureau, Educational Attainment October CPS, 1998 (as cited in “Youth at the Crossroads” by
the Education Trust (2000)
50
The 25-member National Commission on Mathematics and Science Teaching
for the 21
st
Century, chaired by John Glenn, former astronaut and senator, prepared a
report entitled “Before It’s Too Late.” In the report, the commission called for
increased national attention to improve math and science education, justifying their
request for the estimated cost of $5 billion with this alarming reminder: “From
mathematics and the sciences will come the products, services, standard of living,
and economic and military security that will sustain us at home and around the
world” (2000).
State and National Reform Efforts to Improve Math Achievement
In order to respond to the needs to improve student achievement and produce
a highly qualified and skilled workforce able to compete with other countries in the
global market, there must be sustained state and national efforts to improve math
achievement in high schools, especially with regard to state standards, improved
curriculum and instruction and better teacher preparation and selection, along with
other related efforts. In fact, state and national efforts serve as change agents and
sources of external support and leverage for the school-site efforts where the change
actually occurs. As a result of the findings of poor student academic achievement, a
labor force in need of skills remediation, and a high illiteracy rate among the
citizenry, the urgent need for school reform was announced as a national concern in
A Nation at Risk (1983) in the following statement: “If only to keep and improve on
the slim competitive edge we still retain in world markets, we must dedicated
51
ourselves to the reform of our educational system for the benefit of all—old and
young alike, affluent and poor, majority and minority. Learning is the indispensable
investment required for success in the ‘information age’ we are entering” (A Nation
at Risk, 1983, p. 2).
Another recent national wake-up call for school reform was clearly
proclaimed in the No Child Left Behind Act (2001). This was, once again, in
response to the growing dilemma of poor student performance and the labor force’s
declining skills and its increasing inability to compete in the global marketplace.
The NCLB Act of 2001 changed the role of the federal government in public K-12
education through an increased in obligatory high stakes exams and more stringent
school accountability requirements. The law mandated states to require mathematics
and reading assessments based on state curriculum standards for all students in
grades 3-12 (Schiller & Muller, 2003).
What made the new legislation distinct from other educational reform efforts
at the national level was first of all, that it brought the so-called “sub-groups” to the
center of national concerns and efforts to close the student achievement gap.
Additionally, it gave the federal government “teeth” to enforce the new mandates: it
provided punitive actions to support its demand for adequate progress in student
achievement. The law required states to monitor the progress of students who are
economically disadvantaged, belong to racial or ethnic minority groups, fall into
specific disability categories or had limited English language proficiency. A
52
progressive system of sanctions—as severe as reassignment, a state takeover, or
conversion to charter school—were laid out and defined in NCLB for schools which
did not make appropriate progress according to the requirements and expectations of
the state. Schiller and Muller (2003) characterized the scope and focus of the
changes: “The goal of this legislation is to not only raise academic standards and,
thus, performance for American school children, but also to decrease gaps in
achievement between socially advantaged and disadvantaged groups” (p. 300).
Furthermore, the legislation made clear the determination of the U.S. as a
nation to improve student achievement in math and science. It also made explicit the
government’s commitment to help schools in their efforts to bring about those
improvements needed for math and science excellence. The NCLB Act promised
that the National Science Foundation and the U.S. Department of Education would
provide one billion dollars over a five-year period for results-based partnerships
between local districts and universities in order to regain math excellence. On April
18, 2006, President Bush established the National Mathematics Advisory Panel. The
purpose of the panel is to advise the President and the Secretary of Education on the
best use of scientifically based research on mathematics education (U.S. Department
of Education, 2006).
States have numerous other obligations under NCLB. They must administer
annual assessments aligned to state standards and use the results of the assessments
as the principal source to evaluate district and school accountability. States are also
53
expected to develop a well-established statewide accountability system to measure
their public schools and charter schools. The rationale of such an accountability
system is to ensure that all students become proficient in reading and mathematics by
2014. Another mandate from the federal government is for states to establish
rigorous academic content and performance standards for all students in at least the
subject areas of language arts, mathematics, and science. (Learning First Alliance).
These allied demands for establishing academic content standards ultimately led to
strengthened curriculums in the nation’s schools.
As a result of NCLB, states obviously have had to raise their academic
standards and increase academic rigor for all students. In order to meet federal
expectations, states have found it incumbent upon them to maximize their efforts to
bring about the necessary educational reforms. The report Brief on Educational
Progress, 1992-2000, was published by the Executive Office of the President under
the Clinton administration in 2000. According to the report, a great deal of
educational progress was made in the U.S. from 1992 to 2000 in areas such as state
content standards, accountability systems, student performance, and attempts to close
the student achievement gap. The report shows that although only 14 states had state
academic standards in 1992, 49 states had established content standards and 48 states
had put in place assessment systems to measure student performance by the year
2000. The Education Trust (2000) also reported that every state except one had by
then published academic standards for its K-12 students.
54
California is one of the 49 states which responded to the federal mandate by
adopting academic content standards; its efforts can serve to characterize similar
steps taken across the nation. As NCLB was to ESEA (The Elementary and
Secondary Education Act), Aiming High: High Schools for the 21
st
Century was a
follow-up to California’s earlier K-12 agenda, Second to None. The state of
California utilized Aiming High as a blueprint for high school reform intended to
increase the rigor of its standards in order to improve student achievement and meet
the federal requirements. Published by the California Department of Education,
Aiming High begins by spelling out its purpose and fundamental beliefs:
To spur schools to produce graduates with higher levels of achievement and
skills, California educators and policymakers created academic content
standards and a statewide system to measure both schools’ and individual
students’ progress in mastery of the standards…The most important point is
that standards-based education works. It absolutely will raise the achievement
of students across the board, regardless of race, ethnicity, gender, or
socioeconomic background (p.1).
California’s bold assertion of course begs the question of whether its own and
similar national and state policies actually have a positive impact on not only student
achievement and educational practice but on disadvantaged populations as well.
Rose and Betts (2001) noted in their study the need for policies that ensure that
students with economic, language and disability disadvantages will be well served.
They added that efforts to enrich the curriculum in Title I schools might offer an
effective tool for closing the achievement gap between advantaged and
disadvantaged students.
55
Additional questions concerning the efficacy of the legislation efforts also
arise. Among them is the issue of teacher quality. Without an effective teacher
teaching in the classroom, no educational reform can possibly succeed (Stronge,
2005). Under NCLB, teacher quality control has been addressed in its Highly
Qualified Teacher (HQT) provision. All districts are required to ensure that their
teachers are teaching core curriculum to meet the HQT requirements by the end of
the school year of 2006. However, in recognition perhaps of the inordinate
importance of math and science achievement to the nation’s health, President Bush
shifted the primary focus on ensuring teacher quality in NCLB by requiring states to
fill the nation’s math and science classrooms with knowledgeable and experienced
teachers by 2005, instead of 2006. President Bush also supported the idea of paying
math and science teachers more to attract and retain highly qualified teacher
candidates in math and science. (NCLB).
Tucker and Stronge (2000) noted that a significant effect of the NCLB
legislation was the attention it brought to the importance of accountability being
distributed among the states, school districts, and individual schools. This is a result
of its requirements for the establishment and administration of state-wide
assessments and, at the district and school level, the need to meet adequate yearly
progress (AYP), to publish annual report cards, and to ensure highly qualified
teaching staff.
56
These increasingly sophisticated accountability measures implicate all levels
of the education systems but ultimately focused on helping the individual school
sites improve student achievement: the focus is on schools rather than school
districts (Goertz and Massell, 2005). In response to the external accountabilities
imposed on them at the federal and state level, schools have focused their efforts on
school reforms intended to improve student achievement and related school systems
which ultimately support achievement. Almost all states and thousands of districts
have been working on developing high expectations for student learning and
thousands of districts have chosen to adopt school reforms to improve learning and
teaching and to optimize student achievement (Consortium for Policy Research in
Education CPRE, 1998). Goertz and Massell (2005) confirmed in their study that
state accountability systems can be “a powerful force for change” (p.7) to propel
high schools towards school reforms, standard-based instruction, and measured
student performance.
In 1997, Congress approved federal grants to offer annually up to $50,000
per school for comprehensive school reforms. In the following year, Title I schools
became eligible for $120 million of the funds while non-Title I schools competed for
$25 million. The Comprehensive School Reform Development Program (CSRD)
provided funding for states to provide competitive grants to school districts that
submitted applications for their school site to take part in a particular school reform
program (CPRE, 1998).
57
With the federal and state funding, schools have investigated reform designs
that influence the entire context of schooling, including the physical setting, school
operations, curriculum and instruction, school organization, professional
development, and resource allocation in their attempts at comprehensive school
reforms (CPRE, 1998). The article reported (1998) that more than 2,100 schools
have adopted either Bob Slavin’s Success for All program, James Comer’s School
Development Project, or Henry Levin’s Accelerated Schools. Other popular school
reforms are the America’s Choice school design and various implementations of the
collective strategy known as Small Learning Communities (SLC). A brief account of
these programs shows the range of strategies employed in these efforts at reform.
Smith (n.d.) tells us that the Success for All program was a new school design
that the Baltimore School Superintendent used in 1986 to turn around his failing
schools. He called upon Bob Slavin, a researcher from John Hopkins, for assistance
and together they adopted a research driven model, Success for All, with a
philosophy of “All students can be successful in learning.” Slavin and his wife,
Nancy Madden, both former special education teachers, had originated the model in
1987, gathering the most effective tools and strategies that had been especially
influential in working with inner city students. The Success for All model focuses on
a daily 90 minute fast-paced reading block period for all students. The model utilizes
ability grouping, cooperative learning, and continuous assessments
(www.pbs.org/makingschoolswork, 2006). Munoz, et al. (2003) studied the
58
effectiveness of the Success for All model in three elementary schools and their
findings showed that at the school level the model had a positive impact on student
academic achievement especially in reading and attendance as well. According to the
feedback from parents, teachers, and students, the model also had a positive effect on
school climate, educational quality, and job satisfaction.
The Comer School Development Program, a school model commonly called
the Development Program, focuses on a holistic child development model. It
connects student academic performance with their emotional well-being and social
and moral development in a positive, caring school culture conducive to learning.
Since James Comer, a Yale University child psychiatrist, created the model in 1968
with the belief that students perform better when they feel they are supported in a
nurturing environment, the model has been adopted in more than 1,150 schools
across the country. The Comer process views schools as being responsible for
bringing together their stakeholders—teachers, administrators, and parents—to
create an action plan to help students academically and socio-emotionally. According
to the Development Program, it is ideal for schools to operate similarly to a
community center. It places an emphasis on building connections, involving parents
through voluntary opportunities and social services in order to serve students’
individual needs. A study conducted by Thomas Cook, H. David Hunt, and Robert F.
Murphy examined the Comer School Development Program in 10 inner city Chicago
schools over four years. Cook, et al stated (2000) in their study that by the end of the
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first year of the study, students in Comer schools thought that their social climate had
improved, and by the end of the study period student achievement in reading and
math had improved by 3 percentile points along with improvement in student
behavior.
Accelerated Schools Plus, a school design created by Henry Levin at
Stanford University in 1986, was first adopted at two San Francisco Bay Area
elementary schools and has since been implemented at more than 1,300 K-12 schools
nationwide. The primary goal of the model is to provide all students with a rigorous
and enriched curriculum based on the entire school community’s vision of learning.
The model emphasizes “gifted-and-talented” instruction—normally available only to
students formally identified as gifted-and talented—for all students through a process
known as “powerful learning.” The three guiding principles of the design are unity of
purpose, empowerment plus responsibility, and building on strengths. Schools which
implement this new design start their transformation into an “Accelerated School”
with the whole school community evaluating its present status and then build a
shared vision of what the school should be like. Based on the outcome of their
evaluation of the present status and their own vision, they strategize an action plan to
overcome challenges and accomplish their goals (NW regional Educational
Laboratory (NWREL), 2004). The article from NWREL (2004) went on to report
that according to a study by Bloom, et al. (2001) the eight schools which
60
implemented Accelerated Schools showed improvement in reading and mathematics
during the fourth and fifth year of the study.
The Small Learning Communities (SLC) Program is another example of
school reform, which is supported with a $142 million grant by the federal
government. The purpose of the SLC program is to reorganize comprehensive high
schools into smaller learning units for students to build connections with their school
community and for schools to provide students with personalized support. Some of
the common strategies utilized in creating smaller learning units are creating schools
within schools, career academies, restructuring the school day, instituting personal
adult advocates, and developing advisory systems.
The need for such “scaling down” strategies becomes readily apparent when
we look at the available research on the topic. U.S. Department of Education
statistics reveal that about 70% of high school students attend schools with
enrollments exceeding 1,000 and nearly 50% attend schools housing more than 1,500
students. The import of these data becomes clear when viewed in the light of
recommendations such as those underscored in the National Association of
Secondary School Principals (NASSP) 1996 report, Breaking Ranks. The
Association recommended that high schools should reconfigure themselves into self-
operating units with a maximum of 600 students in order to minimize the negative
impact of students’ feelings of anonymity. Breaking Ranks also recommended
reducing the number of students teachers interact with on a daily basis to enable
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them to provide students with individualized support which in turn would
“personalize” the students’ high school experience. The U.S. Department of
Education also noted that smaller schools can offer more resources for students to
expand their connections with school through building relationships with mentors,
tutors, and advisors; helping students purposefully engage in learning by connecting
it to real life through the workplace and the community (U.S. Department of
Education, 2001). Numerous studies such as those of 1996 and 2000 by Cotton, the
1996 and 1999 Raywid studies, and the 1998 study by Klonsky have been conducted
to examine the effectiveness of SLC programs. The consensus appears to be that
these studies demonstrate “an aggressive degree of support for smallness with
respect to academic achievement, academic equity, better preparation for the future,
and higher attendance and lower drop-out rates (U.S. Department of Education,
2001). The 2000 Education Trust report “Youth at the crossroads: Facing high
school and beyond” also noted that when students are taught in a smaller learning
environment with more personal connectedness, they have a tendency to do better.
The America’s Choice School Design refers to a K-12 comprehensive school
reform (CSR) model which was created by the National Center on Education and the
Economy (NCEE). The school design pursues, as Supovitz and Poglinco (2001)
state, high student achievement through rigorous curriculum and stresses the
importance of providing a safety net for all students. It focuses on high expectations,
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literacy, a common core curriculum, standards-based assessments, distributed
leadership, safety nets, and a commitment to teacher professionalism.
While the programs examined above represent the current state of
comprehensive school reform, some schools choose to focus their efforts solely on
instructional reform. These schools make use of a number of strategies to achieve
such instructional reform. One common strategy is to introduce an alternative school
schedule in order to provide the necessary support for students who are far below
grade level in literacy and mathematics. Many schools offer “remedial,” “transition,”
or “make-up” classes—supplementary courses to narrow the gap in fundamental
academic skills, especially in reading and mathematics. The Talent Development
Model brings these instructional reform ideas together in its focus on mathematics. In
this model, the math curriculum is designed with a Transition to Advanced
Mathematics (pre-algebra) course followed by the required Algebra I course. In
addition, The Talent Development Model uses a 4 x 4 “block schedule” to provide
additional time to English as well as mathematics students all year long (McPartland,
2005).
As new research-supported school reform models are increasingly
implemented by schools in their attempts to positively impact student achievement, it
becomes crucial for schools to maximize teaching success and optimize student
learning in order to improve student math achievement.
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Marzano (2003) put forward and ranked five school-level factors that he
believes are needed in order to bring about the changes necessary to improve student
achievement: a guaranteed and viable curriculum, challenging goals and effective
feedback, parental and community involvement, a safe and orderly environment, and
collegiality and professionalism. But learning factors such as these can only be
effective in so far as a school is able to bring them about. For example, as previously
mentioned, in order for schools to provide a “guaranteed and viable curriculum,”
Marzano (2003) asserted that they must maximize opportunities for students to learn
and protect instructional time, while Johnson noted (2002) that it was crucial for the
leadership and school data teams to acquire training in the skills necessary for them
to utilize data properly. In addition, Johnson underscored (2002) the need for
sufficient collaboration time for data collection and analysis.
Grouws and Cebulla (2000) also noted the importance of “opportunity to
learn”: “The extent of the students’ opportunity to learn mathematics bears directly
and decisively on student mathematic achievement” (p.1). In the First International
Mathematics Study, Husen asked teachers in 1965 to rate the degree of student
exposure to specific mathematics concepts and skills. The study finding indicated
that there were strong positive correlations between “opportunity to learn” (OTL)
scores and mean student achievement scores. A number of research findings indicate
that low academic achievement and the significant achievement gap in mathematics
are due to a lack of rigor in the curriculum and ineffectiveness in instruction
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(Education Trust, 2000, 2003; Lara & Pande, 2001; Marzano, 2003; Landgraf, 2004)
and these two factors negatively affect students’ opportunity to learn.
The Education Trust (2003) argued that new standards and accountability
systems would not make any positive impact on student achievement unless a
rigorous curriculum aligned with standards is provided. The study also pointed out
that there is sufficient evidence that all students can make high academic
achievement if they are taught at high levels as long as schools provide those
students who need extra support with more time and systematic support for their
acquisition of the subject matter (Ed Trust, 2003).
There is a strong positive relationship between teacher expectations and
student opportunity to learn (Lara & Pande, 2001; Cotton, 1989). Lara and Pande
(2001) noted that researchers have found that the assumption or belief among some
teachers that minority students possess less competency in meeting rigorous
standards affects their instruction and assignments. The low expectations and the
resulting unchallenging curriculum of such teachers would then affect student
performance; generally leading students to perform below their actual ability (Lara &
Pande, 2001). Cotton (1989) also emphasized that schools should hold high
expectations for student academic achievement and that teachers need to expand
students’ minds by stimulating and encouraging them to achieve at the optimum
level; but not in “protecting” them from failure or embarrassment. Rose and Betts
(2001) also suggested that it is important for schools to ensure accessibility to its
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resources in order to provide all students with an equal opportunity to take more
rigorous math classes and to encourage students to take them. These studies
demonstrate how teacher expectations influence curriculum and instruction and, as a
consequence, student opportunity to learn, which in turn directly affects student
achievement.
Marzano (2003) listed time as the second most important factor that
influences a “guaranteed and viable curriculum.” TIMSS shows the significant
difference in the amount of instructional time among different countries. Stevenson
and Stigler on the organization of schooling, made the argument, however, that the
amount of instructional time was not the real issue, since students in U.S., Chinese
and Japanese schools seemed to spend similar amounts of time in school. Instead,
Stigler argued, we need to take notice of how the school systems in Chinese and
Japanese schools maintain consistency and continuance of student learning by
distributing the total amount of time spent in school in a certain way and providing
curricular activities throughout the school year. In contrast, he maintained, it is
instructive to note how often American schools disrupt valuable instructional time
with PA announcements, socializations, informal breaks, and other non-instructional
activities (Marzano, 2003).
In order to provide students with a “guaranteed and viable” curriculum by
assuring ample opportunities to learn and sufficient time, Marzano recommended
(2003) that schools also should: 1) identify and communicate the essential content
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for all students to learn, 2) ensure that the essential content can be taught in the given
instructional time, 3) sequence and organize the essential content, 4) ensure that
teachers teach the essential content and 4) protect the instructional time.
It is important for schools to have knowledge of key model mathematics
programs and to analyze their characteristics and evidence of success. There have
been a number of key model mathematics programs to improve student achievement
in math. One of them is The Algebra Project, an interactive math curriculum
developed to help inner-city students better comprehend mathematical concepts. It
was designed by Bob Moses, a mathematician and civil rights leader. (North Central
Regional Educational Laboratory, NCREL)
The Algebra Project seeks to impact the struggle for citizenship and equality
by assisting students in inner city and rural areas to achieve mathematics
literacy. High order thinking and problems solving skills are necessary for
entry into the economic mainstream. Without these skills, children will be
tracked into an economic underclass (www.algebra.org, retrieved on 6/30/06)
Two educational concepts were very significant to Moses; 1) All children in
America have a right to free K-12 public education and 2) all children deserve the
best education they can acquire. These two concepts served as the foundation of The
Algebra Project as the concept of “one person one vote” was the fundamental belief
behind his civil rights work in Mississippi during the 1960s. (The principles and
structure of the Algebra project, retrieved from www.learntoquestion.com on
7/3/06).
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Moses formulated The Algebra Project based on some ideas provided by one
of his former Professors, W. Quine, along with teaching theories from Piaget on
learning. Professor Quine emphasized that the language of mathematics has to be
explained to students in everyday language to help them comprehend mathematics
while Piaget stressed that learners utilize their personal experience to acquire new
learning. There are five important steps to follow in implementing the math program:
1) physical events, 2) pictorial representation/modeling, 3) intuitive language, 4)
structured language, and 5) symbolic presentation. Moses designed a math
curriculum in an interactive way by employing these five steps. In using the math
program, students would share their experiences from their daily life related to
algebra, then they would think, discuss, and analyze real life situations. The last step
is to describe the situations using math symbols. Currently the Algebra Project
receives funding support from the McArthur and Lilly Foundations, the National
Science Foundation, and the Open Society Institute (The Algebra Project Today, p.1.
Retrieved July 4, 2006 from www.learningtoquestion.com.
In addition to well-designed math programs like The Algebra Project, schools
need to ensure some research-proven key elements are in place for students to
improve their performance. Martin (2004) shared his findings on the most significant
elements to help minority students achieve at advanced levels. He stated that his
findings were based on numerous studies in achievement gap in mathematics among
different ethnic groups, especially African American and Latino students. In
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addition, the findings were drawn from a growing number of studies in regard to
math education and social equity. Martin (2004), identifies 6 significant elements:
 Access to and experience with high-quality math curricula
 Access to highly qualified mathematics teachers
 Access to teachers who engage in culturally relevant pedagogy
 Access to math-based enculturation and socialization experiences
 Access to coherent instructional systems that link the items above
 Community and family support for mathematics learning
(Martin, 2004, p.11)
Access To and Experience With High-Quality Math Curricula
Marzano (2003) noted that in order for schools to improve student
achievement they need to hold students to high expectations and provide “pressure to
achieve” along with systematic monitoring of the progress of student performance.
Marzano went on to emphasize that, “In fact, high expectations for students,
particularly those from low SES [socioeconomic status], are a cornerstone of the
school effectiveness research” (p.36).
The Education Trust (2003), as has been noted, made the point that there was
ample evidence to show that all students can achieve at high levels if they are
provided with high level instruction. They went on to suggest that the simple change
of placing students in more rigorous courses will result in better achievement as long
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as schools provide extra time and support for students who experience difficulties in
acquiring the content.
Access to Highly Qualified Mathematics Teachers
Much of the research on student achievement shows that teacher
effectiveness is a crucial factor impacting student achievement. Marzano (2003)
studied the effects on student achievement of school and teacher effectiveness. His
findings indicate that teacher effectiveness is the most influential factor affecting
student achievement. For example, if students entering school at the 50
th
percentile
were instructed by the least effective teacher in the least effective school setting, they
would perform at the 3
rd
percentile after two years, while the same students,
instructed in the same school setting but by the most effective teacher, would
perform at the 63
rd
percentile. Marzano (2003) noted that teachers need to show their
effectiveness in the following three areas: instructional strategies, classroom
management, and classroom curriculum design.
The Education Trust (2003) also pointed out that the teacher is the single
most important factor in student learning. They added that if students are expected to
learn high standards, they should be taught by teachers who possess sound
knowledge of the subject matter and also have effective teaching strategies.
Ironically, the study notes, it is not uncommon to find that those students most in
need of the best teachers are instead taught by the teachers least qualified to teach the
subject matter (The Education Trust, 2003).
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Access to Teachers Who Engage in Culturally Relevant Pedagogy
Martin (2004) pointed out that while a great deal of studies on math
education deal with curriculum design, teacher training, student achievement, and
testing results, there have not been too many theoretical examinations of how
ethnicity or race becomes a variable influencing student learning and participation in
mathematics. Martin argued that even though research in sociology, anthropology of
education, and ethnic studies show that race stands out in all aspects of life for
African Americans, Latinos, and Native Americans, educators have little
understanding of the ways each group’s unique characteristics influence their
learning in mathematical contexts (Martin, 2004). Lara and Pande (2001) contend
that it is important for teachers to make use of teaching strategies that “reinforce
students’ strengths and affirm cultural background” (p.3). They indicated that
schools should have an understanding of and respect for their students’ culture,
language and background in order to serve them in a fair, effective manner. Moses’s
The Algebra Project was an example of how instruction should be designed based on
students’ unique background and experiences (NCREL, n.d. Retrieved July 1, 2006
from www.ncrel.org.
Access to Math-based Enculturation and Socialization Experiences
Martin (2004) noted that the Algebra Project and the 1985 Uri Treisman
calculus workshops are reputed to be effective programs in helping African
American students. Both programs are examples for how teachers can design
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curriculum and instruction, particularly through the incorporation of student groups
and lively interactions, to maximize student leaning in mathematics. The Uri
Treisman model grew from graduate student Treisman’s efforts to eliminate the high
failure rates of minority students in his undergraduate calculus classes. Treisman’s
model emphasized collaborative learning to study math, based upon his observations
of how Chinese students, who were successful in the calculus classes, worked as
study communities, incorporating lots of interactions. The model proved successful
and was subsequently modified to fit into the high school setting (Merit workshop
program for emerging scholars in mathematics. Retrieved July 1, 2006 from
www.math.uiuc.edu.
Another example of efforts to design curriculum that focuses on the learners
is the MARS project, mentioned along with The Algebra Project by Rousseau and
Powell. The Mathematics: Application and Reasoning Skills (MARS) Project
originated from the Baltimore City Public School System and the University of
Maryland. They summarized the success of the MARS project as follows:
Curriculum reform within the project began with the design of a new
curriculum guide. Following the design of the curriculum guide, the district
sought out and adopted instructional materials that supported the teaching
and learning of the objectives outlined in the curriculum guide. The
curriculum guide and instructional materials were then used as key
components of subsequent professional development efforts and served as
crucial pieces of the reform process (Campbell, et al., 2003). This and other
examples of systematic reform highlight the importance of curriculum guides
and aligned instructional materials in the reform of mathematics education in
large urban districts (Rousseau & Powell, 2005, P.23)
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Grouws (2000) as well, emphasized that the utilization of small groups of
students can increase student achievement in mathematics. He included the findings
of the 1985 Davidson study that more than 40 percent of students working in small
groups significantly outperformed students in traditional classroom settings. Grouws
(2000) also referred to Slavin’s conclusion from a review of 99 studies of
cooperative learning that cooperative learning was effective in advancing student
achievement when individual students were held accountable while working in a
collaborative learning setting with group goals.
Other Considerations to Improve Mathematics Instruction
Grouws compiled a list of instructional factors and strategies to improve
student achievement that are directly related to classroom instruction (Grouws,
2000, P.1-4):
 The extent of the students’ opportunity to learn mathematics content bears
directly and decisively on student mathematics achievement
 Focusing instruction on the meaningful development of important
mathematical ideas increases the level of student learning
 Students can learn both concepts and skills by solving problems.
 Giving students both an opportunity to discover and invent new knowledge
and an opportunity to practice what they have learned improves student
achievement.
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 Teaching that incorporates students’ intuitive solution methods can increase
student learning, especially when combined with opportunities for student
interaction and discussion.
 Whole-class discussion following individual and group work improves
student achievement.
 Teaching mathematics with a focus on number sense encourages students to
become problem solvers in a wide variety of situations and to view
mathematics as a discipline in which thinking is important
 Long-term use of concrete materials is positively related to increase in
student mathematics achievement and improved attitudes towards
mathematics.
In order, however, for schools to really bring about improvement in student
achievement in mathematics, in addition to instructional reforms of the kind that
have been looked at above, they need systematic reform spearheaded by effective
leadership at the school site. The role of leadership is crucial in the context of school
efforts to improve student achievement. Bennis and Goldsmith (1997) note that
effective organizational leaders always question; pursuing information throughout all
levels of the organization and checking their own understanding. They assess what
works and what does not work. As leaders, school site leadership must master the
ambiguous context, investigate reality, and produce visions, plans, and programs.
Bennis and Goldsmith (1997) characterized effective leadership in this way:
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A leader is someone who has the capacity to create a compelling vision that
takes people to a new place, and to translate that vision into action. Leaders
draw other people to them by enrolling them in their vision. What leaders do
is inspire people, empower them. They pull rather than push. This “pull” style
of leadership attracts and energizes people to enroll in a vision of the future.
It motivates people by helping them identify with the task and the goal rather
than by rewarding or punishing them (p.4-5).
Bennis and Goldsmith (1997) also emphasized that leaders must create trust
in order to lead a team, and in order for them to create trust they should be aware of
four special ingredients they call the four C’s. Leaders, they assert, must possess
Competence, Congruity, Constancy, and Caring. These attributes apply to any school
leader aspiring to effectively lead their team and improve student achievement under
numerous external pressures and internal organizational restrictions.
Bolman and Deal (2003), in a similar vein, argued that it is crucial for leaders
