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The effective implementation of reform strategies, instructional conditions, and best practices to improve student achievement in math: a case study of practices at Land High School
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The effective implementation of reform strategies, instructional conditions, and best practices to improve student achievement in math: a case study of practices at Land High School
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Content
THE EFFECTIVE IMPLEMENTATION OF REFORM STRATEGIES, INSTRUCTIONAL
CONDITIONS, AND BEST PRACTICES TO IMPROVE STUDENT ACHIEVEMENT IN
MATH: A CASE STUDY OF PRACTICES AT LAND HIGH SCHOOL
by
Beverly Ann DeLoach Langford
_________________________________
A Dissertation Presented to the
FACULTY OF THE ROSSIER SCHOOL OF EDUCATION
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF EDUCATION
August 2007
Copyright 2007 Beverly Ann DeLoach Langford
ii
DEDICATION
This dissertation is dedicated to my husband, Michael Jerome Langford and
my children: Bradley, Leah, John and Matthew. Your prayers, sacrifices, and words
of encouragement have been greatly appreciated and acknowledged. Words can
never express how much your support and enthusiasm have meant to me during this
journey. Blessings to our marriage and family!
This dissertation is also dedicated to the memory of my parents, Arthur and
Charlene DeLoach. Your commitment to education and the importance of
persistence coupled with integrity have been pillars of strength during this entire
process. Dad, it was largely your unfilled desire for a quality education that
encouraged and strengthened me to persist, even when faced with tremendous
obstacles. And Mom, your desire to be a teacher, always reminded me of the honor
associated with imparting knowledge and truth.
My sisters, Diane, Darlene, Gwen, Brenda, and Angie, and my brother, Allen
have been consistent sources of encouragement and love. I will always remember the
late night chats and mini celebrations during this journey.
In memory of my parents, Arthur and Charlene DeLoach,
“Teach a child in the way she will go, and
Even when she grows older, she will not depart from it.”
iii
ACKNOWLEDGMENTS
I would like to acknowledge and thank my family, friends, and colleagues
who have generously supported and encouraged me during these past few years
(08/28/04 to 07/01//07) as I worked on obtaining my Educational Doctorate (Ed.D.).
Your words of encouragement and support helped me to move forward when the
thought of finishing seemed impossible. I am truly fortunate to have all of you in my
life.
I would like to express my deepest gratitude to my chair, Dr. David Marsh,
for everything he as done to make this dissertation possible. I am grateful to him for
the well-planned and structured discussions that we had and also for the words of
encouragement that he provided, both academic and personal. I deeply appreciate the
insightful feedback and support provided by the other two committee members, Dr.
Sylvia Rousseau and Dr. Carley Olsen.
A heartfelt thanks to Dr. Richard Clark, to whom, I owe my entire graduate
career. Had it not been for his unwavering support and resolute faith in me, I would
not have survived the intensity of my graduate studies. I feel extremely fortunate that
I had the opportunity to learn so much about life and learning from him.
I would also like to thank Dr. William Maxwell for showing genuine interest
in my academic progress and family life, and for being consistently charitable with
his knowledge, wisdom, and time.
iv
This journey was greatly supported by the leadership team at Northrop
Grumman Corporation. I deeply appreciate the well wishes for my final defense from
Dr. Ron Sugar. I sincerely appreciate the extraordinary support from Mr. John
Berkley, Mr. Brian DePaul, Dr. Peter Leung, Mr. John Shankle, Mr. Mike Smith and
Mr. Al Scsigulinsky. You made it possible for me to finish.
To my life long friends, Dr. Mary Haye, Ms. Mary Ellen Pratty, Ms. Debi
Leach, Ms. Nicole Castillo, Ms. Dale Harbor Day, and Mr and Mrs. Bob and Peggy
Harbor, I am so grateful to you for your faithful prayers, encouraging hugs, and
genuine positive regard. My life is deeply enriched by each of you and I am grateful
to call you friends.
I am deeply grateful to my parents, Arthur and Charlene DeLoach and
parents-in-law, Earnest and Doris Langford for supporting me and always being
proud of all educational achievements.
To my children, Bradley, Leah, John and Matthew whose angelic faces
inspired me everyday to finish this dissertation so I could blow bubbles and take
more ice cream breaks with them. Thank you for being such great children. I’m
honored to be your mom.
This dissertation is not only dedicated to my husband but I need to
acknowledge him as well. You have gently guided me during my studies and this
dissertation period. You encouraged me with tender words of wisdom and brightened
up my days with unrivaled support. Once again, thank you for all the different roles
you took to help me achieve my goal of earning a doctorate degree.
v
TABLE OF CONTENTS
DEDICATION ii
ACKNOWLEDGMENTS iii
LIST OF TABLES vii
LIST OF FIGURES ix
ABSTRACT xi
CHAPTER 1 1
INTRODUCTION 1
Overview 1
Statement of the Problem 10
Purpose of the Study 11
Research Questions 12
Importance of the Study 12
Limitations 14
Delimitations 14
Assumptions 15
Definition of Terms 16
Organization of the Study 21
CHAPTER 2 22
REVIEW OF THE LITERATURE 22
American High School Reform 22
National Achievement Outcomes 26
The Importance of Math 30
The Achievement Gap 37
State and National Reform Efforts to Improve Math 39
New School Designs 51
School Leadership and Math Reform 58
Instructional Leadership 60
Instructional Leadership and Math 73
vi
CHAPTER 3 80
RESEARCH METHODOLOGY 80
Sampling Criteria and Process 82
Selected School Profile 88
Participants in the Study 90
Instrumentation 92
Data Collection Instruments 103
Data Collection 106
Data Analysis 108
Validity and Reliability 109
Conclusion 110
CHAPTER 4 111
DATA FINDINGS, ANALYSIS, AND DISCUSSION 111
Introduction 111
Data Findings 114
Policy 128
School Design 130
Math Program Design 141
Analysis and Discusión 165
Summary 169
CHAPTER 5 171
SUMMARY, CONCLUSIONS AND IMPLICATIONS 171
Background of the Study 171
Purpose of the Study 172
Summary of Methods 173
Summary of Findings 177
Implications for Practice 187
Recommended Future Research 191
REFERENCES 193
APPENDICES 202
A School Profile Data: Simple Criteria 203
B School Selction Criteria: California Department
of Education: California Standards Test Data 204
C Key Leader Interview Guide 208
D Math Teacher Questionnaire 212
E Math Teacher Interview Guide 220
F Non-Math Teacher Questionnaire 221
vii
LIST OF TABLES
1 High School Course Patterns and Distribution of
Postsecondary Degrees 33
2 Gains in State Income from Equalizing Opportunity
for Minorities 36
3 State Grades in Descending Order 48
4 The Four General Elements of Improving Schools based on
13 Emerging Themes from the Research 69
5 Relationship of Data Collection Instruments to
Research Questions 92
6 Bolman and Deal’s Four Frames 98
7 CST Algebra 1 Assessment Data – 2002/2003 116
8 CST Algebra 1 Assessment Data – Racial and Ethnic
Subgroups 117
9 CST Algebra 1 Assessment Data – 2003/2004 118
10 CSTA Algebra 1 Assessment Data – 2004/2005 120
11 Comparison of Land High and Statewide CAHSEE Passing
Rates for the 2002-03, 2003-04, and 2004-05 Academic Years 123
12 Comparison of Passing Rates for Land High and Statewide
Subgroups (2004-05) 124
13 Land School Mathematics-Advanced Placement
Enrollment Information 2002-03, 2003-04, through 2004-05 125
14 Land High School CST Results – 2002/2003, 2003/2004, and
2004/2005 126
15 Math Teacher Questionnaire: Question 1 128
16 Math Teacher Questionnaire: Question 2 128
viii
17 Math Teacher Questionnaire: Question 18 130
18 Math Teacher Questionnaire: Question 19 130
19 Math Teacher Questionnaire: Question 14 130
20 Math Teacher Questionnaire: Question 13 132
21 Math Teacher Questionnaire: Question 14 139
22 Leadership Support and Student Achievement 140
23 Teacher Responses to Standards-Based Instruction Ítems 143
24 Math Teacher Questionnaire: Question 16 144
ix
LIST OF FIGURES
1 Trends in Average Scale Scores for the Nation in Reading,
Mathematics and Science 28
2 Percentage of U.S. 12
th
grade students scoring below basic on
NAEP exams 29
3 Trends in Average Mathematics Scale Scores by Race/Ethnicity 30
4 Requested ACI Funding by Program 43
5 Percent of Entering Freshmen Requiring Remediation, 2003 47
6 Distribution of High Quality Teachers 50
7 Modifications to the Traditional High School
Structure and [Design] 53
8 Bolman and Deal’s Four Frames 54
9 Professional Development: the Consensus View 57
10 Characteristics of Improved School Districts:
13 Themes from Research 70
11 Grade 10 Math Proficiency – 2003 75
12 Framework for Effective School Design 95
13 Effective Math Programs 96
14 Instructional Leadership Framework 99
15 Assessment of Principal’s Expertise in Math 101
16 Strategies to Overcome a Lack of Subject
Matter Competency 102
17 Script for Star Report Cards 135
18 Land High – Student Cumulative STAR Performance Report 138
x
19 Math Teacher Questionnaire – Question 31 147
20 Math Teacher Questionnaire – Question 20 152
21 Math Teacher Questionnaire – Question 41 156
22 Non-Math Teacher Questionnaire – Question 13 157
23 The 2006-07 Land High School Math Department
Master Schedule 158
xi
ABSTRACT
The purpose of this study was to identify how high school leaders in urban
schools successfully integrate policy initiatives and best practices to improve math
performance in their schools. The study investigated how school leaders, who may
not have strong pedagogical content knowledge in mathematics, garner the resources
to improve student achievement and sustain academic growth. Moreover, the study
examined how the school leaders, in the absence of instructional expertise in
mathematics, carried out functions related to fiscal management, personnel
management, change management, organizational leadership, and data collection and
analyses to successfully bring about increased math achievement outcomes.
In order to learn more about how high schools successfully integrate policy
initiatives and best practices to improve math performance in their schools, a case
study was conducted at Land High School of Southern California. The study
consisted of a single, comprehensive and ethnically diverse high school. The study
examined the school’s efforts to improve student achievement in math over a three
year period: the 2002-03, 2003-04 and the 2004-05 academic years.
A comparison of data from math and non-math teachers was presented.
Recommendations for future research were presented, including instructional
improvement and the use of motivation strategies to further promote increased math
achievement and secondary school reform.
1
CHAPTER 1
INTRODUCTION
Overview
“Today there is a new literacy—mathematics, science and technology.” (Tate, 2004,
p. 7). This new literacy is shaping employment opportunities and job structures; and
is intensifying the demand for increased educational achievement in America (Chao,
2006). As the need for a more educated workforce increases, the academic trends in
American high schools are creating a cause for concern.
America’s high schools occupy a critical role and a pivotal position in the
changing economic, technological, educational, and social landscape of the nation
(Chao, 2006; Phelps, 2003; Spellings, 2005). Despite the central position of
secondary schools and the nations growing need for “career and college ready
students,” many high school students—especially those in urban districts—report
they are not engaged in and feel bored with school (Farkas & Johnson, 1997). The
lack of students’ academic engagement and their waning interest in high school
curriculum is most manifested in declining academic outcomes for secondary
students.
The academic decline of American students was the central theme of the
1983 report entitled A Nation at Risk (NAR). The report included many statements
that garnered the attention of the American public; however, the following statement
commanded a considerable amount of attention, "The educational foundations of our
2
society are presently being eroded by a rising tide of mediocrity that threatens our
very future as a Nation and a people" (NCEE, 1983, p. 1).
The report was foundational to many past and current school reform efforts and
proposed remedies to address the academic performance of American high schools. Despite
the reform efforts of the past, the current academic performance of American high school
students is low for many types of students when viewed by national objective standards and by
international comparative studies.
The National Center for Education Statistics (NCES) (1999) estimated that
approximately 10 million American high school students entered twelfth grade
without basic reading skills, 25 million lacked knowledge of basic American history;
and 20 million were incapable of performing basic mathematical calculations. In
2003, the National Assessment of Educational Progress (NAEP) reported that only
32% of fourth graders and 29% of eighth graders tested proficient in math. In this
same report the data revealed that twelfth grade students had declined in both math
and science.
In 1995, the National Center for Education Statistics (NCES) conducted the
Third International Mathematics and Science Study (TIMSS) to investigate the math
and science performance of fourth, eighth and twelfth grade students from
approximately 50 countries. Results from the TIMMS revealed that fourth-grade
students performed well, eighth grade students experienced average outcomes, and
twelfth grade students performed below the international average. Further analysis of
3
the data from the TIMSS revealed that American schools used a less rigorous
curriculum when compared to international schools.
The more recent 2003 TIMSS report reveals minimal academic growth; less than 8%
of America’s fourth and eighth grade students who were tested in math, achieved at
the “advanced” level. The academic performance of American high school students
remains low when viewed by national objective standards and by international
comparative studies. The decline in the academic performance of American high
school students is making secondary education reform a national challenge that has
global implications.
In addition to the economic and global impact, underachievement in math is
correlated with reduce high school completion rates for the nation’s youth, especially
urban youth (Postsecondary Transcript Study (PETS, 2000).
In 2003, data from the PETS 2000 study revealed a strong correlation between
secondary-school mathematics achievement and overall college success. The study
found that students who completed rigorous math courses, such as trigonometry or
pre-calculus, experienced bachelor-degree completion rates above 60%. In addition,
the college completion rates grew to 83% for students who completed a high school
calculus course. The PETS (2000) study highlighted the direct relationship between
math achievement and college graduation rates.
In addition, the study carefully underscored the strong relationship between a
student’s overall college-level math performance and the types and rigor of math
classes completed while in high school. Lubienski (2002) fears that urban youth risk
4
being under prepared for the knowledge economy due to the achievement gap
between African Americans, Hispanics, and low-SES students and white youth.
Furthermore, Lubienski contends the “intergenerational effects of underdeveloped
systems of education continue to plague many groups such as African Americans,
Hispanics, and low-SES students.” This is especially true since students from the
aforementioned groups generally comprise the majority populations in most urban
high schools.
Math achievement is especially important for urban high school students. For
example, for urban, high school students, successful academic outcomes in math
results in increased college attendance and improved college graduation rates (Tate,
2004). In general, math achievement prepares youth, especially urban youth, for both
the workforce and higher education (Martinez & Klopott, 2005). Further, higher
education is closely associated with economic opportunity for urban youth.
According to Moses and Cobb (2001) math achievement must be regarded with a
sense of urgency.
In response to these concerns, State and National efforts to increase math
achievement in high schools have focused on state standards, improved curriculum
and instruction, better prepared teachers and related reform efforts. Currently there
are several programs that target improved math curriculum and effective
instructional practices. These needed improvements are closely associated with the
passage of the No Child Left Behind (NCLB) Act of 2001. The NCLB Act is
intended to help close the achievement gap for students with great academic needs,
5
and to help students achieve real improvements that are based on accountability
models and higher expectations for districts, teachers and students. Just as the 1965
Elementary and Secondary Education Act (ESEA) decreed that every student in the
public school system had a right to receive a quality education, the NCLB ACT
makes the same declaration for students and holds states and schools accountable by
building on a similar foundation of measurement, accountability, and standards-
based reforms.
The NCLB initiative endorsed an accountability system that holds states,
districts, school, and teachers accountable for making Adequate Yearly Progress
(AYP) toward helping students meet established goals that are based on content
standards. The AYP includes incremental targets that help to ensure demonstrated
academic proficiency by the year 2014. Districts and schools that do not meet the
AYP targets are faced with being placed in a Performance Improvement (PI)
category. Administrators, teachers, and schools in PI districts are subject to various
sanctions; and parents are given educational and school choice options to support
and supplement their child’s educational needs.
Teacher quality is another important component of the NCLB Act. The
federal government has instituted a requirement for all teachers to have demonstrated
subject-matter competence as evidenced by obtaining specific educational training
and assessments in core academic areas by the end of 2005/2006.
The overall impact of accountability on school reform has been slowly
reaching secondary schools. Reforms are needed at the high school level and can
6
only be realized if high schools are redesigned and committed to improved results
(Marsh & Codding, 2003). Additionally, in order to diminish the amount of students
who are unprepared to enter college or the work force, the redesign must make a
deliberate effort to include all students (Marsh & Codding, 2003). This is especially
important for low-SES, urban youth
New school designs that focus on student achievement and related school
features have emerged out of school reform efforts. A new kind of high school is
needed; however, the notion of a general course of study is antithetical to school
reform and performance improvement. Marsh and Codding (2003) recommend a
new school design model that emphasizes core academic skills. The school design
must incorporate intense concentration on targeted content areas. General
curriculum in a large comprehensive high school is no longer acceptable and is
contradictory to helping every student achieve to acceptable national and
international performance standards (Marsh & Codding, 2003; Codding & Tucker
2003; Darling-Hammond & Ancess, 2002). Thus, “factory model” schools are
inconsistent with higher achievement.
In large comprehensive high schools, often the curriculum is not aligned with
the instruction; the assessments are not aligned with the curriculum; and the
academic needs of individual students are outside of the teachers’ and school
leaders’ capacities. In contrast, a “small school” approach or design appears to result
in high achievement, decreased dropout rates, diminished rates of violence, and
overall student satisfaction (Darling-Hammond, Ancess, & Ort, 2003).
7
Research organizations such as the School Redesign Network at Stanford
University, and the Small Schools Project at the University of Washington are in the
process of developing tools and other processes to help increase high-performing
high schools. Preliminary findings indicate there are challenges to implementing the
small school strategy. Some of the challenges involve issues related to curriculum
and instruction, teacher expertise, and program costs (Walcott, Owens-West, &
Makkonen, 2005).
In addition to aligning assessment with instruction, accountability, and
smaller class sizes, schools must have tools available to measure and assess
instructional quality. Measuring instructional quality is one of the most important
factors impacting student achievement (Darling-Hammond, 2000). Without good
measurement data, it is difficult for teachers to make data-based decisions regarding
their instructional practices and other teaching strategies. Moreover, there are other
evidence-based instructional strategies that increase instructional quality and
outcomes. It takes effective leadership to ensure the consistent application of these
practices as well as other efforts to improve instruction. Thus, the role of the
instructional leader is central to the process of school reform, and specifically
increased math performance.
In the current climate of standards-based reforms and improved instruction,
building local capacity for improvement must be joined with new policy initiatives,
new school designs and effective instructional practices. Thus, there is a need for
principals to simultaneously adhere to core managerial/business practices in addition
8
to taking on an active and critical role of instructional leader (Supovitz & Poglinco,
2001).
For principals, the current standards-based accountability climate is inherent
with pressures to consistently monitor and measure performance outcomes, influence
and motivate school improvements, support and monitor teachers, and collect and
analyze performance data in order to make adjustments related to teaching and
learning (Supovitz & Poglinco, 2001). Fortunately, a considerable amount of
research has been devoted to studying principals who have successfully implemented
school improvements.
For schools to sustain increased achievement the local capacity for
improvement must be joined with new practices and policy initiatives. The entire
school must have a shared vision for increased student achievement and
accountability. This requires further inquiry into best practices related to
instructional leadership and high school reform, especially in the math content area.
As schools work to meet the required leadership capacity, state and local entities
must work to support instructional leaders in their efforts to improve schools.
Currently, many school districts implement policies to help support school reform.
On the other hand, there are schools that still fail to meet achievement targets and
require Program Improvement. In this context, further inquiry is needed to identify
best practices related to instructional leadership and improved student achievement.
In 2005, The Center for the Study of Teaching and Policy, at Washington
University, investigated the elements needed to build capacity for school
9
improvements and to implement new policy initiatives. The study found high-stakes
accountability and reform measures have produced a considerable amount of
pressure on schools, district leaders and teachers, especially in urban settings. The
study further determined that instructional leaders in urban school settings often face
additional pressures due to persistent achievement gaps, high teacher turnover and
scarcity of leadership support. Given these pressures, a new approach to leadership is
required.
Instructional Leadership is a key element in enacting change initiatives aimed
at increasing student achievement in math and all other content areas. Extensive
research has been conducted to help identify key instructional leadership practices
that support school reform and improved student achievement. According to
Marzano (2003), researchers have discovered that instructional leaders who
experience successful school reform engage in strategic behaviors that promote and
create the capacity for lasting change.
The NCLB goals require all students to be proficient by 2014. In order to
meet this goal, more information is needed to identify how urban high schools and
their leaders bring together policy initiatives and local best practice to actually
improve math performance in their schools. In addition, more information is needed
to understand how instructional leaders who may lack strong pedagogical content
knowledge are effective in improving mathematics achievement outcomes in the
context of standards-based reform.
10
Statement of the Problem
Several urban secondary schools in California have significantly lower
academic performance outcomes in the area of mathematics. Focused attention on
closing the achievement gap in mathematics by national and state agencies through
policy initiatives and published accountability reports such as Annual Yearly
Progress (AYP), the Annual Performance Index (API) and high school exit exams
has resulted in greater pressure for school districts to implement standards-based
reforms to increase students’ mathematics performance outcomes. These reform
efforts are not always easy to implement in urban schools; primarily because urban
schools have to contend with several competing issues, while simultaneously
adhering to reform efforts and practices. For this reason, it is imperative to better
understand how schools that are demonstrating mathematic improvements have
promoted reform and math achievement for all students. Therefore, it is important to
examine the instructional practices that resulted in increased math performance; the
role of the leader and the process used to address dilemmas related to math content
expertise; the issues surrounding school design models and the process of
successfully implementing change.
Effective instructional leadership is viewed as a central component of school
reform success. Effective leaders create a shared understanding of the organizational
goal. They provide support and training to help create an atmosphere that is
conducive to change and instructional improvements. This includes a focus on
academic rigor, teacher training, performance data and content expertise. However,
11
school leaders often do not have strong pedagogical content knowledge in
mathematics education, yet need to carry out functions related to financial
management, staff development, organizational leadership, and decision-making
based on data analysis and review. Little is known about how leaders work
effectively in this context.
Purpose of the Study
The purpose of this study was to conduct a case study of one secondary
school’s mathematics reform design and implementation efforts. It examined factors
that positively influenced the math performance of secondary students. This study
investigated a school’s math achievement as a result of policy initiatives in
standards-based curriculum and instruction. This study investigated the high school’s
instructional practices and design; leadership factors that shaped the design for
mathematics reform; strategies educational leaders used to drive the instructional
reform; the extent of instructional and leadership barriers that needed had to be
addressed during the reform process; and how effective the reform was in sustaining
improved teaching and learning practices. The focus was on the nature of the school
site’s administrative and leadership roles in the mathematics improvement reform
efforts. Additionally, the study examined how instructional leaders, who often lack
strong pedagogical content knowledge in mathematics education, were able to
impact significant mathematics achievement at the school site.
12
Research Questions
1. What was the pattern of math achievement for various students at the
school?
2. What policy initiatives as well as curriculum, instruction and related
conditions seem to be related to improved math achievement at the
school?
3. What change process did the school use to enhance the math program and
strategies to assist students in math?
4. To what extent was strong instructional leadership important in
improving: A) the math programs/strategies and B) math achievement
among students?
5. How did leaders in the school resolve the dilemmas about instructional
leadership?
Importance of the Study
The findings of this study will have relevance to school district leaders,
school site leaders, educational researchers, state policymakers, classroom teachers,
district administrators, site and administrators. This study will contribute to the
existing body of knowledge on the subject of mathematics improvement and
achievement, instructional practices and effective leadership behaviors in the context
of secondary school reform.
The study provides an opportunity for educational researchers, schools and
school districts to benefit from comparative examination of the mathematics
13
program, achievement efforts, and instructional practices within secondary schools
and across other organizations. The study will also provide educational researchers
with a means to evaluate best practices in mathematics instruction for similar
organizations. In addition, the study helps school district leaders acquire a broader
understanding of how to increase mathematics achievement at other school sites.
Although the study investigates a single school, the findings serve to identify how
the instructional practices, mathematics content and instructional leaders serve to
enhance math achievement in secondary schools.
For educational researchers, the study provides insight into the process of
distributed leadership in the context of achieving instructional reform, and provides
strategies for overcoming barriers through the use of distributed leadership at school
sites. This includes teacher leaders and other personnel in formal and informal
leadership roles within the organization.
Classroom teachers need tremendous support when implementing reform
efforts. Given the nature of their role and their sphere of influence, it is important
that they fully understand effective instructional practices and district-led reform
efforts that lead to equitable instruction for all district students. This study will help
teachers clearly identify the significant role they have in implementing change and
sustaining district reform efforts.
Professional organizations will benefit from this study as it provides a
thorough analysis of a single district-led effort to improve math instruction. This
14
study will also provide insight into implementing systemic change to benefit
districts, schools, teachers, and students.
State policymakers need current information to fully understand the process
that school sites must endure to transform mandates into meaningful classroom
practices. Analysis and findings related to mathematics reform strategies may assist
lawmakers in setting policies related to math improvement.
Limitations
The following is a list of limitations of the study and findings:
1. The study was limited to the high schools in California’s Los Angeles
Ventura and Orange counties.
2. The study is not longitudinal; data is collected in a short time frame.
3. The data is subject to participants’ possible biases and willingness to
participate in the study.
4. The findings and data analysis may not be void of the researcher’s
biases and interpretation of the data collected through the interview
and literature review.
Delimitations
This case study is qualitative and quantitative and employs purposeful
sampling in the school selection process. The generalizability of the findings is
beyond the scope of the study and any applicability will be subject to the reader’s
interpretation of how the findings from this case study are pertinent to their own
15
instructional environment and circumstance. In addition, the following parameters
served as delimitations of the study:
1. Only schools in Southern California’s Los Angeles, Orange, or
Ventura counties for this study.
2. School sites were chosen by their steady improvement in student
mathematic achievement as demonstrated by API, AYP and Algebraic
achievement.
3. One school was utilized for the study, which limits the sample size.
4. The study was based on the data and study of one secondary urban
school which impacts the generalizability of the findings.
5. The school was selected based on specific criteria of improved math
achievement.
6. The study was a qualitative case study, which impacts the ability to
draw a definitive cause and effect relationships in the findings.
Assumptions
The study includes the following assumptions:
1. The data collection instruments that were designed and utilized were
effective in eliciting and providing the information sought.
2. The respondents provided honest answers about their experiences and
perceptions when responding to interview questions and completing
questionnaires
16
3. California Standards Test (CST) and the California High School Exit
Exam are valid predictors of student’s skills and thus the schools math
program.
Definition of Terms
For the purpose of this study, the following terms are operationally defined
below:
The Academic Performance Index (API): The API is the cornerstone of the
Public Schools Accountability Act (PSAA). The API ranks school performance, sets
growth targets, and provides similar-school comparisons. The API is a single
number on a scale of 200 to 1,000, indicating how well a school has performed
academically the previous school year (California Department of Education, 2001).
Adequate Yearly Progress (AYP): AYP is an individual state's measure of
yearly progress toward achieving state academic standards. "Adequate Yearly
Progress" is the minimum level of improvement that states, school districts and
schools must achieve each year.
Achievement Gap: denotes differences in the academic achievement in of a
particular group of students. (Bridging the Great Divide (2002): Broadening
Perspectives on Closing the Achievement. North Central Regional Educational
Laboratory (NCREL).
Assessment: The processes used to collect information about student progress
toward educational goals. The form varies with what is being assessed and the
purposes for which the results will be used. Secondary Periodic Assessments
17
measure student proficiency toward California Content Standards for the explicit
purpose of improving teaching and learning (LAUSD, 2005).
Benchmark: Formative uniform measure of student progress relative to
standards. Standards-aligned assessments and assignments provide information
about progress toward the end target (California Department of Education, 2001).
Best Practices: A best practice is a technique or methodology that, through
experience and research, has proven to reliably lead to a desired result. Target Teach,
SearchVB.com Needham, MA.
California High School Exit Examination (CAHSEE): A graduation
requirement, authorized by state law in 1999, which requires California public
students, beginning with the graduating class of 2004, to pass the CAHSEE in order
to receive a high school diploma. The CAHSEE covers the curricular areas of
reading, writing, and mathematics and is 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).
Content Standards: Stated expectations of what students should know and be
able to do in particular subjects and grade levels. They define not only what is
expected of students, but also what schools should teach (LAUSD, 2005).
18
Cultural Capital: 1) Forms of knowledge; skill; education; any advantages a
person has which give them a higher status in society, including high expectations.
Parents provide children with cultural capital, the attitudes and knowledge that
creates an educational system that is a comfortable and familiar place in which they
can succeed easily (Bourdieu, 1986). 2) The term cultural capital represents the
collection of non-economic forces such as family background, social class, varying
investments in and commitments to education, different resources, etc. which
influence academic success (Hayes, E., (N.D.) The Forms of Capital).
Cultural Deficit Theory: Assumes that some student cannot achieve at high
levels because of deficits inherent in their race, ethnicity, language, or culture.
Data-driven decision-making: The process of utilizing multiple indicators to
make decisions about student placements, curriculum and instruction based on the
analysis of classroom data and standardized test data. (Massell, 2000).
Highly Qualified Teacher: 1) The definition of "highly qualified" in the law
requires that public elementary and secondary school teachers have obtained full
state certification or passed the state teacher licensing examination; hold a license to
teach in the state; and not have had a certificate or license requirement waived under
emergency, temporary or provisional. 2) A Highly Qualified Teacher (HQT) as
defined by No Child Left Behind (NCLB) is a teacher 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
19
exams or through a highly objective uniform state standard of evaluation (HOUSSE)
(NCLB, Title IX, section 9101).
Instructional Leadership: An influence that guided the activities designed to
impart knowledge or skills to students (Olsen, 2005).
Leadership: "Leadership is a process of influence leading to the achievement
of desired purposes. Successful leaders develop a vision for their school based on
their personal and professional values [and goals]. They articulate this vision through
their actions and words; they seek to ensure that their staff and other stakeholders
share the vision. The philosophy, structures and activities of the school are geared
towards the achievement of this shared vision." (School Leadership Concepts and
Evidence, Spring 2003).
Master Schedule: This is a construct that reflects the format of the school
day. The following elements are included in and are specified by the master
schedule; the length of each instructional period, when and how frequently courses
are offered, which teachers are assigned to teach specific courses and grouping of
students.
National Assessment of Educational Progress (NAEP): The NAEP is an
ongoing, national assessment of what America’s students in grades four, eight, and
twelve know and can do in various academic subject areas. NAEP is administered
by the National Center for Education Statistics of the U.S. Department of Education.
One NAEP component provides states with a measure of their students’ academic
20
performance over time and a comparison to the results of other states and students
nationwide (California Department of Education, 2001).
Pedagogical Content Knowledge: Identifies the distinctive bodies of
knowledge for teaching. It represents the blending of content and pedagogy into an
understanding of how particular topics, problems or issues are organized,
represented, and adapted to the diverse interests and abilities of learners, and
presented for instruction (Shulman, 1987, p. 4). Reference - Shulman, L. ( 1987).
Knowledge and teaching: Foundations of the new reform. Harvard Educational
Review, 57(1), 1-22.
Performance Bands: Bands that identify levels of student achievement based
on a demonstrated degree of mastery of specified content standards. California has
identified five performance levels for its statewide standards based assessments:
Advanced, Proficient, Basic, Below Basic, and Far Below Basic (California
Department of Education, 2001).
Sanctions: The consequences imposed for not meeting expected performance
outcomes in accountability systems (Olsen, 2005).
Social Capital: The central premise of social capital is that social
networks have value. Social capital refers to the collective value of all "social
networks" [who people know] and the inclinations that arise from these
networks to do things for each other ["norms of reciprocity"].
21
Organization of the Study
This dissertation is comprised of five chapters. Chapter 1 consists of the
introduction to the study and includes; the statement of the problem, the purpose of
the study, the significance of the study, the research questions, the limitations of the
study, the delimitations, the assumptions and definitions of terms to be used in the
study. Chapter 2 is the review of relevant literature. The review addresses the current
status of secondary school performance in math with a focus on urban schools.
Chapter 2 addressed best practices used by math teachers and the nature of the
Principal’s role as an instructional leader and change agent for secondary school
reform efforts and instructional improvements in math. Chapter 3 outlines the
methodology used for the study and describes the data-collection instruments,
conceptual frameworks, the sampling criteria, and the selection process of
participants. The data analysis and overall findings of the study are presented in
Chapter 4 and includes a discussion concerning the meaning of the data. Chapter 5
provides the summary of the study and offered recommendations and potential best
practices that are based on the findings. The references and appendices follow
Chapter 5.
22
CHAPTER 2
REVIEW OF THE LITERATURE
American High School Reform
In August 1981, Terrell Bell, President Ronald Reagan's secretary of
education, called together a committee of education experts and tasked them with
investigating the state of education in America. Eighteen months later, the
committee--the National Commission on Excellence in Education (NCEE)--
submitted the resulting 1983 report entitled A Nation at Risk (NAR). The report
included many statements that garnered the attention of the American public;
however, the following statement commanded a considerable amount of attention,
"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" (NCEE,
1983, p. 1). The Nation at Risk (NAR) report characterized the public schools as “failing”
and called attention to the risks that the failure posed to the economic growth and national
defense of the United States of America (NCEE, 1983). The report was foundational to many
past and current school reform efforts and proposed remedies to address the academic
performance of American high schools. Despite the reform efforts of the past, the current
academic performance of American high school students is low for many types of students
when viewed by national objective standards and by international comparative studies.
To fully identify the nature of the academic performance of American high school
students, it is important to present a review of the literature that is relevant to this study. First,
23
an overview of recent reform efforts need to be reviewed to provide a context for
understanding how American high school students are performing when compared objectively
to their American peers attending public schools. In addition, and due to global competition,
international commerce, and technological advances; it is important to understand how
American students rank in national and international comparative studies, especially in the
subject area of mathematics. Since the growing underperformance in math in America is
critical to the nation’s security and economy, it is important to examine reform initiatives at the
state and local levels that are designed to increase math achievement for economically
advantaged- and disadvantaged-high school students. Furthermore, it is important to identify
the educational leadership and instructional practices that support closing the achievement gap
in math and other educational outcomes.
The current underperformance of American High School students was forecasted by
Glenn Seaborg, a 1983 NCEE commission member and Nobel Prize-winning chemist.
Ten years after the release of NAR, Seaborg was still writing about the priority of the
pre-college educational crisis and the urgent need for reform (Chubb,
Williamson, Chester, & Finn, 2006). Unlike Seaborg, many Americans were jolted by the
findings from the 1983 report, which included common strategies to address the looming
educational crisis such as: new educational agenda, more targeted spending, and increased
high-school graduation requirements.
One of the reforms offered by the NCEE was to require high schools to adopt a core
curriculum for its students. The recommended core high school curriculum included: (a) 4
years of English; (b) 3 years of mathematics; (c) 3 years of science; (d) 3 years of social
24
studies; and (e) one-half year of computer science (NCEE, 1983, Recommendation A section,
1) This was an ambitious recommendation since less than one-fifth of the high school students
in America currently met the recommended course requirements when the NCEE released the
A Nation at Risk report (Frontline, 2002). The academic underachievement of American high
school students created a growing concern for business leaders and educators alike.
Recent History of Education Reform
In 1985 the Carnegie Forum on Education and the Economy revealed the economic
impact of the declining educational performance of American High School students. The
1985 data revealed that almost 75% of the American corporations needed to provide remedial
support in reading, writing, and computation for newly hired employees. In addition, other
countries appeared to be taking over the automobile, manufacturing, and high-tech jobs that
had largely been dominated by American companies; the loss of market share had global
implications for the United States economy (Wong, Guthrie, & Harris, 2003).
When NAR was released in 1983, America was engaged in a significant arms build-
up in response to the Soviet Union. During this era, the national security leaders looked to
American companies for the development of military weapons that were more high-tech and
advanced. Although the military was not the primary audience for the NAR report, the NCEE
committee members equated the findings from the NAR as a national educational challenge to
the military as well. The Department of Navy expressed their concern to the Commission and
reported that over 25% of their recruits were unable to read at a ninth grade level and required
remedial training to be able to read safety-related instructions. Furthermore, the recruits had to
25
complete the remedial training prior to engaging in more sophisticated weapons training
(Wong et al., 1983).
Drawing from the educational, military, and political climate at that time, the NCEE
members wrote, “If an unfriendly foreign power had attempted to impose on America the
mediocre educational performance that exists today, we might well have viewed it as an act of
war. We have, in effect, been committing an act of unthinking, unilateral educational
disarmament (NCEE, 1983, p. 5).
There was a sense of urgency. Many businesses began to partner with government
officials and educators to address the alarming findings from the NAR report. Many changes
resulted from implementing standards-based educational reforms recommended by the NAR.
According to the National Center for Education Statistics, by 1990 almost 40% of graduating
high school seniors met the core curriculum requirements recommended in "A Nation at
Risk." The education reform efforts coupled with government officials and the business
community began to make progress at the state level (Frontline, 2002).
In 1989, President George H. W. Bush summoned the nation's governors to the first
National Education Summit to draft education goals at the federal level. The National
Education Summit identified 6 educational objectives and established a goal to reach them by
the year 2000; thus, they named Bush’s education proposal--America 2000. After President
Clinton was elected, he continued to build on Bush’s education proposal, naming it the Goals
2000: Educate America Act. The Act was signed into law in 1994, giving approval authority
of the states to the federal level. An increased federal role over the states’ education was met
with strong resistance by politicians, state officials, and educational leaders. Since
26
many states had had already began to establish some form of accountability by 1994,
they did not want their state’s education policy governed at the federal level (Elmore,
2006). Consequently, the council for the Educate America Act was never
established.
Today, the No Child Left Behind (NCLB) Act of 2001 is another federal
reform, educational initiative that has bipartisan support. Unlike the previous
educational proposals and reforms -- A Nation at Risk, America 2000, and Goals
2000 -- the NCLB Act concentrates on prioritizing educational efforts, testing
students and holding schools accountable, through standards-based assessments. The
NCLB aims to lessen the achievement gap between the “economically advantage and
disadvantaged students” and targets increasing the reading and math performance of
students in urban and poverty rural communities.
National Achievement Outcomes
Today, 23 years after the release of the Nation at Risk and numerous reform
initiatives; the achievement gap persists and represents a serious national challenge
for us all. Moreover, if the American public schools were a business it would have
closed its doors by now due to failure (Gates, 2004). Recently the American public
schools allowed 25% of it’s students to read below basic levels (Grigg, Daane, Jin,
& Campbell, 2003) failed to graduate 30% of its students (Swanson, 2004); and
prepared more economically-advantaged than disadvantaged students for college-
level work (Wirt, Choy, Gruner & Sable, 2000). According to Bill Gates, “Our high
schools were simply not designed to prepare all students for college learning, high-
27
tech workplaces, and 21st century citizenship” (Gates, 2004). The underperformance
of American students has been a growing concern for the last 20 years and has led
elected officials and educators to call for educational reform initiatives (Elmore,
1997). Many calls for reform were based on comparative studies from national and
international performance data.
The National Assessment of Educational Progress (NAEP), also referred to as
“the Nation's Report Card,” is a nationally reliable organization that conducts
ongoing assessments of the knowledge and performance of American Students. The
NAEP has conducted studies since 1969 to periodically assess student performance
in the content areas of reading, mathematics, science, writing, U.S. history, civics,
geography, and the arts. The NEAP is administered by the National Center for
Education Statistics (NCES) in the U.S. Department of Education and is authorized
by congress to inform the public of the educational progress in grades 4, 8, and 12
(Braswell, Lutkus, Grigg, & Santapau, 2001). In 1999 NEAP conducted the last
assessment of the 20
th
century; targeting the academic performance in reading,
mathematics, and science of a representative sample of 9-, 13-, and 17-year-old
students.
The results from the 1999 NEAP assessment are mixed. The 1980s through
the 1990’s show a stable performance in science and an overall improvement in math
for all age groups; there are modest gains in reading. All three age groups
demonstrate an increase in performance in mathematics. For 9-year-olds, most of
the increase in scores occurs between 1982 and 1990. The 13-year-olds, demonstrate
28
a steady pattern of progress, and a 10-point increase in gains since 1973. Average
scores from 1984 to 1992 were higher than in 1971 for 17-year-olds; however, there
was no significant increase in scores between 1971 and 1999. Figure 1 depicts the
national trends in math scores.
Figure 1. Trends in Average Scale Scores for the Nation in Reading,
Mathematics and Science
*Significantly different from 1999
Note: Dashed lines represent extrapolated data.
Source: National Center for Education Statistics, National Assessment of Educational
Progress (NAEP), 1999 Long Term Assessment
29
The most recent National Assessment of Education Progress (NAEP) reveals
that almost 40% of 12
th
grade students attending public schools scored below the
“basic” level in math (Figure 2).
Figure 2. Percentage of U.S. 12th Grade Students Scoring Below Basic on
NAEP Exams
Source: U.S. Department of Education, National Center for Education Statistics
A more distinctive picture emerges when the trends are divided into
subgroups. The racial/ethnic subgroups measured in the 1999 NEAP assessment
consist of White, Black, and Hispanic students. Other racial/ethnic subgroups are not
reported, as the samples collected were of insufficient size to analyze and report
separately. Overall, students show an increase in math performance; however, White
students achieve higher math scores than their Black and Hispanic peers. The math
achievement gap narrows between White and Black students from 1973 through
1999 for all age groups. Unfortunately, since 1982 the gap widens for 9-year-olds.
Figure 3 shows trends in subgroups in math performance.
30
Figure 3 Trends in Mathematics Scale Scores by Race/Ethnicity
*Significantly different from 1999
Note: Dashed lines represent extrapolated data.
Source: Nacional Center for Education Statistics, National Assessment of Educational
Progress NAEP), 1999 Long-Term Trend Assessment
.
31
The Importance of Math
The link between mathematical reasoning and economic growth is evidenced
as early as 3000 B.C., when the priests of Sumer used mathematical procedures to
better understand agricultural patterns. This was accomplished largely by developing
mathematically-based calendars for agricultural planning. Their agricultural
efficiency resulted in an over abundance of food supplies and the Sumerian workers
were able to temporarily shift from farming and focus on other economically
productive tasks (McNeil, 1999). In the 21
st
century, mathematics education remains
a critical component of schooling and is the key to advancing individual, academic
opportunities and supporting the national economy (Carnevale & Fry, 2004).
Furthermore, high performance in high school mathematics is directly related to
access to competitive colleges and increased earning potential (Carnevale &
Desrochers, 2003).
Math and Academic Access
In 1988, postsecondary data was collected as part of the National Educational
Longitudinal Study (NELS: 88/2000). The majority of participants in the study were
eighth grade students who were seniors in high school in 1992. In 2000, during the
collection of postsecondary transcript data, these same participants were 26 or 27
years old. The analysis of the data resulted in the Postsecondary Transcript Study
(PETS), 2000. The PETS, 2000 study -- released in 2003 -- contained important
information about the relationship between secondary school math achievement and
college success. The study found that students who completed rigorous math courses
32
in high school, such as trigonometry or pre-calculus, experienced bachelor-degree
completion rates above 60%. In addition, the completion rate grew to 83% for
students who completed a high school calculus course (PETS, 2000). Furthermore,
as it relates to college success, the study revealed strong correlations between the
types of math classes completed while in high school and a student’s overall college
math performance, level of persistence, and accrual of college credit and graduation
rates (Table 1). Another key finding of the study is the difference in college
graduation rates between the students who complete Algebra I and Algebra II. Over
30% of the students who completed Algebra II earned a Bachelor’s Degree. In
contrast, only 8% earned Bachelor’s degrees if their highest math course was
Algebra I.
Algebra - The Gatekeeper
The TIMSS 1999 follow-up study revealed that eighth graders in the United
States scored below 18 other nations that participated in the study and ranked 19
th
out of 38 countries in the content area of Algebra. The 2005 National Assessment of
Educational Progress (NAEP) report card shows that less than 24% of eighth graders
have reached proficient levels in mathematics achievement (Giggs & Dion, 2005). In
2003, the NAEP data shows that 83% of schools offered algebra at the eighth grade
level, in comparison to only 3% in 1996. Consistent with this practice, 63% of eighth
grade math teachers report they have adopted more focused instructional practices
when teaching Algebra functions. Developing early instructional practices that help
students engage in mathematical thinking provides the exposure that is needed to
33
reinforce the integration of arithmetic and Algebra (Carpenter, Franke, & Levi,
2003).
Table 1. High School Course Patterns and Distribution of Postsecondary
Degrees (Percentage distribution of the highest postsecondary degree, the
number of college credits completed in calculus and advanced mathematics,
and the number of postsecondary remedial methematics course taken by 1992
12
th
graders, by highest level of mathematics completed in high school: 1992
– 2000).
# Rounds to Zero
Note:. The study consists of all known postsecondary participants for whom the hightest
level of mathematics completed in high school could be determined. Weighted N= 2.0
million. Detail may not sum to total because of rounding .Standard errors appear in
parenthesis.
Source: U.S. Department of Education National Center for Education Statistics, National
Longitudinal Study of 1988 (NELS:88/92/2000): “Second Follow-up High School Transcript
Study, 1992” and “Fourth Follow-up. Postsecondary Transcript Study (PETS) 2000.
34
The earlier students learn higher order mathematical skills, the stronger the
likelihood for college attendance and graduation (NCES, 2001). Early expose to
mathematical thinking is also related to the type of college the student selects, and
what degree the student will earn (Cavanaugh, Gillan, Bosnick, & Hess, 2006). Early
math achievement in Algebra is critical to students selecting and successfully
completing higher-level math courses and attending competitive institutions of
higher learning; algebra is considered a “gatekeeper” course for college admissions,
which has economic implications (Berkner & Chavez 1997; Paul, 2001).
Math and the Economy
Mathematical reasoning is foundational to the flow of the nation’s economy.
It was largely responsible for the shift from the agricultural to the industrial economy
and is partially credited with the shift from the industrial to the knowledge economy
(Carnevale & Desrochers, 2003). According to The National Manufactures
Association (NAM), (2005) increases in math achievement are directly linked to the
nation’s economic growth. Furthermore, NAM predicts if the current trends in
technology continue, by 2012 over 40% of factory jobs will require postsecondary
education; future jobs will go to highly-skilled workers and individuals with
education in science, engineering, and mathematics.
The United States currently trails emerging global forces such as China and
India in technology and engineering (Kappu & Peters, 2006). A recent report –
“Rising Above the Gathering Storm” -- from the National Academy of Sciences
35
points out that with IT and engineering skills being so dependent on math and
science skills, our future as the last remaining superpower is in question. America
now, more than ever before, has to “think globally and act locally” to effectively
respond to secondary students’ increased need for math achievement. Increased
student math achievement is correlated with a decrease in student dropout rates
(Kuttan & Peters, 2003); successful completion of college (NEC, 2003); increased
wage earnings; and national economic opportunity (Chao, 2006). In the new
knowledge economy, solid mathematical skills are critical to increased earning
potential.
When the new information economy emerged in the 1980’s, college-educated
workers experienced an increase in earnings from 37% to almost 60% in 2000
(Carnevale & Fry 2001). Remarkably, the advent of the knowledge economy resulted
in a large gap in wages between high-school educated workers and workers with
some college experience. In the same period between 1980 and 2000, workers with
acquired college experience received a wage increase that went from 43% to 73%
more than workers with only a high school education (Carnevale & Fry, 2001).
Some economists believe that closing the education gap would not increase
only individual economic opportunity, but would result in economic opportunity for
the nation. Creating equity in college matriculation and completion rates would
decrease the number of Hispanic families with insufficient income earnings from
41% to 21%. The inadequate incomes of African American families would go from
33% to 24%. These economic benefits to families would also help increase the
36
nation’s income by $230 billion and provide an additional $80 billion in taxes. The
states would also benefit from creating equitable access to education as well.
“…growth in state wealth would be $73 billion in California, $44 billion in Texas,
and $22 billion in New York, and it would also spread broadly among most states”
(Carnevale & Fry, 2004) (see Table 2).
Table 2. Gains in State Income from Equalizing Opportunity for
Minorities (dollars in billions)
Source: Educational Testing Service. Analyst of U. S. Current Population Survey Data
37
The Achievement Gap
Student Motivation and Self-Efficacy
Although an increase in state revenue is an important economic cause for
closing the achievement gap, increasing academic performance for all students is an
equally notable goal. In general, children enter school without preconceptions of
their math ability; they see math as content that can be learned just as well as reading
and writing. Unfortunately their innocuous view of math changes during middle
school and high school (Middleton & Spanias, 1999; McLeod, 1992) and impacts
whether they will attend college or enroll in college math courses (Middleton &
Spanias, 1999). This should not be interpreted as the student’s lack of interest in
math; however, it may be related to a student’s self-efficacy and motivation (Bishop,
1995; Malloy & Malloy, 1998). The loss of interest in math--as students progress
through school--may be related to their self-concept and not lack of ability (Ingleton
& O’Regin, 1998). In keeping with other reform efforts, the affective aspects of
students must be taken into consideration for math education reform (Geogheghan,
2002).
International Comparisons
There is evidence from the 1995 Third International Math and Science Study
(TIMMS) that American high school students are underperforming in math. U.S.
high school students ranked 19 out of 21 nations, surpassing the performance of
Cyprus and South Africa. John Leo (1998) from US News and World Report,
38
pointed out that the performance might be more dismal than we think. Leo wrote, “If
the Asian countries who ordinarily score very high on TIMSS exams, had
participated, we might have been fighting for 39th place in a field of 41.”
In contrast, the results of the 2003 TIMMS show signs that students in the
United States are making progress in math achievement. In the United States, fourth
and eighth graders scored above the international average and minority students
made a considerable gain at the eighth grade level. In a recent bulletin from the
NCTM (2005), they stated the following:
• U.S. fourth grade students performed above the international average in all
mathematics content areas except measurement, where they scored at the
international average.
• Only six of 25 countries outperformed U.S. fourth graders in patterns,
equations, and relationships, and only four countries did so in data.
• American eighth graders exceeded the international average on mathematics
achievement, outperforming students in 25 other countries. (Only nine
countries earned scores above the U.S. scores.)
• Only eight of 48 participating countries outperformed U.S. eighth grade
students in algebra and in data. The lowest performance of U.S eighth grade
students was in geometry, where 21 countries bested them.
• U.S. Black students in both grades four and eight showed improvement.
• In grade eight, Black and Hispanic students showed large jumps in average
mathematics scores since 1995, improving by 29 and 22 score points,
respectively.
• In grade eight, the achievement gap narrowed significantly among Black,
Hispanic, and White students, with Blacks closing the gap by 20 points. In
1995 there was a 97-point difference between the average mathematics scores
of White and Black students. That gap was reduced to a 77-point difference
in 2003. The difference between average mathematics scores of Whites and
39
Hispanics was reduced by 13 points (down from a 73-point gap in 1995 to a
60-point difference in 2003).
In light of the good news from the 2003 TIMMS, it’s a sobering reality that
American 12
th
grade students are underperforming, especially minority students.
“By 12th grade, the average African American and Hispanic students can only do
math and read as well as a White eighth grader. In addition, high school completion
rates remain markedly lower for students of color” (AERA Research Points, 2004).
Results for the NAEP 2000 Mathematics Assessment show overall gains in
fourth, eighth, and twelfth graders' national average scores since 1990, the first year
in which the current mathematics assessment was administered. Fourth and eighth
graders made steady progress, with higher average scores in 2000 than in 1996,
1992, or 1990. However, this was not the case for 12th graders. Although 12th
graders' average score was higher in 2000 than in 1990, it was lower in 2000 than in
1996.
State and National Reform Efforts to Improve Math
States still have the responsibility for education in the United States, and in
the era of reform, state-level policies influence four important areas: content
standards, student assessments, teacher preparation, and school accountability (Blank
& Langesen, 1999). In the subject of math, many states are leading the effort to align
standards-based reform with math content instructional practices, and assessment
strategies.