to be versatile users of four “frames,” depending on the context of the situation: a
structural frame, a human resource frame, a political frame, and a symbolic frame.
They explained, “Like maps, frames are both windows on a territory and tools for
navigation” (p.13). School leaders also have to utilize the right frame to fit a
particular situation in order to be able to bring about the changes necessary to
improve student achievement. They also added (2003) that only experience and
practice help leaders assess a situation with precision and select the right tools with
precision. According to Bolman and Deal (2003), leaders conduct themselves
differently depending on which frame they apply: through the structural frame,
leaders try to develop and implement a process, or restructure an existing one to fit
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the situation; with the human resource frame, they support and empower their
people; political frames allow leaders to identify their constituencies, establish ties
with them, and handle conflicts in a productive way; and by making use of the
symbolic frame, leaders explore ways to make the best use of the organization’s
traditions and value system as a foundation for creating a cohesive and meaningful
culture.
In order for schools to optimize student achievement, school leaders also
must pay attention to fostering instructional leadership. There are certain ingredients
of instructional leadership we need to ensure, especially at the high school level.
Fink and Resnick (1999) stated that despite the fact that principals are expected to
function as instructional leaders, they usually do not spend enough time on the
matters related to curriculum and instruction. They suggested that in order for school
leaders to create a learning environment where students continue to improve their
achievement they must possess certain leadership qualities, the ability to create trust
and invigorating enthusiasm for constant improvement of instruction. Fink and
Resnick (1999) underscored that effective instructional leaders must “create both
intellectual capital and social capital within their organizations” (p.23). Instructional
leaders can create intellectual capital by taking a substantial part in curriculum
selection, holding high expectations for the quality of student work, and analyzing
opportunities for teachers to improve their instruction (Fink & Resnick, 1999).
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Fullan (2001) opined that leaders must understand the nature of the change
process. It is essential for schools to be able to change the culture of the school and
change dominant values, beliefs, and attitudes of teachers, students, and parents
when necessary. In the process of complex re-culturing, it is critical to establish a
shared vision and purpose that illustrate the developmental aspects of the change
processes. Supovitz and Poglinco (2001) emphasized the importance of a focus on
instruction and of a coherent instructional vision and they further noted that
principals who heighten the school-wide focus on instruction will improve their
students’ achievement. They illustrate their view of instructional leadership in a
descriptive and logical fashion:
But exponential value of instructional leadership comes from the marriage of
an intense organizational focus in instructional improvement with a clear
vision of instructional quality. A concrete vision of instructional quality
provides a tangible representation of what effective instructional planning
and delivery looks like, provides teachers with an instructional portrait they
can work toward, and provides a picture that administrators can measure
implementation against (Supovitz & Poglinco, 2001, p.10).
In addition to trust building, constant focus, and clear vision, it is also crucial
for school leaders to hold high expectations of both student achievement and teacher
instruction. The high expectations of schools trickle down to every member of the
school community in regard to the shared goal of academic excellence and the shared
purpose of the school to enact the vision (Supovitz & Poglinco, 2001). As Cotton
(1989) also pointed out, teachers’ high expectations of their students’ work are
necessary for students’ academic success. According to the findings of Cotton’s
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study (1989), there was causality between inflated teacher expectations on students
and the outcome of student work. Finally, once schools have high expectations and
hold everyone accountable for their part, it is important to provide monitoring on a
regular basis (Marzano, 2003; Supovitz & Poglinco, 2001).
Another ingredient for turning schools into effective learning environments is
for schools to become professional learning communities (PLC). According to Hord
(1997), a professional learning community is defined as a school where the
administrators and teachers constantly seek and share learning to increase their
effectiveness for students, and act on what they learn. As the Southwest Educational
Development Laboratory (SEDL) (1997) reported, Rosenholtz found that teachers
who thought they received support in their own learning and classroom practice were
more committed and effective than those who did not. Peer support and collaborative
work with colleagues enhanced teacher efficacy in meeting student needs.
Mclaughlin and Talbert (1993) also suggested that when teachers were given
opportunities for collaborative work, they developed and shared insights based on
their own experience (SEDL, 1997).
DuFour (2004) illustrated three “big ideas” behind the concept of
professional learning communities: 1) ensuring that students learn, 2) a culture of
collaboration, and 3) a focus on results. These three big ideas actually serve as major
anchors for radical educational reform according to DuFour (2004). The first idea of
ensuring that students learn shifts our focus from teaching to learning that takes place
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within the students. As DuFour puts it, this shift in perspective “has profound
implications for schools” (p.1). When schools commit themselves to the vision of
“learning for all,” they will begin an important body of meaningful work in order to
enact their shared vision. As everyone at the school becomes involved, they will
explore three essential questions that become the driving force of the work taking
place at the school site as a professional learning community: 1) What do we want
each student to master? 2) How will we know when each student has gained
mastery? 3) How will we intervene when a student experiences difficulty in reaching
mastery? DuFour (2004) emphasized that schools need to provide feedback on
student work progress in a timely manner and that schools need to focus on
intervention rather than remediation. He further explained that the key to the success
experienced by Adlai Stevenson High School was the systematic, timely, and
directive intervention program that is designed to help students who show difficulties
in learning (DuFour, 2004).
The second big idea, a culture of collaboration, is the fundamental common
ground for a professional learning community working toward the shared vision of
learning for all. With professional learning communities, collaborative work is a
systematic process which enables teachers to work together in order to make an
analysis of and improvement in their teaching. They get involved with professional
inquiry and promote profound on-going learning experience as a team (DuFour,
2004).
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The third idea, that of focusing on results, forms the basis for common
ground for teachers in regard to their instructional goals and objectives. As DuFour
(2004) pointed out, professional learning communities assess their own work on the
basis of results. Effective PLC’s are adept at gathering necessary data, evaluating
data, and interpreting the collected data in order to make necessary changes in its
practices and programs so that all students can learn. The need for teachers to have
such competence in using data is brought home when DuFour reminds us that
“…data will become a catalyst for improved teacher practice only if the teacher has a
basis of comparison” (2004, p.4).
As schools go through changes and reform, it is useful for school leaders to
be able to identify and recognize numerous stages of concern about the innovation
that each team member may experience. A helpful tool for tracking such issues is the
Concerns-based Adoption Model (CBAM) developed by Hall, Hord, and Rutherford.
The stages the model identifies are awareness (0), informational (1), personal (2),
management (3), consequence (4), collaboration (5), and refocusing (6). By
recognizing them appropriately, school leaders are able to accurately assess the
status of the reform and strategize the next step in order to bring about the reform
needed to improve student achievement. The CBAM is an excellent tool for finding
out how teachers, staff and other related individuals feel about implementation of
new programs or policies.
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It is important for school leaders to be aware that there are ways to connect
mathematics education and instructional leadership at the high school level: leaders
often don’t have strong pedagogical content knowledge in mathematics education,
yet need to employ instructional leadership in that content area. Under the NCLB,
schools are required to shape their reform efforts on the basis of scientifically-based
research instead of untested innovative practices and programs. As Whitehurst
(2002) illustrated, evidence-based reform is an ideal combination of professional
wisdom from individual experience and consensus and empirical evidence from
scientifically based research and empirical information. Due to new research
standards and federal mandates, “evidence-based reform” will become the norm
(NCREL Viewpoints, 2004), which means evidence-based reform models will be
widespread and more known. Such availability will allow instructional leaders to
examine models to fit their context and choose from more options. As a
consequence, instructional leaders should be able to make better decisions without
possessing sufficient knowledge of the subject matter.
It is crucial for school leaders to provide quality professional development
programs to maintain rigor in the math curriculum. Reforms in mathematics
education in the U.S, as can be seen in the National Council for Teachers of
Mathematics, 1989 or the National Science Foundation, 1996, emphasize the need
for rich curriculum that emphasizes problem-solving and instructional strategies that
enhance reasoning and communication skills (Kitchen, 2003). Rousseau and Powell
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(2005) recommended QUASAR, IMPACT, and MARS as exemplary professional
development programs that would address issues of equity. However, it is a well-
known fact that such reform visions and real teaching practices do not necessarily
run parallel (Kitchen, 2003). In order to implement the desired reform in math, there
is an urgent need for on-going access to professional development experiences that
will bridge the gap between the reform model and actual reality. School leaders need
to take advantage of professional development opportunities to train teachers in the
needed area.
As Kitchen recommended (2003), schools leaders should be aware that
professional development experiences for secondary school mathematics teachers
should be organized in certain ways to be effective: 1) programs should be of
sufficient duration rather than too short or broken into incoherent intervals; 2)
teachers should have an active role in defining the content; 3) classroom practice
should be part of regular meetings and 4) programs should be designed in such a way
that would encourage teachers to solve problems in a collaborative manner over an
extended period of time.
Summary
This literature review was a comprehensive presentation of research in
several areas regarding 1) the academic performance of American high school
students based on state and national standards and the findings of international
comparative studies, 2) the persistent achievement gap in math among minority
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students, especially Latino and African American students, 3) the importance of
mathematics affecting postsecondary education and career success, 4) state and
national efforts to improve student achievement in math, 5) new school designs to
improve student achievement, 6) characteristics of math programs to help students
do better, 7) essential ingredients of instructional leadership, and 8) the role of school
leadership to improve student achievement in math.
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CHAPTER THREE: RESEARCH METHODOLOGY
This chapter describes the research design, sample, instrumentation, and
methodology for data collection and analysis employed in the study. The purpose of
the study is to identify how urban high schools successfully bring together policy
initiatives and local best practices to actually improve math performance in their
schools. Several issues seem to be particularly relevant to instructional leadership in
this setting. Leaders often do not have strong pedagogical content knowledge in
mathematics education yet need to carry out related fiscal, personnel, and
organizational leadership functions, as well as data analysis and review. Since little
is known about how leaders work effectively in this context, the study also examines
how instructional leadership is effectively carried out in high schools in the context
of improving math performance for students. The research questions addressed by
this study are:
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—were shown to be related to improved math achievement at the
school?
3. What change process did the school use to enhance its math program and
strategies to assist students in math?
4. 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?
Qualitative Method-Case Study
A qualitative, descriptive case study design was utilized for this study. This
research design was selected because the study requires an examination of an
exemplary school which implemented best practices and programs to improve
student achievement in math. Since the study was also to explore the processes of
school reform in order to bring about necessary changes for student math
achievement, case study is the appropriate strategy of inquiry in this qualitative study
(Creswell, 2003). There is very little known about best practices in improving
student achievement in math. As Patton noted (2002), “Studying information-rich
cases yields insights and in-depth understanding rather than empirical
generalizations” (p.230). It is important to have access to first-hand, in-depth
information from a school which has been able to identify best practices and
implement necessary reform in order to replicate its best practices and programs. The
utilization of a detailed, descriptive study of such a school will provide useful
descriptions of the policies, initiatives, and contexts of the school as possible
contributors of its success. As the National Research Council (2003) points out,
“Researchers often spend long periods of time in the setting or group in order to
understand what decisions are made, what beliefs and attitudes are formed, what
relationships are developed, and what forms of success are celebrated. These
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descriptions, when used in conjunction with causal methods, are often critical to
understand such educational outcomes as student achievement because they
illuminate key contextual factors” (p.106).
The unit of analysis for this case study was a single 9-12
th
grade high school.
Specific research questions, standardized data collection procedures and systematic
data analysis processes were developed and utilized in this study. Four conceptual
frameworks constructed on the basis of key components of the study as expressed in
its research questions—change process, effective school design, math programs, and
instructional leadership—provide a foundation for data collection and analysis in the
study. In order to ensure internal validity, two strategies—triangulation of data and
“member checking”—were employed as Creswell (2003) recommended. Data were
collected through multiple sources including interviews, a questionnaire, and
document analysis for triangulation of data. Findings from one source were cross-
referenced by findings and evidence exhibited from other sources as much as
possible. In addition to triangulation of the data, the respondent served as a check
throughout the interview to ensure the true value and accuracy of the data.
In compliance with the guidelines required by the Institutional Review Board at
the University of Southern California, any information obtained by the researcher for
this study will be kept confidential. No publication following the study will ever be
allowed to reveal participants’ answers or responses connected with this study.
Therefore, participants and the school were assigned pseudonyms to ensure their
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anonymity. Nevertheless, the content of information is factual. Documents and other
artifacts examined in this study were obtained from the school, the websites of the
California Department of Education and Vineyard Union High School District.
Sampling Criteria and Process
Patton (2002) noted, “What would be ‘bias’ in statistical sampling, and therefore
a weakness, becomes intended focus in qualitative sampling, and therefore strength.
The logic and power of purposeful sampling lie in selecting information-rich cases
for study in depth. Information-rich cases are those from which one can learn a great
deal about issues of central importance to the purpose of the inquiry, thus the term
purposeful sampling” (p.230). For this reason, one public high school was
purposefully selected as the unit of analysis in this study. This school was selected
since it satisfied the criteria defined by a group of researchers from the University of
Southern California, Rossier School of Education. The following are the criteria set
for this study:
1. Comprehensive public high school in southern California serving grades 9-12
with at least 1200 students
2. Student demographic information showing at least 50% of its students from
traditionally ethnic minority groups
3. API (Academic Performance Index) score of at least 600
4. Statewide rank of 5 or higher
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5. Improvement of student performance in math as evidenced by results on the
California Standards Test (CST) in Algebra I over a three year period
6. No participation in special grant programs such as IIUSP.
7. Leadership stability defined by at least three years of service at the school site
by the principal during the time the improvement was made.
The eleven students in the Ed. D cohort program led by Dr. Marsh at the
University of Southern California worked collaboratively to design the study and
determined the sampling criteria. There were two phases developing sampling
criteria for this study. The cohort team believed that it was important to study
comprehensive high schools serving at least 1200 students 9th through 12th grades.
The team also agreed that the schools should have diverse populations, including
ELL students, Special Education students, and Title I students. During the first
phase, a sampling criterion was set for a school with a minimum 65% of minority
students. However, such a criterion did not allow enough sampling to conduct the
study. During the second phase, the cohort decided to expand the criterion to a
comprehensive high school with 50% of minority students; this change provided 110
samples available (N=110). Once the team was sure of an ample number of samples
to meet the minority requirement, it proceeded on to the next sampling criterion,
which was student achievement in Algebra I in CST (California State Testing). The
rationale was that Algebra I is a demonstrated “gateway” to higher math courses and
directly related to school performance, college entrance, and career success. In order
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to incorporate all three years of the 2003, 2004 and 2005 CST Algebra I results, the
cohort team made use of two criteria: 1) schools had to show an increase or at least
no decrease in percentage in the top two bands, “Proficient” and “Basic” and 2)
schools had to show a decrease or at least no increase in percentage in the bottom
two bands, “Below Basic” and “Far Below Basic.” According to this formula, 44
potential schools located in Southern California that met these set criteria were
identified and selected (N=44) through data collection and analysis available on the
website of the California Department of Education (CDE). The cohort group then
used the gathered data to create a data chart incorporating school information that
met the criteria based on their three year CST scores in Algebra I. Once the schools
which fit the profile were identified, a map was developed to show school sites
geographically. The geographic map helped the cohort members to select a school
from the pool of qualifying schools. Each member of the cohort was expected to
choose a school site at which to individually conduct the study while conforming to
the guides and rules set by the cohort group. After choosing a school, each researcher
was responsible for finding out whether the school was a recipient of special grants
such as IIUSP and the principal of the school had been served the school as the site
principal for the past three years.
The cohort group also determined who at the school site should be included in
the study, ranging from administrators, key teacher leaders, teachers with leadership
capacity on site, and other classroom teachers. For the interview portion of the study,
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the group decided to include school site administrators and key teacher leaders, using
an interview guide. All classroom teachers at the school were also asked to respond
to a teacher questionnaire. The results of the teacher questionnaire provided the
researcher with school-wide general perceptions by teachers in regard to questions
which had been designed by the cohort to find answers relating to the main topics of
the study. The location of the interview sessions were on campus and the researcher
made sure it was a safe environment, ensuring confidentiality. All interviewees met
with the researcher at least once, while some met more than once depending upon the
needs of the study. Participation in the study was voluntary. The researcher made all
necessary efforts to ensure participants of anonymity and confidentiality on the
researcher’s part.
Selected School Profile
The school purposefully selected for this study, Vineyard High School, is
located in the Vineyard community and is part of the Vineyard Union High School
District in the city of Vineyard in Southern California. The community, which has a
long history of ethnic diversity, especially Mexican Americans who, along with the
native population, were the earliest inhabitants of the region, has long been identified
as one of the most important centers of the agricultural industry in southern
California due to its fertile soil and ideal climate; low flat land spread mile after mile
with one end of the land meeting the Pacific Ocean. Throughout its history most of
the land was used for growing crops, especially strawberries; in recent years
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however, many new extensive housing developments have supplanted the
agricultural sites, welcoming an ever-increasing population taking advantage of the
beautiful climate and large, upscale homes.
The Vineyard School District currently accommodates 16,138 students and
has served the Vineyard community since 1901. It includes six high schools, three
continuation schools and an adult education school. Its student body is diverse; 64
percent Latino and 19 percent white. The district has been challenged by the area’s
changing landscape: a region originally known for its fertile land and farming and a
rural character, today faced with a growing population due to the increasing number
of home developments and becoming more urban each day.
Vineyard High School, one of the districts six high schools, was established
in 1901. It is the oldest school built in the Vineyard community and currently serves
2,900 culturally and socio-economically diverse students. The school takes pride in
its “Bumble Bee spirit” and support from its students, staff, and parents. The present
school site is a state-of-the-art replacement facility that opened in 1995. All of the
permanent classrooms have internet access and the physical plant also includes four
computer labs, a library media center, a career center, a performing arts theatre, an
amphitheater, two gymnasiums, a football stadium with a press box, an all-weather
tartan track, and an Olympic size competition pool.
According to Vineyard High’s School Accountability Report Card (2005),
student demographics exhibited diversity in both the ethnic and economic
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backgrounds of its students. The largest ethnic population was Latino (62.4 %),
followed by white 21.4 %. 20.5% of the student population was identified as English
Language Learners while 9% of the students were students with special needs. In
addition, 30.5% of students were eligible for the free and reduced lunch program.
The school has been designated as a school-wide Title I school.
Student Achievement
According to the academic performance data of Vineyard High School, the
school met state and federal expectations by meeting its API and AYP requirements
as displayed in Table 5. API (Academic Performance Index) numbers had grown 65
points in three years. The school met its API target every year and all subgroups of
the school also met AYP (Adequate Yearly Progress) requirements for the three
years. In regard to API as shown in the table below, it increased 28 points from 2003
to 2004 and then 37 points increased from 2004 to 2005.
Table 5: 2003-2005 API & AYP Comparison Chart
API &AYP
School-wide
Growth*
Met API
Growth Target
Statewide
Rank
School-wide AYP
2003 610 Yes 3 Yes
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2004 638 Yes 4 Yes
2005 675 Yes 5 Yes
*Ethnic and economically disadvantaged student subgroups must show comparable
improvement.
Student achievement in CST Algebra I showed that in 2003 8% of students
met the “Proficient” and “Advanced” levels, in 2004 15% of them did so, and in
2005 21% of students met the two levels, an overall increase of 13% for the period.
In addition, in viewing the bottom two levels of “Below Basic” and “Far Below
Basic,” in 2003 51% performed at those levels, down to 43%in 2004 and in 2005
only 34 %, a 17 % reduction shown from2003 to 2005.
Table 6: CST Algebra I Student Performance Chart
Algebra
1
Advanced Proficient Basic Below
Basic
Far Below
Basic
2005 0% 21% 45% 27% 7%
2004 0% 15% 41% 38% 5%
2003 0% 8% 40% 44% 7%
CAHSEE results from the same three years are shown in Table 7. While
English Language Arts results showed a 7% increase from 2003 to 2005, Math
results rose 24 % during that time.
Table 7: CAHSEE Results from 2003-2005
CAHSEE Results 2003 2004 2005
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ELA 59% 75% 66%
Math 40% 75% 64%
Certificated Staff Information
The school is comprised of 122 certificated staff and 87 classified staff.
Among the certificated staff, five are administrators, six are counselors and 111 are
teachers. Only five were first-year teachers, and eleven were in their second year.
The average years of service among the teachers was 15.3 years in the field of
education and 12.3 years with the district. The administrative team consisted of a
principal and four assistant principals. The principal had been serving at the school
for five years. Before her/his principalship at Vineyard High School, he had been an
assistant principal at another high school in the district.
Selected Participants
For this study, selected participants, such as site administrators and math
teachers, were interviewed for data collection. To ensure that those selected would
provide the necessary and unbiased data, the following guidelines were followed: 1)
include the person who is ultimately responsible for the school operation and
management (the principal), 2) include the person/people who are perceived as
instructional leaders at the school site, 3) include the group which is considered as
the leadership team on campus, and 4) include all math teachers.
School Site Administrators
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The high school principal has a significant influence in determining the
school’s focus, especially instruction. The principal was interviewed two times in
order to gather accurate and inclusive information in regard to how the school was
able to make consistent improvement in mathematics. Since the site principal had
been serving the school for five years, he met the criteria of the study in respect to
stability by having been at the same school site as principal for at least three years. In
addition, the researcher included the assistant principal in charge of instruction and
curriculum at the school site. Assistant principals who oversee instruction and
curriculum assist the principal in the school’s effort to accomplish their school goals
and work toward the school vision. These assistant principals also work closely with
department chairs in articulating and improving instruction at the school site. They
are usually in charge of building the school’s master schedule which, to some degree,
is a representation of the school’s philosophy and practice in utilizing and allocating
teaching staff and facilities.
Key Leaders
The following people were identified by the principal—and this was later
corroborated by various responses during interviews—as instructional leaders
affecting student achievement in math at the school site: the principal, the assistant
principal in charge of instruction and curriculum, the math department chairs, AVID
Coordinator, and English and Math Resource Persons. English and Math Resource
Persons are individuals specially funded through the district office and provided with
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a non-teaching “resource period” which allows them to take charge of student
performance data collection and analysis. These key personnel were also included in
interviews to find out how they assessed school needs, planned and strategized new
initiatives and policies, and introduced new changes to the school community. The
input from the leadership was also expected to show how the change process was
communicated, initiated, assessed, and reviewed. These key leaders collaboratively
worked to discuss school business, review current practices and events, and plan
future school business and events. At various meetings, instructional leaders
reviewed school goals and objectives as well as student performance data.
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Math Teachers
The Math department had nineteen teachers. With the exception of two new
teachers, math department members were veteran teachers who had been at the
school site for a number of years. Their responses were expected to show what took
place in the classroom and department and what teaching strategies and instructional
materials were perceived as effective and influential in order to bring about
necessary changes.
All Certificated Staff
Every teacher—out of a total of one hundred six—was asked to respond to
the teacher questionnaire in order to gather school wide perceptions of instructional
leadership and school culture. The researcher also conjectured that it would be
valuable to compare the school-wide perceptions to the data collected from
interviews with the purposefully selected participants.
Instrumentation
During the spring and summer of 2006, the instrumentation utilized in this
study was designed by a research team of eleven educational doctorate students at
the University of Southern California. They met regularly in a dissertation seminar
under the advisement of Dr. David Marsh, Associate Dean of Academic Programs.
They collaboratively developed conceptual frameworks, planned a methodology for
data collection and analysis, and designed interview guides and a teacher
questionnaire. The team correlated instruments of data collection, data needs, data
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sources, and research questions by creating a data collection/instrument chart (Table
8). An “X” indicates that information from the instrument would address the
corresponding research question(s).
Table 8: Relationship of Data Collection Instruments to Research Questions
Research Question Instrument
RQ 1 RQ 2 RQ 3 RQ 4 RQ 5
School Profile X X
Key Leader Interview X X X X
Math Teacher Interview X X X X
*Teacher Questionnaire X X X X
*There were two versions of the Teacher Questionnaire available: a regular version was for
all teachers while a separate version was provided for math teachers that included math-
specific questions in addition to those of the regular version.
Frameworks for Instrument Design
In order to ensure connections and relevance between data needs and data
collection instruments, after the cohort team determined the five research questions,
corresponding conceptual frameworks were developed. Although no framework was
needed to find answers to the first research question, it was decided that the second
research question would be best conceptualized with two separate frameworks,
resulting in a total of five frameworks. The frameworks further served as means to
focus on the key components of the study in order to find answers to research
98
questions and were designed around the following topics: effective school design,
instructional leadership, the change process, and effective mathematics instruction.
Data Sources for RQ 1: School Profile of Student Performance Data
The first research question asked, “What was the pattern of math
achievement for various students at the school?” The cohort group agreed that the
answers would be found through reviewing, the WASC report, the School
Accountability Report Card, and the School Improvement Plan and examining the
assessment data on the web site of The California Department of Education along
with other student performance data available at the school site. In addition to
student performance data, the research examined the master schedule of math classes
and student grades, and student demographics.
Conceptual Framework for RQ 2: Effective Math Programs and School Design
The second research question asked, “What policy initiatives, as well as
curriculum, instruction and allied conditions, seem to be related to improved math
achievement at the school?” Separate frameworks for School Design and Math
Programs were created for this question. The Conceptual Framework of Effective
School Design, shown in Figure 1, included the key elements of current research
findings such as small school size, curriculum foundations, learning activities, school
cultures, and student performance data. In other words this framework was created to
collect information in regard to these key areas: 1) school strategies to create a small
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learning environment; 2) construction and characteristics of curriculum foundation;
3) types of learning activities for students to optimize learning; 4) school strategies
for formation and maintenance of school culture, particularly as a professional
learning community; and 5) types of student performance assessments and uses of
student assessment data. It is important to note that this framework is not specifically
about Algebra programs; it is, rather, a general framework of curriculum, student
achievement, and school culture.
Figure 1: Conceptual Framework for 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
The Conceptual Framework for Effective Mathematics Instruction in turn,
examines the key components of effective math programs as shown in Figure 2.
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Recent research data point out that it is crucial to focus on key classroom practices
such as effective and coherent lesson design, promotion of student engagement, and
cultural relevance. In addition, standards based instruction is another essential
element. The instruction should be based on state content standards and modified by
analysis of student performance data. The third key component of curriculum design
emphasizes student-centered curriculum driven by learner outcomes. Math
curriculum, designed with scope and sequence based on learning theory, should
stress acquisition of conceptual understanding and problem-solving skills.
Figure 2: Conceptual Framework for Effective Math Programs
Classroom Practices
 Effective and coherent
lesson design
 Promotes high levels of
student engagement
 Makes use of prior
knowledge
 Cultural relevance
 Identifying and providing
accelerated interventions
Curriculum Design
o Student-centered
curriculum
o Driven by learner
outcomes
o Emphasizes
Conceptual
o Focuses on
problem-solving
o Incorporates current
learning theory
o Year-long Scope &
Sequence is
supported by
learning theory
Standards Based Instruction
 Assessments aligned
to standards
 Student achievement
data drives instruction
and decision
 Common performance
rubrics through
collaboration
Effective
Math
Programs
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Conceptual Framework for RQ 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?” The
framework created to collect data in regard to this research question was based on
Bolman and Deal’s four frames (2003)—structural, human resource, political, and
symbolic—for leaders to utilize in their efforts to reframe their organization. The
rationale for adopting Bolman and Deal’s four frames was based on the fact that the
analytical nature of the frames allowed the researcher to examine the organization
from broad analytical perspectives rather than more prescriptive, specific frames.
The use of such broad analytical frames let the researcher tell the story of what was
going on in the organization. This approach also enhances the possibility and its
inherent value of seeing from multiple perspectives in the process of trying to
capture and analyze the background in order to understand what happened at the
school in the process of raising student achievement in math.
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Table 9: Overview of Bolman and Deal’s Four-Frame Model
Frame Structural Human
Resources
Political Symbolic
Metaphor
for
organization
Factory or
Machine
Family Jungle Carnival,
Temple,
Theater
Central
Concepts
Rules, Roles,
goals, Policies,
Technology,
Environment
Needs, Skills,
Relationships
Power,
Conflict,
Competition,
Organizational
politics
Culture,
Meaning,
metaphor,
ritual,
ceremony,
stories,
heroes
Image of
Leadership
Social
Architect
Empowerment Advocacy Inspiration
Basic
Leadership
Challenge
Attune
Structure to
task,
Technology,
environment
Align
Organizational
and human
needs
Develop
Agenda and
Power Base
Create
Faith,
Beauty,
Meaning
Source: Bolman & Deal (2003) Reframing Organizations, p.16.
Conceptual Framework for RQ 4: 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?” The framework was designed to gather data in regard
to five key components that were mainly based upon the California State Principal