40
Math performance results from the 2005 NAEP report reveal strong evidence
that math achievement has improved for the last 15 years for many American
students. For example, 4
th
graders experienced a gain from 50 to 80% during the
1990 to 2005 academic years. In addition to the above noted performance gains, the
number of 4
th
graders performing at or above the proficient level increased from 13
to 36%. During this same period of time, NAEP data indicated that 8th grade
students gained a 50% increase in the number of students achieving “proficient”
levels of performance; however, the performance of 12
th
grade students remained low
and relatively unchanged. The NAEP longitudinal data shows no increase in math
performance between 1999 and 2004 for 12th grade students. This stagnant
performance has resulted in an increase in the achievement gap between the United
States and other nations, and a dismal rank of 24
th
out of 29 nations (PISA, 2003).
The low and declining performance of the nation’s 12
th
graders is prompting
continual state and national reform efforts to improve high school math achievement.
Since the Second World War school improvement studies have flourished.
During the last 30 years a series of school improvement studies have been
undertaken to provide insight and guidance into characteristics of effective schools,
student achievement, and school reform (Marzano, 2000). An overview of school
improvement studies from the three previous decades provides a context for
understanding the current state and national reform efforts to reform math
achievement in high schools.
41
During the 1970s and 1980s--the decade characterized as the School
Effectiveness Movement--researchers focused on identifying “basic” instructional
content, classroom practices, and student achievement factors (Marzano, 2000; van
Meeter, 1998; Cohen & Hill, 1997). The research from the 1980s to the 1990s is
characterized by several seminal works: The NCEE Nation at Risk report (1983);
Bloom’s (1984) instructional practices and strategies, mastery learning and effect
size work, Walberberg’s (1980) productivity model, framework of student
achievement and motivation influences, and Faser’s and Hattei’s (1987) meta-
analyses of factors that influence student achievement.
From 1990 to 2000 educational research (national and international)
proliferated. Researchers shifted the focus of their investigations to educational and
instructional outcomes, such as monitoring students who tests at the “basic” and
“proficient” levels on state assessments and comparative international studies such as
TIMMS and PISA.
This shift in focus lead to the educational proposals and reform efforts noted
earlier: the America 2000 educational proposal enacted by President George H.W.
Bush; the Goals 2000: Educate America Act signed into law by President Clinton;
and the No Child Left Behind (NCLB) Act of 2001. In 2002, when President George
W. Bush signed the NCLB Act into law, many states had already began to adopt
more state-level accountability measures, implement educational standards and
engage in regular assessment practices and studies. When the NCLB Act was signed,
many of the existing state reforms, in the context of math achievement, had their
42
roots in the previous 30 years of school improvement research and national reports
such as, “A Nation at Risk,” 1983; “A Report on the Crisis in Mathematics and
Science Education,” 1984 and the “Curriculum and Evaluation Standards for School
Mathematics” 1989 by the National Council of Teachers of Mathematics (NCTM).
The math achievement reform agenda gained a considerable amount of
momentum after the release of the 1995 TIMMS. According to the Council of Chief
State School Officers (CCSSO) (2003) by the end of 1990 most schools had at least
one of the 4 components comprising school reform established (i.e., content
standards, performance standards, learning assessments and accountability systems).
Between 1995 and 2000 almost all the states had math content standards in place; the
number grew from 25 to 49 states.
American Competitiveness Initiative ACT
Currently, reforms in mathematics instruction are a top priority for many
states, educators, business leaders, military personnel, policymakers, universities and
the federal government. The effort to enact reforms has resulted in various changes
to secondary education including math instruction and a movement toward curricular
alignment with postsecondary institutions (Zapf, Spradlin, & Plucker, 2006).
The most recent initiative, the “American Competitiveness Initiative” (ACI),
presented by President George W. Bush in February, 2006, is intended to help the
United States re-establish its competitive edge through scientific advancement and
innovation (Zaph et al., 2006, p. 5). A key component of the initiative is rigorous
preparation in a secondary education system which provides access to additional
43
math, scientific and technical areas in postsecondary institutions. President Bush has
proposed $380 million in new federal funds to help strengthen the quality of
mathematics, science and technological education in elementary and secondary
schools (Domestic Policy Council, 2006).
The ACI sites the following recommendations to accomplish the secondary
math and science education experience: 1) Expand the Advanced Placement and
International Baccalaureate programs; 2) Encourage mathematics and science
professionals to become adjunct high school teachers; 3) Appoint a National Math
Panel to evaluate and improve mathematics and science instruction; and 4) Establish
a Math Now for Elementary School Students and Math Now for Middle School
Students to promote promising and proven methods of mathematics instruction (see
Figure 4 for funding by program).
Figure 4. Requested ACI Funding by Program
44
Math Content Standard Reforms
Publications, such as A Nation Prepared: Teachers for the 21
st
Century (Carnegie
Forum on Education and the economy, 1986) followed the release of NAR in 1983
and brought attention to the need for common instructional practices in math
education.
The National Council of Teachers of Mathematics (NTCM) brought together
members of its constituency to develop K-12 mathematics standards. This effort
resulted in the Curriculum and Evaluation Standards for School Mathematics
(NCTM, 1989). The standards were intended to provide a single and consistent
curriculum guide for math instruction.
The Professional Standards for Teaching Mathematics was the next set of
standards released by NTCM, (1991). This was followed by the release of the 1995
Standards for School Mathematics. The standards targeted math improvement and
sought to help educators realize that effective math instruction involves more than
memorizing math facts (Weiss, Knapp, Hollweg, & Burrill, 2001). As new
knowledge was gained through educational research and policy initiatives, the
NCTM released the Principles and Standards for School Mathematics (2000) to
establish guidelines for aligning instruction with assessments (Weiss et al., 2002).
According to NCTM, the standards are designed to:
• Set forth a comprehensive and coherent set of goals for mathematics for
all students from pre-kindergarten through grade 12 that will orient
curricular, teaching, and assessment efforts during the next decades;
45
• Serve as a resource for teachers, education leaders, and policymakers to
use in examining and improving the quality of mathematics instructional
programs;
• Guide the development of curriculum frameworks, assessments, and
Instructional materials;
• Stimulate ideas and ongoing conversations at the national, provincial or
state, and local levels about how best to help students gain a deep
understanding of important mathematics (NCTM, 2000, p. 6).
Prior to NCLB, the Mathematical Sciences Education Board (MSEB) (1990)
sought to have states revise their school mathematics programs and align their
content with the NCTM “Standards.” Thus, many states had already begun to adopt
more state-level accountability measures, engage in regular student assessments and
implement math content standards. These content standards served to identify what
students should know and be able to accomplish (Hurst et al., 2003). However, due
to the performance on standardized tests and the need for postsecondary remediation,
there is concern that the math standards are not being consistently applied.
American Colleges and Universities
The growing need for remedial education for students entering colleges and
universities has created a heightened national concern regarding the adequate
preparation of secondary students (Hoyt & Sorensen, 2001). Now more than ever
before are new curricular content reforms and policies needed to give all learners an
opportunity for access to higher education. According to Testone (2001), the
46
mathematics content reform has been studied extensively by several organizations
and professionals. For example, documents from NCTM (1989, 1991, 2000) urged
for changes to the curriculum and outlined standards for math instruction for grades
K-12. Additionally, Moving Beyond the Myth (1991) by the National Research
Council (NRC), proposed changes to the content and pedagogy for mathematics
education for elementary school through graduate school.
As students started attending college, several colleges noticed an increase in
the need for remedial math classes. There were appeals to the state from higher
education math departments to reform high school math content. In addition, scores
from the NAEP showed an increase in the performance gap between White and
minority 17-year-olds, creating a dismal picture for students who were about to
graduate from high school.
California
Students in California and many other states were experiencing declining
math scores on standardized math tests (see Figure 5), making it necessary for many
states to focus on math reform efforts by adopting state standards. Some states
adopted new curricula, others focused on teacher professional development. Still
others incorporated technology with math instruction (Walcott, Owens-West, &
Makkonen, 2005). Statewide academic standards were needed to promote
consistency in instructional content and materials as well as goal- directed
instruction.
47
Further, tests needed to be aligned with state standards to form the core of
professional development programs for teachers as well (Klein, 2003).
Figure 5. Percent of Entering Freshmen Requiring Remediation, 2003
Note: Because each system develops in its own standards for remdiation, the figures are not
comparable.
Source: Hill, E. (2005, May) Improving high school: A strategic approach. Sacramento, CA
Legislative Analyst’s Office p. 57
To support this process, the Thomas B. Fordham foundation devised a set of
criteria to evaluate the effectiveness of the math content standards adopted and
implemented by the states. Each state’s math standards were rated in 4 categories:
clarity, content, reasoning, and negative qualities. California was one of 3 states that
received an “A” for its content standards framework. The other states earning an
48
“A” were Indiana and Maryland (see Table 3). The average grade was D and more
than half received grades of D or F.
Table 3. State Grades in Descending Order
Increased Accountability
The NCLB legislation has resulted in a considerable amount of efforts to
increase school accountability. Public schools throughout the nation are now
accountable in two key areas. First, the public schools are required to increase all
student performance to the proficient level in core subjects, such as math and
reading, by 2014. As such, schools and districts are accountable for the Adequate
Yearly Progress (AYP) of students as they work to achieve 100% proficiency for all
students. Schools that fail to meet the AYP targets are labeled “Program
Improvement Schools,” and are subject to state-mandated corrective action. This
includes mandated leadership and staff changes, loss of federal funding and other
corrective actions.
49
The second NCLB accountability metric is the Highly Qualified Teacher
(HQT) requirement. The NCLB legislation required all teachers to become "highly
qualified" by the end of the 2005-2006 school year.
According to the HQT definition, teachers were required to have:
• State certification or licensure
• A bachelor’s degree or higher
• Demonstrated competency in the subject(s) he or she teaches
The demonstration of subject matter knowledge is achieved by accomplishing the
following: 1) passing a test in the subject-matter content area, 2) earning a college
major in the subject, 3) completing a state-defined peer review (for veteran teachers):
High Objective Uniform State Standard of Evaluation (HOUSSE).
There is strong evidence that teachers are one the most critical elements in
student achievement (NCES, 2000). Yet, many urban, high-poverty and high-
minority schools have high teacher turnover rates and a greater percentage of
inexperienced teachers than schools with fewer poor and minority students
(Figure 6).
The retention and recruitment of highly qualified teachers (HQT) in urban
schools are critical to increasing student achievement and overall school reform.
Many of the studies that examine the effectiveness and sustainability of reform, often
address the issue of teacher buy in and teacher quality. This is because teachers are
critical to the academic success of all students (Sanders & Rivers, 1998; Sanders &
Jordan, 2000; Tyack & Cuban, 1995). Despite the AYP and HQT accountability
50
measures, many states have instituted additional reform measures to further monitor,
support and sustain the reform process.
Figure 6. Distribution of High Quality Teachers
Source: National Center for Education Statistics. “Monitoring Quality: An Indicators
Report,” December 2000
California initiated additional legislation to support NCLB Act. California
developed the Academic Performance Index (API) measure as part Public Schools
Accountability Act of 1999. The API is a measure of the schools progress in
increasing student achievement as evidenced by student performance on standardized
tests. Schools are required to achieve a minimum score of 800. Schools already
scoring 800 are still required to verify progress by at least 1 API point each year.
51
The new accountability requirements are placing increasing pressures on
districts, schools, principals, teachers and students, and are increasingly playing an
important role in school reform.
New School Designs
The current high school reform movement requires many changes in the
school as a whole unit. The need for comprehensive, high school reform has resulted
in efforts to create new school designs that concentrate on student achievement and
increasing student performance. This includes changes in “its leadership,
management, and organization; in its climate, ethos, and priorities; in the way it uses
the money and human resources available to it; in the things it values and its
aspirations for its students” (Marsh & Codding, 1999, p. 137). There is a widely held
belief among educational leaders that when students are expected to achieve their
performance increases (Marsh & Codding, 1999; Fisher, Tietelbaum, & Emanuel,
1999). The high-level student expectation and performance must be embraced by the
entire school for the change to occur. In addition, making changes that result in
instructional improvement has to be the main goal of the educational leader (Elmore,
2001).
In the context of school reform, Marsh and Codding (1998) also identify five
important elements of the school that need to be considered for new-school design
initiatives:
• school cultures
• school size (smaller)
52
• learning activities
• performance assessments
• instructional curriculum
These 5 components that comprise Marsh and Codding’s model for new school
designs evolved from a considerable amount of research led by Ron Edwards starting
in 1970. The research conducted by Edwards and other is foundational to current
studies that examine new school design.
The high schools in America were not designed to change with the needs of
the nation’s knowledge-based economy or major reform efforts. The majority of
high schools are based on a century-old design that was intended to accommodate a
small portion of high school graduates and an even smaller group of students
enrolling in postsecondary studies. A “factory model” characterizes the design of
high schools. In this model both the teachers and students are accustom to large
groups of students working independently from the teachers and attending up to
eight different subjects a day (Walcott, Rose Owens, West, & Makkonen, 2005).
The Marsh and Codding (1998) model and other school design efforts are
more student-focused and incorporate many of the elements listed in Figure 8. These
new school designs were adopted to support high school reform efforts and to
promote standards-based instruction in schools. However, implementation of these
designs required the instructional leader to also function as a change agent.
53
Organizational Change
According to Bolman and Deal (2003), change can only occurs when the
leader addresses specific aspects of the target organization. Principals face an even
greater challenge when it is commonly known that they are tasked with making
changes and designated to serve as a change agent. Bolman and Deal's (1984; 2003)
reframing theory provides school leaders with a systematic way to view and navigate
through the organizational change process. The theory consists of 4 frames: (1)
structural, (2) human resources, (3) political, and (4) Symbolic.
Figure 7. Modifications to the Traditional High School Structure [and
Design]
Modifications to the Traditional High School Structure and [Design]
Curricular
Alignment
Alignment between secondary schools and postsecondary institutions can help define what
students need to know to be successful. This curricular alignment can help prepare
students for success in college or the workplace by ensuring they have attained the
necessary skills.
Smaller
Learning
Communities
Smaller learning communities (SLC) in high schools, such as career academies or
freshman centers, break students up into subgroups to provide an environment where
students are able to develop closer relationships with teachers and peers. SLCs such as
career academies emphasize the relationship between academics and the workplace and
have been shown to decrease drop-out rates and improve work attendance and job
performance (Maxwell & Rubin, 2002).
Alternative
Schools
Alternative schools provide an option for students who do not function well in traditional
schools. Alternative schools use different curricular and structural methods to help
students complete their high school education in an environment that is more suited to
their academic and social needs (Raywid, 1994).
Middle
College High
School
Middle college high schools provide at-risk students with the opportunity to attend high
school on a college campus. In addition to being able to complete high school and prepare
for college, students also have the opportunity to earn college credit during high school.
These high school structures have been shown to decrease drop-out rates, increase college
attendance, and improve students’ writing proficiency (Conley, 2002)
Competency-
based
Promotion
Competency-based promotion allows for grade promotion based on students’
demonstrated competency. It allows those students who demonstrate a need for additional
instruction to receive it, and students who demonstrate mastery in certain areas to progress
to the next educational level (Webb & Bunten, 1988).
Source: Plucker, Zapf, & Spradlin (2004, p. 5)
54
These 4 frames serve as a conceptual framework for practices by instructional
leaders that lead to positive outcomes and instructional improvements (see Figure 8).
A single, focused, goal of instructional improvement is consistent with several
researchers approach to school reforms supported by the instructional leader
(Andrews & Soders, 1987; Elmore, 2001; Datnow, 2003).
Figure 8. Bolman and Deal’s Four Frames
Frame Structural Human Resources Political Symbolic
Metaphor
for
organization
Factory or
Machine
Family Jungle Carnival,
Temple, Theater
Central
Concepts
Rules, Roles,
goals, Policies,
Technology,
Environment
Needs, Skills,
Relationships
Power, Conflict,
Competition,
Organizational
politics
Culture,
Meaning,
metaphor, ritual,
ceremony,
stories, heroes
Image of
Leadership
Social
Architect
Empowerment Advocacy Inspiration
Basic
Leadership
Challenge
Attune
Structure to
task,
Technology,
environment
Align
Organizational and
human needs
Develop Agenda
and Power Base
Create Faith,
Beauty, Meaning
The Structural Frame
The structural fame of leadership is concerned with the extent to which
leaders articulate goals clearly and consistently, act logically, and hold themselves
and others accountable (Bolman & Deal, 2003). In the current climate of school
reform there is a tremendous degree of mutual accountability. “Pressure is on actors
at all levels, from students themselves to teachers, principals and superintendents. In
these times of heightened concern for student learning, school leaders are being held
accountable for how well teachers teach and how much students learn”(Leithwood &
55
Riehl, 2003, p. 3). In the context of educational reform, effective leadership
translates to effective instructional leaders.
The impact of effective school and instructional leadership on student
achievement is significant. Students who attend effective schools have an increased
(44%) passing rate on tests (Marzano, 2003). Bolman and Deal’s structural frame
provides a means by which instructional leaders can work to develop organizational
goals and objectives; and create the strategies and structures across the school unit
from which to achieve them. More importantly, this often has to be done in an
environment of scarce or limited resources and requires strong organizational and
people skills. The human resources frame provides leaders with the means to be
effective and efficient in handling scarce resources at the school site.
Human Resource Frame
In this age of accountability and standards-based reform there is often a need
for shared or distributed leadership to make positive changes. Bolman and Deal’s
(2003) human resource frame indicates that the process of leadership is just as
important as the task of leadership. In this climate of increased demands it is
important for educators and educational leaders to realize that standards- and
performance-based accountability is intended to increase academic performance
outcomes for all students. This can only be accomplished using strategies that
include collaborative and professional development, shared leadership and
reorganization of traditional educational structures (Elmore, 2003). This includes
integrating professional development during the routine course of everyday work
56
(Elmore, 2003). However, what professional development activities are effective for
education reform? Figure 9 contains of summary of a growing consensus of
effective professional development strategies. Elmore (2003) posits that effective
development strategies include the following elements listed in Figure 9:
In addition to effective professional development, the human resource frame
provides the educational leader with a frame from which to monitor and measure
interactions with the teachers and other staff members. Moreover, professional
development is a central component in the context of educational reform and is a
critical responsibility of educational and instructional leaders (McLaughlin, 1991).
As cited in Vavasseur (2003) the current research indicates the principal’s primary
role is to support teacher learning and increase retention (Blasé & Blasé, 2000;
Bolman & Deal, 2002; Fleming, 1999; Fullan, 2002; McLaughlin, 1991; Morrissey,
2000), and consistently focus on the teaching and learning process (Darling-
Hammond, 2003; Elmore, 2002; Fullan, 2004). It is important for the educational
leaders to promote trust within and between the teacher groups and to create a
climate that is conducive to collaborative and professional training and support.
Symbolic Frame
Bolman and Deal’s (2003) leadership frames include the importance of
organizational traditions and rituals that are symbolic and deeply rooted within the
57
Figure 9. Professional Development: the Consensus View
Source: Richard Elmore (2003), Bridging the Gap between Standards and Achievement.
The account of the consensus view draws heavily on the original standards for professional development
adopted by the National Staff Development Council in 1995 (Sparks & Hirsch 1997; Sparks, 1995).
organizational culture. Further, an effective educational leader understands that the
change process "intrudes upon deeply rooted symbolic forms, traditional ways, and
ritual behavior” (p. 370). Often the teachers, parents and other educational leaders
will need to be guided through the process. This often occurs as the instructional
leader increases classroom visits, provides consistent development opportunities and
arranges teacher and leader collaboration.
Political Frame
According to Marzano, Waters, and McNulty (2003) effective leaders use
immediate or situational awareness as a means to remain aware of the political
climate of the school at all times. The effective instructional leader uses the
58
information to address issues and to work through upcoming barriers. Barriers and
enablers are part of the change process and educational leaders must be aware of
both and take the time to reflect on how to navigate through or around barriers to
achieve lasting change. By adhering to a moral, political process for compromise, the
leader also motivates the teachers and helps them to consistently align instruction
and assessment measures with performance standards (Sergiovanni, 1994).
School Leadership and Math Reform
Many advocates of mathematics reform in the United States are beginning to
call for math lessons that include “conceptual teaching.” International comparative
studies reveal that high-performing countries such as Japan and Singapore, utilize
conceptual math teaching models (Federal Publications, 2003). However, there is
still a growing debate about the correct balance between conceptual and
computational teaching approaches (Carpenter & Fennema, 1991; Loveless, 2001).
In the United States, there is now an increasing interest in the conceptual
approach to math instruction and the push for conceptual instruction is gaining
strength. This instructional strategy is now an important element in current
educational policies (see the NCTM Principles and Standards for School
Mathematics-Executive Summary, 2001, p. 4). The NCTM and other proponents of
conceptual teaching conclude that student’s benefit greatly from this approach; it
allows students to engage in real-world problem solving and authentic math tasks. In
addition, it helps students acquire the skills need to understand math-related
phenomena (NCTM, 2001).
59
Another math improvement effort involves the integration of innovative math
programs with new school design and reform efforts. The term “content-driven
reform” is used to describe this effort. Elmore and Burnery (1999) describe this
reform effort as the approach that districts use to make specific academic content
central to their schools’ improvement efforts.
Following is a summary of the math reform programs that are integrated within
new school designs:
• Since 1983, the “University of Chicago School Mathematics Project (UCSMP),”
funded by Amoco, General Electric, and the Carnegie Corporation, has
developed a six-year secondary mathematics curriculum encompassing a broad
scope of content and emphasizing real-world applications. In focusing on both
procedural and conceptual knowledge, student understanding is developed in
four domains: skills, concepts, applications, and representations. Reading
mathematics is stressed for all students, and appropriate use of computers and
graphing calculators is presumed. “UCSMP” is currently developing a K-6
curriculum structured as a helix, with skills and concepts developed over time
and revisited in varying contexts. The materials assume the use of calculators and
manipulatives.
• The Calculator and Computer Pre-calculus (C2PC) Project at Ohio State
University has produced a curriculum based on computer/calculator-generated
graphs. Students use the power of visualization to solve realistic, interesting
applications through exploration and experimentation. Because technology
enables interactive instruction that casts teachers in nontraditional roles, C2PC
conducts workshops to assist teachers in moving beyond transmission of
knowledge to facilitation of learning.
• The Graphing Calculator-Enhanced Algebra Project--funded by NSF, the
Interlochen Arts Academy, and Texas Instruments--starts with the premise that
students have access to graphing calculators and teachers have comparable
technology for in-class demonstrations. The curriculum materials feature fewer
problems considered in greater depth, emphasis on small group work, analysis of
graphical representations, and development of mathematical concepts in real-
world contexts accessible to high school students.
• The Oregon State University Calculus Curriculum Project has developed a
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curriculum that uses super-calculators (e.g., HP-48SX) and emphasizes multiple
representations of functions, graphical interpretations, conceptual understanding,
real-world applications, mathematical modeling, and the intelligent use of
technology with full awareness of its limitations.
The principal can only experience success with the aforementioned math-
reform programs when there is active engagement in the teaching and learning
process and a relentless pursuit to have all children succeed (Elmore, 2000). This
often requires the principal to adopt the role of the instructional leader within the
school structure.
Instructional Leadership
In the context of school reform, the role of the school principal has become
essential to leading the efforts to improve student performance and close the
achievement gap (Elmore, 2000; Walters, Marzano, & McNulty, 2003). In addition,
schools are rapidly changing to adjust to increasing state and local pressures for
standards-based reforms and demands from community partners, institutions of
higher learning, and technology-based businesses. A new kind of principal is needed
to meet the school demands of the 21st century; one whose role will be defined in terms of
instructional leadership, community leadership and visionary leadership (Institute for
Educational Leadership [IEL], 2000). In the context of school reform, the principals in the
21
st
must be able to accomplish the following:
“…principals today also must serve as leaders for student learning.
They must know academic content and pedagogical techniques. They
must work with teachers to strengthen skills. They must collect, analyze
and use data in ways that fuel excellence. They must rally students,
teachers, parents, local health and social service agencies, youth
development groups, local businesses, and other community residents
and partners around the common goal of raising student performance.
61
And they must have the leadership skills and knowledge to exercise the
autonomy and authority to pursue these strategies (IEL, 2000; p. 2)
In the context of school reform, the principal’s role as an instructional leader
involves improving teaching and learning, providing professional development, engaging in
data-driven-decision making, and committing to instructional accountability. This includes
maintaining the conviction that all children can achieve and inspiring others in the school
and community with the same vision (IEL, 2000).
In addition, schools are rapidly changing to adjust to increasing state and
local pressures for standards-based reforms and demands from community partners,
institutions of higher learning, and technology-based businesses. These new and
changing demands for principals to establish processes and practices for effective
instruction and increased student achievement are now requiring a different
framework for school and instructional leadership.
During the effective schools movement of the 1980’s the notion of
instructional leadership emerged with the principal operating as the expert in
instructional practices (Barth 1986). Many teachers grew to resent this top-down
organizational management-model approach and sought to become more
empowered. Teachers wanted to be more involved in making decisions about
instructional practices and learning materials, especially since they have first hand
knowledge about student learning behaviors (Hallinger,1992; Sykes,1990).
According to Darling-Hammond and Goodwin, 1993, teacher involvement in the
instructional and curriculum decisions results in improved student achievement and
62
greater teacher satisfaction. In other words, educational reform efforts are more
effective when the principal involves the teachers in the process (Blasé and Kirby,
2000).
Over the past decade, a new view of the instructional leader is forming. The
new view involves more delegation of responsibilities and a refocus on “teaching for
learning and student success.” This view of instructional leadership is emerging from
the Interstate School Leaders Licensure Consortium (ISLLC) Standards for School
Leaders. The ISLLC Standards were developed by the chief school officers of each
of the 50 states - the Council of Chief State School Officers (CCSSO) and are now
shaping the process of developing school leaders.
More than 15 years ago, the National Policy Board for Educational
Administration (NPBEA) and representatives of 23 state departments of education
formed the ISLLC. One of the key accomplishments of the ISLLC was establishing a
set of 6 standards and assessments for the licensure requirements for school leaders
(Shipman & Murphy, February 2001). The ISLLC standards help establish the
training and practices needed to become an effective instructional and school leader
that is skilled in helping all students succeed. The following ISLLC standards
represent the practices and knowledge of effective instructional leaders:
• Vision of learning
• A Culture of teaching and learning
• Management of Learning
63
• Relationships With The Broader Community To Foster Learning
• Integrity, Fairness, And Ethics In Learning
• The Political, Social, Economic, Legal, And Cultural Context Of Learning
Each standard is characterized by specific leadership practices. The vision for
learning standard focuses on establishing, communicating, implementing and
consistently evaluating the school’s vision for learning. The culture of teaching and
learning standard identifies the school leader’s practices in terms of advocating,
supporting, and sustaining a culture of student achievement and professional growth.
The third standard focuses on school management in terms of ensuring a quality
learning environment and efficient school operations. The community focused
standard, the fourth standard, emphasizes targeting community resources and
collaboration with families and members of the community. Ethical behavior and
practices are emphasized in the fifth standard and educational policies, laws and
regulations are the elements that comprise standard 6, the last standard.
The six standards are foundational to forming a framework for effective
school leaders and for establishing the baseline for additional leadership practices.
These additional practices are referred to as the 24 components that further describe
the behaviors of effective instructional leaders (Hessel & Holloway, 1001).
Many of the behaviors and practices that grow from the ISLLC standards are
identified in the list of 21 leadership responsibilities that correlate with student
achievement. According to Waters, Marzano and McNulty (2003), researchers at the
64
Mid-Continent Research for Education and Learning (McREL), the 21 leadership
responsibilities form the balanced leadership framework. Over 30 years of research
meta-analysis was used to form the leadership framework, which identifies the
knowledge, skills, techniques and tools that leaders need to positively influence
student achievement. Their findings suggest that the following leadership, high-level
behaviors are highly correlated with student achievement:
1. “Situational awareness in which the leader is aware of details and
undercurrents in the running of the school and uses this information to
address current and potential problems.”
2. “Intellectual stimulation in which the leader ensures the faculty and staff
is aware of the most current theories and practices and makes the
discussion of these a regular aspect of the school’s culture.”
3. “The leader is a change agent who is willing to and actively challenges
the status quo.”
4. “The leader seeks input by involving teachers in the design and
implementation of important decisions and policies.”
5. “Manages the culture of the school by fostering shared beliefs and a
sense of community and cooperation.”
The relationship between effective leadership and student achievement is
very strong. One study contained a correlation of .50 (McREL, 2003). This can
result in an achievement differential of as much as one standard deviation. In
65
addition, their findings indicated that professional development is a key component
of educational reform and positive results
The McREL's balanced leadership framework does not focus only on
leadership responsibilities; the framework also emphasizes knowing when, how, and
why the responsibilities need to be carried out. According to the McREL researchers,
effective leaders understand how to “balance pushing for change, while, at the same
time, protecting aspects of culture, values, and norms worth preserving. They know
which policies, practices, resources, and incentives to align and how to align them
with organizational priorities” (McREL, 2003, p. 2). In addition, effective
instructional leaders know how to balance the behaviors associated with the 21
leadership responsibilities. Student achievement increases according to the extent to
which the principal:
1. Fosters shared beliefs and a sense of community and cooperation.
2. Establishes a set of standard operating procedures and routines.
3. Protects teachers from issues and influences that would detract from their
teaching time and focus.
4. Provides teachers with materials and professional development necessary for the
successful execution of their jobs.
5. Is directly involved in the design and implementation of curriculum, instruction,
and assessment practices.
6. Establishes clear goals and keeps those goals in the forefront of the school's
attention.
7. Is knowledgeable about current curriculum, instruction, and assessment practices.
8. Has quality contact and interactions with teachers and students.
9. Recognizes and rewards individual accomplishments.
10. Establishes strong lines of communication with teachers and among students.
11. Is an advocate and spokesperson for the school to all stakeholders.
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12. Involves teachers in the design and implementation of important decisions
and policies.
13. Recognizes and celebrates school accomplishments and acknowledges failures.
14. Demonstrates an awareness of the personal aspects of teachers and staff.
15. Is willing to and actively challenges the status quo.
16. Inspires and leads new and challenging innovations.
17. Communicates and operates from strong ideals and beliefs about schooling.
18. Monitors the effectiveness of school practices and their impact on student
learning.
19. Adapts leadership behaviors to the needs of the current situation and is
comfortable with dissent.
20. Is aware of the details and undercurrents in the running of the school and uses
this information to address current and potential problems.
21. Ensures that faculty and staff are aware of the most current theories and
practices and makes the discussion of these a regular aspect of the school
culture.
The above findings are significant; however, the McREL, (2003) meta-
analysis revealed two equally important variables related to effective leadership and
student achievement. The first variable is the focus on change. It addresses the
leader’s ability to make improving the school and classroom practices a direct area of
focus. And the focus must be narrowed down to the practices that will yield the
highest increases in student achievement. The second variable is whether the school
leader thoroughly comprehends the extent or “magnitude” of the change needed to
increase student achievement. In other words, an effective school must have a clear
understanding of the scope of the change and must target, monitor, evaluate and
refine their leadership practices to achieve the desired outcome.
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In the 2005 National Educational Summit on High Schools, the U.S.
Secretary of Education, Margaret Spellings, reminded the summit’s participants of
the urgent challenge facing educators. She stated,
...Getting every child to graduate high school with a meaningful
diploma in their hands is one of the biggest challenges our
country faces. Today only 68 out of 100 entering ninth-graders
will graduate from high school on schedule. Fewer than 20 will
graduate on time from college. Meanwhile, 80 percent of the
fastest-growing jobs will require some postsecondary education.
(Education Trust, 2005, p. 3)
The leadership challenges and opportunities associated with the NCLB Act,
and the requirements to close the achievement gap and improve student learning,
requires redefining the roles, responsibilities, and relationships between the school
leaders and staff members (Shannon & Bylsma, 2004).
In the context of school reform, principals, teachers, students and schools are
increasingly held accountable for student learning and academic achievement. In
addition, it is now becoming easier to measure and analyze outcome data based on
the performance of educational leaders (principals), classroom teachers, and student
groups (Marsh, 2000). Thus, the principal’s role includes the twin partners that have
been found to support instructional improvement: educational leadership and
instructional leadership.
Defining Instructional Leadership
Spillane, Hallett and Diamond (2003) define instructional leadership as “an
influence relationship that motivates and supports teachers’ efforts to learn about and
change their instructional practices” (p. 1). To further expand the definition, Blase
68
and Blase (2003) define instructional leadership according to 4 categories that have
emerged from educational researchers. According to Blase and Blase (2003)
instructional leadership consists of the following 4 general type tasks: 1)
instructional leadership as a set of integrated tasks related to teacher assistance, staff
development, curriculum design, instructional practices, and action research; 2)
instructional leadership as shared decision-making, curriculum development,
equitable pedagogy, and performance growth; 3) instructional leadership as inquiry
and teacher advocacy; and 4) instructional leadership as close examination of
classroom interaction to support equity and social justice.
Emerging Themes of Effective School Leadership
In a recent study that investigated the essential elements of improved schools,
Shannon and Bylsma (2004) found 13 themes that emerged from the 80 research
reports and articles that they analyzed (see Table 4). The 13 themes were organized
using 4 general categories: 1) Effective Leadership, 2) Quality Teaching and
Learning, 3) Support for systemwide [schoolwide] improvement, and 4) Clear and
Collaborative relationships (Table 4).
The goal of the study was to identify the characteristics of improved schools
within Districts and to identify specific elements that each of the schools had in
common.
69
Table 4. The Four General Elements of Improving Schools based on13
Emerging Themes from the Research
Effective
Leadership
Quality Teaching
and Learning
Support for
Systemwide
Improvement
Clear &
Collaborative
Relationships
Research Studies
Focus on all students learning
Dynamic/distributed leadership
Sustained improvement efforts
High expectations for adults
Aligned curriculum & assess
Coordinated/embedded prof dev
Quality classroom instruction
Effective use of data
Strategic resource allocation
Policy/program coherence
Prof. culture & collaboration
School & district roles /relations
Interpret/manage external envir
1. Cawelti, Protheroe
(2001) X X X XX X X X * X
2. David, Shields
(2001) * X X X X X X X X X X * X
3. Firestone (1989) X X X X X X X X X X
4. Marsh (2001) X X X X X X X X X
5. Massell (2000) X X * X X X X X X X
6. McLaughlin,
Talbert (2003) X X X * * X X X X X X X *
7. Skrla et al. (2000) X X X X X X X X X X X X
8. Snipes et al. (2002) X X X X X X X X X X X X
9. Spillane, Thompson
(1997) X X X X X X X X X *
10. Togueri, Anderson
(2003) X X X X X X X X X X X X X
Source: Shannon, G.S. and Bylsma, P. (2004). Characteristics of Improved School Districts: Themes from
Research. Office of Superintendent of Public Instruction. Olympia, WA. X indicates theme is explicitly discussed
in the report and * indicates the theme is strongly implied.
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What is most apparent in the matrix from the Shannon and Bylsma (2004)
study is the central role of leadership to improved schools. Although the role of
instructional leadership is implied, it is not explicitly discussed or identified; instead,
it is integrated throughout the 4 general categories of improved schools. This is
further evidenced in Figure 10.
Figure 10 is an expansion of Effective Leadership, which is one of the 4
general categories that derived from the 13 emerging themes of the Shannon and
Bylsma (2004) study. Although Figure 10 does not contain instructional leadership
as one of it explicit elements, much of its content is consistent with Leithwood’s
(2003) concept of instructional leadership. According to Leithwood (2003), when
instructional leaders have learning-focused goals, it does not limit the scope of their
leadership, as older leadership models revealed. Instead, leadership that includes
learning-focused goals helps leaders focus their attention and actions on ensuring
that everyone is fully engaged in supporting student learning and achievement.
Hallinger and Heck (1997) assert that the principal’s influences on student
outcomes are often mediated through other activities such as professional
development, teacher collaboration, teacher commitment, and shared or distributed
leadership. These elements appear to be closely associated with helping instructional
leaders increase math performance, especially if they lack strong content knowledge.
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Figure 10. Characteristics of Improved School Districts: 13 Themes from
Research
Effective Leadership
Focus on Student Learning
• Focus on all students learning to
high standards
• Share beliefs & values, have
clear goals and shared vision of
change
• Hold all district staff, programs
and operations responsible for
student learning
DynamicLeadership
• Exhibit dynamic leadership,
united in purpose, visible in
schools, interested in
instruction
• Expand to encompass
central office, principals,
teacher leaders and others
• Provide moral leadership
that moves from talking to
doing, to ensure students
learn
Sustained Improvement
Efforts
• View educational
improvement as long-term
commitment and processes
• Persevere, persist, and stay
the course
• Help staff internalize the
changes
Quality Teaching and Learning Support for Improvement Collaborative Relationships
• High Expectations and
Accountability for Adults
• Hold all adults accountable for
student learning
• Expect excellence, monitor
performance, provide feedback
• Make high expectations part of
personnel decisions
• Coordinated and Aligned
Curriculum and Assessment
• Align curriculum with standards,
assessment, policies
• Centralize and coordinate
curriculum approaches and
decisions
• Use multiple measures to assess
learning
• Coordinated and Embedded
Professional Development
• Provide high quality, ongoing
professional development focused
on classroom instruction
• Include school-based coaching and
support for instruction
• Support professional develop-ment
based on teaching and learning
needs in schools
• Quality Classroom Instruction
• Pay close attention to instruction,
provide guidance and
oversight to improve
teaching and learning
• Develop a common vision of good
instruction
• Monitor instruction, curriculum,
and changes in practice
• Effective Use of Data
• Use data to monitor results,
equity, accountability, and for
resource allocation
• Use data for instructional
decisions and professional
development
• Provide time and training to
staff to use data
• Strategic Allocation of
Resources
• Provide, allocate, reallocate,
and find resources for quality
instruction
• Provide additional resources
to support low performers
• Give schools flexibility
within parameters for
resource use
• Policy and Program
Coherence
• Develop and implement
policies that promote equity
and excellence
• Review and revise policies as
needed to link programs and
practices to goals and ensure
coherence
• Monitor coherence of actions
and programs to district
focus, goals
• Professional Culture and
Collaborative Relationships
• Build a culture of mutual
respect, collaboration, trust,
and shared responsibility
• Support school communities
of practice for continuous
learning for adults
• Develop central offices as
professional learning
communities
• Clear Understanding of
School and District Roles and
Responsibilities
• Set expectations, decentralize
responsibility, and serve as
change agents
• Support learning, serve as
mentors, and help seek
solutions
• Balance district authority
with school flexibility and
autonomy
• Interpreting and Managing
the External Environment
• Analyze, interpret, and
mediate state and federal
policy with local policy
• Buffer schools from external
disturbances and internal
distractions
• Mobilize community and
business support
• Involve family and
community
Source: Shannon, G.S. & Bylsma, P. (2004). Characteristics of Improved School Districts: Themes
from Research. Office of Superintendent of Public Instruction, Olympia, WA.
72
Instructional Leadership and Math
Hallinger and Heck (1997) assert that the principal’s influences on student
outcomes are often mediated through other activities such as professional
development, teacher collaboration, teacher commitment, and shared or distributed
leadership. These three elements appear to be closely associated with helping
instructional leaders increase math performance, especially if they lack strong
content knowledge.
According to Stein and Nelson, (2003), instructional leaders and teachers do
not need more advanced knowledge related to content. Instead, they need knowledge
that they can use to help others learn the content. This construct is referred to as:
pedagogical content knowledge. Further, the paradigm--pedagogical content
knowledge--will require principals to acquire and construct “leadership content
knowledge” (p. 3). Although the construct is in its infancy, Stein and Nelson (2003)
define leadership content knowledge as the knowledge that leaders need related to
subject matter content, instructional strategies, and student learning. This is in
addition to their management and organizational knowledge and skills. Further, Stein
and Nelson offer the following recommendations:
• All administrators should have solid mastery of at least one subject and
expertise in other subjects; this includes learning and teaching the subject in
small sections.
• Use a process referred to as postholing to allow administrators to explore
small and complete slices of the subject; examine how the subject is learned
and how it is best taught.
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• Administrators should learn how knowledge is built in a specific subject,
what constitutes solid instructional practices, and what tasks are critical to
learn.
• Administrators must learn what constitutes good instruction.
• Where administrators lack knowledge, develop instructional support through
networks and other teams or groups to ensure that expertise is available.
• Every administrator must possess knowledge of how adults learn.
Stein and Nelson (2003) suggest that this kind of knowledge that will help
administrators to become strong instructional leaders. However, many school leaders
do not have strong pedagogical content knowledge in the subject area that is focus of
their reform efforts. When instructional leaders do not possess strong content
knowledge, there are several strategies available to them that have emerged from
school improvement research. For example, Northouse (2001) suggests the
delegation approach. That is, the instructional leader may be required to delegate
leadership to the assistant principal or other members of the staff with stronger
content knowledge, especially in a content area like math. In terms of instruction,
effective instructional leaders who lack content knowledge, but understand how to
learn, can draw upon several key strategies: 1) quality instructional strategies, 2)
increased student engagement, and 3) input from feeder schools (Marzano, 2003)
Another instructional leadership strategy for overcoming a lack of
pedagogical content knowledge is improving staff development by using outside and
expert resources (Marzano, 2003). A similar process was used in the Success for All
(SFA) program to develop instructional leaders.
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The SFA math model has two components: reading and math. The math
component is entitled Math Wings and schools implementing the Math Wings
component of SFA are required to select Math Facilitators. The roles and
responsibilities of the Math Facilitators are clearly defined and the positions are
thoroughly described in formal program documents, as are expectations about the
role of principal and other members of the leadership team. Math Facilitators receive
3.5 days of training and principals are mandated to also attend training sessions. This
is an effort to increase the teacher’s math content knowledge. And the training is
ongoing to ensure the teachers and instructional leaders have a shared understanding
of the instructional methods. Additional professional development focuses on
quarterly assessment and monitoring implementation. One of the methods used to
help the instructional leader overcome a lack of content knowledge is the use of pre-
assembled curriculum that includes formal training.
The 2005 Education Trust, Inc report, Gaining Traction Gaining Ground:
How Some High Schools Accelerate Learning for Struggling Students, presents a
study and analyses of schools that achieved unusually high performance gains from a
population with large concentrations of poor children and children of color. The
Education Trust (ET) team collected school data and observed instructional practices
to better understand how the students reached such high levels of achievement.
The study’s aim was to identify the characteristics and practices of successful
schools--characterized as high impact schools--that are especially effective in
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improving the academic performance of previously low-performing students; the
students who make greater-than-expected gains (Education Trust, 2005).
Figure 11. Grade 10 Math Proficiency – 2003
Academic Growth Over Time
2003- met expected gains
2004- met high gains
Source: North Carolina Department of Public Instruction. Jack Britt High School is located
in Fayetteville, NC and has a total of 1,820 students enrolled, about half of whom are African
American. It contains grades nine through 12 and has a student-teacher ratio of 17.2 students
to one teacher. Jack Britt did not make Adequate Yearly Progress in 2003 in reading for
economically disadvantaged students. In 2004, Jack Britt did make AYP.
Their findings reveal the principal’s instructional leadership was key to the
academic gains. The report cites the following practices as characteristic of effective
instructional leaders (i.e., principals, assistant principals and department chairs) in
high-impact- schools.
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Academic Goals
• In high-impact high schools, teachers and administrators express consistent
views about achievement-related school goals.
• High-impact faculty members and administrators speak more consistently about
working toward common goals than their counterparts in average-impact schools.
The evidence suggests more agreement – among administrators, among teachers
and between teachers and administrators – on important academic issues.
• In high-impact schools, more principals talk about the importance of getting
students into tougher classes to ready them for postsecondary choices, and their
actions reinforce that goal.
Accelerated Strategies
• Administrators report a conscious effort to keep ninth-grade classes smaller for
struggling and average-performing students. Administrators offset this by
increasing the size of advanced classes.
• In high-impact schools, administrators and teachers take responsibility for
ensuring that struggling students get the additional help that they need.
• High-impact schools have in place early warning systems to identify students
who need help before it’s too late.
• Administrators at high-impact high schools adjust class sizes to provide more
attention for struggling students and are not averse to larger student-teacher ratios
for students who are able to work more independently.
• Administrators recognize that a student who is struggling in a class may not
necessarily want to work with the teacher of that class and make alternatives
available.
Data-driven Decisions
• Administrators in high-impact schools tend to communicate test-score
information more formally than their peers in average-impact schools and make
more of an effort to use the information to improve future curriculum and
instruction.
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• In the high-impact school that has a traditional six-period schedule,
administrators provide struggling students with two math (or English) classes,
one at grade-level and another to support that class. These support classes
provide help to students who entered ninth grade under-prepared.
Professional Development/Staffing
• Principals at high-impact high schools exert more control over who joins their
staff than those at average-impact schools.
• High-impact school administrators reported assigning teachers based on criteria
such as qualifications, subject-matter expertise and performance as measured by
student test scores.
• The principal “requires his teachers to work together by department and subject
level.”
Structured Support for New Teachers
• This high-impact school also offered specific programs for new teachers, such as
an in-school instructional “coach” for all the new teachers.
• Administrators assign new teachers and veteran teachers the same courses, so
that new and veteran teachers are both delivering the same content to their
students.
• It was common practice for administrators to walk in and out of teachers’
classrooms – new teachers’ and veteran teachers’ – in order to offer support and
evaluate new teachers.
According to Calhoun (1994) an effective instructional leader has the ability
to identify problems with the curriculum and make improvements, develop
innovative ways to provide professional development to teachers, support students in
their efforts for academic achievement. In addition, effective instructional leaders
effectively use data as a source for decision-marking related to instruction and are
skilled in the ability to align standards, curriculum, teaching materials, and
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instructional practice for the common good of the student and continuous
improvement. Effective instructional leaders use the data to revise the course scope
and sequence when needed (Marzano, 2003).
Pedagogical Content Knowledge
In 1986, Lee Shulman concluded there was a “missing paradigm” in learning-
related research and embarked on education research that investigated content-
specific subjects such as math, English, etc. Shulman’s research led to a construct
related to the teacher’s subject-matter knowledge, referred to as pedagogical content
knowledge. As noted earlier, He defined pedagogical content knowledge as
knowledge that is used to help others to better understand specific subject matter.
Moreover, he concluded that teachers and leaders need a level of knowledge that was
qualitatively different than practicing professionals. In other words, the
mathematician may possess and need deep and advanced knowledge of math
concepts, procedures and problems solving, but the instructional leaders still needs to
support teachers to enable them to make math concepts understandable to students
who are building their math knowledge domains (Shulman, 1986). This leads to
increased math achievement and improved math programs.
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CHAPTER 3
RESEARCH METHODOLOGY
This chapter discussed the research methodology that was used to conduct the
study. Included are a description of the school being researched and a description of
the research design, sampling criterion, and the participant selection process, as well
as a description of the methodology to be used for data collection and analysis. The
study investigated the best practices, instructional strategy, organizational structure,
and leadership behaviors in an urban high school that helped to promote and sustain
increased student achievement in mathematics for a minimum of three consecutive
years. The study also examined programs, curriculum and policies that contributed to
math improvement.
The purpose of this study is to identify how high school leaders in urban
schools successfully integrate policy initiatives and best practices to improve math
performance in their schools. In addition, the study investigated how school leaders,
who may not have strong pedagogical content knowledge in mathematics, garner the
resources to improve student achievement and sustain academic growth. Therefore,
this study examined how these leaders, in the absence of instructional expertise in
mathematics, carried out functions related to fiscal management, personnel
management, change management, organizational leadership, and data collection and
analyses to successfully bring about increased math achievement outcomes.
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The school selection criteria, as defined in the school profile instrument,
resulted in a specific cadre of Southern California high schools. Out of this group of
schools, Land High School was selected for the study. The data collected from Land
High School consisted of the following: student achievement data; teacher and
administrator survey data; and questionnaire and interview data. The collected data
was analyzed to examine the following research questions:
1. What was the pattern of Math achievement for various students at the
school?
2. What Policy initiatives as well as curriculum, instruction and related
conditions seem to be related to improved math achievement in the
school?
3. What change process did the school use to enhance its math program and
strategies to assist students in math?
4. How was instructional leadership important in improving a) the math
programs/strategies and b) math achievement among students?
5. How did instructional leaders respond in academic areas in which they
were not experts?
This study was a case study “provide depth, detail, and individual meaning”
(Patton, 2002, p. 16). Collecting qualitative data supported developing a conceptual
framework for a specific case. The data from participants constructed a
comprehensive picture, by using findings based on the participants’ perspective,
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insights and practices. Qualitative data was gathered from multiple sources to
provide an in-depth narrative, which is the essence of qualitative inquiry (Patton,
2002). Data was gathered from questionnaires, interviews, and existing documents
within the setting of the school site. The questionnaire and interview instruments
were specifically developed for the study and are addressed specific research
questions. The school site’s existing documents were reviewed and rendered
information that was pertinent to the research questions for the study.
The school site for this case study was one public southern California high
school. All of the instruments in the case study were based on current educational
research and produced responses relevant to the research questions being
investigated. Conceptual frameworks were used to provide a set of related ideas or
concepts that are organized to communicate the context and support the analytical
style used in this study. Evidence found in document analysis was cross-referenced
with interview data and questionnaire findings wherever possible. Triangulation was
used to help establish the credibility of the study’s findings. The information about
the school and participants was factual; however, the case study incorporated the use
of pseudonyms to provide anonymity and maintain confidentiality.
Sampling Criteria and Process
A purposeful sampling process was used to provide an opportunity to conduct
a thorough investigation and to explore more deeply the processes related to the
research questions of this study. The school selected for the study was chosen
consistent with the following criteria:
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1. Improvement in math achievement as evidenced by results on the California
Standards Test (CST) in Algebra I.
2. Student diversity as defined by a student population of at least 50% from
traditionally ethnic minority groups.
3. Public high school in the Southern California region of at least 1200 students.
4. An Academic Performance Index Score of at Least 600
5. A State Wide Rank of 5 or higher
6. Leadership stability as defined by a Principal being at the school for at least
three years during the time the improvement was made.
The 11 members in the cohort group led by Dr. Marsh worked together to
develop the sampling criteria, and then to identify schools in southern California that
met those criteria. Qualifying high schools were identified using the following
process:
1. A data file was downloaded from the California Department of Education’s
web site using the DataQuest service.
2. The data file was exported into Microsoft Excel to create a spreadsheet that
was used to analyze and filter the available data in an effort to identify
schools fitting the profile (see Appendix B).
3. Knowing that the group would need to research improvement in CST in
Algebra 1 in a later step and that many schools would not have demonstrated
improvement, the group set a goal of a sample size of no less than 100
schools in the southern California region.
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4. Preliminary efforts to use more stringent requirements did not yield a
sufficient sample so adjustments had to be made. For example, when the
student enrollment parameter was set to 1500; the percentage of minority
students was set at 65%; the statewide rank set at 6 or higher, the sample was
limited to only 28 schools in southern California.
5. The second iteration included adjusting the parameters to an enrollment of no
less than 1200; a minority population of 50% or more and a statewide rank of
5 or higher. The sample population then rose to a satisfactory level of 110
schools in the southern California region.
6. Students in the group were then assigned to research 10 schools each by
looking up and recording CST scores in Algebra I for the years 2003, 2004
and 2005 onto a common spreadsheet which one person in the group
compiled.
7. The group then assigned an absolute value to the improvements made in two
areas. First, decreasing the number of students scoring in the bottom two
performance bands; and second, increasing the number of students scoring in
the top two performance ands. These totals were added to indicate an overall
level of improvement. For example, if a school decreased the numbers of
students scoring in the bottom two performance bands by 3% and increased
the number of students scoring in the top two performance bands by 5%, the
school would have an overall improvement score of 8%.