Standards and a framework by Hassel and Halloway (2002) for school leaders which
was an attempt to align ISLLC standards to real life practice. The five key
components, shown in Table 10, include a broad area requiring principals’ skills and
knowledge in building a shared vision of learning, establishing practices in effective
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monitoring and supervision of instructional programs, building collaboration among
families and community members to mobilize community resources, building and
sustaining a school culture and instructional programs, and using data to guide
instructional programs and support student learning.
Table 10: Framework for Instructional Leadership
I n s t r u c t i o n a l L e a d e r s h i p F r a m e w o r k
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
Facilitates the
development,
articulation,
implementation,
and
stewardship of a
vision of learning
that is shared and
supported by the
school community.
A- Develops
vision
B- Communicates
the vision
C- Implements the
vision
D- Monitors and
evaluates the
vision
E- Addresses
obstacles to the
vision and its
implementation
and realization
Observes and monitors
instructional program.
Provides constructive
feedback in a timely
manner to all teachers.
A- Classroom
observations on a
daily/weekly basis.
B- Allocates resources to
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
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
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 to inform
instruction
and support
learning
A- Utilizes
data to place
students
appropriately
B- Formative
benchmark
school site
assessments
C- Summa-
tive
standardized
assessment
D- Disaggreg
ate data by
students,
classes and
cohorts
E- Use data
to guide and
improve
teachers
instructional
program
F- Use data
to create
master
schedule
G- Use data
to inform and
improve
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Conceptual Framework for RQ 5: How did instructional leaders respond in
academic areas in which they were not experts?
Next, based on the Framework of Instructional Leadership (Table 10), the
researcher examined an array of strategies that were implemented at the school site
by the principal in order to ameliorate any instructional deficits due to any
deficiencies in teacher subject matter competency. These strategies are outlined in
Table 11.
Table 11: Instructional Strategies to Overcome a Lack of Subject Matter
Competency
Item Strategy Approach/Source
1
Delegate Leadership to Assistant
Principal 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)
pacing of
instructional
plans
105
6
Emphasize strategies to engage
students in the learning process
Student Engagement
(Marzano, 2003 pp. 149-150)
7
Emphasize articulation with feeder
schools
Guaranteed, Viable Curriculum
(Marzano, 2003 pp. 22-34)
8
Emphasize raised expectations
Challenging Goals and Effective
Feedback (Marzano, 2003 pp. 35-
46)
9
Emphasize Strategic Teacher
Assignments
HR Frame
(Bolman & Deal, 2003)
10
Emphasize Revised Course Scope
and Sequence and/ or Curriculum
Guaranteed, Viable Curriculum
(Marzano, 2003 pp. 22-34)
11
Emphasize Interventions for lower
performing students
Supplemental Services
(NCLB, 2001)
12
Emphasize Professional
Development
Meaningful Staff
Development Activities
(Marzano, 2003 pp. 65-66)
In addition, making use of the definition by the state of California of a highly
qualified teacher (HQT) as required by NCLB, the principal’s competency in the
subject matter knowledge was assessed and determined as shown in Figure 3.
Figure 3: Process of Assessment of Math Expertise
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Data Collection Instruments
The data collection instruments for this study were created after numerous
revisions as the cohort developed and finalized conceptual frameworks for them in
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
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an attempt to design instruments that would best address each particular research
question. These Data Collection Instruments were then used to gather relevant
information about the pattern of student achievement in math, math programs and
instructional practices, the change process, and instructional leadership. Five
instruments for data collection were designed to provide qualitative data and to
gather information relevant to each research question. Through the employment of a
variety of instruments, the school profile, key leader interview guide, math teacher
interview guide, math teacher questionnaire, and general teacher questionnaire, the
researcher was able to triangulate data (Gall, Borg, and Gall, 1996).
School Profile
The research cohort team led by Dr. Marsh designed the school profile
instrument to identify characteristics of the school community in an attempt to create
a comprehensive understanding of the school being researched. The areas of data
collection integrated into the school profile included demographics, student
performance, and school information in general. The researcher was able to collect
the necessary data through the web site of the California Department of Education.
Data for student body demographics included ethnic and percentage
breakdowns for English Language Learner and Special Education students and the
percentage of students eligible for the free or reduced lunch program. Data for
teacher demographics included an ethnic breakdown, the number of teaching staff,
the percentage of teachers meeting the requirement of highly qualified teachers
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(HQT) under NCLB, and years of teaching experience. Demographic data revealed
specific needs and challenges that the selected school site had to focus on.
Student performance data, closely linked with the purpose of the study,
consisted of the school’s Academic Performance Index (API) and Annual Yearly
Progress (AYP) results, student performance results in CAHSEE for the past three
years and local benchmark assessment results and student performance data in a
variety of math classes at the school site. Student performance data showed the trend
of student achievement in math, strengths and weaknesses in math subject areas, and
the characteristics of the achievement gap. Data from the school profile helped the
researcher gather information relevant to Research Questions 1 and 2.
Key Leader Interview Guide
Structured, formal interviews were conducted with the site principal, assistant
principal in charge of instruction and curriculum, math department chair and math
coach using the Key Leader Interview Guide. This provided the researcher a
standardized open-ended interview for the study, a format which requires all
respondents to answer the same questions. As a result, it increases comparability of
the collected responses and enhances organization and analysis of the data (Patton,
2002). The intention of conducting the key leader interview was to gather
information to answer Research Questions 2, 3, 4, and 5. Interviews were conducted
with each participant for one or two sessions of no more than 40 minutes in length.
All were held in the school’s conference room except for the individual interviews
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with the principal and assistant principal, which were held in their respective offices.
A semi-structured interview process, using specific questions developed by the
researcher, was employed for the interviews with key leaders (Creswell, 2003).
Teacher Interview Guide
The research cohort team designed the Teacher Interview Guide to gather
additional data on Research Questions 2, 3, 4 and 5. Participants for teacher
interviews included teachers who taught at least one section of math class at the
school site. Their input was gathered to examine their perceptions and experiences
regarding the causes for an improvement in student achievement in math, the change
process, and instructional leadership. Utilization of the Teacher Interview Guide
enabled the researcher to ask semi-structured questions to elicit relevant information
to answer specific research questions. The Teacher Interview Guide was designed
for a half-hour long interviews. The interviews with teachers were held in the
conference room.
Teacher Questionnaire
The Teacher Questionnaire was developed to gather data on school-wide
perceptions regarding general school-wide issues related to the Research Questions
2, 3, 4 and 5. A Total of 25 questions were created to be utilized for the teacher
questionnaire portion of the data collection. There were two versions of the Teacher
Questionnaire available: a regular version was for all teachers while a separate
110
version was provided for math teachers that included math-specific questions in
addition to those of the regular version.
Data Collection
Prior to the collection of data, the team of researchers had to receive approval
from the Institutional Review Board (IRB) at the University of Southern California.
For this study, the research cohort team led by Dr. Marsh submitted one IRB
proposal, representing the multiple studies by the cohort members. Upon meeting the
university’s requirements, the researchers received an Approval Notice for Research
Involving Human Subjects, an Information Sheet for Non-Medical Research, and a
Telephone Contact Protocol. Following approval from the IRB to commence the
study, each team member chose a research school site and made contacts with the
school. Once the researcher received approval and consent from the principal of the
school site, the researcher shared information about the study and the plan of data
collection with the selected site. The data collection took place from September 2006
through November 2006. Participation in the study was voluntary for all participants.
The data to acquire answers to the research questions was collected in four phases.
The first part of Phase One of the data collection concentrated on gathering
school-wide hands-on information. The researcher collected and examined the
master schedule, the School Improvement Plan, the WASC (Western Accreditation
of Southern California) report, and other relevant documents. The researcher also
met school personnel to establish a favorable relationship with the school personnel,
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visited classrooms, and spent time on campus to gather informal information about
the school. In addition, the researcher held the first interview with the site principal
to review the nature of the study, review the data collection instruments, and review
IRB assurances of confidentiality and voluntary participation. The researcher also
used this initial interview with the principal to acquire general information about
school culture, key leaders, student achievement in math and other issues relevant to
the study. Before beginning the next phase, the researcher examined and analyzed
the data compiled from this initial phase.
In addition, during the initial phase the researcher met the principal for an
introductory/planning meeting. At this meeting, the principal identified whom he
considered to be the instructional leaders at the school, and the researcher and
principal then strategized the specifics of the data collection process such as when
the researcher would be introduced to the faculty and to the math department, how
questionnaires would be distributed and collected, and where and when interviews
with key leaders and math teachers would be conducted.
Once these logistics of data collection were configured, Phase One began. It
consisted of conducting key leader interviews and distributing the teacher
questionnaire to the faculty, including the special version provided only to math
teachers. The researcher began the key leaders interviews in the conference room at
the school; the interviewees included the site principal, the assistant principal in
charge of instruction and curriculum, who also oversaw the math department, the
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AVID Coordinator, the math department chairpersons comprising the two current co-
chairs and the recently retired department chair as well since she was perceived as
the key person who had brought about improvement of the math curriculum,
instruction, and student achievement. In addition, the two Resource Persons were
interviewed since they were regarded as a major part of instructional leadership. The
Key Leader Interview Guide was employed to ensure that the information gathered
related to the research questions. The Teacher Questionnaire was distributed to the
teachers after an introductory meeting explaining the purpose and nature of the
study.
Phase Two involved compiling interview notes, reviewing and analyzing
documents, and identifying emergent themes. During Phase Two, the researcher
visited classrooms to observe math instruction, especially Algebra and Pre-Algebra
classes. Math Lab was also visited since many of the interview respondents
frequently referred to it during interviews.
Phase Three completed the key leader interviews, this time targeting the math
department chair and math coaches, and conducted the teacher interviews. Teacher
interviews were held with teachers who taught at least one section of math. The
Teacher Interview Guide was used, again in order to gather information which
addressed the research questions. The researcher took handwritten notes to record
their responses and reviewed them with the participants to ensure the accuracy of the
note taking. In addition, the researcher followed up with questions focusing on
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emergent themes that had been identified in Phase Two. Follow-up interviews were
held with key leaders to clarify facts and more documents were gathered. Additional
observations were also made to confirm the facts and findings. Also during this
stage, the Teacher Questionnaires were collected from the faculty.
Data Analysis
The purpose of this study was to learn more about how comprehensive high
schools successfully bring together policy initiatives and local best practice to
improve math performance in their schools. The study explored the extent of the
impact of policies and initiatives, the design of math curriculum and programs, the
utilization of instructional leadership, and the school reform process. Five research
questions addressing that purpose had been developed along with conceptual
frameworks based upon them which, in turn, shaped the data collection instruments
that were then designed to gather information relating to the five research questions.
Qualitative data collected included the researcher’s transcripts from
interviews and field notes, and they were utilized to identify and analyze the trends
and commonalities in responses from the participants. Interview notes and field notes
were cross-filed with themes categorized by the key points of the conceptual
frameworks. A spreadsheet was employed to manipulate the data collected using the
research questions and data collection instruments in order to obtain a more thorough
and systematic analysis of the collected data. In addition to the spreadsheet, visual
charts were created. Each chart consisted of those research questions and conceptual
114
framework or frameworks which had emerged during the data collection. The
researcher then categorized field notes and interview notes by placing them in the
matrix thus created by the visual charts.
Validity and Reliability
In an effort to ensure validity and reliability, this study utilized triangulation
of data and member-checking as Creswell (2003) recommended. As far as internal
validity is concerned, data was collected through multiple sources including
interviews, a questionnaire, and a school profile and document analysis for
triangulation of data. The utilization of multiple sources of data allowed the
researcher to clarify and investigate relevant factors to the study. In addition to
triangulation of the data, the participants served as a check throughout the interview
to ensure the true value and accuracy of the data. However, external validity is not
within the reach of this study which employed a single case study methodology. Also
due to the nature of case study methodology, caution must be used in any attempts to
generalize from the findings.
Summary
The purpose of this chapter was to discuss the research methodology
used in this study. The discussion included a detailed explanation about the design,
the sampling criteria, the collection instruments, the data collection process, and data
analysis used in this study. The data collection procedures were collaboratively
developed by the research cohort team led by Dr. Marsh and were approved by the
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Internal Review Board of the University if Southern California. The regulations
established by the IRB were explained to the site principal and implemented
throughout the study. The study was comprised of a school profile analysis, key
leader interviews, math teacher interviews, and a teacher questionnaire. Results of
data analysis and findings are provided in the next chapter.
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CHAPTER FOUR: FINDINGS, ANALYSIS AND DISCUSSION
Introduction
The purpose of the study was to identify how urban high schools successfully
bring together policy initiatives and local best practices to improve math
performance in their schools. In addition, the study examined how instructional
leadership is effectively carried out in high schools in the context of improving math
performance for students and how school leaders respond in academic areas in which
they do not have expertise.
This chapter examines the data collected for a case study of one high school’s
successful practices and efforts which resulted in improved student achievement in
math. Qualitative data collected included the researcher’s transcripts from interviews
and field notes which were then utilized to identify and analyze the trends and
commonalities in responses from the participants. Interview notes and field notes
were cross-filed with themes categorized by the key points of the conceptual
frameworks. In addition to the findings, an analysis and discussion of the collected
data follow, based upon the data findings.
The data were collected according to the guidelines defined in Chapter Three for
each of the following five research questions:
1. What was the pattern of math achievement for various students at the school?
2. What policy initiatives—as well as curriculum, instruction, and related
conditions—were related to improved math achievement at the school?
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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 collected data included student performance results, the master schedule,
WASC report, Single Plan, School Accountability Report Card, the 2003 Ventura
County Superintendent’s Schools’ Office Curriculum Audit report, informal
observations, and interviews with key leaders and math teachers as well as
questionnaires that were distributed to the whole faculty.
This chapter is organized and structured by the five research questions of the
study. The first part of the chapter deals with the data findings in reference to the five
research questions while further analysis and discussion are included in the second
part of the chapter.
Data Findings
Research Question One
The first research question asked, “What was the pattern of math
achievement for various students at the school?” For this question a school profile
was used, utilizing a variety of student performance data from high stakes math
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exams such as CST and CAHSEE. In addition to overall student achievement results,
sub-groups’ academic performance outcomes were examined.
CAHSEE Results
As shown in Table 12 below, Vineyard High School has seen a dramatic
improvement in student achievement shown in the CAHSEE, the state-mandated
examination to qualify for high school graduation.
Table 12: Comparison of Passing Rates of Vineyard High School Students on the CAHSEE
Math Section from 2003-2005
2003 2004 2005
Overall 40% 75% 64%
10th 53% 75% 76%
11th 21% - 32% Grade
12th - - -
Male 40% 72% 63% Gender
Female 40% 79% 66%
African-American 22% 72% 60%
Asian 58% 100% 100%
Filipino 68% 96% 88%
Latino 34% 70% 59%
Ethnicity
White 58% 86% 76%
English Only 44% 78% 67% Language Status
English Learners 33% 62% 45%
Non-economically Disadvantaged 45% 80% 75% Economic Status
Economically Disadvantaged 28% 70% 53%
Special Education Participation Students Receiving Services 7% 17% 21%
Source: http://dq.cde.gov.ca/dataquest/cahsee Retrieved on December 10, 2006
Overall Student Achievement Pattern.
119
As shown in the chart, there were overall improvements in student
achievement in math at Vineyard High School. The data showed a 35% increase
from 2003 to 2004 and a lesser but still substantial 24% increase over the two years
(2003 to 2005), a 9% decrease from 2004 to 2005. It is worth noting that there were
no 11
th
graders’ participating in 2004, while the performance results of 10
th
grade
students from 2004 to 2005 actually increased by 1%. The 9% overall decrease from
2004 to 2005 resulted from factoring in the 32% passing rate of 11
th
graders in 2005.
In fact, a little closer look at the student performance data also shows that students in
every category showed some degree of decrease from 2004 to 2005 with three
exceptions: 10
th
graders, Asian students, and students with special education
services. It is presumable that these decreases were due to the participation of the
11
th
graders in these categories.
Achievement Pattern by Grade Levels (10
th
and 11
th
).
According to the data, 10
th
graders consistently showed higher passing rates
than 11
th
graders over the three years. For 10
th
graders, it was their first attempt to
pass the stated mandated exam. 11
th
graders, on the other hand, had taken the exam
previously and failed to pass it on their first attempt. Students in both grades showed
improvement in their performance over the three years; however, 10
th
graders made a
larger gain with a 23% increase while 11
th
graders improved by 11%. It should be
noted that the 11
th
graders consisted of the 25% of the previous year’s 10
th
graders
who had failed to pass.
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Achievement Pattern by Gender.
The data depicted females showing higher achievement in math than male
students at Vineyard High School. In 2003, students of both genders showed a 40%
passing rate, but in 2004 female students performed at 79%, with males trailing at
72%, females performing seven percent higher than their peers of the opposite
gender. In 2005, female students again outperformed male students by three percent.
Achievement Pattern by Ethnicity.
The CAHSEE data showed that there was a significant increase among all
ethnic student groups for the three years. Between 2003 and 2004, the African-
American student group showed the highest achievement increase at 50%. For the
entire three year period, 2003 to 2005, Asian students along with African-American
students had the highest achievement of all groups; Asian students showing a 42%
increase, closely followed by African-American students at 38%. Latino students
showed a 36% increase from 2003 to 2004 and 25% from 2003 to 2005. However,
comparing the student achievement data among the sub-groups by ethnicity showed
that the absolute student achievement pattern in Vineyard High school parallels the
national trend—Latino and African-American student groups showed the lowest
passing rates compared to their peer groups in spite of the significant increases
shown in their performance results.
Achievement Pattern by Language Status.
121
While English Only speaking students demonstrated a 34% increase from
2003 to 2004 and 23% from 2003 to 2005, English Learner students showed only a
29% increase from 2003 to 2004, dropping to 12% for 2003 to 2005, their
improvement lagging behind their English Only speaking peers.
Achievement Pattern by Economic Status.
According to the CAHSEE data as shown in the chart, economically
disadvantaged students showed a 42% increase in their performance results from
2003 to 2004 and a 25% increase from 2003 to 2005 while their non-economically
challenged peers demonstrated a 35% increase from 2003 to 2004 and 30% from
2003 to 2005.
Achievement Pattern by Special Education Services.
At Vineyard High School, students who received special education services
showed a 10% increase from 2003 to 2004 and an additional increase to 21% in
2005. They are one of only three sub-groups which showed consistent improvement
for the three years from 2003 to 2005.
CST Algebra I Results
When the achievement results in CAHSEE at Vineyard High School were
compared to the state results, they showed similar patterns: a 43% passing rate in
2003, 74% in 2004, and 63% in 2005. It is important to understand however, in light
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of this study, that Vineyard High School’s achievement is not merely part and parcel
of a state trend towards higher scores, unrelated to the specifics of the individual site.
The analysis of the CST results which follows, demonstrates, on the other hand, that
in fact, the improvement in student math achievement at Vineyard was quite distinct
from statewide trends and, we argue, results from the implementation of their
particular efforts and strategies described in this study.
CST State Algebra Results showed that the percentage of students who
performed at a Proficient or Advanced level was erratic and generally modest over
the three-year period. Among 9
th
graders it was 19% in 2003, 12% in 2004, and 16%
in 2005. For 10
th
graders the results were 8% in 2003, 2% in 2004, and 7% in 2005
while 11
th
graders achieved at 6%, 2% and 4% over the three years. In contrast, as
we find in the data below, despite a substantial deficit in the first year, Vineyard
High School showed a consistent and, in most instances, a substantial increase in
their CST scores across all grade levels over the three years, ultimately displaying a
large lead over their statewide peers. There was clearly something special going on
at Vineyard.
Table 13 following, shows this strong improvement in student achievement
on the math section of the annual state- mandated California Standards Test (CST) at
Vineyard.
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Table 13: Comparison of Vineyard High School’s Student Performance
Results of CST Algebra I Competency from 2003-2005
2003 2004 2005
Overall 8% 15% 21%
9th 10% 21% 29%
10th 8% 14% 22% Grade
11th 3% 6% 6%
Male 8% 19% 24%
Gender
Female 7% 11% 18%
#
tested
%
proficiency
& above
#
tested
%
proficiency
& above
#
tested
%
proficiency
& above
African-
American
22 0% 22 14% 41 15%
Filipino 14 21% 17 29% 17 35%
Latino 214 6% 307 14% 360 21%
Ethnicity
White 94 7% 116 16% 100 19%
English Only 291 9% 383 16% 356 19%
Language
Status
English
Learners
71 4% 92 10% 97 19%
Non-
economically
Disadvantaged
277 9% 280 14% 282 21%
Economic
Status
Economically
Disadvantaged
86 5% 194 17% 257 21%
Special
Education
Participation
Students
Receiving
Services
16 0% 23 9% 27 11%
As the table makes evident, without any exception, students at Vineyard High School
showed improvement in their academic achievement in Algebra I on the CST.
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Overall Student Achievement Pattern in CST Algebra I.
The percentage of students who performed at a Proficient or Advanced level
increased consistently for three years from 2003 to 2005; by 7% from 2003 to 2004
and 6% from 2004 to 2005.
Achievement Pattern by Grade Levels (9
th
-11
th
).
Since 12
th
graders do not take the CST, the student performance results of
three grades, 9
th
through 11
th
, were compared. Among the three grade levels, 9
th
graders showed the most improvement, 19% from 2003 to 2005. 10
th
graders
displayed a 14% increase while 11
th
graders showed only a 3% increase.
Achievement Pattern by Gender.
Male students showed more improvement than their female peers. While
male students increased their performance by 16% from 2003 to 2005, female
students demonstrated an 11% increase. Looking at the 2003 performance data, both
genders performed at a similar level; however, in the following year 19 % male
students scored at the Proficient or Advanced level while their peers with the
opposite gender increased their performance only by four percent. Then in 2005,
female student performance in the CST Algebra I went up by 7% while their male
peers improved by five percent. Overall, male students outperformed female
students.
Achievement Pattern by Ethnicity.
125
An examination of the CST student performance results by ethnicity showed
that there was an average 15% increase among the major sub-groups. For African-
American students, the same number, 22, took the CST Algebra I test in 2003 and
2004. None of the African-American students scored at the Proficient or Advanced
level in 2003, but the next year 14% of the 22 students showed that they were
competent in Algebra I. In all three years Filipino students displayed the highest
percent of math proficiency in algebra I among the sub-groups while African-
American students, despite their 15 % improvement, had the lowest proficiency
among their peers. The 2005 results showed that 21% of Latino students scored at
the Proficient or Advance level while 19% of white students scored at the same
levels.
It is worth noting the changes in the number of students who participated in
the exam. In order to take the CST Algebra I exam, students have to be enrolled in an
Algebra or equivalent course. Students who take a remedial math class or a math
class below Algebra are not allowed to take the exam. There was a very slight
change among Filipino and white students in general; respectively, three and six
students from 2003 to 2005. On the other hand, the number of African-American
students who took the exam almost doubled, from 22 students to 41, in those two
years. Latino student groups also experienced a significant increase in the number of
students taking the exam; 214 students in 2003 increasing to 360 students in 2005.
Achievement Pattern by Language Status.
126
The CST student performance data showed that English Learner (EL)
students showed more improvement than English Only (EO) students in Algebra I.
Only 4% of EL students—compared to 9% of EO—met the level of competency in
2003 but they demonstrated a 15% increase over the two years, compared with a
10% increase over the same period for English Only students. In 2005, 19% of EL
students scored at the Proficient or Advanced level, exactly the same as the English
Only students.
Achievement Pattern by Economic Status.
A close look at the academic achievement data of Vineyard High School revealed
that economically disadvantaged students made more improvement than students
who were not economically disadvantaged; a 16 percent increase versus 12 percent.
The 2005 CST results showed that the same percent of both groups, 19 %, scored at
the Proficient or Advanced level. There was a significant increase in the number of
economically disadvantaged students taking the exam in two years; in 2003 only 86
of them participated in the exam but in 2004, 257 students took the CST Algebra I
exam.
Achievement Pattern by Special Education Services.
In 2003, of the 16 students receiving special education services who took the
exam, none of them showed competency. However, in 2004 nine percent of 23
students and in 2005 11% of 27 of the special education students scored at the
Proficient or Advanced level.
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Based on the CAHSEE and CST data available at the website of the
California Department of Education, the findings on student achievement in math at
Vineyard High School revealed a consistent improvement from 2003 to 2005. Such
improvement was shown across the board, regardless of grade level, gender,
ethnicity, language status, economic status, and special needs.
Advanced Placement Examination Results in Math
In addition to CAHSEE and CST results, Advanced Placement examination
results were reviewed to acquire an understanding of student achievement in math in
Vineyard High School. As shown in Table 14 below, the pattern of student
achievement in AP math exams showed a different tendency from those of the CST
and CAHSEE. As opposed to the consistent increases shown in the latter two
assessments, the AP results showed a decrease in the passing rate on the three math
AP exams in 2004 and 2005 from the results of 2003; however, according to the
2006 results, the passing rate showed an improvement.
Table 14: Comparison of Vineyard High School’s Student Performance Results of AP Math
Exams
2003 2004 2005 2006
Attempted 19 3 11 13
Passed 1 0 0 1
Calculus AB
Pass Rate 5.2% 0% 0% 7.6%
Attempted 19 23 14 14
Passed 4 3 3 7
Calculus BC
Pass Rate 21% 13% 21.4% 50%
Attempted 36 14 13 25
Passed 13 5 1 9
Statistics
Pass Rate 36.1% 35.7% 7.6% 36%
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Research Question Two
The second research question asked, “What policy initiatives—as well as
curriculum, instruction, and related conditions—were shown to be related to
improved math achievement at the school?” For this question, two Conceptual
Frameworks were employed to guide the data collection and data analysis: The
Conceptual Framework of School Design and the Conceptual Framework of
Effective Math Programs. As detailed in Figure 1, the School Design Framework
focuses on four areas that center on student learning factors in the learning-teaching
equation: 1)Student Performance Assessments to capture various student capabilities,
2) Learning Activities that affect student learning and various components of 3)
School Curriculum and 4) School Culture. The Framework for Effective Math
Programs (Figure 2) on the other hand, focuses on those areas affecting the teaching
side of the equation, specifically the components comprising Classroom Practices,
Curriculum Design and Standards Based Instruction. It should be kept in mind
during the following discussion of the findings that despite their seemingly unrelated
titles, both of the frameworks, School Design as well as Effective Math Programs—
albeit from the distinct perspectives of teaching and learning—were intended to
invoke responses concerning, and thus ascertain staff perceptions of, improved
achievement in math.
Interviews with the principal, assistant principal in charge of instruction and
curriculum, department chairpersons, Data Resource Persons (two main people in
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charge of data for the school), AVID coordinator, and math teachers provided the
necessary data to answer the second research question. In regard to math department
chairpersons, three individuals participated in the key leader interview; the two
current department co-chairs were joined by the department chair from the previous
year who had retired but was still deferred to, having been the driving force and
leader of the math department for decades during her service at Vineyard High
School. The report of the 2003 curriculum audit, composed by the Ventura County
Superintendent’s Schools Office was also reviewed.
In addition, two versions of teacher questionnaires, one for math teachers and
one for non-math teachers, offered information in regard to the second research
question. Ten math teacher surveys and 59 non-math teacher surveys were
completed and collected for data analysis.
Influence of Policy Initiatives
The report of the 2003 Curriculum/Instruction Audit of Vineyard High
School contained the following information:
As initially required by the Improving America’s Schools Act of 1994
(IASA), and then again by the No Child Left Behind Act of 2001 (NCLB),
California’s State Board of Education instituted rigorous Academic Content
Standards (K-12) and processes for measuring public schools’ success in
helping all students master standards. Within this broad system of academic
accountability, largely defined by California’s Public Schools Accountability
Act of 1999, Vineyard High School [pseudonym] became identified as an
under-performing or Program Improvement (PI) school in 2000-2001.
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Vineyard High School had a certain prestige and was subject to high
expectations from the community, being the first school opened in the area.
Designation as an under-performing school thus placed a great deal of external and
internal pressure on them.
Based on interview and questionnaire responses, the school staff believed that
policy initiatives greatly affected the school culture and student achievement of
Vineyard High School. Their responses are summarized in Table 15 below,
distributed over the three relevant policy categories.
Table 15: Summative Survey Results for Policy Initiatives
Questions 1 2 3 4 5
Non-Math
Teacher
Survey
11% 15% 19% 41% 14% The No Child Left Behind Legislation has promoted
increased student achievement at our school.
Math Teacher
Survey
10% 0% 30% 50% 10%
Non-Math
Teacher
Survey
3% 5% 10% 47% 35% The requirement that students pass the CAHSEE to earn a
high school diploma has contributed to the school’s effort
to improve student achievement.
Math Teacher
Survey
0% 10% 0% 20% 70%
Non-Math
Teacher
Survey
7% 5% 58% 20% 10% Board Policies in our district have contributed math
achievement in our school.
Math Teacher
Survey
0% 10% 60% 30% 0%
(1=Disagree Strongly, 2=Disagree Somewhat, 3=Neutral, 4=Agree Somewhat, 5=strongly Agree)
Their responses to these interview and questionnaire items regarding policy
initiatives showed that the faculty of Vineyard High School felt that policy initiatives
131
have directly or indirectly affected student achievement in math. Some policy
initiatives, as Table 15 indicates, were found to be more influential than others.
Passage of the CAHSEE.
The requirement of passage of the CAHSEE in order to earn a high school
diploma was regarded by the staff as the most significant policy that influenced the
school’s efforts to increase student achievement in math. Moreover, it affected the
attitude of students in regard to their academic achievement in math. Students cared
about the high stakes exam because it was required to graduate with a diploma. Data
from the first three survey questions, represented in Table 15, demonstrate that 90%
of math teacher respondents and nearly the same percentage (82%) of non-math
teacher respondents agreed that the CAHSEE requirement had influenced the
school’s efforts to improve student achievement in math. During interviews, 100% of
the participants referred to the CAHSEE requirement as the most influential policy
affecting school’s efforts to help students improve their performance in math. One
participant stated, “The CAHSEE requirement is the biggest influence. It directly
influenced student achievement in math.” Another respondent said, “Students are
more influenced and motivated by CAHSEE than anything else while the CST’s
(California Standards Tests) have no buy-in from students. It [CAHSEE] matters to
them because they know that they must pass it to graduate.”
No Child Left Behind Legislation.
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The second most influential policy seemed to be the No Child Left Behind
(NCLB) Legislation. This legislation caused some dissent among staff due to what
some perceived as its unrealistic dogma characterized as “all students will reach (a
particular achievement level) by (a particular time)” and its punitive sanctions
toward schools which had not been successful in meeting state-mandated goals.
Despite these perceptions, however, there was a general consensus that the federal
legislation was an external accountability system that helped the school and district