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8. The group then reviewed the scores of all schools in the sample and
eliminated any school that:
a. Evidenced a decrease in the number of students scoring in the top two
performance bands from 2003 - 2005.
b. Evidenced an increase in the number of students who scored in the
bottom two performance bands.
c. Failed to evidence an overall improvement score as calculated in the
example detailed in number 7 above.
9. Using this process resulted in 44 schools qualifying for the study.
10. A geographic map was then developed of the qualifying schools to help
cohort members select a school for their study based on proximity and other
relevant factors.
Research team members reviewed the list of schools that were identified
based on the criteria above. The eleven members in the cohort group led by Dr.
Marsh worked together to develop the sampling criteria, and then to identify schools
in southern California that met those criteria. The research team met in a
collaborative cohort model in January of 2006. The team worked together to
develop research questions and relevant academic literature was discussed to prepare
for the study. The team continued to meet through the summer of 2006 and into the
beginning of the 2006-2007 academic year at which time individual researchers
commenced their detailed studies at their selected sites.
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Qualifying high schools in the study were selected through an analysis of
available data on the California Department of Education’s web site. The
researchers developed a spreadsheet of data from schools fitting the profile in terms
of their CST scores in Algebra I (see Appendix B). The team then created a
geographic map to plot the selected schools and to help cohort members select a
qualifying school for their study based on proximity and other relevant factors.
A flyer was distributed to all potential participants of this study, which will
included a detailed description of the research procedures, purpose of the study and
will also indicate that participation in the study will remain anonymous and is
entirely voluntary. A recruitment letter approved by the university’s Institutional
Review Board (IRB) was sent directly to potential participants following the
distribution of the initial flyer. Recruitment letters for teachers were placed in their
individual mailboxes, and clearly stated that participation in the study was
completely voluntary. Teachers were required to return a signed letter indicating
their desire to be part of this study without any coercion from their principal or any
other superior. A returned, signed letter from the teachers and others denotes
agreement to participate. Thus, no further consent letters were required.
The subjects involved in this study were limited to teachers, administrators,
and some support staff member. Subjects in the teacher category were identified for
participation based on their response to the recruitment letter given to them early in
the process. The participants consisted of math teachers and other teachers who
appeared to have a leadership role at the school. Upon agreement, the educational
86
professional was provided with a recruitment letter specifying the purpose and
process for the study.
All site administrators and key teacher leaders were interviewed using the
interview guide attached as Appendix C. The school site’s math instructors were
asked to complete a 50-item teacher questionnaire (see Appendix D). The data from
completed teacher questionnaires provided the researcher with teacher perceptions
and classroom practices information; this information related to the research
questions being examined. Teachers at the school site who are not math teachers
were asked to complete a shorter questionnaire designed to obtain their impressions
about school-wide factors linked to the research questions.
Participants were scheduled for at least one interview, while some key
leaders were interviewed more than once for follow up and additional questions
related to leadership, staff development and support. All interviews were held at the
school site and in an environment that protects confidentiality.
The Principal Investigator, Dr. Marsh, and Co-Investigators working on this
study visited research sites between 8 – 10 times consisting of approximately seven
hours per visit from September 2006 until November 2007. The visits included
interviews and other research activities related to this study. The Principal
Investigator, Co-Investigators and Graduate Student Research Assistant met formally
at least monthly to evaluate and discuss research findings gathered at individual
research sites. There were ongoing meetings that also took place between the
Principal Investigator and Co-Investigators to ensure that deadlines are met while
87
following the protocols of effective research. This combination of investigation,
collaboration and discussion provided adequate time to conduct and complete the
research at each of the high school sites selected for this study.
Selected School Profile
Land High School was selected for this study. The school is located
approximately 50 miles from the University. The school district, established in
1898, educates continuation students, junior high and traditional high school students
in grades 9 through 12. The stated mission of the district is, “The Learning Force
since 1898.” The district is comprised of 8 middle schools, 10 comprehensive high
schools and 7 continuation high schools. The total district enrollment during the
2005-06 school year was 33,112.
Land High School has an 11% mobility rate; the lowest in the district. The
two largest ethnic groups in the school are Hispanic and Asian with 61% and 9%
respectively. The remainder of the school is comprised of 22% White; 3% Filipino;
2% Pacific Islander; 2% African American; and 1% American Indian. More than
29% of the high school students in the District are English Language Learners
(ELL). There are approximately 2,213 students at the Land High School and 1043
(47%) qualify for free or reduced lunch. Land High School has 86 teachers and a
teacher to student ratio of 25 students to 1 teacher.
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Purposive Sampling
The school and research respondents were purposively chosen for this study because
were relevant to the research question and provided rich and detailed information
about math achievement in secondary schools as well as the role of instructional
leadership. In addition, purposive sampling allowed the researcher to adjust the
process of data collection as various themes emerge and to stop or start data
gathering to the extent that new information was needed.
Student Achievement
The school profile (Appendix A) listed most of the demographic and student
performance data used as criteria for the final selection of the research school site.
Demographic indicators comprised the first section of the school profile. Additional
sections of the profile included demographic indicators such as subgroup
aggregation, school size and other subgroup data as defined by API. The California
Basic Education Data System (CBEDS), and the School Accountability Report Card
(SARC) were sources used to find additional important data. The school profile also
included another source of important information--human resource data. Human
resource data was critical to the study in that it provided important information
related to the average years of the staff’s teaching experience, compliance with the
NCLB standards concerning highly qualified teachers, and the number of years each
teacher had been part of the school staff. Other important information for the study is
data that related to the school Administrator. Administrator data provided
information related to the number of years the school site leader had been a school
89
site administrator. In addition, the human resource data indicated the leader’s length
of service as an instructional leader and experience or knowledge in math education.
Student performance data included graduation rates, CAHSEE passing rates,
the percent of students achieving at the proficient level in math, and the percent of
students taking Advanced Placement (AP) classes. This was pertinent information
since college entrance requirements are directly related to school reform efforts and
levels of math completed. All of the data contained in the school profile is relevant to
the study and the literature related to school reform and effective math programs.
Participants in the Study
All site leaders and over 65% of the math teacher population participated in
the study; more than half of the non-math teacher population participated. The study
used mixed measures to conduct research in a manner that allowed for triangulation
of data. Triangulation of data is especially important in qualitative case studies to
reduce the incidence of individual or cultural bias.
Site Administrators
On the high school campus, the school site principal serves as the primary
instructional leader. For the purposes of this study the principal was interviewed
during several interview sessions in an effort to collect second-level and detailed
information about how the school achieved math improvements in the context of
school reform. In general, the principal relied extensively on his assistant principals
to execute the day-to-day logistics of program operations, instructional activities and
staff development. In light of this, the assistant principals were interviewed to help
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determine the extent to which the math program implementation plan and staff
development activities aligned with policy. The assistant principals also provided
information related to how the principals communication patterns, use of data, and
other leadership behaviors related to math achievement.
Teacher Leaders
Teacher leadership is an inescapable component of school reform (Cuoco,
2006) in general and a key component in this study as well. The teacher leaders
participating in the study included: math department chairs, instructional and
curriculum specialists, and data coaches.
Other Key Leader
In addition to administrators and teacher leaders, guidance counselors have a
degree of influence in promoting student enrollment patterns and encouraging
academic achievement. Data was collected from additional important leaders and
follow up interviews were held to obtain additional insight into the pattern of
achievement at Land High School.
Classroom Teachers
Classroom teachers were one of the most critical components of successful
policy implementation. Moreover, they were in the optimal position to gain first
hand knowledge of how well students performed against the goals and expectations.
Classroom teachers were surveyed and interviewed to learn about their practices and
perceptions related to the school reform efforts and math improvement. They were
best suited to discuss the efficacy of staff development, teacher collaboration, student
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achievement and support strategies for struggling students. In addition, classroom
teachers offered important information related math improvement based on their
perceptions about the effectiveness of the instructional leadership and administrative
support.
Instrumentation
The instrumentation used in this study was developed collaboratively by 11
members of a dissertation cohort at the University of Southern California. These
Doctoral candidates met regularly during the Spring and Summer of 2006 in a
research seminar led by Dr. David Marsh, Associate Dean of Academic Programs
and professor at the university. This collaboration period is characterized by open-
ended discussions of the topics to be covered in the study and effective data
collection methods required to obtain the data needed to address the research
questions noted above. The research team developed four data collection instruments
and designed the instruments to be consistent with the study’s conceptual
frameworks.
The conceptual frameworks were grounded in research that presented best
practices and models related to improving student achievement at the secondary
level. The data collection tools and instruments were the teacher interview guide, key
leader interview guide and questionnaires math and non-math teachers. The data
collection tools such as the teacher interview guide and key leader interview guide
were integrated with the data collection instruments (i.e., teacher questionnaire to
support a rich and consistent data collection process. The cohort members also
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collaborated to identify the relationship between the research questions and the data
collection instruments to ensure maximum efficiency in the data collection process.
Table 5 depicts the relationships between the various data collection
instruments and tools used in the study and the research questions examined. The
teacher questionnaire (Appendix D) consists of 50 questions using a five point Likert
scale. The questionnaire is divided into four sections each addressing research
questions two, three, four and five. The questionnaire is designed to ask teachers to
rate the school’s effectiveness based on their own perceptions of school-wide
practices, policy initiatives and the school’s math program and leadership.
Table 5. Relationship of Data Collection Instruments to Research Questions
Instrument Research Questions
RQ1 RQ2 RQ3 RQ4 RQ5
School Profile X X
Key Leader Interview X X X X
Teacher Interview X X X X
Teacher Questionnaire X X X X
Conceptual Frameworks
Members of the research team worked collaboratively to develop the
instruments using research-based processes. From this collaboration effort the
research team also identified the relevant literature needed to develop conceptual
frameworks. These frameworks helped the researchers to identify constructs for
each research question. For example, the research question, “What was the pattern
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of math achievement for various students at the school?” requires a construct or
framework that helps to define and operationalize math achievement and patterns of
math achievement in order to develop questions that specifically and effectively
target math achievement data. Thus, the researcher’s collaboration resulted in four
major themes or conceptual frameworks associated with each research questions.
These four frameworks guide the process of developing data collection instruments
and appropriate questions that comprise each data collection instrument.
Framework for Research Question 1: School Profile /Achievement Data. .
Research Question One asked about the pattern of mathematic achievement
for various students at the school. The aforementioned school profile information
served as the framework for research question one in that it provided a template for
identifying areas of student achievement in math where quantifiable data was
available for analysis. Appendix E includes the data used to identify the pattern of
student achievement in math at the site.
Frameworks for Research Question 2: Math Programs and School Design.
Research Question 2 targeted data related to the policy initiatives, curriculum
and instructional practices and related conditions associated with improved math
achievement in the school. Two separate frameworks were developed to help in the
development and analysis of the associated questionnaire and interview questions.
The first is a framework describing effective school design. The elements of this
framework consist of Marsh and Codding’s model of school design. The School
Design conceptual framework is made up of four components: curriculum, school
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culture, learning activities and student performance assessments. The basic elements
are reflected in Figure 12. The framework highlights curriculum foundations built on
student-centered approaches and outcomes. The framework addresses school
cultures that enhance effective school design and indicates that these school cultures
are effective because they have meaningful interactions between students and staff,
ongoing professional development and enhanced learning opportunities. The
framework also included learning activities and suggests that effective activities are
ones that challenge students to use higher-order thinking skills, solve problems and
collaborate across the learning environment. Finally, the framework included student
performance assessments and indicated that effective communication and problem-
solving which emphasizes conceptual understanding is foundational to effective
student performance assessments.
Framework for Effective Mathematics Programs.
The second framework highlights the elements of effective math programs
and is depicted in Figure 13. The components of the effective math programs
framework are: (1) student-centered curriculum that emphasizes conceptual
understanding and which promotes in-depth mastery of computations and
manipulations of mathematical symbols and procedures as tools in the problem-
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Figure 12. Framework for Effective School Design
School
Design
Curriculum Learning
Activities
Challenge
Students to
Think
Students
Solve
Problems
School
Culture
Based on
Enhanced
Learning
Meaningful
Staff-Student
Interactions
Ongoing
Professional
Development
Collaborative
School-to-Career
Applications
Constructivist
Knowledge
Based on
Student
Outcomes
Student Performance
Assessments
Capture
Conceptual
Understanding
Capture
Problem
Solving
Capture
Communication
Skills
solving process; (2) rigorous, standards-based instructional practices based on the
alignment of content standards and assessments, data-driven decision-making, and
effective catch-up strategies. This framework also illustrates that effective math
programs incorporate coherent and effective classroom pedagogy, includes sound
lesson design, makes use of prior knowledge, and is culturally relevant.
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Figure 13. Effective Math Programs
97
Framework for Research Question 3: The Change Process.
Research Question 3 targets information related to the change process used
by the school to improve the math program and strategies used to support students.
Bolman and Deal’s Leadership model (2003) emphasize that an effective
instructional leader uses the 4 frames (i.e., structural, human resources, political and
symbolic) from which to view the operation of the organization or school (Table 6).
The Bolman and Deal model (2003) was an especially important model for
an instructional leader in terms of the change process. An effective instructional
leader must be able to view the change process from individual and organizational
points of view. This framework is depicted in Table 6. In addition, an effective
instructional leader aligns rules, roles, goals and policies to the goals of the school
and the objectives of the change initiative. These included: clarification and
realignment of goals; matching people to appropriate assignments or other aspects of
the organization; effectively working with diverse interest groups or stakeholders
such as labor unions, school boards, and classroom teachers; and building meaning
for the students and teachers from within the school culture.
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Table 6. Bolman and Deal’s Four Frames
Frame Structural Human
Resources
Political Symbolic
Metaphor
for
organization
Factory or
Machine
Family Jungle Carnival,
Temple,
Theater
Central
Concepts
Rules,
Roles, goals,
Policies,
Technology,
Environment
Needs, Skills,
Relationships
Power,
Conflict,
Competition,
Organizational
politics
Culture,
Meaning,
metaphor,
ritual,
ceremony,
stories, heroes
Image of
Leadership
Social
Architect
EmpowermentAdvocacy Inspiration
Basic
Leadership
Challenge
Attune
Structure to
task,
Technology,
environment
Align
Organizational
and human
needs
Develop
Agenda and
Power Base
Create Faith,
Beauty,
Meaning
Framework for Research Question 4: Instructional Leadership
Research Question 4 seeks to identify how instructional leaders helped bring
about improved math strategies and programs as well as student achievement in
math. Figure 14 depicts the instructional leadership framework used in this study.
According to Sweeney’s meta-analysis (1982) principals who make instructional
improvements emphasize achievement. Blase and Blase (2004) outlined three basic
components of effective instructional leadership. First, instructional leadership
involves integrating all activities to directly relate to classroom instruction and other
learning events. Another component of effective instructional leadership involves
interacting and collaborating with teachers to foster trusting relationships. This
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includes peer coaching and observing classroom instruction. Finally, another
component of effective instructional leadership is promoting continued professional
development for teachers (see Figure14).
Figure 14. Instructional Leadership Framework
Instructional Leadership Framework
What an effective leader must have knowledge of…
Vision for
learning
Supervision and
monitoring of
Instruction
Community
and Political
Climate
Culture of
Teaching and
Learning
Data Driven
Decision-
making and
Analysis
Facilitates the
development,
articulation,
and
stewardship of
a vision for
learning that is
shared and
supported by
the school
community.
A – Developing
the vision
B –
Communicatin
g the vision
C – Implement
the vision
D. Monitor and
evaluate the
vision
E- Addresses
obstacles to
vision
implementatio
n and
realization
Observes and
monitors
instructional
program.
Provides
constructive
feedback in a
timely manner to
tall teachers.
A- Classroom
observations on a
daily/ weekly
basis.
B- Allocates
resources ensures
successful
teaching and
learning.
C- Supervision of
personnel
D- Hiring
personnel that
support the
learning goals
and vision of the
school
Collaborates
with families
and
community.
Responds to
diverse
interests and
needs and
mobilizes
community
resources.
A-
understands
the value of
diversity
B-
Understands
Community
needs
C- Involves
the
community
in the school
D- Provides
opportunity
for
community
involvement
Advocates,
nurtures and
sustains a school
culture and
instructional
program.
A- Value the
students and staff
B- Develop and
sustain the
school culture
C- Respects
diversity
D- Implementati
on practices for
culturally
relevant teaching
and learning
E- Celebrates
students,
teachers and
staff.
Uses data as a
tool to support
student learning
A- uses
assessment data
to place students
and guide and
improve teachers
B- Formative
benchmark
school
assessment
C- summative
standardized
assessment
D- Dis-
aggregates data
by classes
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Framework for Research Question 5: Assessment of Individual Leader.
Research Question 5 examined how instructional leaders responded in
academic settings in which they were not math content experts. The framework
developed to deal with this question has two components: (1) an assessment, which
was developed to help determine the level of expertise the principal had in math and
(2) a process that is based on the state of California’s definition of a highly qualified
teacher (HQT) under NCLB. This is framework was appropriate since the research
question that was designed to assess the teacher’s qualification is primarily based on
math competency. The assessment involved is detailed in Figure 15 and results in
one of three levels of expertise being assigned to the leader – high, medium, or low.
Second, a range of strategies based on the literature around school improvement was
devised to help the researcher identify broad categories of efforts associated with
which to view each of the school’s efforts to improve student achievement in math.
This second part of the framework is detailed in Figure 16.
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Figure 15. Assessment of Principal’s Expertise in Math
Source: NCLB Teacher Resource Guide [electronic version] located at
http://www.cde.ca.gov/nclb/sr/tq/documents/nclbresourceguide.pdf
Assessment of Principal’s Expertise in Math
Step 1
Is the Principal
HQT Compliant?
Yes No
High
Expertise
Step 2
Does the
Principal have a
credential or
major in math?
Yes No
Medium
Expertise
Has Principal
minored in or
taught math?
Yes No
Medium
Expertise
Low
Expertise
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Figure 16. Strategies to Overcome a Lack of Subject Matter Competency
Item Strategy Approach/Source
1
Delegate Leadership to Assistant
with greater expertise
Delegation Approach
(Northouse, 2001 p. 58)
2 Empower Department Chair Teacher Leadership (Gabriel, 2005)
3 Bring in Outside Expertise
Meaningful Staff
Development Activities
(Marzano, 2003 pp. 65-66)
4
Emphasize inquiry and problem
solving
Action Research
(Stringer 1999)
5 Emphasize quality instruction
Instructional Strategies
(Marzano, 2003 pp. 78-87)
6
Emphasize strategies to engage
students in the learning process
Student Engagement
(Marzano, 2003 pp. 149-150)
7
Emphasize articulation with
feeder schools
Guaranteed, Viable Curriculum
(Marzano, 2003 pp. 22-34)
8 Emphasize raised expectations
Challenging Goals and Effective
Feedback (Marzano, 2003 pp. 35-
46)
9
Emphasize Strategic Teacher
Assignments
HR Frame
(Bolman & Deal, 2003)
10
Emphasize Revised Course Cope
and Sequence and/ or
Curriculum
Guaranteed, Viable Curriculum
(Marzano, 2003 pp. 22-34)
11
Emphasize Interventions for
lower performing students
Supplemental Services
(NCLB, 2001)
12
Emphasize Professional
Development
Meaningful Staff
Development Activities
(Marzano, 2003 pp. 65-66)
Data Collection Instruments
Instrument 1 - School Profile
The School profile instrument was designed to provide a framework of the
myriad of characteristics that make up the school community. The secondary school
reform cohort led by Dr. Marsh worked to identify those elements most likely to
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provide a comprehensive picture of the school being studied. The cohort organized
the data into three main categories: demographics, student performance, and general
school information. The majority of the data is available on the California
Department of Education’s web site.
Demographic data included both student and teacher demographic traits.
Teacher demographics included total numbers of teachers; credential and NCLB
Highly Qualified status; and years of experience. Data collected for students
included ethnicity, English Language Learner (ELL) status; free and reduced lunch
status; and student enrollment patterns.
Student performance data (Appendix E), such as CST for Algebra 1 for the
recent three years; CAHSEE pass rates; standardized test score data; and AP
enrollment classes, was is directly responsive to one of the research questions related
to the academic achievement pattern in the school.
Instrument 2 – Key Leader Interview Guide
The Key Leader Interview Guide (Appendix C) was developed to facilitate
the collection of data relevant to research questions numbers 2 through 5. In
particular, key leaders were interviewed to help identity their perceptions of the
practices and strategies that resulted in math improvement. The interview guide is
designed to help the interviewer follow up on themes and patterns; this semi-
structured process is based on Creswell’s protocol (1998).
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Instrument 3 – Teacher Interview Guide
The Teacher Interview Guide (Appendix F) is developed to facilitate the
collection of data relevant to research questions numbers 2 through 5. The teacher
interview guide is designed to help illicit teacher perceptions related to improvement
in student achievement in math. The cohort group aligned the questions and
conceptual frameworks for the 30-minute teacher interview and added open ended
questions to the guide. The teacher leader interview guide was developed
collectively and by specific research questions. The semi-structured interview
process is based on Creswell’s protocol (1998).
Instrument 4 – Math Teacher Questionnaire
The Math Teacher Questionnaire (Appendix D) is designed to target the
collection of data relevant to research questions numbers 2 through 5. Teachers were
asked to complete the questionnaire to provide the researcher with their perceptions
of the factors that contributed to increased student achievement in math. The cohort
group collectively developed the teacher questionnaire and ensured it aligned with
the proposed research questions and conceptual frameworks. The teacher
questionnaire incorporated the use of a 5-point Leikert scale ranging from Strongly
Agree to Strongly Disagree. It was designed to take approximately 30 minutes to
complete. In addition, the possibility of follow up visits to collect the questionnaires
and clarify information was articulated by the researcher.
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Instrument 5 – General Teacher Questionnaire
The General teacher questionnaire was developed to include 30 items
providing teachers in subjects other than math with an opportunity to share their
perceptions around school-wide issues. This instrument is attached as Appendix G.
Data Collection
For the study, data was collected over a two-month period from October 2006
through November 2006. The data was collected in three distinct phases to allow for
a more thorough review and analysis of data sets and documents between each data
collection phase. After each data collection event, interview notes were compiled. In
addition, a follow up strategy was used to further examine emerging themes or
patterns and the data collection process was triangulated to help increase reliability.
A key step in the process of data collection was obtaining the approval of the
Institutional Review Board (IRB) prior to the collection of any data. Once the IRB
gave final approval for the study to begin, the cohort group reviewed the list of
qualified schools and commenced with data collection activities after contacting the
site principals and briefing the principal on the purpose, intent and method of the
study. Participants were informed of the voluntary consent requirement and that they
can end their participation at will. Completion of the questionnaire was voluntary as
well and the researcher made the appropriate efforts to collect all completed
questionnaires.
During the first round of data collection, the intent was to obtain a high-level
understanding of the school. To achieve this, the first interview was with the site
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principal. The interview with the principal was designed to gather information about
key leaders and instructional programs, specifically the math program. In addition,
the researcher spent time visiting the classroom and the general campus to gain a
better overall understanding of the school. During the first phase of the data
collection, the researcher reviewed the school’s master schedule and school site plan.
The teacher questionnaire was distributed with the intent to continuously work to
maximize and increase the questionnaire return rate.
The second phase of the data collection consisted of interviewing key leaders
such as the assistant principals, department chairs, and teacher leaders. In addition,
completed teacher questionnaires were collected for content and data analysis and a
second interview was conducted with the principal to get a more thorough
understanding of the information gathered during the initial interview in phase one.
If required, the second phase included gathering second-level data related to the
school culture, instructional programs, and school-related information obtained
during the first phase of the data collection.
The third and final data collection phase consisted of collecting teacher
questionnaires and conducting brief interviews as needed in response to the ongoing
data analysis process. This process of iterative clarification of the data allowed the
researcher to achieve a high level of accuracy in the data collection and analysis
process.
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Data Analysis
The purpose of this study was to acquire a better understanding of how
effective instructional leadership works to improve student achievement in
mathematics. Data was collected and analyzed and existing documents were
reviewed. Specifically, the study explored the various aspects of the role of the
instructional leader during the math improvement process. Particular attention was
given to instructional leadership, the components of effective math instruction, and
the design model of the mathematics curriculum at the site in order to arrive at a
preliminary explanation for the school’s math achievement. Five research questions
were designed to help target and uncover the appropriate data.
The data analysis process consisted of several steps. First, interview notes
were taken during and after the interviews and transcribed to be reviewed by the
participants. The notes were verified with the participants and copies were made and
cross referenced with the appropriate conceptual framework. This effort assisted with
retrieval of data and in identifying themes that emerged as more than one person
noted a particular dynamic on campus. A spreadsheet was developed to compile
similar patterns and emerging themes were sorted and grouped by research question
and data collection instrument. From this process the content was further analyzed to
identify the frequency of similar responses.
A key analysis enabler for data that was collected for this study involved the
development of a spreadsheet using Microsoft Excel in which rows and columns
were designated for the specific recording of relevant information, according to the
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framework, collection instrument, and research question. The spreadsheet allowed
the researcher to aggregate and analyze the data in a manner that reveals patterns,
anomalies, and frequency of specific responses.
The results of the teacher questionnaire were handled in a similar manner.
Scores for each question were compiled and entered in the aforementioned
spreadsheet. The data entries were associated with the most relevant research
question for the purpose of data analysis. After the interview and questionnaire data
was entered, the data was sorted and analyzed to identify emerging patterns.
Finally, existing and source documents was analyzed and entered in the
spreadsheet in the same manner to reveal patters of similar responses.
Validity and Reliability
This study used multiple sources of data in an effort to minimize threats to
rater reliability. This process of triangulation of data and the use of conceptual
frameworks served to ensure consistency and guide the scope of the investigation.
The triangulation of data included interviews with key informants, and document
analyses. This process allowed the researcher to follow-up with additional questions,
clarify information, and verify data form multiple participants. In addition,
participants reviewed their interview notes to validate the content. External validity
is beyond the scope of the study which used a single, case study methodology. While
the findings in this study are reasonable given the data collected, via a careful
analysis, they are not generalizable to other settings. However, the findings may
offer patterns or actions that may result in further investigation by other researchers.