to focus on curriculum and student achievement outcomes. Table 15 shows that 55%
of the non-math teachers and 60% of math teachers agreed that the NCLB legislation
had been a factor to improve student achievement at their school. It is also worth
noting that 26% of non-math teachers and only 10% of non-math teachers disagreed
with the view that the NCLB promoted student achievement. During the interviews,
though similarly mixed feelings and differing views were voiced, a clear majority of
the responses showed that the NCLB legislation had helped the school to improve
student achievement in math.
One interview participant explained, “The sanctions or punitive consequences
of the NCLB are external pressure to motivate people to move forward. It’s a huge
pressure for schools, especially for principals, to show student achievement. It’s been
a great wake-up call.” Another participant stated, “The NCLB legislation helped the
school do the right thing, such as putting best teachers in most needed classes.” One
teacher interview participant declared, “NCLB helped to get dialogues going and
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open eyes to problems that our school was having. Before NCLB, with doors closed,
we did our thing. After NCLB we started having dialogues about test scores and
standards. For the first time we evaluated results.” One interview participant
mentioned the NCLB’s positive impact on student achievement in spite of his own
doubts: “I have a mixed feeling about NCLB. However, it really helped us focus on
all sub-groups and I think that’s very positive.”
Board Policies.
Among the three initiatives of Board Policies, NCLB and CAHSEE, Table 15
shows that Board Policies were deemed to be the least influential: Thirty percent of
the survey respondents, regardless of what they teach, agreed that board policies
have affected student achievement in math in their school while 58% of non-math
teachers and 60% of math teachers took a neutral position on the question.
Practices and Related Conditions Positively Affecting Student Achievement
The policy initiatives identified above as most relevant to Vineyards staff
were obviously designed to pressure districts and schools to implement practices that
would bring about expected student performance outcomes. Much of this pressure
was external, especially after the district became an underperforming district. Such
pressure forced the district to focus on instruction and curriculum. Although the
district had put some effort into improving student achievement since 2000, a more
systematic, concerted effort was placed on curriculum and instruction after the
district became a “PI” district in 2002. Vineyard Union High School District focused
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on instruction and curriculum in order to improve student achievement so that it
would be able to remove its PI (Program Improvement) status as required by the
NCLB legislation. Vineyard High School also, along with its parent district, was
categorized as “under-performing,” with the status of a Program Improvement (PI)
school, in 2000-2001. The school did not meet its Academic Performance Index
(API) goals in 2001-2002 or in 2002-2003. As a result, the school was given the
more serious “Year 2 PI” status. However, in 2003-2004, for the first time under the
PI status, the school was successful in making its API goal. In the following year it
again met its annual API goal, which meant that the school was finally able to exit its
PI status.
As a result of this history, the school district adopted new practices, including
revamping existing practices such as improved implementation of its Benchmark
assessments, the establishment of pacing calendars for core subject areas, updating
technology for more efficient access to student performance data, and reallocation of
financial and human resources. These district initiatives were, of course, reflected in
the practices of its school sites, including Vineyard High School and implemented in
turn by its teaching staff.
Table 16, shown below, shows us how these practices were perceived by
Vineyard’s teachers. Two of these district-wide practices were found to be most
influential in bringing about the necessary improvement of student achievement in
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math at Vineyard High School; Benchmark assessments and data driven decision-
making in the area of curriculum and instruction.
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Table 16: Summative Survey Results by Percentages for Effective Instructional and
Curriculum Practices and Conditions
Questions 1 2 3 4 5
Non-Math
Teacher
Survey
3% 3% 27% 44% 23% Our school has successfully implemented
common assessments that support increased
student achievement.
Math Teacher
Survey
0% 20% 20% 50% 10%
Non-Math
Teacher
Survey
2% 3% 8% 53% 34% Teachers at our school teach standards-based
instruction.
Math Teacher
Survey
0% 0% 10% 50% 40%
Non-Math
Teacher
Survey
0% 14% 25% 46% 15% Teachers at our school use research-based
instructional strategies to increase student
achievement.
Math Teacher
Survey
0% 10% 30% 40% 20%
Non-Math
Teacher
Survey
10% 15% 19% 39% 17% Periodic benchmark assessments provide useful
data that our teachers use to drive instruction.
Math Teacher
Survey
0% 30% 10% 50% 10%
Instruction of standards-based instruction has
served as an important foundation in improving
student achievement in math.
Math Teacher
Survey
0% 20% 10% 40% 30%
Changes in the curriculum have played a key
role in increasing student achievement in math.
Math Teacher
Survey
10% 0% 20% 70% 0%
Support classes have been included in our master
schedule to improve student achievement in
math.
Math Teacher
Survey
0% 0% 10% 30% 60%
Teachers have helped develop strategies used at
our school to improve instructional practice in
math.
Math Teacher
Survey
0% 10% 20% 50% 20%
Our school has implemented effective
intervention strategies for students having
difficulty in math.
Math Teacher
Survey
0% 10% 40% 50% 0%
Our school has effective strategies to support
students of various learning modalities.
Math Teacher
Survey
10% 0% 30% 60% 0%
(1=Disagree Strongly, 2=Disagree Somewhat, 3=Neutral, 4=Agree Somewhat, 5=strongly Agree)
Benchmark Assessments.
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Benchmark assessments for the subject areas of English and math had been
implemented district wide in Vineyard Union High School District since 2000.
However, according to responses during the interviews, the original math benchmark
exams were not aligned to the sequence of math instruction used in classes. It was
the math department at Vineyard High School which initiated assistance to the
district in its effort to align the benchmark assessments to curriculum, as was
expressed by one of the interview respondents: “Four or five department members,
under the leadership of department chairs, got involved in rewriting benchmark
exams. We took it seriously, with ownership.”
Benchmark assessments helped the departments create a culture of
collaboration and focus on individuals through student performance data. Every
interview participant referred to them as one of the most influential practices. One
interview participant stated, “The first time it was implemented it didn’t work
because it was out of sequence. Once it was sequenced, everyone looked at the
results and the results meant something.” Another interview participant said,
“Benchmark exams help us evaluate curriculum. It helped me understand and
interpret standards objectively.” Another participant noted that, “After implementing
benchmark exams and data review, district wide improvement was prevalent in CST
results, not limited to my school.” According to the survey results seen in Table 15,
67% of non-math teachers and 60% of math teachers agreed that the school had
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successfully implemented common assessment to support increased student
achievement.
Data-Driven Decision Making in Areas of Curriculum and Instruction.
Along with implementation of the improved benchmark exams for student
achievement, the district emphasized the use of student performance data. In order
for school sites to have access to meaningful data on student achievement, the
district made Edusoft software available at each school site through updated
technology and provided Edusoft training for the schools. Due to the upgraded
technology, the results of benchmark exams were available without delay. Immediate
feedback of student performance prompted discussion among teachers in regard to
student performance and instruction as well as curriculum. Teachers used the student
performance data as a reflection tool to revamp their instruction. One interview
participant noted, “Edusoft provides opportunities to see the results right away after
students take benchmark exams. The results clearly show me what part of instruction
went well and did not go too successfully. I know what I need to go over again with
my students. It is like a road map to teaching.” Another participant stated, “Edusoft
enables teachers to provide individual student support to strengthen learning and
instruction. In addition, creating common assessments and uploading them on
Edusoft help teachers create dialogues about teaching and student learning.” Another
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participant shared this: “An availability of student performance data is powerful,
especially benchmark exam data. They were the very first data that were meaningful
to teachers. Teachers compared to each other’s results. They took ownership of their
own students’ performance and reflected on their own instruction.” Table 15 shows
that fifty-six percent of non-math teachers and 60% of math teachers agreed that
periodic benchmark assessments provided useful data that teachers used to design
instruction.
Standards-Based Instruction.
A focus on looking at student achievement data on high stakes exams as well
as benchmarks also helped the math department strengthen its standards-based
instruction. Since Benchmark assessments were based on standards, the results of
student performance data such as CST and CAHSEE showed the strengths and
weaknesses of each teacher’s instruction in addressing individual standards. The data
also indicated department-wide strengths and weaknesses—crucial to their focus on
reinforcing areas that help teachers align instruction to state standards in an effective
way. As one teacher interview participant put it, “When we started working around
student performance data and the blueprints of CAHSEE and CST as well as
benchmark exams, it was easy to understand how to plan instruction based on
standards.” One of the difficulties in delivering standards-based instruction that the
math department had experienced in the past was that students were not placed
properly; the problem was even more severe with incoming freshmen since the only
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tool for placement was teacher recommendation from feeder schools. However, “the
problem was solved,” according to one interview participant, “by the use of multiple
student performance results including placement assessment and CST results as well
as teacher recommendations.” Proper placement at the beginning of the school year
and semester was beneficial for teaching and learning since it minimized any waste
of instructional time.
According to the survey results in Table 15, 87% of non-math teachers and
90% of math teachers agreed that teachers at Vineyard High School implemented
standards-based instruction. In addition, 70% of math teachers agreed that the use of
standards-based instruction had served as an important foundation in improving
student achievement in math.
Curriculum Design.
In November 2003, when the school district was under PI status, they
contracted with the Ventura County Superintendent of Schools Office to conduct an
examination in depth of their schools’ curriculum and instruction in order to help
their under-performing schools improve student achievement and thereby eliminate
the undesirable status. This audit process and its findings apparently helped
Vineyard High School to clearly understand its strengths and weaknesses in
curriculum and instruction and also assisted its teachers learn to work collaboratively
when taking part in school wide efforts to improve instruction. One key leader
interview participant stated, “The curriculum audit played a major role in improving
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curriculum and instruction. The findings of the curriculum audit suggested 12 areas
to work on and four major areas. It was a revelation.” In addition to the heightened
awareness of the need for enhancement of curriculum and instruction, the outcome of
the curriculum audit helped the school site put concerted effort into creating a pacing
calendar in order to align the CAHSEE diagnostic testing, CST math exams,
identified essential standards, and math programs.
One of the major curriculum changes in math was an offering of tri-semester
Algebra coursework designated as Algebra A, B and C. This change was begun four
years ago in order to help students who were not prepared to take Algebra since
Algebra had become necessary to meet high school graduation requirements and pass
the CAHSEE. One key leader interview participant stated, “The tri-semester Algebra
classes offer more structure and more time for concept building, which is beneficial
especially for students who struggle.” Table 15 shows that 70% of math teachers
agreed that changes in the curriculum had played a key role in increasing student
achievement in math and that teachers had helped develop strategies used at their
school to improve instructional practice in math.
In regard to curriculum design, during the interviews with key leaders—
especially department chairs and the assistant principal in charge of instruction and
curriculum—and math teachers, there were two common elements they referred to as
factors that helped students improve their achievement in math: use of the computer
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lab using the New Century Education (NCE) software program and intervention
programs.
Student Learning in Computer Lab Using NCE Software.
At Vineyard High School students who take math classes below Algebra,
including Pre-Algebra, were required to take tutorial math as a support class. During
tutorial classes teachers took students to Math computer lab at least once a week. In
the lab there was a computer technician who assisted students along with the teacher.
There was consensus in the math department interviews among the department chairs
and math teachers that the use of the computer lab, using the NCE software program,
had contributed to the improved student achievement, especially for low achievers.
One key leader interview participant stated, “NCE serves as a tool to provide
an opportunity for individualized learning. It assesses individual student skills and
offers independent lessons that are paced for individual students. Students receive
challenging curriculum at their own pacing as well as individual monitoring.”
Another participant noted, “There are more multi-level students in non-
college prep classes. They don’t have prerequisite skills to be successful in Algebra
class. NCE provides an opportunity to close the gap in essential skills with
individualized learning opportunities.” During observation in the computer lab,
students agreed that they enjoyed coming to the lab to work on their math skills. One
student put it this way: “It helps me. If I don’t get it right, it tells me and shows me
how to get the right answer.” Based on the math teacher survey results in Table 15,
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we find that 90% of math teachers agreed that support classes had been included in
their master schedule to improve student achievement in math.
Interventions: After-School Tutoring, CAHSEE Pullout Sessions.
There was also consensus among math department members that one of the
influential factors that contributed to improved student achievement in math at
Vineyard High School was the after-school tutoring program. When it was
introduced, it was mandatory for students who struggled academically in math and
English and, as a key leader explained, “When after-school tutoring was mandatory,
students took it as negative, punitive action against them.” When it was changed to
voluntary participation, on the other hand, the intervention program worked.
Students volunteered to participate in the program which was well-organized and
well-run as a result of the collaboration between the Special Programs Counselor and
the ELD (English Language Development) Coordinator. Their collaborative work
helped sub-group students, especially English Learner students and students eligible
for services provided by Title I funding. One key leader summed up the change:
“Now it’s open to everyone and it’s voluntary. Students who go, they are motivated
to learn. The after-school intervention program is going very well.”
In addition to the lab, the department also had a Math Resource Person who,
besides being in charge of school-site data, was responsible for providing pullout
sessions for 12
th
graders who did not pass the CAHSEE. This too was seen as an
important factor in improved student achievement. As one key leader noted during
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the interview, “The purpose of the pullout sessions is to identify each student’s
strengths and weaknesses based on their performance data. It’s been very effective.”
Table 15 reveals that 50% of math teachers agreed that their school had
implemented effective intervention strategies for students having difficulty in math
and 60% of them agreed that the school had effective strategies to support students
of various learning modalities.
The data we have discussed here provide some important insights our
research question. In terms of policy initiatives, the state exam, CAHSEE, was seen
as having a powerful motivational effect on student achievement, while the federal
NCLB mandate was perceived as less so, but nevertheless still important. In the area
of classroom practice and curriculum two department changes stood out as most
influential to Vineyard’s success; the use of Benchmark assessments and the addition
of support classes to the math program’s curriculum.
Research Question Three
The third research question asked, “What change process did the school use
to enhance its math program and strategies to assist students in math?” For this
question, the Four Frame Model of Bolman and Deal guided the data collection and
data analysis of the change process at the school site. Key leader interviews
including the principal, assistant principal in charge of curriculum, English and Math
Resource/Data Persons, department chairs, and AVID coordinator along with math
teacher interviews based on Bolman and Deal’s four Frames offered important data
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for understanding the change process that took place at Vineyard High School in
order for the school to show improved student achievement in math. In addition, the
Non-Math Teacher Survey and the Math Teacher Survey provided quantitative data
in relation to the third research question.
Background Information
Vineyard High School was the first school built in the district and many of its
alumni had become leaders in the community. The average years of service among
the teachers at the school was 15.3 years and 12.3 years with the district. One key
leader shared, “This school has gone through the most political events in the district.
It has had the most number of principals. The faculty has a reputation for being
difficult and tough, especially for principals. I have been here in this school for
fourteen years. The faculty got rid of some principals. They made it clear when they
do not want certain principals.”
When the principal was assigned to Vineyard High school in 2002, his first
principalship, the school was already categorized as an under-performing school,
having been designated as a Program Improvement (PI) school in 2000-2001. During
the interview, the principal stated, “The PI status of the school made me rethink what
should take place. I needed all the input I could get from everyone and started
looking at student achievement data.” As previously described, the school did not
meet its API goals for two years (2001-2003) and had received a “Year 2 PI” status
as a result. Over the next two years however, it met its annual API goals and was
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able to finally shed its PI status. In order for the school to have met that challenge,
many changes had to take place.
During the key leader and teacher interviews, every participant pointed to the
principal as one of the main contributors to improved student achievement at
Vineyard High School. There was a consensus that it was the principal who made
this happen: he brought the staff together, made them feel like the best team, and
supported teachers and motivated them. One teacher participant said, “The principal
was a direct contributor to improved student achievement. He directly impacted
things.” Another teacher stated, “The principal communicated, in a positive way, the
need to move out of PI status. He created a sense of “home” or “family” and used
those words all the time in his communication. I want to do it for him.” In addition to
the interview findings, the math teacher survey results also supported the principal’s
significant contribution to the improvement of student achievement in math. Table
17, shown below, summarizes the results of this survey and in this case reveals that
80% of math teachers agreed that the principal had served as a “change agent” for
improved student achievement in math.
Table 17: Summative Survey Results by Percentages for the Change Process
Questions 1 2 3 4 5
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.
Non-Math
Teacher
Survey
7% 12% 20% 42% 19%
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In an effort to improve instruction on our
campus, our school has focused on personnel
issues including quality teachers and
fostering a positive working environment
amongst peers on campus.
Non-Math
Teacher
Survey
14% 20% 17% 32% 17%
In an effort to improve instruction on our
campus, our school has focused on
overcoming political obstacles and gaining
necessary support to move the school
forward.
Non-Math
Teacher
Survey
17% 15% 22% 37% 8%
In an effort to improve instruction on our
campus, our school has focused on
motivating students and staff as well as
celebrating successes.
Non-Math
Teacher
Survey
7% 20% 20% 36% 17%
Our school has added the use of math
coaches or experts to assist in the effort to
improve student achievement in math.
Math
Teacher
Survey
30% 20% 40% 10% 0%
The principal has served as a “change agent”
for improved student achievement in math.
Math
Teacher
Survey
10% 10% 0% 50% 30%
Student achievement in math was made a
priority as the school allocated its financial
resources.
Math
Teacher
Survey
0% 10% 50% 40% 0%
Teacher assignments in the math department
are made strategically and with student need
in mind.
Math
Teacher
Survey
10% 0% 50% 40% 0%
Non-Math
Teacher
Survey
17% 27% 20% 24% 12% The master schedule at our school is built
based on student need.
Math
Teacher
Survey
0% 20% 10% 60% 10%
1=Disagree Strongly, 2=Disagree Somewhat, 3=Neutral, 4=Agree Somewhat, 5=Strongly Agree
According to the original research design, the collected data related to the
change process, which the principal brought about and which the school went
through to achieve improvement of student achievement in math, were examined
through four lenses. The non-math teacher survey responses in Table 17 showed the
following results: 1) 61% of teachers agreed that the school had focused on ensuring
that structures and policies that supported student achievement were in place, 2) 59%
of them agreed that the school had focused on personnel issues including quality
teachers and fostering a positive working environment, 3) 45% of them agreed that
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the school focused on overcoming political challenges and gaining necessary support
to move the school forward, and 4) 53% of them agreed that the school had focused
on motivating students and staff as well as celebrating successes. Beyond these
results, the interviews provided further informative data in regard to the change
process that took place at Vineyard High School.
Structural Frame
NCLB & CAHSEE.
The 2001 NCLB Act and the CAHSEE requirement for a high school
diploma were prominent structural elements influencing the school’s efforts to
improve student achievement at Vineyard High School. Under the 2001 NCLB Act,
the Year 2 PI status imposed a great deal of pressure, not the least of which was the
threat of sanctions and punitive consequences, including the possibility of the
principal being removed, relocation of the faculty, and a state take-over. One
interview participant remembered, “The principal said at the faculty meeting and
rallies that he wanted to stay at this school for a long time but he could be removed if
we did not make the API goal again. Students love him. They did not want him to
leave. Teachers also did not want to lose the principal. We wanted to do it for him.”
The immediacy and urgency of the NCLB Act provided opportunities for the
principal to make tough changes, including reassigning teachers and requiring them
to work collaboratively to accomplish their shared goal. One teacher interview
participant stated, “NCLB helped to get dialogues going and open eyes to problems
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that our school was having. Before NCLB, with doors closed, we did our thing.
After NCLB we started having dialogues about test scores and standards. For the
first time we evaluated results.”
The influence of the CAHSEE was also significant and, as shown previously
in the discussion of the second research question, it many instances it was actually
perceived as most influential. One key leader interview participant stated, “CAHSEE
is the biggest influence on student achievement. It affected school wide attitudes
about testing. It helped teachers identify and work on each type of questions students
were having trouble with.” Another key leader interview participant stated,
“CAHSEE influenced student achievement in math. It matters to students, while CST
has no buy-in from students.”
Alignment of Board, District and School Priorities.
Another influential factor revealed in the data was the alignment of priorities
among the school board, district, and school sites, which promoted shared goals and
focus. The principal stated, “Every year the district shares annual goals and focuses
on human resources, facilities and curriculum. A partnership has been established by
aligning board priorities, district priorities, and school priorities.”
Edusoft: Access to Technology and Student Performance Data.
Another important structural characteristic that was seen as a contributor to
improved student achievement in math was being equipped with Edusoft, an upgrade
in technology which provided quick, easy access to student performance data. One
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teacher interview participant stated, “We had ‘SAT-CHAT.’ While students were
working alone, teachers spent time with individual student to go over CST results
using Edusoft. I think it was very helpful. Students saw that teachers cared, so they
cared about CST’s.”
Each teacher’s access to Edusoft also helped the math department in creating
a new culture. Benchmark exam results were available on Edusoft right after
administering the test. It provided an opportunity for teachers to view their students’
results and reflect on their own teaching. As a group, they soon began to discuss and
compare student performance results, curriculum, essential standards, and
instructional plans and activities. One teacher interview participant shared, “An
availability of student performance data is powerful, especially benchmark exam
data. They were the very first data that were meaningful to teachers. Teachers
compared their own to other’s results. They took ownership of their own students’
performance and reflected on their own instruction.”
Physical Layout of Campus.
Seen through Bolman and Deal’s structural frame, the most simple and
physically evident characteristic of the school is the layout of the campus. The
numerous buildings on the school’s beautiful new campus were, for the most part,
assigned according to subject matter. Building F was allocated to the Math
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department. All math teachers were located in the building except for three who, as
a result of increased student enrollment, had been assigned to portable buildings.
The Math Computer Lab was also located in Building F. Math teachers felt that easy
access to the lab was important. One interview participant’s remarks underlined this:
“I moved to a classroom I did not want. However, for students, I moved in order to
be near the lab.”
Human Resources Frame
The principal at Vineyard High School was proficient in utilizing the
characteristics of Bolman and Deal’s human resources frame to make the best use of
his own leadership and human resources in order to improve student achievement in
math.
Principal’s Leadership.
The leadership style of the principal was regarded highly by staff, as
evidenced in interviews. Some of the common descriptors that interviewees chose to
describe him were “inspiring,” “motivating,” “fair,” “open-minded,” “supportive,”
and “empowering.” One participant stated, “He always tells us we are the best. When
we did not meet our API goals, he said we could do better because we were the best
team. He made us feel that we could do it. I think it really helped. It is so powerful.
So now I do the same thing to my students, telling them they are the best, so they can
do it.”
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Respect toward the principal was evident. In their responses, many of the
interview participants expressed the idea that they did not want to let him down:
“He’s been there for us. Now we want to be there for him,” “We want to do it for
him.” The principal himself stated, “I want to be seen as a democratic leader, not as
autocrat.” One key leader interview participant stated, “He brought changes. He is
very supportive. These days, principals need to know what’s going on in every
department. He knows, and lets people know that he’s not the expert. He makes it
clear that he wants to get involved and know what’s going on. We know that ideas or
information he gets from staff is important to him. I have known the principal for
many years. I have worked with many principals. I think his approach is very
effective and empowering.”
Teaching Assignments and Master Schedule.
In addition to his inspiring interpersonal leadership style, the principal was
regarded as a leader who was willing to do what was necessary. Teaching
assignments was an example of this. Two years ago, the principal saw a need for
improving teaching assignment practices so that he could make sure that the best
teachers teach the neediest students. One interview participant stated, “The principal
and department chairperson came to the math department and said, ‘Let’s do what’s
right for students.’” One teacher participant stated, “With the principal’s leadership
and department chairpersons using their leadership, we try to place the best teachers
with the most needy students. The math department is on its way. But not there yet.”
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As a result, according to interview results, one significant change was that every
teacher in the math department teacher teaches at least one standard level class. One
key leader interview participant stated, “All college prep or honors teachers now
teach standard level classes as well; in the past, Vineyard High School had a
reputation for teachers teaching only certain subjects and levels.” According to the
survey results from Table 16, 40% of math teachers agreed that teacher assignments
in the math department were made strategically and with students in mind while 50%
of them took the “neutral” position.
In addition to teaching assignments, another key area in which the principal
was involved was the school’s master schedule. The principal explained, “The math
department focuses on Pre-Algebra and Algebra classes. The support class, tutorial
class, is for students who need extra help.” Table 16 reveals that while only 36% of
non-math teachers agreed that the master schedule was built based on student need,
70% of math teachers agreed it was.
Math Resource/Data person.
Another important element for the change process according to the human
resources frame was found in the positions of the Math and English Resource
Persons who were in charge of collection, analysis, and dissemination of student
performance data. This year was the second year with the specially assigned
position. One teacher participant stated, “Having a resource person made department
meetings more informative and helped us produce products together based on data.”
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During interviews, the math resource person was regarded as one of the leaders in
the department. One teacher interview participant stated, “The resource/data person
definitely has leadership. He goes to district meetings, receives information
regarding testing, runs pullout sessions for seniors who have not passed the
CAHSEE, and helps teachers with resources.”
Highly Qualified Teachers (HQT): Veteran Teachers and Strategic New
Teacher Selection Process.
Vineyard High School has a total of 19 teachers in its Math Department: 17
are veteran teachers and two are new. According to the retired department chair, all
veteran teachers were well trained in both the College Preparatory Math (CPM) and
Interactive Math Programs (IMP) curriculums. There was a consensus among the
participants that the district had taken a proactive approach to securing highly
qualified teachers since 2002. In early March a career fair was held to offer contracts
to applicants for teaching positions for the following school year. The top priority
was to secure teachers or teacher candidates who met the HQT criteria and did well
on interview sessions with school site administrators in the subject areas of math,
science, and special education. The principal stated, “The district effort has been
immense. The annual career fair is a careful selection process. And as a principal, I
put in place a new teacher selection process at the school site involving department
chairs and assistant principals.” One key leader stated, “I find these days that new
teachers are better prepared and come on board with more qualifications, such as a
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master’s degree. They have already received training in standards-based instruction.
The whole standards movement has really impacted teacher preparation.” According
to NCLB Teachers and Paraprofessionals Data 2005 from the California Department
of Education, 405 classes were identified as NCLB core classes and 389 classes,
96% of them, qualified as NCLB compliant classes. In addition, 100% of 18
paraprofessionals were qualified as NCLB compliant.
Political Frame
Interview participants also agreed that there was a major difference between
the previous administration and the current one. The perceived differences in the
changes brought about by the new administration were regarded as beneficial for the
school and as a contributor to improved student achievement. One teacher participant
described the old school culture in his response: “With the previous administration, it
used to be us against them. There was no teacher buy-in.” As previously quoted, the
principal stated during an interview that the school’s PI status had led him to
“rethink what should take place.” He sought out input from everyone and looked
carefully at student achievement data. He also made his open door policy known to
everyone and listened to what everyone had to say and went so far as to establish a
Principal Concerns Committee to provide a channel for open communication with
everyone on campus. One key leader participant stated, “The principal allows
teachers to be leaders. He never talks down. He empowers teacher leaders.” In
addition to open communication and empowering teacher leaders, he also was
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diligent about bringing up new leaders on campus and was perceived as good at
finding the right people to create a school culture centered on students. One teacher
participant put it this way: “He did a good job of bringing in new blood as a leader
who is a strong student advocate.” Another teacher participant stated, “Some key
leaders left, but new people stepped up. Establishing leadership with a mix of new
and veteran teachers is a good idea. Mixing experience and expertise helps in
building a strong team.”
In addition to establishing a system to hear out what people have to say and a
leadership team combining veteran and new teachers, the principal also had to
construct strategies to overcome other political challenges in order to improve
student achievement. Two examples were master scheduling and teaching
assignment. The principal made some significant changes over the years to meet
student needs. One teacher participant noted, “He overcame reticence bit by bit.
Then he started getting more involved with and controlled the master schedule. I
think school leaders need to own the master schedule. If it’s put together for the
students, it works out.” The principal also involved himself with teaching
assignments so that best teachers could teach the neediest students. One key leader
participant stated, “It can be like opening a can of worms for principals to make
changes with teaching assignment.” One teacher stated, “The principal got more
involved with teaching assignment. He looks at teachers’ strengths, skills, and
abilities and then matched them to student needs. He simply says that students who
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need extra support need to be taught by the best teachers.” When the principal was
asked what the major challenge was and how he overcame the challenge, he replied,
“It was the most challenging when I had to establish working relationship with
teachers who had not been “on board.” I went to those teachers and asked for their
help. I told them that I did not have answers but I wanted them to be part of the
process.” In spite of the potential for a political uproar over his initiatives in these
sensitive areas, the principal was able to bring about major changes in both the
master schedule and teaching assignments by earning trust and respect from his staff
through a leadership style that invited everyone to participate as part of a team to
solve problems.
Symbolic Frame
During interviews, there was evidence provided through interviews that the
principal served as a “change-agent,” who changed the school culture from “us vs.
them” to “we” and “family.” He fostered a learning environment which centered on
and valued students. These perceptions were also evidenced in the math teacher
survey results. Table 16 shows that 70% of them agreed that the master schedule at
the school is built based on student need while 80% of them agreed that the principal
served as a “change agent” for improved student achievement in math.
In addition to the principal’s contributions to creating a positive school
culture, there had also been a variety of student activities that increasingly placed