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Conclusion
The purpose of this chapter was to describe the methodologies used in this
study. This description included a detailed review of the sampling criteria, the data
collection instruments, the data collection process and the data analysis methods. The
procedures used for this study were collectively developed by the students in the
cohort led by Dr. David Marsh and were approved by the IRB of the University of
Southern California. The concepts and methodologies were reviewed by and gained
the approval of the school principal at Land High School. Data collection efforts
were confined to math teachers and key leaders using interview guides and teacher
questionnaires. Document analysis was performed as needed. The findings and data
analysis presented in the Chapter 4 are based on a thorough content analysis of the
data collected and was expressed in terms of the research questions that have guided
this study.
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CHAPTER 4
DATA FINDINGS, ANALYSIS, AND DISCUSSION
Introduction
The Nation at Risk (NAR) report characterized the public schools as “failing” and
called attention to the risks that the failure posed to the economic growth and national defense
of the United States of America (NCEE, 1983). The report was foundational to many past and
current school reform efforts and proposed remedies to address the academic performance of
American high schools. During the 1990’s the school reform efforts resulted in an increased
focus on school accountability and standardized curriculum for each state.
Today, the No Child Left Behind (NCLB) Act of 2001 is another federal
reform, educational initiative that has bipartisan support. Unlike the previous
educational proposals and reforms -- A Nation at Risk, America 2000, and Goals
2000 -- the NCLB Act concentrates on prioritizing educational efforts, testing
students and holding schools accountable, through standards-based assessments. The
NCLB aims to lessen the achievement gap between the “economically advantage and
disadvantaged students” and targets increasing the reading and math performance of
students in urban and poverty rural communities. In addition, there is an increased
focus on secondary school reform, specifically in math education. Primarily, because
strong math performance increases college attendance and graduation rates; and
strong math performance improves the quality of job opportunities that are available
for high school graduates.
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A review of the current literature revealed that for the last 24 years and since
the release of the Nation at Risk report, the underperformance of American students
was a growing concern that led elected officials, educational leaders, and educators
to call for many educational reform initiatives (Elmore, 1997). These reform
initiatives had many elements that were often characterized as “best practices” due to
resulting in increased student achievement. Furthermore, a review of the literature
revealed there were common elements shared by schools that experienced
performance improvement. These common elements were: 1) alignment of
assessments with standards, 2) use of data for instructional decisions, 3) participation
in teacher development, and 4) participation in instructional leadership development.
The purpose of this study was to identify how high school leaders in urban
schools successfully integrate policy initiatives and best practices to improve math
performance in their schools. The study investigated how school leaders, who may
not have strong pedagogical content knowledge in mathematics, garner the resources
to improve student achievement and sustain academic growth. Moreover, the study
examined how the school leaders, in the absence of instructional expertise in
mathematics, carried out functions related to fiscal management, personnel
management, change management, organizational leadership, and data collection and
analyses to successfully bring about increased math achievement outcomes.
In order to learn more about how high schools successfully integrate policy
initiatives and best practices to improve math performance in their schools, a case
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study was conducted at Land High School of Southern California. The study
consisted of a single, comprehensive and ethnically diverse high school. The study
examined the school’s efforts to improve student achievement in math over a three-
year period: the 2002-03, 2003-04 and the 2004-05 academic years.
Land High School of Southern California was selected for the study. The data
collected from Land High School consisted of the following: student achievement
data; teacher and administrator survey data; and questionnaire and interview data.
The collected data was analyzed to examine the following research questions:
2. What was the pattern of Math achievement for various students at the
school?
2. What Policy initiatives as well as curriculum, instruction and related
conditions seem to be related to improved math achievement in the
school?
3. What change process did the school use to enhance its math program and
strategies to assist students in math?
4. How was instructional leadership important in improving a) the math
programs/strategies and b) math achievement among students?
5. How did instructional leaders respond in academic areas in which they
were not experts?
This study investigated Land High School’s efforts to improve student
achievement through the frameworks of effective instructional leadership,
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organizational design, sound instructional practices and supportive educational
policies and initiatives. The five data collection instruments developed for the study,
were specifically designed to gather data relevant to the above research questions.
The data collection instruments included: (1) A Key Leader Interview Guide
(Appendix C); (2) A Teacher Interview Guide (Appendix D); (3) A School Profile
(Appendix E); and, (4) A Teacher Questionnaire with two versions (Appendices F
and G). These data collection instruments were used to gather findings for the study.
The findings for this study consisted of data gathered from interviews with key
leaders and teachers, results from teacher questionnaires, data gathered from source
documents, classroom observations, and quantitative data from the California
Department of Education Data Quest web site.
Gathering related data from multiple sources made it possible to triangulate
the data, which supported the increased reliability and validity of the findings. The
findings in this chapter were presented with the five research questions for the study
and were followed by a detailed analysis and discussion of the data.
Data Findings
Research Question 1: Pattern of Achievement in Math.
The first research question asked, “What was the pattern of Math
achievement for various students at the school?” The pattern of math achievement is
evidenced in the review of assessment measurement data from the California
Department of Education (CDE). There were three types of assessment
measurement data used to examine the pattern of math achievement at Land High:
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1) Algebra I CST results, 2) CAHSEE passing rates, and 3) Advance Placement (AP)
taking/passing rates for the 2003 through 2005 timeframe.
An analysis of the data using the three aforementioned assessment measures
revealed the following general findings for Land High School:
1. Almost 50% of the students performed at a scale score at or above
proficient on the Algebra I section of the CST in 2005.
2. Hispanic students out gained their peers statewide by a wide margin
during the time period examined.
3. Economically disadvantaged student significantly out gained their peers
statewide during the time period examined.
4. ELL students out gained their peers statewide by a wide margin during
the time period examined.
5. The number of students enrolled in Advanced Placement mathematics
courses increased 33% from the 2002 through 2005 time period.
6. Over 60% of economically disadvantaged students consistently passed
the CAHSEE during the time period examined.
California Standards Test (CST) Algebra 1 Assessment. The CST Algebra 1
assessment is administered as part of the Standardized Testing and Reporting
(STAR) Program under policies established by the State Board of Education. The
CST Algebra 1 assessment is designed to demonstrate progress toward the state
standards in the content area of Algebra 1. Each academic year, the CST Algebra 1
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assessment is administered to all students in grades 9 through 11 in the state of
California.
The questions on the CST are evaluated by committees comprised of teachers
and administrators that are Algebra 1 content experts. These committees work to
make certain the CST questions adequately measure the academic content standards
in Algebra I. And the committees help to ensure the CST assessment items are void
of biases related to gender, ethnicity, and language.
This study examined CST Algebra 1 assessment data for Land High for three
consecutive academic years: 2002-03, 2003-04, and 2004-05. An analysis of CST
Algebra I assessment data for the 2002-03 academic year (see Table 7), revealed that
Land High School demonstrated a mean scale score of 328.2. When examined
according to primary subgroups, the mean scale scores span a range of 342.8 (Asian)
to 322.0 (Hispanic).
When comparing Land High School’s score with statewide results, the mean
scale score for the state is slightly higher, with a mean scale score of 336.8. The
statewide gap in achievement between subgroups is consistent with the achievement
patterns for subgroups at Land High. The state’s CST assessment results reveal that
Asians demonstrated strong performance with a mean scale score of 386.3 and
Hispanics scoring at 306.3. In addition, these scores for the 2002-03 academic year,
revealed that Asians at Land High scored below the state average while Hispanics
scored above state average at the school and district levels. Moreover, the ELL
students and those characterized as SES disadvantaged both performed better than
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Table 7. CST Algebra 1 Assessment Data - 2002/2003
2002/2003 CST Algebra 1 Mean Scaled Score
Total Number Tested at Land High =185
Land High School -
Subgroups/% enrolled
School District State
African American * 303.9 301.9
Amer. Indian or Alaska
Native
* * 319.5
Pacific Islander * 369.2 321.7
Asian 342.8 403.6 386.3
Filipino * 373.7 342.6
Hispanic or Latino 322.0 333.2 306.3
White (not Hispanic) 329.8 355.0 352.1
Economically Disadvantaged 327.2 323.1 310.7
English Language Learners 325.0 318.4 295.4
All Students 328.2 328.4 336.8
Data reported are the percent of students achieving at Proficient or Advanced level
(meeting or exceding the state standards) for 2002/2003 timeframe. *No score reported
if less than 10 students tested.
their peers statewide. The ELL students at Land High realized a mean scale score of
325.0 compared to a statewide average of 295.4. SES students at Land High had a
mean scale score of 327.2 compared with statewide score of 310.7.
The pattern of achievement for Hispanics was equally evident when the
percentage of students scoring proficient and above was used as the measure. The
number of students scoring proficient and above grew from 15% to 48% during the
timeframe examined. In 2002-03, 15% of Hispanic students at Land High scored
proficient or above, while in 2004-005, a full 48% of Hispanic students scored
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proficient and above (Table 8). In comparison to other Land High subgroups,
Hispanics had the largest growth in the number of students scoring proficient or
above.
Table 8. CST Algebra 1 Assessment Data–Racial and Ethnic Subgroups
Algebra 1 African
American
American
Indian or
Alaska
Native
Pacific
Islander
Asian Filipino Hispanic
or Latino
White not
Hispanic
Economically
Disadvantaged
ELL
2002/2003 * 36 * 15 32 20 22
2003/2004 * 39 15 24 32 23 29
2004/2005 * 57 * 48 36 47 33
Data reported are the percent of students achieving at the Proficient or Advanced level
(meeting or exceeding the state standards) for the 2002, 2003, 2004, and 2005 timeframe.
*No score reported if less than 10 students tested.
During the timeframe for the study, there was a slight drop in Land High’s
mean scale score, but there were increases in the number of students scoring
proficient and above. Hispanics students grew from 15% to 48%, while Asian
students realized an increase from 36% to 57%. White students grew from 32% to
36% scoring proficient and above. Overall, Asian, White, and Hispanic students
experienced an increase in the number of students scoring proficient and above at
Land High, while there were declines in these same subgroups statewide (Table 8).
In 2003-04, the second year examined (see Table 9), Hispanic students at
Land High School outperformed their peers statewide. At Land High, Hispanic
students achieved a mean scale score of 325.8; this is higher than the state’s mean
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scaled score of 303.3 for Hispanic students. As noted earlier, Hispanic students at
Land High demonstrated consistent performance gains during the time period
examined. Their mean scale scores for the 2002/2003 and 2003/2004 academic years
were 322.0 and 325.8 respectively.
Economically disadvantaged students experienced continuous growth in their
mean scale score over a three-year period. Their mean scale score was 237.2 in
2002-03 (Table 1) and 323.8 in 2003-04 (Table 9). In addition, the percent of
economically disadvantaged students scoring proficient and above grew from 20%
during the baseline year to 47% in the 2003-04 timeframe. Overall, growth occurred
at Land High for English Language Learners (ELL). In 2002-03, 22% of the ELL
students at Land High scored proficient or above. In the 2003-04 timeframe, 29%
achieved proficient and above (Table 8).
Table 9. CST Algebra 1 Assessment Data - 2003/2004
2003/2004 CST Algebra 1 Mean Scaled Score
Total Number Tested =185
* No score reported if less than 10 students tested.
Land High School -Subgroups
School District State
African American * 370.0 297.6
Amer. Indian or Alaska Native * * 320.2
Pacific Islander * 387.7 322.6
Asian 338.2 417.2 381.9
Filipino 327.2 402.0 380.4
Hispanic or Latino 325.8 358.1 303.3
White (not Hispanic) 327.5 374.3 350.7
Economically Disadvantaged 323.8 370.3 306.0
English Language Learners 312.8 365.1 287.5
All Students 327.4 384.6 330.8
Data reported are the percent of students achieving at Proficient or Advanced level (meeting or
exceedingthe state standards) for 2003/2004 timeframe. *No score reported if less than 10
students tested.
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The 2004-05 academic year, represented the third and final year of analyzing
CST Algebra 1 assessment measures (see Table 10). In the 2004-05 academic year,
Land High students demonstrated math achievement gains in all significant sub-
groups with particularly strong gains made by the Hispanics and ELL students. For
example, Hispanic students at Land High outperformed their peers statewide with a
mean scale score of 345.7. During this same time period, the statewide score was
304.5. ELL students also experienced increased math achievement. In 2003 ELL
students earned a mean scale score of 325.0. The score grew to 335.0 in 2005
timeframe.
During the 2004-05 assessment period, the number of economically
disadvantaged students scoring proficient and above increased by more than 50%. In
the 2002-03, only 20% of economically disadvantaged students scored proficient and
above; the number scoring proficient and above increased to 47% in the 2004-05
academic year (see Table 8).
For ELL students, the gains were also significant. In the 2004-05 academic
year, nearly two-thirds of ELL students at Land High scored proficient or above.
This was an increase from 22% in 2002-03 to 33% in 2004-05 scoring proficient and
above. During the same time period, the number of economically disadvantaged
students scoring proficient and above increased by more than 50%. In the 2002-03,
only 20% of economically disadvantaged students scored proficient and above; the
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Table 10. CST Algebra 1 Assessment Data - 2004/2005
2004/2005 CST Algebra 1 Mean Scaled Score
Total Number Tested =185
* No score reported if less than 10 students
tested.
Land High School -Subgroups/%
enrolled
School District State
African American * 377.3 347.9
Amer. Indian or Alaska Native * * 369.5
Pacific Islander * 361.5 360.0
Asian 357.9 435.3 386.3
Filipino * 386.9 346.3
Hispanic or Latino 345.7 369.5 304.5
White (not Hispanic) 339.7 393.8 349.4
Economically Disadvantaged 348.1 381.6 306.5
English Language Learners 328.2 407.7 285.5
All Students 346.2 377.3 330.4
Data reported are the percent of students achieving at Proficient or Advanced level (meeting or
exceeding the state standards) for 2004/2005 timeframe. *No score reported if less than 10 students
tested.
number scoring proficient and above increased to 47% in the 2004-05 academic year
(see Table 8).
When using CST Algebra 1 data as an assessment measurement, the data
revealed that Hispanic and economically disadvantaged students at Land High,
demonstrated the strongest gains in the number of students scoring proficient and
above. For example, in 2002-03, only 15% of Hispanic students scored proficient
and above; whereas in 2004-05, almost half the Hispanic student population (48%)
scored proficient and above. During this same time period, statewide assessment
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measures were considerably lower and slightly declined for the Hispanic population.
In 2002-03, statewide data revealed that 17% of Hispanic students scored proficient
and above. This same statewide measurement number dropped to 16% during the
2004-05 assessment period.
CAHSEE Passing Rates. In 1999, the state law approved the development of
the California High School Exit Exam (CHSEE). The CAHSEE, designed by content
experts in English-language arts and mathematics, reflects the expert panel’s
recommendation for the content that students should master to be able to succeed in
higher-level education.
Although grade 9 students can voluntarily take the CAHSEE, grade 10
students are required by state law to take the exam. If the exam is not mastered,
students will have opportunities for additional instruction and are permitted to retake
the mandated exam and must pass the exam to obtain a high school diploma.
In keeping with this requirement, the pattern of achievement for Land High is
also evidenced in the number of students passing the CAHSEE. During the time
period examined, the passing rates for Land High students almost always surpassed
the CAHSEE statewide passing rates (Table 11). For example, during the time period
examined, African American and Hispanic students at Land High experienced gains
in the number of students passing the CAHSEE, while statewide the rate of passing
for these same subgroups declined.
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Also noteworthy was the similarity between the statewide CAHSEE passing
rates and the Land High passing rates for both Asian and White students. In 2004-05
the statewide passing rate for Asians was 73% and the school-passing rate was very
similar with 75%. White students statewide experienced an 83% passing rate, while
the statewide passing rate for the same student group was 82%.
Although the 2004-05 timeframe is used to illustrate the similar school and
statewide passing rates for the Asian and White subgroups and the differences in
school and statewide rates for African American, Filipino, Hispanic and Pacific
Islander subgroups, the same pattern is evidenced in both the 2002-03 and the 2003-
04 timeframes (Table 11).
Advance Placement (AP) Enrollment/Passing Rates. The Advanced
Placement (AP) Program is administered by The College Board of New York and the
instruction for AP classes is provided at local high schools. Providing AP classes at
local high schools enables high school students to enroll and participate in college-
level courses.
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Table 11. Comparison of Land High and Statewide CAHSEE Passing Rates
for the 2002-03, 2003-04, and 2004-05 Academic Years
Race/Ethnicity
Number
Tested
Land
High
Number
Passed
Land
High
Percent
Passed
Land
High
Percent
Passed
CA State
Number
Not
Passed
Land High
Percent
Not
Passed
Land
Mean
Scaled
Score
Land
2002-03 CAHSEE Passing Rates
American Indian
or Alaska Native 0 -- -- 68%
--
-- --
Asian 65 49 75% 73%
16
25% 380
Pacific Islander 4 -- -- 66%
--
-- --
Filipino 19 19 100% 81%
0
0% 395
Hispanic or Latino 452 292 65% 53%
160
35% 361
African American 19 10 53% 56%
9
47% 351
White 152 130 86% 84%
22
14% 387
ELL Students 271 124 46% 33%
147
54% 343
Economically Dis. 341 227 67% 51%
114
33% 362
2003-04 CAHSEE Passing Rates
American Indian
or Alaska Native 2 -- -- 73% -- -- --
Asian 63 55 87% 85% 8 13% 392
Pacific Islander 6 -- -- 71% -- -- --
Filipino 23 22 96% 87% 1 4% 397
Hispanic or Latino 302 216 72% 62% 86 28% 368
African American 10 -- -- 63% -- -- --
White 122 102 84% 88% 20 16% 386
English Learner 137 58 42% 39% 79 58% 345
Economically Dis. 255 176 69% 60% 79 31% 367
2004-05 CAHSEE Passing Rates
American Indian
or Alaska Native
7 --
-- 64%
-- -- --
Asian 65 51
78% 75%
14 22% 382
Pacific Islander 14 12
86% 64%
2 14% 382
Filipino 30 28
93% 81%
2 7% 397
Hispanic or Latino 501 321
64% 53%
180 36% 361
African American 18 13
72% 54%
5 28% 362
White 181 148
82% 83%
33 18% 379
English Learner 284 120 42% 33%
164 58% 342
Economically Dis. 504 323 64% 51%
181 36% 360
Source: California Department of Education: Supplemental Information for the California High
School Exit Examination (CAHSEE).
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Overall there is minimal difference between the statewide and school passing
rates for Asian and White students. In contrast, African American, Hispanic,
Filipino, and Pacific Islander students experience a distinctively higher passing rate
at Land High in comparison to statewide subgroups (Table 12).
Table 12. Comparison of Passing Rates for Land High and Statewide
Subgroups (2004-05).
Subgroups Land High
Passing Rate
CA Statewide
Passing Rate
White
82% 83%
Asian
78% 75%
African American
72% 54%
Filipino
93% 81%
Hispanic or
Latino
64% 53%
Pacific Islander
86% 64%
The math department at Land High School participates in the AP program
and offers Advanced Placement classes in Calculus A and B. In keeping with the
pattern of math achievement, enrollment in the Calculus AP class increased from 24
students in 2002-03 to 33 students in the 2004-05 timeframe (Table 13).
Overall, the pattern of math achievement at Land High is evidenced by the
CST Algebra I increased mean scale score for almost all subgroups, the consistently
increasing CAHSEE passing rates and the growth in the rate of enrollment in the AP
Calculus classes during the timeframe studied.
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Table 13. Land High School Mathematics-Advanced Placement
Enrollment Information 2002-03, 2003-04, through 2004-05.
Course Name Male
Enrollment
Female
Enrollment
Total Course
Enrollment
Number of
Classes
Advanced Placement
Calculus AB
(2002/2003)
8 16 24 1
Advanced Placement
Calculus AB
(2003/2004)
10 12 22 1
Advanced Placement
Calculus AB
(2004/2005)
18 15 33 1
Source: California Department of Education
The CST Algebra 1 mean scale score grew from 328.2 in 2002-03 to 346.2 in
the 2004-05 timeframe. During this same timeframe, Asian students experienced a
scale score growth of more than 15 points, White students improved by 10 points and
Hispanic students improved by 21 points. Statewide, there were improvements in
the Hispanic and White student populations as well, but the improvements were less.
At the school level, Hispanic students experienced the largest gain in mean scale
scores. There was minimal change in Asian student achievement at the school level;
however, during the 2003 to 2005 timeframe the Asian student population at Land
High demonstrated the third highest gain in mean scale scores. Economically
disadvantaged students demonstrated the second highest gains.
The increased-enrollment pattern in the math department AP classes and the
CAHSEE passing rates further evidenced increased math achievement. Also worthy
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of note are the decreases in the students scoring below basic and far below basic.
For example, in 2003-03 almost 20% of the students scored below basic. In the
2004-05 timeframe the number decreased to 10% of the students scoring below basic
(Table 14).
Table 14. Land High School CST Results –2002/2003 2003/2004, and
2004/2005
Students Tested Mean Scaled Score % Below Basic
Test
Year
Grade
School
District
State
School
District
State
School
District
State
Algebra I 2003 9 185 1273 187396 328.2 328.4 306.1 18 8 34
Algebra I 2004 9 210 1373 222333 327.4 333.5 301.2 20 8 30
Algebra I 2005 9 216 1306 248498 346.2 347.6 304.2 10 4 27
Source: California Standardized Testing and Reporting Program. The California Standards
Tests (CSTs) are developed by California educators and test developers specifically for
California. They measure progress toward California's state-adopted academic content
standards, which describe what students should know and be able to do in each grade and
subject tested.
In summary, analysis of the assessment measurement data related to Research
Question 1 reveals a strong pattern of achievement in math at Land High in
comparison to statewide patterns of achievement. At the school level, all significant
sub-groups out performed their peers statewide, in terms of performance gains on the
Algebra I CST. In addition, the increased-enrollment pattern in the math department
for the AP class and the CAHSEE passing rates evidenced increased achievement.
Finally the gap closed for students scoring below basic and far below basic in that
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students were allowed to increase skills by taking Algebra classes (Algebra A and
Algebra B) over a full year. Closing the gap for students scoring below basic and far
below basic will be discussed when the findings from research question 2 are
presented.
Research Question 2: Policy and Practice
The second research question asked, “What policy initiatives as well as
curriculum, instruction, and related conditions seem to be related to improved math
achievement in the school?” The findings related to the policy initiatives, school
curriculum, instructional practices and school conditions that supported improved
math achievement are outlined in this section. These findings have been discussed in
the context of the framework for research question 2: Marsh and Codding’s school
design (1998) and math program design. Therefore, findings for this research
question have been discussed in terms of policy initiatives, school design, and math
program design.
Policy
Policy Initiatives Related to Improved Student Achievement. In general, math
teachers at Land High School do not agree that NCLB has promoted increased
student achievement. Only 22% of math teachers agree that the NCLB Legislation
has promoted increased student achievement at Land High School (Table 15). In
contrast, a full 89% of math teachers agree that the requirement to pass the CAHSEE
has contributed to the school’s efforts to improve math achievement (Table 16).
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Table 15. Math Teacher Questionnaire: Question 1
The NCLB Legislation has promoted increased student achievement.
Scale Mean = 2.89 Range Frequency Percentage N= 9
Strongly Agree 5 0 0
Agree Somewhat 4 2 22
Neutral 3 5 56
Disagree Somewhat 2 1 11
Strongly Disagree 1 1 11
Table 16. Math Teacher Questionnaire: Question 2
The CAHSEE requirement has contributed to efforts to improve math achievement.
Scale Mean = 4.44 Range Frequency Percentage N= 9
Strongly Agree 5 6 67
Agree Somewhat 4 2 22
Neutral 3 -- 0
Disagree Somewhat 2 1 11
Strongly Disagree 1 -- 0
Almost all administrators at Land High School repeatedly expressed that
accountability measures and policies such as NCLB, AYP, API, CAHSEE and HQT
have greatly influenced their focus on increased student achievement. Land High
principal, Paul Grey, indicated that policies such as NCLB and the CAHSEE have
had a “significant impact at all levels” and have led to many district-level
administrators being “fired up.” Paul Grey, concluded his remarks on policy
initiatives by stating that policies such as NCLB and the CAHSEE have had a
“significant impact at all levels” of the school. Grey further explained that he
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perceived improved math achievement also resulted from overall changes in the
school design such as teacher commitment and student effort.
As previously mentioned, the effective school design framework for research
question 2 is based on Marsh and Codding’s model (1998), which consists of the
following four components: student performance assessment, curriculum, school
culture, and learning activities. Land High School reported significant use of three of
the components of the effective school design framework and very limited use of the
curriculum component.
School Design
Findings in this case study indicated that the math teachers at Land High
worked diligently to promote a positive school culture that emphasized and
supported student achievement in math. Moreover, the findings revealed that the
majority of the math teachers believe the leadership and collaboration from within
the math department greatly influenced the use of the 3 aforementioned components
in Land High’s efforts to improve math achievement (Tables 17 and 18).
Overall, the findings revealed that math teachers devoted a considerable
amount of attention to student assessments and changing the school culture as it
relates to standardized tests: less time and attention was given to the math curriculum
and to learning activities. Moreover, most math teachers perceived the school design
approach for improved math achievement is largely driven by standards-based
instruction (Table 19).
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Table 17. Math Teacher Questionnaire: Question 18
Teachers have developed strategies to improve math instructional practices.
Scale Mean = 4.22 Range Frequency Percentage N= 9
Strongly Agree 5 4 45
Agree Somewhat 4 3 33
Neutral 3 2 22
Disagree Somewhat 2 0 0
Strongly Disagree 1 0 0
Table 18. Math Teacher Questionnaire: Question 19
The principal has served as a change agent for improved math achievement.