high value on academic achievement. These activities were planned by the
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Associated Student Body (ASB) under the direction of its Activity Director. One
teacher participant stated, “ASB really got involved. They talked to students,
stressing the importance of improving scores and school pride. They also offered
prizes and raffle tickets for students who participated in testing. Students responded
positively to these activities.” Another participant mentioned that there were school-
wide awards and ceremonies such as “Night under the STARs” and the school’s
“Renaissance” program. One key leader participant remarked, “Academic success
and learning are celebrated at the Back to School Night events. Without emphasis on
learning and academic success, we cannot sustain what we are doing.”
In summary, the change process that Vineyard’s faculty found most relevant
to its success was not really a particular process but the leadership of the principal.
There was a consensus that it was the principal who made everything happen. He
brought the staff together, made them feel like the best team, and motivated and
supported his teachers.
Research Question Four
The fourth research question asked, “To what extent was strong instructional
leadership important in a) the math programs/strategies and b) math achievement
among students?” For this question, the data collection and analysis on the
importance of strong instructional leadership were guided by the Conceptual
Framework of Instructional Leadership. Along with math teacher interviews, key
leader interviews with the principal, the assistant principal in charge of curriculum,
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math department chairs, and the Resource/Data persons, provided the primary data
for the fourth research question. The Non-Math Teacher and Math Teacher Surveys
also offered quantitative data to support the interview data.
Shared Instructional Leadership
Based primarily on the data collected through interviews, it was quite evident
that instructional Leadership at Vineyard High School was shared among the
principal, math department chairpersons, and the Resource/Data person. The
principal took an active role as the site leader in creating a school culture which
focused on student achievement. On the other hand, he valued and relied on the
leadership of the math department chairpersons in helping students improve their
achievement in math. When the principal was asked who would be considered as
instructional leaders for the math department, he included the retired department
chairperson, one of the current department co-chairpersons, and the resource/data
person. The same responses were received throughout the interviews; 100% of
interview respondents referred to these same individuals as leaders of the
department, especially the retired department chairperson and one of the current
department chairs. The principal stated, “Their work is invaluable. They created the
tutorial program and reorganized math programs to meet student needs. Because of
their work, students are more properly placed in math classes and do better. They are
real leaders.” During teacher interviews, one participant stated, “Department chairs
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are very positive and influential figures. The resource/data person will also make a
positive impact in the future. It can only help.”
Components of Shared Leadership
In regard to the various components of shared instructional leadership, it was
evident on the basis of an analysis of the data collected in this study using the five
components of the Conceptual Framework of Instructional Leadership that four of
the five components of the framework were considered as key contributors to
improved student achievement in math at Vineyard High School: A clear vision for
learning, the supervision and monitoring of instruction, a positive school culture of
learning and teaching, and data driven decision making. The Community/Political
component did not emerge here as significant as it did in the previous discussion of
Research Question Three.
Vision for Learning.
At Vineyard High School, there was a clear vision for improved student
achievement. The principal developed the vision for the school with school
stakeholders and clearly communicated it to his staff. When the school was a PI
school, exiting the PI status was a school wide, strongly shared vision. This can be
seen below in Table 18 where in the non-teacher survey responses we find that 63%
of respondents agreed that the school had a clear vision for increased student
achievement. Similarly, according to the math teacher survey results, 60% agreed
that district personnel, school site leaders, and teachers shared a vision for increased
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math achievement. The principal was committed to placing the school’s first priority
on improvement of student achievement.
Table 18: Summative Teacher Survey Results for the Vision for Learning
Component of Instructional Leadership
Questions* 1 2 3 4 5
There is a shared vision for increased
student achievement at our school.
Non-
Math
Teacher
Survey
3% 15% 19% 44% 19%
Our school had a clear strategic plan
to improve student achievement.
Non-
Math
Teacher
Survey
5% 17% 24% 37% 17%
The district personnel, school leaders
and teachers all have a shared vision
for increased math achievement.
Math
Teacher
Survey
10% 20% 10% 50% 10%
The math achievement goals and
measures for my school were clearly
articulated and easy to understand.
Math
Teacher
Survey
0% 10% 30% 40% 20%
The school leader is aware of the
mathematics instruction and
academic progress of the students in
my class.
Math
Teacher
Survey
0% 10% 40% 50% 0%
My district and school leaders seem
knowledgeable about instructionally
effective math practices and
assessment strategies.
Math
Teacher
Survey
0% 20% 20% 50% 10%
*1=Disagree Strongly, 2=Disagree Somewhat, 3=Neutral, 4=Agree Somewhat, 5=Strongly
Agree
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In addition to the principal’s instructional leadership and the shared vision for
the school, it was clear from the interviews that the math department had its own
strong leadership and vision to promote improvement of student achievement.
During the key leader and teacher interviews, it was evident that instructional
leadership was provided from department chairpersons and the Resource/Data
person, especially the former department chairperson and one of the current
department chairpersons. One key leader interview participant, referring to the
department’s efforts to team teachers who taught the same classes, stated that “Due
to [the department leaders’] leadership, the math department is the first department
working on ‘job-alikes.’” Another teacher participant stated, “She (the retired
department chairperson) was involved with everything. She was part of the school
leadership team. She had a big picture and a vision for the department and she also
had answers.” Another participant mentioned, “She [referring to the old department
chairperson] is the one who brought up student achievement. She was very
influential school wide, not just in the math department. She had long and deep
relationships with the district and the school board.” One of the current department
chairpersons was also referred to by interview participants for his expertise and
resourcefulness. One teacher participant stated, “Everyone goes to him to seek help
in regard to instruction and situations. He is amazing.” Another participant stated,
“He and the old department chairperson are the major change-agents for our
department.” When the current department chairperson was asked about instructional
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leadership in the department, he too noted the previous chairperson’s valuable work,
but then added, “Instructional leadership in our department is really distributed
among the department members.”
It was also evident from the teacher survey results that there were clear and
comprehensible math achievement goals and measures at Vineyard High School and
that the school’s primary leader was aware of the mathematics instruction and
academic progress of the students in each teacher’s class. Table 18 bears these
perceptions out, indicating only 10% of teachers in disagreement with the prevailing
views.
Supervision and Monitoring of Instruction.
According to the Conceptual framework of Instructional Leadership, the
supervision and monitoring of instruction component had four key areas: 1) regular
classroom observation, 2) allocation of resources such as time, peer support,
materials, and professional development, 3) supervision of personnel and 4) hiring of
personnel supporting the learning goals and vision of the school. Based for the most
part on interview data, the second of these key areas, the allocation of resources,
especially in the area of professional development, was the most influential
contributor to improved student achievement in math at Vineyard High School.
Classroom visitation was seen as the second most influential contributor.
With its shared vision and goals for student achievement in mind, the math
department had a clear need for professional development that allowed them to
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collaboratively work on student performance data, curriculum, and instruction; the
principal took an active role in providing the necessary support to promote this type
of staff development in order to bring about improved student achievement in math.
The principal stated, “I put aside money for professional development. I send them
throughout the state and sometimes out of state, too, if necessary.” The assistant
principal in charge of curriculum added, “The school’s single plan helps us focus on
those student sub groups who need additional support. We allocate resources
following the school’s Single Plan, which strongly supports professional
development for student learning such as ELD (English Language Development),
SDAIE (Specially Designed academic Instruction in English), resource teams,
instructional strategies, and student performance data analysis. We also support
attending conferences as teams. Now we make a yearly plan for professional
development. The district is very supportive of professional development as well.”
Data from the teacher surveys also supported these views; not a single response on
the math teacher responses, seen in Table 19 below, disagreed that the school leader
provided opportunities for faculty members to discuss mathematics instruction.
Table 19: Summative Survey Results for the Supervision and Monitoring of Instruction Component of
Instructional Leadership
Questions* 1 2 3 4 5
School achievement is a priority when
the school allocates its financial
resources.
Non-Math
Teacher
Survey
7% 20% 25% 27% 21%
The principal works hard to monitor and
supervise instruction in the classroom.
Non-Math
Teacher
Survey
8% 20% 20% 26% 26%
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I have gained valuable resources from
math coaches/instructional leaders that
have improved the quality of my math
instruction.
Math
Teacher
Survey
70% 10% 10% 0% 10%
I have regular support from proven
instructional leaders in math instruction.
Math
Teacher
Survey
10% 30% 20% 40% 0%
My school’s instructional leader
provides professional development
resources that I use in my mathematics
instruction.
Math Teacher
Survey
30% 10% 30% 30% 0%
The school leader provides opportunities
for faculty members to discuss
mathematics instruction.
Math Teacher
Survey
0% 0% 40% 50% 10%
*1=Disagree Strongly, 2=Disagree Somewhat, 3=Neutral, 4=Agree Somewhat, 5=Strongly Agree
With financial support, the math department was able to collaborate on
curriculum and instruction throughout the school year, including over the summer
and during after-school hours throughout the school year. In the course of the
interviews, department chairpersons and teachers stated that summer training and
after-school training were very valuable. One department chairperson stated, “We
have on-going professional development and it is a tremendous and consistent
support and force for us.” It was evident during the interviews with key leaders and
teachers that due to the school’s support for professional development all math
teachers were able to attend IMP (Interactive Mathematics Program) and CPM
(College Preparatory Mathematics) training before they started teaching class.
Another type of professional development taking place within the math
department was the implementation of “data gathering walk-throughs,” which was
recommended by the curriculum audit team from the Ventura County office in 2003.
The math department was the first department to put it into practice and most of the
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math department members voluntarily participated. Utilizing Marzano’s “higher
thinking” guide, in small teams the teachers did ten minute walk-throughs, visiting
four classrooms during their conference period. Using Marzano’s guide, they
observed a class, took notes of what they saw on a card and left the note with the
teacher being observed. After visitation, visiting teachers compared their
observations with each other. One teacher participant stated, “The important thing to
remember is that it’s not for evaluation; the first time it was strange, and a bit
uncomfortable.”
There was consensus among the interview participants that the pressure from
outside, especially NCLB, as a result of the PI status, helped promote dialogue
among the department members about student learning and motivated them to work
collaboratively. It was routine for them to examine the student performance data and
discuss the data, standards, instructional goals and activities, and common
assessments. Their discussions were centered on student achievement, teaching, and
learning. One teacher participant summed it up by noting, “NCLB helped us have
dialogues on student achievement. We had to work together. I think changes have
been made, especially in instruction that resulted in student achievement.”
Culture of Teaching and Learning
With their clearly shared vision and goals in mind, Vineyard High School
cultivated a school culture that valued teaching and learning. Both staff and students
were highly valued, and their successes were celebrated and recognized at school
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functions. According to Table 20 below, 66% of the non-math teacher respondents
agreed with the view that students and staff at Vineyard High School were valued
and their successes were celebrated. The principal was perceived as the person who
had created this nurturing school culture. As one participant had observed, “[The
principal] made us feel that we could do it. I think it really helped. It is so powerful.”
The principal fostered a learning environment where student achievement was
valued and centered. These perceptions were also evident in the survey results of the
math teachers. As shown in Table 20, 70% of them agreed that the master schedule
at their school is built based on student need and 80% of them agreed that the
principal served as a “change agent” for improved student achievement in math. Also
shown in Table 20, the school principal was perceived as an instructional leader who
encouraged staff to get involved in dialogues about instruction (“discuss effective
math instructional strategies”).
Table 20: Summative Survey Results for the Culture of Teaching and
Learning Component of Instructional Leadership
Questions* 1 2 3 4 5
Students and staff are valued and
their successes are celebrated.
Non-
Math
Teacher
Survey
3% 8% 22% 42% 24%
The school leadership works to
establish and maintain a respect for
cultural diversity.
Non-
Math
Teacher
Survey
12% 22% 15% 36% 15%
The school instructional leader
encourages faculty members to
discuss effective math instructional
Math
Teacher
Survey
0% 0% 40% 50% 10%
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strategies.
My school’s math instructional
practices are developed from
evidence-based strategies.
Math
Teacher
Survey
0% 0% 50% 20% 30%
The principal has served as a
“change agent” for improved student
achievement in math.
Math
Teacher
Survey
10% 10% 0% 50% 30%
Non-
Math
Teacher
Survey
17% 27% 20% 24% 12% The master schedule at our school is
built based on student need.
Math
Teacher
Survey
0% 20% 10% 60% 10%
*1=Disagree Strongly, 2=Disagree Somewhat, 3=Neutral, 4=Agree Somewhat, 5=Strongly
Agree
Data-Driven Decision Making
For the math department at Vineyard High School, many changes had
occurred in curriculum and instruction as a result of student performance data
analysis; the school single plan itself was designed based on student needs as
revealed by student achievement data. Such emphasis on student data arose at the
district level. While this was discussed previously under Research Question Two, it
is worth reviewing some of that discussion here to recall its importance to the
faculty, this time in the context of instructional leadership. In the prior discussion we
pointed out that the district had made Edusoft software available at each school site
through updated technology and training in order for school sites to have access to
meaningful data regarding student achievement. The availability of student
achievement data through the upgraded technology helped the math department
169
members to work as a team to improve teaching so that they could improve student
achievement. One participant noted that “Edusoft enables teachers to provide
individual student support to strengthen learning and instruction” as well as “creating
common assessments and...dialogues about teaching and student learning.” Another
participant remarked that “An availability of student performance data is
powerful…[and very] meaningful to teachers…They took ownership of their own
students’ performance and reflected on their own instruction.”
The principal made sure that he had a sound understanding of student
performance trends by working closely with the school’s data team, which consisted
of 18 certificated and classified staff members. He also made important decisions for
the school based on what was revealed in student performance data. As evidenced
below in Table 21, while respondents were divided on the relevance of student data
to professional development offerings, a substantial number of them (68% of non-
math teachers) agreed “somewhat” or “strongly” on the survey that the school
leaders used data-driven information to address problems or issues related to student
achievement.
Table 21: Summative Survey Results by Percentages for the Data Driven
Decision Making Component of Instructional Leadership
Questions* 1 2 3 4 5
Professional development offerings
at our site are based on student
achievement data.
Non-
Math
Teacher
Survey
10% 20% 22% 32% 14%
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The school leaders used data-driven
information to address
problems/issues related to student
achievement.
Non-
Math
Teacher
Survey
10% 7% 15% 54% 14%
*1=Disagree Strongly, 2=Disagree Somewhat, 3=Neutral, 4=Agree Somewhat, 5=Strongly
Agree
In summary then, although data show the key leadership contributors to
improved student achievement in math at Vineyard High School to be a clear vision
for learning, meaningful professional development, a positive school culture of
learning and teaching, and data driven decision making, it was also recognized by the
faculty that the underlying and most significant ingredient was the culture of
collaboration that had been created. Shared leadership was the real key.
Research Question Five
The fifth research question asked, “How did instructional leaders respond in
academic areas in which they were not experts?” For this question, while the data
collection and analysis were based on the Framework of Instructional Leadership,
the researcher focused on how leaders created effective reform and maintained
resulting changes and policies when they did not possess content knowledge in the
subject matter. In addition, the researcher examined an array of strategies that were
implemented at the school site by the principal in order to ameliorate any
instructional deficits due to deficiencies in teacher subject matter competency. Along
with math teacher interviews, key leader interviews including the principal, the
assistant principal in charge of curriculum, math department chairs and
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Resource/Data persons, provided primary data for this research question. The Non-
Math Teacher and Math Teacher Surveys provided further quantitative data
There were 12 coping strategies that were identified by the cohort team as
essential strategies that instructional leaders would apply when they do not possess
expertise in a subject matter which they supervise. Based on the interviews and
surveys, there was evidence that the following four of the twelve identified
strategies—Emphasis of High Expectations, Emphasis of Quality Instruction,
Empowerment of Department Chairpersons and Quality Interventions—were
effectively put into use by the principal at Vineyard High School in order to bring
about the improved student achievement in math.
Emphasis of High Expectations
The principal of Vineyard High School emphasized having high expectations
for student achievement. He also made it clear that he had high expectations for his
staff; the goal of the school had now moved beyond merely meeting API goals and
removing the PI status. Through an expansion of the AVID (Advancement Via
Individual Determination) program on campus, the school had doubled up the
numbers of AP classes being offered on campus. According to the principal,
Vineyard High School had the highest number of AP (Advanced Placement) classes
in the district.
During interviews with key leaders and teachers, the respondents pointed to
the emphasis on high expectations as the most distinct style and most effective
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strategy of their principal that helped students improve their achievement. One of the
key leaders stated, “He is a great motivator. He directly impacted student
achievement. He always says to staff and students that we are the best. He also says
that Vineyard High School is going to be an 800 school on the API. He has changed
the way we do business to get our goals achieved.” Another respondent stated,
“Now our school is college and career centered, instead of being career centered
only. For the past two years, we have almost doubled the sections of AP classes. This
is a major change and the principal has to be given the credit for it. He has high
expectations for students and tells us to have higher expectation for our students.”
When the principal was invited to share an example of his emphasis on high
expectation for student achievement, he responded, “I always ask the faculty and
department chairs to have high expectations for their students as well as themselves.
I think I was able to help students and staff understand the importance of having high
expectations.”
According to the survey results exhibited in Table 22 below, 80% of non-
math teachers and 70% of math teachers were in agreement that site leaders
emphasized the importance of having high expectations for student achievement.
There was no disagreement on this view from math teacher respondents and only
10% disagreement from non-math teacher respondents.
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Table 22: Summative Survey Results by Percentages for School Leaders’ Coping Strategies
Questions 1 2 3 4 5
The principal makes effective use of the
department chairs and relies on their
expertise when making important
curricular decisions.
Non-Math
Teacher
Survey
14% 8% 20% 38% 20%
The Math Department Chair has been
entrusted with and is empowered to
make important curricular decisions.
Math
Teacher
Survey
0% 20% 20% 50% 10%
Non-Math
Teacher
Survey
8% 22% 31% 29% 10% Outside experts have been used to
promote greater capacity in the area of
instruction.
Math
Teacher
Survey
20% 30% 30% 20% 0%
The principal has delegated some
curricular authority to an assistant
principal with greater expertise in
curriculum and instruction.
Non-Math
Teacher
Survey
8% 12% 32% 28% 20%
Site leadership fosters a culture of
inquiry and collaborative problem
solving.
Non-Math
Teacher
Survey
14% 19% 27% 25% 15%
Non-Math
Teacher
Survey
10% 7% 10% 42% 31% The school’s leaders emphasize the
importance of quality instruction as a
primary mission of the school.
Math
Teacher
Survey
0% 10% 10% 30% 50%
Non-Math
Teacher
Survey
5% 5% 10% 49% 31% Site leaders emphasize having high
expectations for student achievement.
Math
Teacher
Survey
0% 0% 30% 20% 50%
Non-Math
Teacher
Survey
14% 24% 29% 25% 8% Professional development in math has
been a key tool used by site leaders in
our effort to improve instruction on our
campus. Math
Teacher
Survey
20% 10% 30% 30% 10%
Non-Math
Teacher
Survey
7% 12% 25% 49% 7% Quality interventions have been
implemented on our site to help students
at risk of failing academically.
Math
Teacher
Survey
0% 10% 40% 40% 10%
Our site leaders emphasize a culture of
collaboration as a means of improving
instruction at our site.
Math
Teacher
Survey
0% 20% 40% 30% 10%
Teacher assignments in the math
department are made strategically and
Non-Math
Survey
22% 19% 20% 29% 10%
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with student need in mind. Math
Survey
10% 0% 50% 40% 0%
*1=Disagree Strongly, 2=Disagree Somewhat, 3=Neutral, 4=Agree Somewhat, 5=strongly Agree)
Emphasis of Quality Instruction
It was evident that the principal’s emphasis on high expectations for student
achievement was directly connected with an emphasis on quality instruction. In order
for teachers to help students improve academic achievement in their class, their
instruction had to be effective. There was consensus among the interview
respondents that high expectations for student achievement naturally called for
quality instruction. The principal stated, “Students do not have the right to fail so we
need to create the right environment for teachers and their outstanding performance
as instructors.” One teacher participant stated, “High expectations and quality
instruction go hand in hand. High expectations wouldn’t do anything unless quality
instruction is provided.” Indeed, the survey results regarding the high expectation
strategy and the quality instruction strategy showed similar responses. We see in
Table 21 that in line with the data that showed 80% of non-math teachers and 70% of
math teachers being in agreement that site leaders emphasized having high
expectations for student achievement, 73% of non-math teachers and 80% of math
teachers agreed that the school’s leaders emphasized the importance of quality
instruction as a primary mission of the school.
Empowerment of Department Chairpersons
175
It was clear from the data that the math department chairpersons felt they
were empowered by their principal. In particular, they felt they were much more
involved with the teacher selection process for new hires than ever, with the final
decision for teacher selection left to the department chairperson. As well, in the
process of building a master schedule they felt that the principal and the assistant
principal in charge of curriculum worked collaboratively with them. The principal
created a school culture of trust and collaboration and then he let the people with
expertise do what needed to be done. One department chairperson stated, “The
principal allows teachers to be leaders. He empowers teacher leaders.” Another
department chairperson stated, “Once the key concept is understood, he lets people
perform. There is no micro-management.” One department chairperson described the
master schedule building process as “an honest, open approach, emphasizing
working together.” The math chairpersons also agreed that they were entrusted to
make curricular decisions for the math department. Again, as shown in Table 21, the
survey results revealed similar results between non-math teachers and math teacher
respondents in regard to the strategy of empowerment of the department
chairpersons: 58% of non-math teachers and 60% of math teachers agreed that the
principal made effective use of department chairs and relied on their expertise.
Quality Interventions
Based on the interview and survey results, it was evident that the school
implemented quality interventions to help students at risk of failing academically.
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First, juniors and seniors who did not pass the CAHSEE were monitored by the
school data team and offered pull-out sessions to provide individual monitoring and
instructional support. After-school tutoring was also perceived as an effective
intervention. Students voluntarily participated in the program which was a well-
organized collaboration between the Special Programs Counselor and the ELD
(English Language Development) Coordinator. Their work helped sub-group
students, especially English Learner students and students eligible for services under
Title I funding. One key leader stated, “Now it’s open to everyone and it’s voluntary.
Students who go, they are motivated to learn. The after-school intervention program
is going very well.”
The survey results seen in Table 21 revealed that only 19% of non-math
teachers and a still smaller 10% of math teachers disagreed that quality interventions
had been implemented on their site to help students at risk of failing academically.
In summary then, four strategies seemed to emerge as the answer to the
question of how leaders can bring about improved student achievement in math
despite unfamiliarity with the subject area: These were high expectations, emphasis
on quality instruction, empowerment of department chairpersons and quality
interventions. The instructional staff seemed to understand that the use of these
tactics by the leaders did not rely on math knowledge but instead, empowered those
who did have the subject expertise to affect the desired changes in the students.
Analysis and Discussion
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Analysis of the data obtained through interviews and surveys at Vineyard High
School, along with objective school, community, student and personnel data
collected through various sources focused on answering the underlying, fundamental
question of this study: What did Vineyard High School do, or alternatively what does
it have, that enabled its students to achieve remarkable performance gains over the
past three years? From the data, the following salient factors emerge that seem to
answer this question and provide a convenient framework for understanding how
these factors function and organize themselves in the discussion of the findings that
will follow:
1. External pressures such as CAHSEE or NCLB helped the school focus on
student achievement.
2. The school leader established a shared vision and purpose for the school with
his leadership.
3. The school leader built a culture of trust and instructional leadership by
empowering teachers.
4. The school leader was competent in using Bolman and Deal’s (2003) four
frames to bring about a change process.
5. Teachers enhanced curriculum and instruction based on student performance
data.
6. The school built a professional learning community with a culture of
collaboration.
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Employing this set of corollaries we can characterize the achievements at
Vineyard in a simple manner. Motivated by pressures arising from external
mandates, the school’s principal was able to motivate his teachers by creating with
them and the district a shared vision of what might be. He then empowered teachers
by providing them with resources of time, technology and structure as well as a safe
and nurturing environment. He was able to do so by drawing on his personal
qualities as well as his professional knowledge and skills. In a nutshell, the success at
Vineyard was a direct result of its Principal’s leadership. The following discussion
expands, contextualizes and corroborates the various components inherent in this
process.
Pressure of External Accountabilities
Since 2000-2001 when Vineyard High School was identified as an under-
performing or Program Improvement school under the 2001 No Child Left Behind
Act, the school found itself under increasing pressure from external mechanisms of
accountability such as CAHSEE and NCLB. As has been noted, in 2002-2003 the
school was designated with a “Year 2 PI” status due to its continuing failure to meet
its annual API goals until in 2003-2004, as well as the following year, it met its API
goals and was finally able to exit its PI status. Along with its accomplishment in
reaching its API goals, the school also showed continuous improvement in student
achievement in math based on CST and CAHSEE results.
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There are two views of the affect of such external pressures: As some of the
teacher interview responses revealed, teachers and others often see them as inhibiting
or counter-productive, yet the legislation itself offers them up as motivators and
guides for change and progress. It seems clear, however, that for Vineyard High
School external accountabilities such as NCLB and CAHSEE requirements provided
clear opportunities to establish a shared vision and goals, build a culture of trust and
collaboration, and, ultimately, improve teaching and learning. Goertz and Massell
(2005) confirmed in their study that state accountability systems can, indeed, bring
about such changes, noting that they can be “a powerful force for change” (p.7) to
propel high schools towards school reforms, standard-based instruction, and
measured student performance.
Tucker and Stronge (2000) noted as well that a significant effect of the
NCLB legislation was the attention it brought to the importance of accountability
being distributed among the states, school districts, and individual schools. This is a
result of its requirements for the establishment and administration of state-wide
assessments and, at the district and school level, the need to meet adequate yearly
progress (AYP), to publish annual report cards, and to ensure highly qualified
teaching staff.
These increasingly sophisticated accountability measures implicate all levels
of the education systems but ultimately focus on helping the individual school sites
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improve student achievement: the primary focus, that is, is on schools rather than
school districts (Goertz and Massell, 2005).
The data from this study make it clear that Vineyard High School was
affected by precisely the scenarios described above, and that these were the primary
motivators for its principal as well.
Importance of Leadership to Create Shared Vision and Purpose
In order to truly bring about improvement in student achievement in
mathematics, Vineyard High School needed systematic reform spearheaded by
effective leadership at the school site. The role of leadership was crucial in the
context of school efforts to improve student achievement. In response to the pressure
and climate of external accountabilities, the principal at Vineyard High School was
able to bring about necessary changes in the school organization in order to
accomplish improvement of student achievement by “knotting together rigorous
external accountability systems and local capacity building” (Goldberg & Morrison,
1999, p.59).
Interview participants were in agreement that the principal created a broad
vision as well as specific goals for exiting from the undesirable “PI” status and
moving toward becoming an API 800 school. Goldberg and Morrison (1999) pointed
out that successful leaders are “able to create a clear sense of purpose among the
school community members and shared understanding of how and what the school
community members are held accountable for.” The authors asserted (1999) that
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when the school community members focus on their shared goals, it is possible to
achieve them with concerted efforts and action.
The Inquiry Process for Building Common Ground and Empowering Teachers
The principal continuously asked for information from the school community
members, especially from department chairpersons and teachers, so that he could
gather the information necessary for him to monitor and evaluate their progress and
also ensure that all their views and actions would be congruent. This process of
inquiry was beneficial since it provided an opportunity to empower teachers and
department chairpersons, focus on tasks, and foster a culture of trust. Bennis and
Goldsmith (1997) note that effective organizational leaders always question, pursue
information throughout all levels of the organization, and check their own
understanding. They assess what works and what does not work. As leaders, school
site leadership must master the ambiguous context, investigate reality, and produce
visions, plans, and programs. Bennis and Goldsmith (1997) characterized effective
leadership in this way:
A leader is someone who has the capacity to create a compelling vision that
takes people to a new place, and to translate that vision into action. Leaders
draw other people to them by enrolling them in their vision. What leaders do
is inspire people, empower them. They pull rather than push. This “pull” style
of leadership attracts and energizes people to enroll in a vision of the future.
It motivates people by helping them identify with the task and the goal rather
than by rewarding or punishing them (p.4-5).
Bennis and Goldsmith (1997) also emphasized that leaders must create trust
in order to lead a team, and in order for them to create trust they should be aware of
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four special ingredients they call the four C’s. Leaders, they assert, must possess
Competence, Congruity, Constancy, and Caring. The principal at Vineyard High
School seemed to consistently embody these four special ingredients; as a result, he
was able to create a culture of trust. The interviews and surveys we have examined
provide ample evidence of this: His “Competence” clearly embodied in his ability to
continually move the change process forward through judicious use of his human
and material resources, “Congruity” evidenced in his promotion and management of
shared visions and attitudes across a wide cross-section of participants, his
“Constancy” evidenced in his ability to focus disparate and at times diverging
initiatives towards a single goal and, finally, his “Caring” side abundantly attested to
by so many of the respondents in this study. As Bennis and Goldsmith (1997)
suggested, these attributes must apply to any school leader aspiring to effectively
lead their team and improve student achievement under numerous external pressures
and internal organizational restrictions.
The Principal’s Competency Viewed through Bolman and Deal’s Frames
In addition to empowering teachers by creating a shared vision and goals and
a culture of trust, the principal showed he possessed the necessary professional
competencies to bring about the organizational changes required to allow his
teachers to improve student achievement. His competence can perhaps best be seen
by viewing his actions through the four frames of Bolman and Deal. He made use of
external pressures such as NCLB to bring everyone together and focus on student
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achievement. He turned these pressures into opportunities for making necessary
changes such as teaching assignments in order to maximize human resources. In
conflicting situations he brought everyone’s focus on the shared vision and goals and