Scale Mean = 1.67 Range Frequency Percentage N= 9
Strongly Agree 5 0 0
Agree Somewhat 4 0 0
Neutral 3 3 33
Disagree Somewhat 2 0 0
Strongly Disagree 1 6 67
Table 19. Math Teacher Questionnaire: Question 14
Standards-based instruction served to improve student achievement in math.
Scale Mean = 4.33 Range Frequency Percentage N= 9
Strongly Agree 5 4 45
Agree Somewhat 4 4 44
Neutral 3 1 11
Disagree Somewhat 2 0 0
Strongly Disagree 1 0 0
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Student Performance Assessments. Math Department Chair, Rhonda Castillo,
described the extensive assessment process that the math department takes to ensure
that entering ninth grade students are placed in the proper math class. Castillo reports
this is important for two reasons: (1) The students need to obtain the appropriate
level of instructional support and remediation, if needed and (2) Land High School
has designed its math department to help students develop the skills needed to
successfully complete the Algebra course. The first assessments are conducted in the
summer, proceeding eighth grade graduation. These assessments are completed prior
to the students’ officially entering ninth grade at Land High.
Castillo further explained that these assessments are critical because Land
High has designed the Algebra course to include two sections: Algebra 1 and
Algebra 2. According to Principal Grey, the math teachers use the incoming-
students’ math assessment data from eighth grade and the summer assessment data to
determine which Algebra course is needed. Students who need to “catch up” are
provided an opportunity to take Algebra 1 for a full year and complete Algebra 2
during their sophomore year. The students who enter ninth grade with stronger math
skills skip Algebra 1 and only take Algebra 2 during their freshman year of high
school. Principal, Grey explained that the Algebra course structure helps to ensure
that all students are given an opportunity to succeed.
Castillo, reports that extensive and regular assessment efforts directly
contribute to increased student achievement. Furthermore, she described the
additional assessment that occurs two weeks after school starts. Castillo explains that
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students are re-assessed two weeks after school starts to identify students who need
support in math instruction or remediation. For example, if the student was originally
assigned to Algebra 2, but the most recent assessment data indicates that additional
instructional support or remediation is needed, the same student would be reassigned
to Algebra 1. The decision is a collaborative decision between the math teachers and
the math department chair.
Principal Grey reports that a concerted effort is made to provide ongoing
support to students who need instructional support in mathematics. Land High math
teachers arrange for the students to participate in extra math support classes on
Saturday morning or during one of the student’s elective class periods. Principal
Grey explained the arrangement is usually designed in agreement with the student’s
parents since it involves modifying the student’s school week or school day. The
majority of math teachers agree that support classes are intended to improved student
achievement in math (Table 20)
Table 20. Math Teacher Questionnaire: Question 13
Support classes are included to improve math achievement.
Scale Mean = 4.22 Range Frequency Percentage N= 9
Strongly Agree 5 4 45
Agree Somewhat 4 3 33
Neutral 3 2 22
Disagree Somewhat 2 -- 0
Strongly Disagree 1 -- 0
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Math Department Chair, Castillo, reports that data-driven decisions that
include the use of grades from classroom instruction in addition to outcomes form
standards-based tests are critical to improved math performance. He explained that
the math teachers routinely examine students’ grades, in-class performance, and
math test data to determine how best to support students who are underperforming.
Castillo notes the process is not a formal, data-driven, decision-making process, but
it’s nonetheless effective because the teachers have the most instructional time with
students and are keenly aware of the students’ instructional needs.
Although the research indicates that coherent math curriculum is a key factor
in math achievement (NCTM, 2000), Principal Grey and Department Chair Castillo,
did not highlight the role of curriculum in improving student math achievement.
School Culture. Principal Grey explained that Math Department Chair,
Castillo and math teachers implemented a process that changed the school culture as
it relates to the Standardized Testing and Reporting (STAR) program, specifically in
the content area of math. Principal Grey, School Administrators and Math
Department Chair, Castillo, reportedly increased the students’ sense of control
regarding their personal outcomes related to standards-based testing by creating a
school-wide communication strategy just prior to the testing event. The goal of the
communication strategy is to motivate students to increase their focus and
achievement efforts during the testing process. In addition, the strategy is designed to
increase the value that students place on effort and persistence when taking the tests.
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Assistant Principal, Mehia emphasized that school administrators and math
teachers adopted a testing awareness/communication strategy that had been
successfully used by another school in the Orange District, and reported that many
students had benefited from the strategy. Principal Grey, further explained that the
testing/communication strategy first started by carefully crafting how they would
present the information to a student.
Principal Grey, Math Department Chair, Castillo and the other Assistant
Principals, recounted their efforts to create a STAR-program communication strategy
that resulted in increased student awareness and motivation. First, they developed a
script to support the strategy. The script consisted of three key elements: (1) general
steps, (2) class presentation/talking points, and (3) individual [student/teacher]
meetings (Figure 17).
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Figure 17. Script for Star Report Cards
General Steps: Pass out report cards to each student at the beginning of your time there.
• Make a brief presentation about the different parts of the report card and why one should try
their best on the STAR Test
• Meet with the individual students in the back of the classroom, setting goals and encouraging
student to do their best on the STAR Test.
- Classroom teachers can help too [meeting with students from 1 to 2 minutes each]
• Any problems, such as missing sheets, etc? Please note and contact STEVE.
Class Presentation Talking Points (Use these and adopt/adapt them as you see fit)
• “Note on the left side of your STAR Report Card you will find your GPA, credits earned and a place
to set a goal for your GPA. This should be a realistic goal for your GPA to accomplish by this time next
year.”
• “On the right side of your STAR Report Card you will find your STAR performance over the past two
years. Hopefully you will see growth in this area. Your performance level is determined by using the
scales found on the bottom right hand corner (FYI – Advanced, Proficient, etc.).”
• “We are here today to meet with each of you individually and develop goals with you. We believe
that everyone can improve by one quintile level. Getting just one more question correct is worth
approximately 5 to 10 scaled points. A few more correct can move you up a lot!!! (Pause for dramatic
effect!)”
• “Why should you do well on the STAR Tests?” Tests officially begin on (date)
- #1 – Your performance on these tests is part of our permanent record. Your score should be a
reflection of what you are capable of and how much you are growing from year to year.
- Class placement is often done using the scores from these tests.
- Double block classes (2 periods of Math and 2 periods of English) began this year for students who
scored in the below basic level.
- This test is excellent practice for the CASHSEE and the SAT/ACT college entrance exams.
• “We want you to do your best and want to set realistic goals with you individually.” Please finish the
bar graphs after we meet and bring this sheet home and share it with your parents. Have your parents
sign the STAR Report card and show it to your teacher. Then keep it in your notebook and review it
once a day to review your future goals.”
Individual Meetings
• Consider the GPA and credits (current credit guidelines would have 9th =30, 10th =90, 11th =150). Set a
realistic goal with the student for the GPA for a year from now.
• Consider the STAR performance for the past two years (if a score is missing work with the one score). Note
growth or decline in scores (a decline will be in parenthesis) and any discrepancy with the GPA (e.g. if a
student has a GPA of 3.5, but is below basic in performance – something is very wrong!).
• Set the STAR goals with the student, attempting to move the student to the next performance quintile. If the
student is already in the advanced band or if they are too far way from the next band, make a goal that shows
improvement (hopefully 20 points at a minimum).
• Have the student finish the bar graph for homework and have them get a parent signature.
• On to the next student…no time to rest!
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Principal Grey reported that the SCRIPT outlined the process for how to best
increase student awareness, motivation, and accountability when presenting the
STAR program information. Additionally, the script was designed to provide a
consistent message from school administrators and teachers. According to Principal
Grey, the SCRIPT was crafted with the intent to make students cognizant of the
importance of persistence and personal effort. Finally, the SCRIPT was designed to
enable the student to set goals and to foster parent participation in helping students
persist toward achieving the goals.
Principal Grey was surprised to learn that “Most of the students were not
aware they could positively impact their performance outcomes if they correctly
answered one or two additional questions during the test.” Principal Grey recounted
that when the students were informed of this, many of the student reportedly said,
“They would have focused more and taken more time had they known this.”
According to Principal Grey, the SCRIPT for the STAR program is also
intended to increase the utility value that students place on standardized performance
test like the CAHSEE, Scholastic Assessment Test (SAT) and the American College
Test (ACT). Moreover, the SCRIPT directs the administrator or teacher to state,
“This test is excellent practice for the CASHSEE and the SAT/ACT college entrance
exams.” Principal Grey comments, that this is stated to help students link their STAR
achievement outcomes to the future standardized tests required for high school
graduation and college admission. According to Assistant Principal, Mehia linking
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performance on the STAR test to other standardized tests is helpful because “the
students can see the tangible results needed.”
In general, the Math teachers at Land High have a similar point of view
regarding the benefits of standardized tests. This is evidenced by their responses to
the following item on the Math Teacher Questionnaire: The requirement that
students pass the CAHSEE to earn a high school diploma has contributed to the
school’s effort to improve student achievement. A full 89% of the math teachers
agree with the above item and the mean scale score for the item is 4.44 (based on 5
point Likert scale).
In addition increasing student awareness to help drive reform, Land High
developed additional measures to increase student motivation and accountability.
These measures are directly related to the students’ cumulative STAR performance
report (Figure 18). Principal Grey reports the cumulative STAR report is prepared
and given to students as part of a goal setting process for students. The SCRIPT for
the STAR report contains the discussion points that teachers and administrators use
to help the student focus on their past performance and set goals for their future
STAR performance.
The three sections of the SCRIPT (Figure 17) are designed to help
administrators and teachers provide the same message to all students. The first
section of the SCRIPT directs the administrators and teachers to distribute the
cumulative STAR report to students. After the reports are distributed, the
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administrator and teachers discuss the report data and other elements with students
and are required to follow the prescribed set of talking points.
Principal Grey explains that students are often surprised by what they see on
the report, especially when they see their achievement patterns. Some students are
pleased and others see failure; however, all students are encouraged to increase their
effort and persistence. In addition, the students have an opportunity to individually
meet with administrators and teachers to discuss the cumulative STAR report and to
set new goals.
Figure 18. Land High – Student Cumulative STAR Performance Report
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Assistant Principal, Mehia concluded the discussion about the STAR
awareness and goal setting strategy by stating that students are now more aware of
what is expected and work to meet the expectations. According to Mehia, the goal
setting process has help teachers monitor their instructional practices, especially as it
relates to teaching standards-based lessons. This is further evidenced by the
teachers’ responses to the following item on the Math Teacher Questionnaire: The
implementation of standards-based instruction has served as an important
foundation in improving student achievement in math. Eighty-nine percent of math
teachers agree that standards-based instruction has contributed to student
achievement in math (Table 21).
Table 21. Math Teacher Questionnaire: Question 14
Standards-based instruction served as an important foundation for math
achievement.
Scale Mean = 4.33 Range Frequency Percentage N= 9
Strongly Agree 5 4 45
Agree Somewhat 4 4 44
Neutral 3 1 11
Disagree Somewhat 2 -- 0
Strongly Disagree 1 -- 0
Learning Activities. The findings from the observation, interview, and
questionnaire data indicate there are limited formal and specific learning activities at
Land High that are directly intended to increase math achievement. Almost all math
teachers perceive they are the primary impetus for math achievement at Land High.
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Moreover, they believe learning activities are limited to the routine teaching
practices required to help the students meet the California standards. The majority of
math teachers also report there is limited use of math coaches and experts. This is
evidenced by a mean score of 1.78 to item 15 and a mean score of 1.67 for item 19
on the math teacher questionnaire (Table 22).
Table 22. Leadership Support and Student Achievement
Item
#
Math Teacher Questionnaire Item
Strongly
Disagree
Disagree
Neutral
Agree
15 Our school has added the use of math
coaches or experts to assist in the effort to
improve student achievement in math.
56% 11% 33% 0
19 The principal has served as a “change
agent” for improved student achievement in
math.
67% 0 33% 0
The math teachers attribute the math achievement at Land High to teacher,
leadership, teacher collaboration, standards-based instruction and student motivation.
Assistant Principal Mehia reported that some students are so self-motivated that a
select group of high achieving students started their own math club, using the public
library for their Saturday meetings.
Math Program Design
In contrast to the teacher’s perception, Math Department Chair, Castillo,
identified formal learning activities that are embedded in the math program design
and are specifically structured to support math achievement. Castillo noted that most
of his math teachers are highly qualified, in terms of years of teaching and formal
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training in math instruction. In addition, Castillo and three of the 14 math teachers
have advanced degrees in math instruction.
Classroom Practices. Math Department Chair, Castillo, described two
important classroom practices: teacher collaboration/mentoring and prescriptive
learning. According to Castillo, “The math teachers closely collaborate to make sure
that they use similar instructional practices.” He notes that this is important because
it ensures continuity of instructional content and instructional methods. According to
Castillo, both elements are needed.
There are typically two teachers in lower-level math classes. One provides
the primary instruction and the other observes the instructional practices and
provides instructional support to struggling students or to students that may need the
information clarified.
When asked about the process of monitoring new teachers, Math Department
Chair Castillo, commented, “New teachers are paired with veteran teachers and
struggling students are moved to math classes taught by veteran teachers.” Castillo
also noted that math teachers regularly review classroom-performance data in order
to prescribe and provide additional instructional support in specific content areas.
The math teachers use the student grades and classroom test data to determine the
extent of additional instructional support needed. Once this is determined, they target
individual instruction to meet the student’s learning needs.
Curriculum Design. In addition to teacher collaboration, Math Department
Chair, Castillo described another formal process for helping students increase math
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achievement. He commented that students who enter ninth grade without the
required math foundation are required to enroll in Pre-Algebra for one full year. The
Pre-algebra course is designed to help students refine the basic math skills needed to
successfully complete higher-level math courses such as Algebra and Geometry.
Castillo noted that the teachers at Land High are committed to helping their
students achieve in math. She provided several examples of how the math teachers
support their students by using their personal funds and time to help meet student
needs. Castillo emphasized that most math teachers are highly motivated and
routinely collaborate with other math teachers to help struggling students. Before
declaring she needed to prepare for the next class, Castillo pointed out that similar
attention is given to students who are excelling to help those students continue to
succeed.
Direct observations revealed that several students entered Castillo’s
classroom before class started. Castillo and the students were actively engaged in
conversations and appeared to have an authentic interest in each other as evidenced
by personal and school-related conversations. The students smiled as they talked and
Castillo made constant eye contact with the students during the conversations.
Standards-based Instruction. Among the most critical findings in this case
study are the teacher perceptions regarding standards-based instruction. This
perception is evidenced from math-teacher questionnaire responses. First, all math
teachers agree that they teach standards-based lessons. Second, a full 78% agree that
assessments were linked to standards. Finally, 88% agree that student achievement
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data was used to drive instruction. Table 23 lists the questions that examine
standards-based instructional practices. The responses received an averaged rating of
at least 4.4 on the 5-point Likert scale where a rating of 1 or 2 would indicate
“Disagree,” a rating of 4 would indicate “Agree,” and a rating of 5 would indicate
“Strongly Agree.”
Table 23. Math Teacher Responses to Standards-Based Instruction Items
Questionnaire
Item
Question (Math Teacher) Mean
Math Teacher
Item # 5
Teachers at our school teach standards-based lessons.
4.83
Math Teacher
Item # 4
Our school has successfully implemented common
assessments that support increased student achievement
3.78
Math Teacher
Item #8
Periodic benchmark assessments provide useful data
that our teachers use to drive instruction 4.58
Results from the interviews and questionnaires indicate that both math
teachers and school administrators link increased student success to standards-based
instruction. According to Math Department Chair, Castillo, the students also have a
significant role in the achievement patterns. “They [the students] take the instruction
more seriously.”
According to principal Grey and assistant principal, Mehia, standards-based
instruction is also supported by the District as evidenced by the District’s
requirement for benchmarks related to math instruction. Department Chair, Castillo
points out that common instructional practices help ensure that all students are
receiving the same curriculum. Castillo reports that the math teachers routinely
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collaborated to develop common assessments and rubrics to help ensure that all
students received the same curriculum and instructional rigor (Table 24).
Table 24. Math Teacher Questionnaire: Question 16
Teachers collaborate to develop common assessments and rubrics.
Scale Mean = 4.33 Range Frequency Percentage N= 9
Strongly Agree 5 5 55.6
Agree Somewhat 4 2 22.2
Neutral 3 2 22.2
Disagree Somewhat 2 -- 0
Strongly Disagree 1 -- 0
Math Department Chair Castillo, concluded her comments about standards-
based instruction by providing additional evidence of the math teachers’
commitment to success for all students. Castillo emphasized that the math teachers
have formed a supportive instruction and learning system that is standards-based and
student focused. She comments, “Teachers help new teachers out” and work closely
to develop “group-work strategies” to support student engagement and to increase
learning.
In summary, the math department leader, school administrators, and math
teachers agree that policies such as NCLB and CAHSEE have served a significant
role in math achievement reform at Land High. In addition, standards-based
instruction and assessments have help to drive increased student achievement in
math. The communication strategy adopted for standards-based instruction was
implemented to motivate all students to increase their focused effort during the
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testing process. Furthermore, the communication strategy made students aware of the
importance of the test results as it relates to CAHSEE passing rates and attending
college in the future.
Research Question 3: The Change Process. The third research question
asked, “What change process did the school use to enhance its math program and
strategies to assist students in math?” The findings for this research question are
discussed from the framework of Bolman and Deal’s Four Frames of Leadership
consisting of the following frames: 1) Structural, 2) Human Resource, 3) Political,
and 4) Symbolic (Bolman & Deal, 2003).
The Four Frames of Leadership provide “lenses” from which to view the
organization in the context of the change process. Therefore, the data for research
question 3 is presented according to the four frames which are detailed in Table 6 in
Chapter 3.
The Structural Frame. Assistant Principal Nara Dim, is the administrative
team member assigned to the math department. His role is to work with Math
Department Chair, Castillo to ensure “teachers have what they need” and to support
teachers with the math achievement process. He is also responsible for obtaining
District level resources for teacher development and plays a significant role in the
school’s standards-testing communication and awareness campaign. His additional
responsibilities include student assessments and math curriculum review.
Math Department Chair, Castillo, views the support from a member of the
administrative team as crucial to the teachers feeling supported in their efforts to
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improve math instruction. According to Castillo, this alignment allows the school’s
leadership to efficiently meet the needs of the math department. The math teachers
have a different perception regarding the benefits of this alignment and many report
the alignment adds little value to the quality of their math instruction (Figure 19).
This is evidenced by the math teachers’ responses to the following item: I
have gained valuable resources from math/instructional leaders that have improved
the quality of my math instruction. Teachers responded to this item with a mean
rating of 1.67. The majority of the math teachers would like to receive more
resources that add to the quality of their math instruction.
Principal Grey agreed that teacher support and development is needed in the
current atmosphere of high stakes testing and accountability. With that said, Grey
reportedly is pleased that Title 1 funding is available for the 2006/2007. Title 1
funding was not available during the academic years targeted in this study.
Grey recalled the crucial role that Assistant Principal Dim played in
increasing students, parents and teachers awareness of the importance of standards-
based testing. He commented that the structure of the campaign placed the school
leadership at the forefront and placed students and teachers in the center of it.
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Figure 19. Math Teacher Questionnaire - Question 31
Principal Grey further commented that requiring the students to participate in
goal setting activities and face-to-face discussions with teachers and school leaders
was central to the overall plan as it created mutual ownership and buy-in between the
leadership, the teacher, and the student.
In addition to mutual ownership, the math program was structured to allow
the ongoing assessment of students to enable teachers to make data-driven decisions.
The teachers used information from classroom performance and math tests to
determine if students needed additional instructional support. If a need was
identified, the students schedule was adjusted to accommodate a two-period math
class. Typically, the student’s elective class was dropped and the student started
attending the two-period math class.
6
5
4
3
2
1
Neutral Disagree Somewhat Disagree Strongly
I have gained valuable resources from math/instructional leaders that have
improved the quality of my math instruction.
66.7% 22.2%
11.1%
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Finally, the math department was structured to offer intervention math
courses, such as Math Studies and Pre-Algebra, for students who entered ninth grade
lacking basic math skills. In addition, the Algebra 1 course was divided into Algebra
1A and Algebra 1B for students whose pre-enrollment assessment data indicated a
need for additional math support before enrolling in Algebra 1. The Algebra 1
course was designed for students with stronger math competencies and skills.
The Human Resources Frame. An important finding in this study was the
role that the math teachers played in promoting improved student achievement in
math. The principal and Math Department Chair both agree that the math teachers’
dedications were crucial to increased student achievement. In the initial interview
with Assistant Principal Dim, who is aligned with the math department, he expressed
that the math teachers at land high are very collaborative; and veteran math teachers
routinely partner with new teachers to ensure the overall quality of the math
instructional practices and strategies.
Math Department Chair, Castillo, emphasized that “all departments are
concerned about the success of students” and that math department teachers are some
of the most dedicated teachers at Land High. Castillo also discussed the role of the
student in the math achievement process. Castillo appeared genuinely pleased to
report that the students often engaged in academically supportive behaviors. For
example, he appeared pleased to report that students initiated and formed a math club
that meets on Saturdays. He further elaborated by saying that he often observes
students engaged in peer-to-peer tutoring and other supportive behaviors.
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Department Chair Castillo has a 10-year history with Land High and reports
that he has a personal interest in the success of his students and has an “open door
policy.” During the interview, several students entered the classroom and smiled as
they greeted him. He often interrupted the interview to ask students about personal-
and school-related matters.
The Political Frame. Math department chair, Castillo, provided very little
insight into the political elements of change during her interview. He did not
perceive that there were political issues that the math department had to deal with
during the years studied. Principal Grey provided a different perception regarding
political issues. He recalls the math teachers were very resistant to some of the
standards-related initiatives.
As mentioned earlier, Principal Grey joined Land High during the 2003/2004
academic year. Prior to Grey becoming the principal, Mr. Victor Rojas served as the
principal during the 2002/2003 academic year. Mr. Rojas was hired after Mr. Luke
Holtz, retired. Grey reports that Holtz had been the principal at Land High for over
10 years and many of the current teachers had worked with Mr. Holtz. After Holtz
retired, it was reportedly, very difficult for Mr. Rojas to provide leadership and get
“teacher buy-in” for activities related to the California Standards. Grey notes that one
such activity was the standards-test awareness campaign.
According to Grey, in 2002 the standards-test awareness campaign was
initiated at the district level. Grey recalls that the awareness campaign was initiated
around the same time that Mr. Holtz was preparing for retirement and suggests that
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the campaign was not implemented since it was too close to the timeframe for Mr.
Holtz retirement.
Mr. Rojas became the principal at Land High after Mr. Holtz retired. One of
Mr. Rojas’ first projects was to initiate the standards-test awareness campaign in the
math department. His goal was to help students better understand what the
performance measures meant and the benefits of improving their performance. In
addition, Mr. Rojas had successfully conducted this campaign at another school site
and attributed his schools positive outcomes to the awareness campaign. However,
when he tried to introduce it to the math department at Land High, he was met with a
considerable amount of resistance. As a result of the resistance, Principal Grey
reports that Mr. Rojas solicited district support. This resulted in teacher resistance
and Mr. Rojas resigned after several months. Mr. Rojas reportedly resigned to
accept a position at another school within the same District.
In 2003, Principal Grey joined Land High. Principal Grey was aware of the
math teachers’ resistance and reports that he decided to use a different approach.
Prior to meeting with the teachers, Principal Grey contacted the district and asked for
a representative from the District-leadership team to help him present the standards-
test awareness campaign to the math teachers. The representative from the District
complied with Grey’s request. Shortly thereafter, Principal Grey and the District
representative met with the teachers. Principal Grey stated the math teachers “finally
got it” and they “knew that the District was serious.” In addition, Grey hired several
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Assistant Principals who had positive experiences with implementing the awareness
campaign at other schools.
Grey reports that the district leadership support, the Assistant Principal’s real-
world experience, the math teachers’ participation and the student’s increased
motivation and effort have resulted in positive outcomes for standards-based testing
at Land High. During interviews with the Assistant Principals, several of them
reported that they understand the benefits of the awareness campaign and note that
most math teachers are now supportive, despite their initial misgivings.
Another important finding related to the political frame of reference was that
the math teachers at Land High took on the role of teacher leader in their efforts to
improve math achievement. Although the school leaders initiated the standards-test
awareness campaign, the majority of math teacher’s report they have received very
little professional development related to math achievement (Figure 19).
In addition, 89% of math teachers report that student achievement in math
was not a priority of the school in terms of financial allocations. This is evidenced by
the math teachers’ responses to item 20 on the math teacher questionnaire: Student
achievement in math was made a priority as the school allocated its financial
resources. Teachers responded to this item with a mean rating of 1.78.
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Figure 20. Math Teacher Questionnaire - Question 20
The Symbolic Frame. Site Leadership at Land High made little use of
ceremonies and symbolism to support increased student achievement in Math. This
is reportedly due to budget issues. Math Department Chair, Castillo noted that many
teachers used their personal resources and conference time to support and encourage
students. According to Castillo, the math teachers’ personal interest and commitment
to students is evidenced and communicated daily.
Assistant Principal Dim expressed that the school had limited resources for
math teacher professional development and symbolisms. He noted that Land High
schools was not able to qualify for Title 1 status and resources because “many
students are too embarrassed to report that they qualify for free and reduced lunch.”
Disagree Somewhat Disagree Strongly
66.7%
22.2% 11.1%
Neutral
Student achievement in math was made a priority as the school allocated
its financial resources.
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He noted that this is because of a perceived stigma and other students seem to know
who gets free and reduced lunch.
Assistant Principal, Mejia did not use the word “symbolism,” but noted that
the Student Cumulative STAR Performance Report form served as a contract
between the student, the teacher and the parent since the form required both the
student’s and the parent’s signature. In addition, the form contained the student’s
goals for increased math performance. The student was provided a copy and the
math teachers added copies to the student’s classroom files. Mejia reported that the
signed STAR Performance Report form helped enable students to focus on the goal
and to reflect on making efforts to reach their goals.
The symbolism associated with the school’s mascot, the Saxon, appeared
throughout the entire school and schools web site with the caption: “Saxon Pride.”