built a culture of trust and collaboration by empowering his teachers. Under his
leadership, the school valued the staff and students and celebrated their successes.
Bolman and Deal (2003) noted that it is crucial for leaders to be versatile
users of their four frames, depending on the context of the situation the structural
frame, the human resource frame, the political frame, or the symbolic frame. They
explained, “Like maps, frames are both windows on a territory and tools for
navigation” (p.13). School leaders also have to utilize the right frame to fit a
particular situation in order to be able to bring about the changes necessary to
improve student achievement. According to Bolman and Deal (2003), leaders
conduct themselves differently depending on which frame they apply. Through the
structural frame, leaders try to develop and implement a process, or restructure an
existing one to fit the situation, and with the human resource frame, they support and
empower their people. Political frames, on the other hand, allow leaders to identify
their constituencies, establish ties with them, and handle conflicts in a productive
way, and finally, by making use of the symbolic frame, leaders explore ways to make
the best use of the organization’s traditions and value system as a foundation for
creating a cohesive and meaningful culture.
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In his effort to bring about a desirable organizational culture, the principal at
Vineyard High School showed his ability to create trust among the school
community members as well as enthusiasm for improvement of student achievement
and teacher instruction. Fink and Resnick (1999) stated that despite the fact that
principals are expected to function as instructional leaders they usually do not spend
enough time on the matters related to curriculum and instruction. Fink and Resnick
(1999) suggested that in order for school leaders to create a learning environment
where students continue to improve their achievement they must possess certain
leadership qualities: the ability to create trust and invigorating enthusiasm for
constant improvement of instruction.
In addition to his concerted efforts on trust building, constant focus, and clear
vision, it was also evident that the principal of Vineyard High School held high
expectations for both student achievement and teacher instruction. Supovitz and
Poglinco (2001) noted that the high expectations of schools trickle down to every
member of the school community in regard to the shared goal of academic
excellence and the shared purpose of the school to enact the vision.
Enhancement of Curriculum and Instruction Based on Student Performance
Data
High expectations and a primary focus on student achievement and quality
instruction, along with the external pressure resulting from the school’s PI status
under NCLB, opened dialogues among teachers in respect to instruction. Supovitz
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and Poglinco (2001) emphasized the importance of a focus on instruction and of a
coherent instructional vision and they further noted that principals who heighten the
school-wide focus on instruction will improve their students’ achievement.
Focusing on student achievement, the math department at Vineyard High
School was able to bring about its own reform in order to improve student
achievement. Due to the increased external pressure and the school’s shared vision
and goals, a change was taking place; math teachers started talking about student
achievement results and instruction. They reviewed student performance data and
identified essential standards based on the CST and CAHSEE test blueprints.
Johnson (2002) underscored how student performance data can be utilized as “a
fundamental tool” (p.11) in the school organizational change process. Johnson
(2002) also emphasized that a school reform leadership team has to be instrumental
in initiating and maintaining on-going communication with the school community
and in bringing about consensus regarding the change process based on the
meaningful use of data.
Provided by the District with constant support in the form of upgraded
technology along with a congruent movement toward improvement of student
achievement, especially from the district’s person in charge of professional
development in math, the math department staff at Vineyard High School began their
own reform. The instructional leadership in the math department, mainly from
department chairpersons, contributed to aligning curriculum and instruction to state
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standards, sequencing benchmark assessments in accordance with classroom
curriculum, and collecting and analyzing student performance data. As Johnson
(2002) suggested, they created “a culture of inquiry” (p.11). They started to engage
in self-evaluating questions regarding what the data showed about their instructional
strengths and weaknesses, trends in academic performance and the need for changes
or improvement of their practice.
Since it was crucial to accurately interpret student performance data, the
school had its own 18-member data team and, under the direction of the district so as
to assist the school leadership with effective data collection and accurate data
analysis, Data/Resource persons for math and English. Johnson (2002) noted that it
was crucial for the leadership and school data teams to acquire training in skills
necessary in order for them to properly utilize data.
As a result of this high accessibility to student performance data by
individual teachers, the math department staff, as a team, was able to examine
student performance data, especially benchmark assessment data, and thereby
effectively monitor student learning. Marzano (2003) noted that in order for schools
to improve student achievement they need to hold students to high expectations and
provide “pressure to achieve” along with systematic monitoring of the progress of
student performance. Such systematic monitoring on a regular basis was provided by
benchmark assessments and their results in math instruction at Vineyard High
School. Based on these types of student performance data, interventions were
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instituted. Tutorial classes and a computer lab utilizing NCE provided individualized
support while after-school tutoring offered school-wide support. These efforts were
clearly in line with DuFour’s (2004) emphasis that schools need to provide feedback
on student work progress in a timely manner and that schools need to focus on
intervention rather than remediation.
Building a Professional Learning Community with a Culture of
Collaboration
One of the most valuable gains the math department obtained, and one of the
most influential contributors to improved achievement at the school, was the culture
of collaboration they created. DuFour (2004) noted that a culture of collaboration is
the fundamental common ground for a professional learning community working
toward the shared vision of learning for all. With professional learning communities,
collaborative work is a systematic process which enables teachers to work together
in order to make an analysis of and improvement in their teaching. They get involved
with professional inquiry and promote profound on-going learning experience as a
team (DuFour, 2004). Such a culture of collaboration within the math department at
Vineyard High School contributed to improved curriculum and instruction which, in
turn, brought about improved student achievement in math. Continuously realigning
instruction and curriculum to essential state standards on the basis of student
performance data helped math teachers focus on being mindful of a variety of
learning modalities.
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It seems clear from the data examined that Vineyard High School’s efforts to
improve their math program and the positive results that ensued, when viewed from
the various perspectives touched upon in the research literature as proven elements in
successful reforms in general and math in particular, can be attributed to the six
factors described above: the external accountabilities, establishment of a shared
vision and purpose, a culture of trust and instructional leadership through teacher
empowerment, a school leader’s competency in Bolman and Deal’s four frames,
enhancement of curriculum and instruction based on student performance data, and a
professional learning community with a culture of collaboration. At Vineyard High
School these factors came together to create the environment in which led to so
successfully improved student achievement in math.
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CHAPTER FIVE: SUMMARY AND IMPLICATIONS
Summary
Despite a host of alarming national reports published over many years and
the subsequent and inevitable array of urgent proclamations and policies and the
decades of reform that ensued, current student performance data reveal a continuing
and seemingly incurable deficit in public education in the United States when viewed
by its own objective national standards as well by international comparative studies.
Such inadequacies in education bode ill, of course, for the future of our students and
for the nation as a whole.
We live in the age of information and it is more crucial than ever in the
nation’s history to have a highly qualified and skillful workforce to compete with
other countries in the global market. This urgent need calls for national and local
attention to the outcome of public education, especially mathematics due to its
inordinate role as the primary gateway to college education, technology, and
advanced science. Student achievement at the high school level is progressing only
marginally, especially in the critical area of math. Such inadequate student
achievement in math has been a national concern for the last few decades, in spite of
the great deal of attention at the national and state level that has been placed on
schools and districts to make them accountable for student achievement. As a result,
a national urgency has come about to establish effective policy initiatives in order to
improve student achievement in math.
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In addition, there is a potential socio-political crisis in the nation due to the
student achievement gap in math. As Rose and Betts’s study (2001) shows, the rigor
of math classes that students take in high school affects their success in their career
and their financial well-being over the ten years following their high school
graduation. Such a finding implies that high school math placement is closely
related to economic status and social status. According to the results of numerous
high stakes examinations such as NAEP, the California Standards Test (CST), and
CAHSEE, Latino and African-American students perform at a significantly lower
level than Caucasian and Asian students nationwide. This makes it crucial to narrow
the current gap between ethnic groups in academic performance in math in order to
prevent the resultant economic disparities.
Math education has been bombarded with constant public criticism, a stream
of new initiatives, and a variety of external accountabilities. But as they address the
criticism and respond to the new mandates, it is important for policymakers,
educational leaders, and practitioners to know which policy initiatives can be shown
to be related to improved math achievement at the school. Under the increased
scrutiny, there has been a quest for the best practices and the most effective
curriculum and instruction to improve student achievement in math. Therefore, it is
crucial to identify what factors comprise these best practices; what curriculum,
instruction and related conditions are most likely to actually promote improvement
of math achievement.
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Moreover, in order to enhance math programs and instructional strategies,
just as for any attempt at organizational improvement, schools cannot avoid going
through a change process. It is thus worthwhile to examine effective change
processes that have been implemented at the school level to improve student
achievement in math. Successful change processes, for the purpose of enhancing
math programs and strategies and improving student achievement in math, require
effective leadership at the site, especially strong instructional leadership, in spite of
the many challenges and dilemmas that are inevitable in the change process.
Purpose of the Study
The purpose of the study is to identify how urban high schools can
successfully bring together policy initiatives and local best practices to effectively
improve math performance in their schools. In addition, the study examines how
instructional leadership is effectively carried out in high schools in the context of
improving math performance for students. Several issues seem to be particularly
relevant to instructional leadership in this setting. To begin with, school leaders
often don’t have strong pedagogical content knowledge in mathematics education
and yet need to motivate and guide those who do, as well as provide data analysis
and review of their efforts. Little, however, is known about how leaders work
effectively in this context.
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Research Questions
Five questions framed the research, and are addressed by this study. They are
listed here in the order they are discussed in the study.
1. What was the pattern of math achievement for various students at the school?
2. What policy initiatives—as well as curriculum, instruction, and related
conditions—were shown to be related to improved math achievement at the
school?
3. What change process did the school use to enhance its math program and
strategies to assist students in math?
4. 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?
Research Method
A qualitative, descriptive case study design was utilized for this study. This
research design was selected because the study requires an examination of an
exemplary school which implemented best practices and programs to improve
student achievement in math. Since the study also intended to explore the processes
of school reform used to bring about needed changes in student math achievement,
case study was deemed the most appropriate strategy of inquiry for a qualitative
study of this type (Creswell, 2003).
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Sampling Criteria
The eleven students in the Ed. D cohort program led by Dr. Marsh at the
University of Southern California worked collaboratively to design the study and
determine the sampling criteria. The following are the criteria set for this study:
1. Comprehensive public high school in southern California serving grades 9-12
with at least 1200 students
2. Student demographic information showing at least 50% of its students from
traditionally ethnic minority groups
3. API (Academic Performance Index) score of at least 600
4. Statewide rank of 5 or higher
5. Improvement of student performance in math as evidenced by results on the
California Standards Test (CST) in Algebra I over a three year period
6. No participation in special grant programs such as IIUSP.
7. Leadership stability defined by at least three years of service at the school site
by the principal during the time the improvement was made.
Research Instrumentation
The instrumentation utilized in this study was designed by a research team of
eleven educational doctorate students at the University of Southern California. They
collaboratively developed conceptual frameworks, planned a methodology for data
collection and analysis, and designed interview guides and teacher questionnaires.
These Data Collection Instruments were then used to gather relevant information
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about the pattern of student achievement in math, math programs and instructional
practices, the change process, and instructional leadership. Five instruments for data
collection were designed to provide qualitative data and to gather information
relevant to each research question. Through the employment of a variety of
instruments, the school profile, key leader interview guide, math teacher interview
guide, math teacher questionnaire and general teacher questionnaire, the researcher
was able to triangulate data. In addition, four conceptual frameworks—the change
process, effective school design, math programs, and instructional leadership—
constructed on the basis of key components of the study as expressed in its research
questions, provide a foundation for data collection and analysis in the study.
Data Collection
As mentioned in Chapter Three, the unit of analysis for this case study was a
single 9
th
-12
th
grade high school, Vineyard High School. The data to acquire
answers to the research questions was collected in four phases at the school site as
follow:
The first part of Phase One of the data collection concentrated on gathering
school-wide hands-on information. The researcher collected and examined the
master schedule, the School Improvement Plan, the WASC (Western Accreditation
of Southern California) report, and other relevant documents. The researcher held
an initial interview with the principal to acquire general information about school
culture, key leaders, student achievement in math and other issues relevant to the
195
study. Before beginning the next phase, the researcher examined and analyzed the
data compiled from this initial phase.
Phase I consisted of conducting key leader interviews and distributing the
teacher questionnaire to the faculty, including the special version provided only to
math teachers. The researcher began the key leaders interviews in the conference
room at the school; the interviewees included the site principal, the assistant
principal in charge of instruction and curriculum, who also oversaw the math
department, the AVID Coordinator, the math department chairpersons comprising
the two current co-chairs and the recently retired department chair as well since she
was perceived as the key person who had brought about improvement of the math
curriculum, instruction, and student achievement. In addition, the two
Resource/Data Persons were interviewed since they were regarded as a major part of
instructional leadership. The Key Leader Interview Guide was employed to ensure
that the information gathered related to the research questions. The Teacher
Questionnaire was distributed to the teachers after an introductory meeting
explaining the purpose and nature of the study.
Phase Two involved compiling interview notes, reviewing and analyzing
documents, and identifying emergent themes. During Phase Two, the researcher
visited classrooms to observe math instruction, especially Algebra and Pre-Algebra
classes. Math Lab was also visited since many of the interview respondents
frequently referred to it during interviews.
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Phase Three completed the key leader interviews, this time targeting the math
department chair and math coaches, and conducted the teacher interviews. Teacher
interviews were held with teachers who taught at least one section of math. The
Teacher Interview Guide was used, again in order to gather information which
addressed the research questions. The researcher took handwritten notes to record
their responses and reviewed them with the participants to ensure the accuracy of the
note taking. Follow-up interviews were held with key leaders to clarify facts and
more documents were gathered. Also during this stage, the Teacher Questionnaires
were collected from the faculty.
Summary of Findings
It seems clear from the data examined that Vineyard High School’s efforts to
improve their math program and the positive results that ensued, when viewed from
the various perspectives touched upon in the research literature as proven elements in
successful reforms in general and math in particular, can be attributed to the six
factors described above: the external accountabilities, establishment of a shared
vision and purpose, a culture of trust and instructional leadership through teacher
empowerment, a school leader’s competency in Bolman and Deal’s four frames,
enhancement of curriculum and instruction based on student performance data, and a
professional learning community with a culture of collaboration. At Vineyard High
School these factors came together to create the environment which led to so
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successfully to improved student achievement in math. In the following sections, the
findings will be examined in detail for each of the research questions.
Research Question One
For this question data were obtained from available school profiles providing
a variety of student performance data including the CST and CAHSEE high stakes
math exams. In addition to overall student achievement results, sub-groups’
academic performance outcomes were examined. Based on the CAHSEE and CST
data available at the website of the California Department of Education, the findings
on student achievement in math at Vineyard High School revealed a consistent
improvement from 2003 to 2005. Such improvement was shown across the board,
regardless of grade level, gender, ethnicity, language status, economic status, or
special needs.
There was a dramatic improvement in student achievement shown on the
CAHSEE, the state-mandated examination to qualify for high school graduation, as
well as overall improvements in student achievement in math at Vineyard High
School. The data showed a 35% increase from 2003 to 2004 and a lesser but still
substantial 24% increase over the two years from 2003 to 2005. It is worth noting
that there were no 11
th
graders’ participating in 2004, while the performance results
of 10
th
grade students from 2004 to 2005 actually increased by 1%. The 9% overall
decrease from 2004 to 2005 resulted from factoring in the 32% passing rate of 11
th
graders in 2005. In fact, a closer look at the student performance data shows that
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students in every category showed some degree of decrease from 2004 to 2005 with
three exceptions: 10
th
graders, Asian students, and students with special education
services. It is presumable that these decreases were due to the participation of the
11
th
graders in these categories.
Similar improvement in student achievement was also shown in the results of
student performance in Algebra I on the CST (California Standards Test). The
percentage of students who performed at a Proficient or Advanced level increased
consistently for the three years from 2003 to 2005; by 7% from 2003 to 2004 and by
6% from 2004 to 2005. As with the CAHSEE results, improvement was shown
across the board, regardless of grade level, gender, ethnicity, language status,
economic status, or special needs.
Research Question Two
There are two views of the affect of such external pressures: As some of the
teacher interview responses revealed, teachers and others often see them as inhibiting
or counter-productive, yet the legislation itself offers them up as motivators and
guides for change and progress. It seems clear, however, that for Vineyard High
School external accountabilities such as NCLB and CAHSEE requirements provided
clear opportunities to establish a shared vision and goals, build a culture of trust and
collaboration, and, ultimately, improve teaching and learning.
According to interview and questionnaire responses, the school staff believed
that policy initiatives greatly affected the school culture and student achievement at
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Vineyard High School. Their responses to the interview and questionnaire items
regarding policy initiatives showed that the faculty of Vineyard High School felt that
policy initiatives have directly or indirectly affected student achievement in math.
Some policy initiatives were found to be more influential than others. The
requirement for passage of the CAHSEE in order to earn a high school diploma was
regarded by the staff as the most significant policy influencing the school’s efforts to
increase student achievement in math. Moreover, they believed it affected the
attitude of students in regard to their academic achievement in math. Teachers also
felt that students cared about the high stakes exam because it was a requirement for
graduating with a diploma.
The second most influential policy, according to the results, seemed to be the
No Child Left Behind (NCLB) Legislation. This legislation caused some dissent
among staff due to what some perceived as its unrealistic dogma of “all students will
reach (a particular achievement level) by (a particular time)” and its punitive
sanctions toward schools which had not been successful in meeting state-mandated
goals. Despite these perceptions, however, there was a general consensus that the
federal legislation was an external accountability system that helped the school and
district to focus on curriculum and student achievement outcomes.
These policy initiatives pressured districts and schools to implement practices
that would bring about expected student performance outcomes. There was a lot of
pressure externally, especially after the district was classified as an underperforming
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district. Such pressure forced the district to focus on instruction and curriculum.
According to the collected data, two components of these district-wide practices
were found to be most influential in bringing about the necessary improvement of
student achievement in math at Vineyard High School; Benchmark assessments and
data driven decision-making in the area of curriculum and instruction.
Benchmark assessments, teachers thought, helped the departments create a
culture of collaboration and focus on individuals through student performance data.
Along with implementation of the improved benchmark exams for student
achievement, the district emphasized the use of student performance data.
Immediate feedback of student performance prompted discussion among teachers in
regard to student performance and instruction as well as curriculum. Teachers used
the student performance data as a reflection tool to revamp their instruction.
A focus on looking at student achievement data on high stakes exams as well
as benchmarks also helped the math department strengthen its standards-based
instruction. Since Benchmark assessments were based on standards, the results of
student performance data such as CST and CAHSEE showed the strengths and
weaknesses of each teacher’s instruction in addressing individual standards. The data
also indicated department-wide strengths and weaknesses—crucial to their focus on
reinforcing areas that help teachers align instruction to state standards in an effective
way.
Research Question Three
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The most salient theme that arose during the key leader and teacher
interviews was the importance of the principal to Vineyard’s reforms: Every
participant pointed to the principal as the main contributor to improved student
achievement at Vineyard High School. There was a consensus that it was the
principal who made everything happen: he brought the staff together, made them feel
like the best team, and motivated and supported teachers.
In order to truly bring about improvement in student achievement in
mathematics, Vineyard High School needed systematic reform spearheaded by
effective leadership at the school site. The role of leadership was crucial in the
context of school efforts to improve student achievement. In response to the
pressure and climate of external accountabilities, the principal at Vineyard High
School was able to bring about necessary changes in the school organization in order
to accomplish improvement of student achievement.
In addition to empowering teachers by creating a shared vision and goals and
a culture of trust, the principal showed he possessed the necessary professional
competencies to bring about the organizational changes required to allow his
teachers to improve student achievement. His competence can perhaps best be seen
by viewing his actions through the four frames of Bolman and Deal. He made use of
external pressures such as NCLB to bring everyone together and focus on student
achievement. He turned these pressures into opportunities for making necessary
changes such as teaching assignments in order to maximize human resources. In
202
conflicting situations he brought everyone’s focus on the shared vision and goals and
built a culture of trust and collaboration by empowering his teachers. Under his
leadership, the school valued the staff and students and celebrated their successes.
Research Question Four
Based on the data collected through interviews and surveys, it was quite
evident that instructional Leadership at Vineyard High School was shared among the
principal, math department chairpersons, and the Resource/Data person. The
principal took an active role as the site leader in creating a school culture which
focused on student achievement. On the other hand, he valued and relied on the
leadership of the math department chairpersons in helping students improve their
achievement in math.
With shared instructional leadership, on the basis of an analysis of the data
collected in this study using the five components of the Conceptual Framework of
Instructional Leadership, it was evident that there were a few components that could
be considered as key contributors to improved student achievement in math at
Vineyard High School: a clear vision for learning, meaningful professional
development, a positive school culture of learning and teaching, and data driven
decision making. One of the most valuable gains the math department obtained, and
one of the most influential contributors to improved achievement at the school, was
the culture of collaboration they created. The culture of collaboration within the math
department at Vineyard High School contributed to improved curriculum and
203
instruction which, in turn, brought about improved student achievement in math.
Continuously realigning instruction and curriculum to essential state standards on the
basis of student performance data helped math teachers focus on being mindful of a
variety of learning modalities.
Research Question Five
Based on the interviews and surveys, it appeared that four out of the
Framework’s twelve strategies were effectively put into use by the principal at
Vineyard High School in order to bring about the improved student achievement in
math: These were high expectations, emphasis on quality instruction, empowerment
of department chairpersons and quality interventions.
The principal of Vineyard High School emphasized the need for having high
expectations for student achievement. He also made it clear that he in turn had high
expectations for his staff; the goal of the school had now moved beyond merely
meeting API goals and removing the PI status. Through an expansion of the AVID
(Advancement Via Individual Determination) program on campus, the school had
doubled the numbers of AP classes being offered on campus.
It was evident from the data that the principal’s emphasis on high
expectations for student achievement was directly connected with an emphasis on
quality instruction. In order for teachers to help students improve academic
achievement in their class, their instruction had to be effective. There was consensus
204
among the interview respondents that high expectations for student achievement
naturally called for quality instruction.
It was also clear from the data that the math department chairpersons felt they
were empowered by their principal. In particular, they felt they were much more
involved with the teacher selection process for new hires than ever before, with the
final decision for teacher selection left to the department chairperson. As well, in the
process of building a master schedule they felt that the principal and the assistant
principal in charge of curriculum worked collaboratively with them. The principal
created a school culture of trust and collaboration and then he let the people with
expertise do what needed to be done.
Based on the interview and survey results, it was evident that the school
implemented quality interventions to help students at risk of failing academically.
Juniors and seniors who did not pass the CAHSEE were monitored by the school
data team and offered pull-out sessions to provide individual monitoring and
instructional support. Vineyard’s after-school tutoring program was also identified
as an effective intervention for its at-risk students.
Implications
The case study presented here of Vineyard High School’s path to reform and
high achievement reveals a host of factors, skills, strategies, and understandings that
were key components in their success. This study, it is hoped, can thus serve as a
205
resource and guide to other school leaders and practitioners who wish to follow a
similar path.
Recommendations for Future Research
Two significant questions arise based on the findings of this case study; one
explicit, the other implicit. Future research in this field would help to clarify these
questions and add to our understanding of how leadership affects reform efforts.
The first question that arose from the study was generated by a discrepancy in
student achievement results. The patterns in student achievement on Advanced
Placement exams did not coincide with those for CST and CAHSEE. For future
research, it is suggested that the cause of this incongruity be examined in order to
explore whether or not the leadership factors examined here are applicable to
students at higher levels.
A less obvious but perhaps more fundamental question that came out of the
study was this: To what extent can the findings from this particular case be
generalized to other settings? A different perspective on this fundamental query
would be to ask if the findings in this case would apply to sites which had not
achieved success in their reform efforts. Future research, therefore, may look into
other schools in the Vineyard School District or similarly constituted districts in
order to conduct a comparison study across school sites.
Implications for Practice
206
The findings of this study have suggested a number of practices which would
benefit a broad segment of those involved in schooling: policy makers, district
leaders, school leaders, and teachers—anyone interested in understanding current
policies, practices and programs that are effective in improving student academic
achievement.
Implications for Policy Makers
The events at Vineyard High School make it clear that policy makers need to
acknowledge the effect of external accountabilities on public education whether
coming from federal or state agencies. It can help schools focus their efforts on
student achievement to meet the challenges. One practice that would serve policy
makers well would be to establish a system to acquire and disseminate the results of
student achievement on state mandated exams in a timely manner. If the exams are
to be the instruments to propel academic rigor and measure the growth of schools,
the immediate availability of student achievement data is crucial to modify
curriculum and instruction and serve students with better placement and
individualized services. One particular practice in this regard that would serve policy
makers well would be to establish a system to acquire and disseminate the results of
student achievement on state mandated exams in a timely manner. At Vineyard High
School, the instant availability of benchmark assessment data propelled teachers to
zero in on what’s really important—curriculum and instructional modification. Such
a system could be enhanced through the requirement of an “Action Plan” from those
207
receiving the data at all levels of the system; this “feedback” requirement would
serve to motivate and guide the use of the data in effective ways.
Implications for District Leaders
District leaders, the study indicates, must exert their leadership in focusing on
concerted efforts and aligning resources to student academic achievement. Vineyard
Union High School District aligned their annual objectives and goals to those of the
schools. Such alignment provided coherence and a shared vision between the district
and the school. School districts should make every effort to implement similar
practices that insure cohesiveness between the district and the school site. They also
need to build capacity for instructional leadership among site leaders and teachers
through well-defined professional development. As was done at Vineyard Union
High School District, they should take on the role of providers of resources to assist
schools in accomplishing their goals for student achievement.
Implications for Site Leaders
Implications for site leaders, based on the study’s findings, focus on their
need for effective leadership and an understanding of the change processes needed to
bring about effective reform to better improve student achievement. The key to the
success achieved at Vineyard High School was their shared vision and purpose. They
built a culture of trust and instructional leadership by empowering teachers and they
created a culture of collaboration and data-based decision-making practices. Those
wish to emulate that success therefore, must establish a shared vision and purpose for
208
their schools through their leadership. They also need to build a culture of trust and
instructional leadership by empowering teachers. Site leaders must build a
professional learning community with a culture of collaboration and, at the same
time, strengthen the internal capacity of instructional leadership in order to enhance
teaching and learning at the site. They also must organize their professional
development plans so that it maximizes the skills and competence of staff to make
productive use of student achievement data.
Implications for Classroom Teachers
Implications for classroom teachers who wish to emulate the successes at
Vineyard include the use of student performance data to design instruction and
monitor the progress of student achievement. They should collaboratively work with
their peers to build common ground in instruction and curriculum among their own
department members as well as with teachers outside of their own departments.
They also should build a culture that stresses constant evaluation of the effectiveness
of its own teaching and of student learning. Finally, teachers need to create common
assessments with their peers in order to be able to measure student achievement in a
timely and objective manner.
209
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APPENDICES
215
APPENDIX A: KEY LEADER INTERVIEW GUIDE
Key Leader Interview Guide
Research Question Two: What policy initiatives as well as curriculum,
instruction and related conditions seem to be related to improved math
achievement in the school?
Directions to Interviewer:
Describe the purpose of the interview, expected timeline, and introduce
each topic as the RQ changes. For this section,:
“The first part of our interview, I will be asking you to describe your
perceptions about how policy issues have affected your efforts to improve
student achievement in math. Specifically, we will cover policy issues related to:
POLICIES
 NCLB- AYP/HQT
 District
 State Policies/API
 CAHSEE
Are you ready?
1. How do you perceive NCLB as having influenced your efforts to increase student
achievement?
AYP?
HQT?
2. What board policies and/or practices (if any) are in place that support increased
student achievement in math?
 Benchmarks assessments
 Financial resources
 Additional Staffing / CSR

3. How has Standardized testing and the requirements to meet your API growth
target influenced your efforts to increase student achievement in math?
4. How do you feel the CAHSEE requirement has influenced your efforts to increase
student achievement in math?
216
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. Here is a copy of the framework 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
1. What structural changes have you made that you feel have contributed to
improved math achievement?
o School design
o Leadership
o Facilities
o CSR
2. What personnel changes have been implemented that has positively influenced the
math achievement?
o Teacher assignments
o Leadership roles
3. How did you negotiate the political aspects associated with the change process?
o Site level
o District level
o Community level
4. What did you do symbolically to support and engage in the change process that
has been implemented to improve math achievement?
o Vision/mission
217
o Culture climate
o Ceremonial/awards
Leadership Instrument RQ 4
Research Question 4: To what extent was strong instructional leadership
important in improving (a) the math programs/strategies and (b) math
achievement among students?
“I would now like to ask you about issues specifically related to the role of
instructional leadership in your efforts to improve student achievement in math.
Specifically, I will be asking about the roles leaders played and issued related to
the development of a professional learning community on your campus.”
1. Who were the leaders on your campus who helped bring about the improved
achievement in math?
a. What were there roles?
2. How was the professional growth of the math teachers supported?
3. To what degree was teacher collaboration and/or reflection fostered and
encouraged?
4. How has the school leadership worked to implement a professional
community on you campus?
a. Teacher empowerment
b. Teacher leadership
c. Peer collaboration
d. Reflection
5. In what ways have site leaders attempted to make the focus on student learning
and results?
Leadership Questionnaire RQ5
Research Question 5: How did leaders in the school respond in academic areas
on which they were not experts?
“Now let’s talk a little about how the site leadership went about overcoming any
obstacles you may have faced as you worked to improve student achievement in
math.” You may find it useful to refer to the frameworks on change that I
provided to you earlier.
218
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
219
APPENDIX B: TEACHER INTERVIEW GUIDE
Teacher Interview Guide
1. What is your current position?
2. Describe your educational background, credentials held, years of experience
and any specialized training you have had in math instruction.
3. What policy initiatives and/or curricular programs do you feel have
contributed to improved student achievement in math?
4. What teaching strategies, methods and/or instructional materials do you feel
have contributed to improved student achievement in math?
5. Over the past few years, what changes, if any do you feel have made a
significant impact on student achievement in math? How were they
implemented?
6. What role did school leaders (administrators, department chair, lead teachers,
math coaches) play in the development and implementation of the math
program?
7. What actions taken by school leaders most directly affected student
achievement in math?
220
APPENDIX C: MATH TEACHER QUESTIONNAIRE
Math Teacher Questionnaire
Thank you for taking the time to complete this survey. It is hoped that the results
will serve as a rich source of data that may serve to better inform schools seeking to
improve in math achievement. Please return the survey in the sealed envelope
provided to the principal’s secretary by November 14, 2006. Please be assured
the questionnaires will only be viewed by the researcher and not be viewed at all by
site leaders. Once again, your assistance is greatly appreciated.
Directions: Please rate each item on the following scale by circling the response of
your choice:
5 = Strongly Agree
4 = Agree Somewhat
3 = Neutral
2 = Disagree Somewhat
1 = Disagree Strongly
1. The No Child Left Behind
Legislation has promoted
increased student achievement
at our school.
2. The requirement that students
pass the CAHSEE to earn a
high school diploma has
contributed to the school’s
effort to improve student
achievement.
3. Board Policies in our district
have contributed to improved
math achievement in our
school.
4. Our school has successfully
implemented common
assessments that support
increased
student achievement.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
221
Directions: Please rate each item on the following scale by circling the response of
your choice:
5 = Strongly Agree
4 = Agree Somewhat
3 = Neutral
2 = Disagree Somewhat
1 = Disagree Strongly
5. Teachers at our school teach
standards-based lessons.
6. The master schedule at our
school is built based on
student need.
7. Teachers at our school use
researched-based instructional
strategies to increase student
achievement
8. Periodic benchmark
assessments provide useful
data that our teachers use to
drive instruction
9. Student need is a major
consideration when making
teacher assignments in math at
our school.
10. The NCLB Act has been one
of the main external pressures
for improved math
achievement at this school.
11. The requirement that students
pass the CAHSEE in math in
order to earn a high school
diploma has contributed to the
school’s effort to improve
math achievement.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
222
Directions: Please rate each item on the following scale by circling the response of
your choice:
5 = Strongly Agree
4 = Agree Somewhat
3 = Neutral
2 = Disagree Somewhat
1 = Disagree Strongly
12. Our school’s effort to improve
student achievement in math
instruction had nothing to do
with external accountability
such as NCLB regulations and
the CAHSEE requirement.
13. Support classes have been
included in our master
schedule to improve student
achievement in math.
14. The implementation of
standards-based instruction
has served as an important
foundation in improving
student achievement in math.
15. Our school has added the use
of math coaches or experts to
assist in the effort to improve
student achievement in math.
16. Teachers collaborate to
develop common assessments
and rubrics.
17. Professional development
offerings at our site are based
on student achievement data.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
223
Directions: Please rate each item on the following scale by circling the response of
your choice:
5 = Strongly Agree
4 = Agree Somewhat
3 = Neutral
2 = Disagree Somewhat
1 = Disagree Strongly
18. Teachers have helped
develop strategies used at our
school to improve
instructional practice in math.
19. The principal has served as a
“change agent” for improved
student achievement in math.
20. Student achievement in math
was made a priority as the
school allocated its financial
resources.
21. Our school had a clear
strategic plan to improve
student achievement in math.
22. Professional Development has
played a key role in increasing
student achievement in math
23. Teacher collaboration has
played a key role in increasing
student achievement in math.
24. Changes in the curriculum
have played a key role in
increasing student
achievement in math.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
224
Directions: Please rate each item on the following scale by circling the response of
your choice:
5 = Strongly Agree
4 = Agree Somewhat
3 = Neutral
2 = Disagree Somewhat
1 = Disagree Strongly
25. Our school has implemented
effective intervention
strategies for students having
difficulty in math
26. My district supports teachers
with effective staff
development in Mathematics
Instruction.
27. My principal actively supports
opportunities for staff
members to collaborate and
plan Mathematics lessons and
units.
28. Teachers learn by watching
each other teach and
discussing best practices.
29. Our school has effective
strategies to support students
of various learning modalities
30. Our school uses math
coaches to help teachers
become more reflective with
their math instruction
31. I have gained valuable
resources from math
coaches/instructional leaders
that have improved the quality
of my math instruction.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
225
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
32. My school's instructional
leader provides professional
development resources that I
use in my mathematics
instruction.
33. The school leader is aware of
the mathematics instruction
and academic progress of the
students in my class.
34. The school leader provides
opportunities for faculty
members to discuss
mathematics instruction.
35. The school instructional
leader encourages faculty
members to discuss effective
math instructional strategies.
36. My school's math
instructional practices are
developed from evidence-
based strategies.
37. I have regular support from
proven instructional leaders in
math instruction.
38. The math achievement goals
and measures for my school
were clearly articulated and
easy to understand.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
226
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
39. I received coaching and
mentoring from instructional
leaders or peer coaches.
40. The district personnel, school
leaders and teachers all have a
shared vision for increased
math achievement.
41. My district and school
leaders seem knowledgeable
about instructionally effective
math practices and assessment
strategies.
42. The Math Department Chair
has been entrusted with and is
empowered to make important
curricular decisions.
43. Outside experts have been
used to promote greater
capacity in the area of math
instruction.
44. The school’s leaders
emphasize the importance of
quality instruction as a
primary mission of the school.
45. Professional Development in
math has been a key tool used
by site leaders in our effort to
improve instruction on our
campus.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
227
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
46. Site leaders emphasize having
high expectations for student
achievement in math.
47. Quality interventions in math
have been implemented on our site
to help students at risk of failing
academically
48. Our site leaders emphasize a
culture of collaboration as a means
of improving instruction at our
site.
49. Teacher assignments in the math
department are made strategically
and with student need in mind.
50. Our school has emphasized
articulation with our feeder
schools as a means of improving
student achievement in math
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
228
APPENDIX D: NON-MATH TEACHER QUESTIONNAIRE
Non-Math Teacher Questionnaire
Thank you for taking the time to complete this survey. It is hoped that the results
will serve as a rich source of data that may serve to better inform schools seeking to
improve in math achievement. Please return the survey in a sealed envelope to the
principal’s secretary by Date TBA, 2006. Please be assured the questionnaires will
only be opened by the researcher and not by viewed at all by site leaders. Once
again, your assistance is greatly appreciated.
Directions: Please rate each item on the following scale by circling the response of
your choice:
5 = Strongly Agree
4 = Agree Somewhat
3 = Neutral
2 = Disagree Somewhat
1 = Disagree Strongly
1. The No Child Left Behind
Legislation has promoted
increased student achievement
at our school.
2. The requirement that students
pass the CAHSEE to earn a
high school diploma has
contributed to the school’s
effort to improve student
achievement.
3. Board Policies in our district
have contributed to improved
math achievement in our
school.
4. Our school has successfully
implemented common
assessments that support
increased
student achievement.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
229
Directions: Please rate each item on the following scale by circling the response of
your choice:
5 = Strongly Agree
4 = Agree Somewhat
3 = Neutral
2 = Disagree Somewhat
1 = Disagree Strongly
5. Teachers at our school teach
standards-based lessons.
6. The master schedule at our
school is built based on
student need.
7. Teachers at our school use
researched-based instructional
strategies to increase student
achievement
8. Periodic benchmark
assessments provide useful
data that our teachers use to
drive instruction
9. In an effort to improve
instruction on our campus, our
school has focused on
ensuring that structures and
policies that support student
achievement are in place.
10. In an effort to improve
instruction on our campus, our
school has focused on
personnel issues including
hiring quality teachers and
fostering a positive working
environment amongst peers
on campus.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
230
Directions: Please rate each item on the following scale by circling the response of
your choice:
5 = Strongly Agree
4 = Agree Somewhat
3 = Neutral
2 = Disagree Somewhat
1 = Disagree Strongly
11. In an effort to improve
instruction on our campus, our
school has focused on
overcoming political obstacles
and gaining the necessary
support to move the school
forward.
12. In an effort to improve
instruction on our campus, our
school has focused on
motivating students and staff
as well as celebrating
successes.
13. There is a shared vision for
increased student achievement
at our school.
14. Our school had a clear
strategic plan to improve
student achievement.
15. Student achievement is a
priority when the school
allocates its financial
resources.
16. Professional development
offerings at our site are based
on student achievement data
17. The principal works to gain
the support of the community
for the school’s academic
efforts.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
231
Directions: Please rate each item on the following scale by circling the response of
your choice:
5 = Strongly Agree
4 = Agree Somewhat
3 = Neutral
2 = Disagree Somewhat
1 = Disagree Strongly
18. The school leadership works
to establish and maintain a
respect for cultural diversity
19. Students and staff are valued
and their successes celebrated.
20. The school leaders used data-
driven information to address
problems/issues related to
student achievement.
21. The principal works hard to
monitor and supervise
instruction in the classroom
22. The principal makes effective
use of the Department Chairs
and relies on their expertise
when making important
curricular decisions.
23. The principal has delegated
some curricular authority to
an assistant principal with
greater expertise in curriculum
and instruction.
24. Outside experts have been
used to promote greater
capacity in the area of
instruction.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
232
Directions: Please rate each item on the following scale by circling the response of
your choice:
5 = Strongly Agree
4 = Agree Somewhat
3 = Neutral
2 = Disagree Somewhat
1 = Disagree Strongly
25. Site leadership fosters a
culture of inquiry and
collaborative problem solving.
26. The school’s leaders
emphasize the importance of
quality instruction as a
primary mission of the school.
27. Site leaders emphasize
having high expectations for
student achievement.
28. Quality interventions have
been implemented on our site
to help students at risk of
failing academically.
29. Professional Development
has been a key tool used by
site leaders in our effort to
improve instruction on our
campus.
30. Teacher assignments are
made strategically and with
student need in mind.
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5

Abstract (if available)

Abstract The purpose of the study was to identify how urban high schools can successfully bring together policy initiatives and local best practices to effectively improve math performance in their schools. In addition, the study examined how instructional leadership is effectively carried out in high schools in the context of improving math performance for students. Several issues seemed to be particularly relevant to instructional leadership in this setting. To begin with, school leaders often don't have strong pedagogical content knowledge in mathematics education and yet need to motivate and guide those who do, as well as provide data analysis and review of their efforts. Little, however, is known about how leaders work effectively in this context. A qualitative, descriptive case study design was utilized for this study. This research design was selected because the study requires an examination of an exemplary school which implemented best practices and programs to improve student achievement in math. The study was anchored with five research questions to address these critical areas and established conceptual frameworks for research questions in order to interpret collected data through a certain perspectives.

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Asset Metadata

Creator Schwartz, Kyunghae Hong (author)

Core Title Leading the way: the effective implementation of reform strategies and best practices to improve student achievement in math

School Rossier School of Education

Degree Doctor of Education

Degree Program Education (Leadership)

Publication Date 04/25/2007

Defense Date 03/29/2007

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

Tag best practices,OAI-PMH Harvest,student achievement in math

Place Name California (states), educational facilities: Vineyard High School (geographic subject), Sacramento (counties), USA (countries), Vineyard (city or populated place)

Language English

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

Creator Email khschwar@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m468

Unique identifier UC1272576

Identifier etd-Schwartz-20070425 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-495205 (legacy record id),usctheses-m468 (legacy record id)

Legacy Identifier etd-Schwartz-20070425.pdf

Dmrecord 495205

Document Type Dissertation

Rights Schwartz, Kyunghae Hong

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