Observations noted that Saxons were displayed in the school yard, the library, the
student and teacher newsletters and the school’s front office area to gain the attention
of visitors, teachers, students and administrators as they entered the school’s front
office. Observations further noted that the daily audio broadcast from Principal
Grey’s office began with, “Good morning fellow Saxons” and ended with a muted
crescendo “Remember the Saxon Pride.” Principal Grey displayed several images
and illustrations of the Saxon throughout his office. Many students wore T-shirts and
carried bags that were adorned by the red and gold Saxon.
In summary, analysis of the assessment measurement data related to
Research Question 3 reveals that Principal Grey joined Land High shortly after there
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was a considerable amount of change and school initiatives. At the school level,
Principal Grey had a goal to implement the districts practices and to solicit support to
help him initiate district mandates. The mandated standards-based communication
and awareness strategy was critical to the overall school culture. It involved the
teachers, department chair, school leaders and the students. These are all critical
components of a learning community.
Research Question 4: Instructional Leadership. The fourth research question
asked, “How was instructional leadership important in improving a) the math
programs/strategies and b) math achievement among students?” The instructional
leadership framework used to analyze data for this research question is based on five
critical components that are facilitated and supported by instructional leaders: 1)
vision for learning, 2) supervision and monitoring of instruction, 3) community and
political mobilization, 4) culture of teaching and learning, and 5) data-driven
decision-making and analysis. The five critical components that comprise the
instructional leadership construct are based on the work of Johnson (2002) and
Hessel and Holloway (2002) as outline in Chapter 3 in Figure 13.
The findings reveal the principal and teacher-leaders at Land High school
effectively used all five of the constructs from the Instructional Leadership
framework. However, since the math teachers and the math department chair were
actively engaged in many of the math reform process, the findings for three of the
constructs were previously discussed in detail in this chapter when presenting
information about the practices of the math teachers and the math depart chair.
155
For instance, findings related to the data-driven decision-making and analysis
component were discussed with research question 2 (p. 22). Findings related to the
involvement of the parents (community/political component), were discussed with
the findings related to school culture in research question 2 (p. 23). Finally, the
process of monitoring instruction was presented in research question 2 in the
learning activities (p. 31) and classroom practices (p. 33) sections.
To avoid redundancy, the findings presented for research question 5 are
limited to data-driven decision-making and analysis, shared vision for learning and
the culture of teaching and learning components of the instructional leadership
framework. The findings presented here will also include a comparison of data from
math teachers and non-math teachers at Land High School.
Shared Vision for Learning. Reponses from the math teacher questionnaires
indicate that the school leadership at Land High has a shared vision for student
achievement. The Math Teachers were asked to rate the following item: The district
personnel, school leaders, and teachers all have a shared vision for increased math
achievement. Math Teachers responded to this item with a mean rating of 3.22 on
the 5-point Likert scale. Although there wasn’t overwhelming agreement, 44% of the
math teachers expressed agreement and 66% expressed disagreement with this item
(Figure 21).
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Figure 21. Math Teacher Questionnaire - Question 41
Non-math teachers where asked to rate a similar question: There is a shared
vision for increased student achievement at our school. Non-math Teachers
responded to this item with a mean rating of 4.22 on the 5-point Likert scale (Figure
22). A full 70% of non-math teachers agree that Land High has a shared vision for
student achievement.
Although the study investigated earlier academic years the Math Department
Chair, Castillo expressed that she is currently concerned about the “shared vision”
for students who perform at the basic and below basic levels on the CST. She noted
that the master schedule (Figure 23) is designed to especially support struggling
students. The Pre-Algebra, Algebra 1A and Algebra 1B are all courses designed to
Disagree Somewhat Strongly Agree
44%
11%
44.4%
Disagree Somewhat
The district personnel, school leaders, and teachers all have a shared
vision for increased math.
157
Figure 22. Non-Math Teacher Questionnaire - Question 13
Disagree
Somewhat
Disagree
Strongly
5% 18%
43%
Agree
Somewhat
Neutral
7%
Strongly
Agree
27%
Shared vision for increased student achievement at our school.
158
Figure 23. The 2006-07 Land High School Math Department Master
Schedule
Teacher Period 1 Period 2 Period 3 Period 4 Period 5 Period 6
Teacher A Geometry Algebra 1B Geometry Algebra 1B Geometry I
Teacher B Pre-Algebra Algebra 1B Algebra 1B Pre-Algebra Algebra 1B
Teacher C Algebra 1A Geometry Algebra 1A Geometry Algebra 1A
Teacher D Algebra 2 Algebra 2 Geometry Geometry Algebra 2
Teacher E Algebra 2 Math Apps Algebra 2 Algebra 2
Elements of
Geometry
Teacher F Algebra 1 Algebra B Algebra 1 Algebra G Algebra 1
Teacher G Math 1B Geometry Algebra 1A Algebra 1A Geometry
Teacher H
Elements of
Geometry Algebra 1A Pre-Algebra
Elements of
Geometry Algebra 1A
Teacher I See Science Algebra 1B
See
Science Algebra 1B See Science
Teacher J Calc AB AP Algebra A Algebra A
Algebra 2
/Trig
Algebra 2
/Trig
Teacher K Algebra 1A Algebra 1 Algebra 1A Algebra 1 Algebra 1
Teacher L Pre Calc Algebra 1 Algebra 1 Pre Calc Algebra 1
Teacher M Trig/Ana Geo Geometry
Trig/Ana
Geo Pl Sol Geo Pl Sol Geo
help students “catch up” and to help reduce the number of students who score basic
and below basic on the CST.
Castillo believes the “catch up” courses are directly responsible for reducing
the number of students scoring basic and below basic during the timeframe of this
study. She noted that the District has decided to remove these “catch up” courses
from the 2007/2008 High School curriculum. This is where she believes her vision
for learning may vastly differ from the district’s vision.
159
To help support a shared vision of learning during the 2003-05 timeframe,
Principal Grey reported that the school leadership worked with outside sources such
as the district’s math curriculum specialist and instructional specialist from the High
Quality Teaching and Instruction Center. In addition, Assistant Principal Dim is
assigned to work directly with the math department chair to identify professional
development opportunities for the math teachers.
Another important component of the shared vision for teaching and learning
is the Beginning Teacher Support and Assessment (BTSA) program. Principal Grey
notes that this program supports new teacher development and monitors the teacher’s
progress. Consistent with this practice, Math Department Chair, Castillo reports that
she always pairs experienced teachers with new teachers to ensure the coherent
instructional practices.
A Culture of Teaching and Learning. Assistant Principal, Dim reported that
Land High used student achievement from classroom performance, standards tests,
and Data Director, the district database, to help increase math achievement.
However, Assistant Principal, Dim noted that the math teachers were in the process
of being trained to use Data Director.
As mentioned earlier, every year before the students arrived at Land High,
school and district leaders worked to thoroughly assess the incoming students in
order to provide an effective student profile for the teachers. In addition, the
assessment data provided the teachers and school leadership a good baseline measure
of the knowledge level of incoming students.
160
Data-Driven Decision-Making and Analysis. Having a good baseline,
performance measure allowed the teachers to better monitor the process of the
students within the first few weeks of school. In addition, it allowed the teachers to
respond proactively in meeting the needs of the students. If students were struggling,
they were immediately reassigned to a class that was designed to help the student
catch up with his peers. Math Department Chair, Castillo noted that the students
were also assessed on an ongoing basis. They were provided additional resources,
such as double periods of math instruction and given individual support from math
teachers and their peers.
In summary, findings for research question 4 revealed that the math teachers
actively engaged in many of the functions in the instructional leadership framework.
The math teachers and the math department chair actively monitored student learning
and engage in data-driven decision-making to support a culture of teaching and
learning. However, it’s important to note that the findings revealed also that the
principal worked diligently to establish this culture upon arriving at the school and
enlisted the support of the district leadership to help establish a culture of teaching
and learning.
The math teachers (67%) reportedly perceive that the leadership at Land High
does not possess a shared vision for student achievement in math. In contrast, almost
the same percent of non-math teachers perceive that there is a shared vision for
student achievement (70%). Math department chair, Castillo commented that the
elimination of the Algebra A (Pre-Algebra) class from the 2007-2008 academic year
161
will make it difficult to help students who currently score below basic and far below
basic. This is where he reports that his vision differs from the District’s vision for
learning.
Research Question 5: Strategies to Overcome Lack of Subject Matter Expertise
The fifth research question asked, “How did instructional leaders respond in
academic areas in which they were not experts?” Many of the strategies discussed in
this chapter were detailed in earlier findings as they were the practices of the math
teachers and the math department chair. In addition, Principal Grey characterized
the math teacher and math department chair as highly qualified. Nevertheless, there
are strategies identified in the framework for this research question for school leaders
that lack subject matter expertise.
The framework for research question 5 consisted of two distinct components
designed to answer the research question. The first component was a three-step flow
chart used to assess a principal’s knowledge domain in math (see Figure 14 in
Chapter 3). Principal Grey, reportedly had limited experience and training in math
instruction. Therefore his level of expertise in math was identified as “low.”
The second component of the framework for research question 5 is based on
the research related to strategies for school improvement. These include strategies
that the instructional leader employs to achieve improved math achievement. The
strategies (see Figure 15 in Chapter 3) are grounded in the research literature and are
aligned with the findings from research question 5.
162
Delegation Approach. Although the site leaders did not drive the math reform
process, Chapter one indicated that an assumption of this study was that school
leaders must actively work to overcome their own lack of expertise in the math
content area. In this study, the principal delegated leadership (Northhouse, 2001) to
assist the math department chair and math teachers in their math reform efforts.
Principal Grey primarily relied on Assistant Principal Dim to work with Math
Department Chair Castillo. Although the math teachers did not perceive of this as an
“instructionally supportive” gesture, Math Department Chair, Castillo reported that
he worked with AP DIM to make sure the teachers had what they needed to do their
jobs.
Emphasized Raised Expectations. Math Department Chair Castillo, worked
with Assistant Principal Dim to support the communication and awareness strategy
for the standardized testing program in order to actively involve teachers, students,
and parents in the goal-setting process (Marzano, 2003).
Empowered Department Chair. Another important strategy was identified by
Assistant Principal Mehia. She recalled that school leaders worked closely with the
math department to help assess students before the students arrived on campus. Once
the students were attending classes, the math department chair encouraged the math
teachers collaborated with each other to monitor student data in order to help
increase math achievement (Gabriel, 2005). Math teachers used classroom
performance data, periodic assessment data, and standards test data to “informally”
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track student achievement and to engage in data-driven decision-making as it relates
to instructional practices
Emphasized Inquiry and Problem-Solving. Another strategy identified in the
framework is that math teachers engaged in practices of inquiry and problem-solving
(Stringer, 1999) by consistently reviewing student achievement data. Examples of
these practices have been previously discussed and reportedly have contributed to the
improved math achievement at Land High School. The following characterized the
math teachers’ inquiry and problem solving practices:
1. Engaged in teacher collaboration as a process for reviewing student
achievement data.
2. Analyzed classroom performance data and teacher input to adjust
students’ course of instruction and time on task.
3. Worked with school leaders and students to help students set
standards-based achievement goals and objectives.
In addition, many of theses strategies were identified in the interviews,
questionnaires, and follow up discussions with the school leadership and math
teachers.
Finally, according to Math Department Chair, Castillo, the revised
instructional scope and sequence is was a key strategy that improved student
achievement in math (Marzano, 2003). Castillo believes “remedial” classes such as
Pre-Algebra, Algebra 1A and 1B, all attributed to decreasing the number of students
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scoring basic, below basic and far below basic. Castillo believes these classes were
critical to helping students “catch up” and transition to the Algebra 2 class.
In summary, there were several strategies employed by the instructional
leader and math teacher/leaders to improve math achievement. The strategies
included the principal delegating school leaders with greater expertise to assist the
math department chair and math teachers. Principal Grey also empowered the math
department chair and math teachers to engage in inquiry and problem-solving by
encouraging teachers to collaborate with other math teachers and engage in data
review and analysis improve instructional practices and support student learning.
The active review of student performance and assessment data enabled the
leaders and math teachers to help students set achievement goals and allowed math
teachers to modify the scope and sequence of instruction. All the strategies used in
research question 5 were grounded in effective research-based practices.
Analysis and Discussion
The findings in this study were analyzed and presented in the context of the
conceptual frameworks for each research question. This section reflects on the
findings of the study and discusses what the findings mean. In general, the findings
of the study offered more evidence to support the importance of helping students to
establish achievable goals, empowering others with greater expertise, engaging in
strategic leadership practices and focusing on student-centered learning.
Achievable Goals and Motivation. The pattern of achievement detailed
earlier in this chapter included an analysis of the CST scores for both school and
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statewide sub-group populations. In general, the data revealed CST scores for Land
High sub-group populations grew much more than their peers statewide. Motivation
research and the findings suggest that increased student achievement may be
attributable to teachers’ and the student’s receiving a clear understanding of the goals
and how they would be supported in working to achieve the goals.
Assistant Principal Mejia stated that she specifically told the students that
their improved performance on standards-based test results in better performance on
the CAHSEE. The standards communication and awareness strategy and Assistant
Principal Mejia’s comment might have resulted in increasing student motivation.
For example, the expectancy-value theory of motivation posits that the
amount of effort that a student expends to complete a task is positively related to the
value that the student places on the task (passing the CAHSEE), outcome
expectations, and the individual’s perceived probability for success (Wigfield &
Eccles, 2000). “When students value a task, they will be more likely to engage in it,
expend more effort on it, and do better on it” (Wigfield, 1994, p. 102).
According to Principal Grey, the students were surprised to learn that making
an effort to just answer two additional questions correctly could result in increased
student achievement on standardized tests. Principal Grey stated that the students
indicated that they would have focused (focused effort) more had they known this.
The standards communication strategy that Land High implemented was
pivotal to communicating and setting expectations for students and teachers and
allowed students and teachers to partner in the process of improving student
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achievement. In addition, the school leadership made the standards communication
campaign a school-wide event and set aside time to meet with students and teachers
to discuss the importance of focused-effort during the test taking process
Standards and Accountability. Establishing an environment of increased
expectations and accountability appeared to be a key factor in the school’s success.
Almost all teachers and school leaders agreed that standards and accountability
policies have contributed to efforts to improve instruction. In this era of high stakes
testing, the site leaders at Land High adhered to standards-based instructional
practices and benchmark assessments and made a considerable effort to address the
teaching and learning needs of all students.
Almost all the administrators and teachers reported that policies such as
NCLB and CAHSEE have contributed to increased student achievement and have
helped to shape their instructional and testing practices. As noted earlier in this
chapter, the site leaders and teachers at Land High adhered to standards-based
instructional practices, established benchmark assessments and adopted strategies to
support underperforming students. According to Elmore (2001), making changes
that result in instructional improvement has to be the main goal of the educational
leader (Elmore, 2001).
As detailed in Chapter 2, there is a widely held belief among educational
leaders that when students are expected to achieve their performance increases
(Marsh & Codding, 1999; Fisher, Tietelbaum, & Emanuel, 1999).
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Instructional Practices. The math teachers at Land High worked closely
together to ensure the math instruction was aligned with benchmark assessments and
instructional practices. The math teachers also showed personal interest in helping
students succeed. This resulted in increased student motivation as it possibly
modified the student’s sense of self-efficacy. Providing instructional support is an
important element of high school reform EdTrust West (2004)
With Principal Grey’s delegation, the math teachers and math department
chair engaged in regular assessments and data analysis. Furthermore, they and used
the information to make instructional adjustments to support student learning.
The current research indicates the principal’s primary role is to support
teacher learning and increase retention (Blasé & Blasé, 2000) and consistently focus
on the teaching and learning process (Darling-Hammond, 2003; Elmore, 2002;
Fullan, 2004).
Delegate Leadership. Math Department Chair, Castillo, viewed the support
from a member of the administrative team as crucial to the teachers feeling supported
in their efforts to improve math instruction. According to Castillo, this alignment
allowed the school’s leadership to efficiently meet the needs of the math department.
This was only accomplished using strategies that include collaboration, shared
leadership, and reorganization of traditional educational structures (Elmore, 2003).
Assistant Principal Dim’s alignment with the math department was a key and
strategic factor.
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As noted in Chapter 2, According to Marzano, Waters, and McNulty (2003)
effective leaders use immediate or situational awareness as a means to remain aware
of the political climate of the school at all times. The effective instructional leader
uses the information to address issues and to work through upcoming barriers.
Barriers and enablers are part of the change process and educational leaders must be
aware of both and take the time to reflect on how to navigate through or around
barriers. Marzano (2003) has pointed out that leaders are key to effective school
reform and specific strategies.
Effective leadership was also evident in the way Principal Grey managed the
standards-based communication and awareness strategy. For principals, the current
standards-based accountability climate is inherent with pressures to consistently
monitor and measure performance outcomes, influence and motivate school
improvements, support and monitor teachers and collect and analyze performance
data in order to make adjustments related to teaching and learning (Supovitz &
Poglinco, 2001). Principal Grey worked to create a shared vision for learning and to
get buy-in from teachers, students and other site leaders for standards testing and
goal setting.
Summary
This chapter reviewed the findings using the data collected for this study. The
review of the findings follows the analysis of the five research questions. The
discussion includes a discussion related to role of student motivation and goal
setting. In addition, the importance of standards-based practices, are discussed and
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linked to increased student performance. Finally, the discussion examined the role of
the math teachers in supporting increased student achievement. The findings
presented in this study were based on the triangulation of data from multiple sources.
This strengthens the overall validity of the findings. The next chapter contains the
summary, conclusions, and implications of this study.
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CHAPTER FIVE
SUMMARY, CONCLUSIONS AND IMPLICATIONS
Background of the Study
The academic performance of American high school students remains low
when viewed by national objective standards and by international comparative
studies. The decline in the academic performance of American high school students
is making secondary education reform a national challenge that has global
implications.
When high school math performance declines, college graduation rates also
decrease. For urban high school students, successful academic outcomes in math
result in increased college attendance and improved college graduation rates. In
general, math achievement prepares urban youth for both the workforce and higher
education.
In the 21
st
century, mathematics education remains a critical component of
schooling and is the key to advancing individual, academic opportunities and
supporting the national economy. Furthermore, performance in high school
mathematics is directly related to access to competitive colleges and increased
earning potential.
The earlier students learn higher order mathematical skills, the stronger the
likelihood for college attendance and graduation (NCES, 2001). Early exposure to
mathematical thinking is also related to the type of college the student selects, and
what degree the student will earn. Early math achievement in Algebra is critical to
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students selecting and successfully completing higher-level math courses and
attending competitive institutions of higher learning; algebra is considered a
“gatekeeper” course for college admissions, which has considerable economic
implications.
Currently, reforms in mathematics instruction are a top priority for many
states, educators, business leaders, military personnel, policymakers, universities and
the federal government. The effort to enact reforms has resulted in various changes
to secondary education including math instruction and a movement toward curricular
alignment with postsecondary institutions.
Now more than ever before are new curricular content reforms and policies
needed to give all learners, especially urban youth, an opportunity for access to
higher education and to close the achievement gap.
Purpose of the Study
The purpose of this study is to identify how high school leaders in urban
schools successfully integrate policy initiatives and best practices to improve math
performance in their schools. The study examined factors that positively influence
the math performance of secondary students as a result of policy initiatives in
standards-based curriculum and instruction. Moreover, the study investigated the
high school’s math program design; the leadership factors that shaped the design for
mathematics reform; the leadership strategies used to drive the instructional reform;
and the instructional and leadership barriers that had to be addressed during the
reform process. The five research questions identified by the cohort defined the areas
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being studied and helped guide the research at the sites studied. The five research
questions were:
6. What was the pattern of math achievement for various students at the
school?
7. What policy initiatives as well as curriculum, instruction and related
conditions seem to be related to improved math achievement at the
school?
8. What change process did the school use to enhance the math program and
strategies to assist students in math?
9. To what extent was strong instructional leadership important in
improving: A) the math programs/strategies and B) math achievement
among students?
10. How did leaders in the school resolve the dilemmas about instructional
leadership?
1. How did instructional leaders respond in academic areas in which
they were not experts?
Summary of Methods
This study employed a case study approach and largely qualitative methods
to investigate a single school’s efforts to increase student achievement in math. The
research data was collected using data collection instruments that included site-
leader interviews, non-math and math-teacher questionnaires, site source documents,
direct observations, and quantitative data from the California Department of
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Education’s web site. Using multiple data sources supports triangulation of data
which increased the validity of the findings of the study.
Frameworks
Conceptual frameworks were designed to support each of the five research
questions. Each conceptual framework was grounded in research that presented the
best practices and models related to improving student achievement at the secondary
level. Moreover, the data collection questionnaires and interview instruments used in
the study contained design elements that were with the study’s conceptual
frameworks. The questionnaires and interview instruments were developed by eleven
doctoral students attending the University of Southern California.
Sampling
A purposeful sampling process was used in order to provide an opportunity to
conduct a thorough investigation and to explore more deeply the processes related to
the research questions of this study. The school selected for this study was
purposively selected based on its enrollment of more than 1200 students, its diverse
population and its improvement in Algebra I CST scores between the years of 2003
and 2005. This type of sampling allowed the researcher to develop an in depth
inquiry and respond to emergent themes of inquiry. These factors also helped the
researcher develop a rich description of the specific efforts made by the site to
improve student achievement in math.
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Data Collection and Analysis
Data for the study were collected in October through March of 2006. The
conceptual frameworks were deployed as the basis for the data collection
instrumentation. Research Question One asked about the pattern of mathematic
achievement for various students at the school.
The aforementioned school profile information served as the framework for
research question one in that it provided a template for identifying areas of student
achievement in math where quantifiable data was available for analysis. Appendix E
includes the achievement used to identify the pattern of student achievement in math
at the site.
The conceptual framework for RQ 2 (Appendix D) consisted of elements
related to effective school design and effective math program design. The effective
school design model was based on the work of Marsh and Codding (1999) and was
comprised of the following components: (a) curriculum incentives, (b) school
culture, (C) learning activities and (d) student performance assessments. The model
fore effective math program design consisted of those that evidenced strong
standards based curriculum and assessments, “catch up strategies” and effective
classroom and instructional practices. Bolman and Deal’s leadership model provided
the framework for RQ3. The four frames of model provided the bases from which to
view and effectively handle the school’s change process in improved student
achievement. The four frames focused on efforts that related to the structure, politics,
human resources, and symbolism of the organization.
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The framework developed for RQ 4 focused the key components of effective
instructional leadership and included (a) vision for learning, (b) supervision and
monitoring instruction, (c) community and political, (d) culture of teaching and
learning and (e) data-driven decision making. The framework for RQ 5 identified
twelve strategies that a leader might use to overcome a lack of expertise in math.
These frameworks served as the basis for the development of four data
collection instruments used in the collection and analysis of data.
1. The School Profile (Appendix E) provided a reference point from
which to examine the school’s pattern of math achievement. This
included the examination data related to CAHSEE passing rates, AP
enrollment/pass rates and CST data.
2. The Key Leader Interview Guide (Appendix C) was used as the
interview protocol for the six key administrative and math leaders.
These six leaders included (a) the principal, (b) three Assistant
Principals (c) the Curriculum and Instruction Specialist, and (d) the
Math Department Chair.
3. The Teacher Interview Guide (Appendix D) was used as the interview
protocol for math teachers at the school site and was designed as an
open-ended instrument to allow teachers to reveal their perceptions
related to increased math achievement.
4. The Questionnaires consisted of two versions: one for math teachers
(Appendix F) and one for all other teachers (Appendix G). Both
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versions of the questionnaire clearly aligned with the research
questions to support data collection and analysis.
In addition to the data collection instruments other sources of data were
examined to further validate the data collected from the aforementioned instruments.
The additional sources were provided by source documents from the research site.
For example, the master schedule confirmed student enrollment patterns of and
teaching assignments. Other key source documents included the teacher’s
standardized test script and the student’s standardized test performance and goal
setting guide.
Summary of the Findings
The data collection and analysis process used in this study led to key findings
related to each of the five research questions. This section will summarize key
findings related to each research question and note the primary data sources analyzed
that led to each of the findings.
Research Question 1: Pattern of Achievement in Math
The first research question asked, “What was the pattern of Math
achievement for various students at the school?” The pattern of math achievement
was evidenced in the review of assessment measurement data from the California
Department of Education (CDE). There were three types of assessment
measurement data used to examine the pattern of math achievement at Land High: 1)
Algebra I CST results, 2) CAHSEE passing rates, and 3) Advance Placement (AP)
taking/passing rates for the 2003 through 2005 timeframe.
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An analysis of the data using the three aforementioned assessment measures
revealed the following general findings for Land High School:
7. Almost 50% of the students performed at a scale score at or above
proficient on the Algebra I section of the CST in 2005.
8. Hispanic students out gained their peers statewide by a wide margin
during the time period examined.
9. Economically disadvantaged student significantly out gained their
peers statewide during the time period examined.
10. ELL students at Land High achieving proficient and above grew from
22% in the baseline year to 38% in 2005.
11. The number of students enrolled in Advanced Placement mathematics
courses increased 33% from the 2002 through 2005 time period.
12. Over 60% of economically disadvantaged students consistently
passed the CAHSEE during the time period examined.
When using CST Algebra 1 data as an assessment measurement, the data
revealed that Hispanic and economically disadvantaged students at Land High,
demonstrated the strongest gains in the number of students scoring proficient and
above. For example, in 2002-03, only 15 % of Hispanic students scored proficient
and above; where as in 2004-05, almost half the Hispanic student population (48%)
scored proficient and above. During this same time period, statewide assessment
measures were considerably lower and slightly declined for the Hispanic population.
In 2002-03, statewide data revealed that 17% of Hispanic students scored proficient
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and above. This same statewide measurement number dropped to 16% during the
2004-05 assessment period.
Research Question 2: Policy and Practice
The second research question asked, “What policy initiatives as well as
curriculum, instruction, and related conditions seem to be related to improved math
achievement in the school?” The findings are discussed in the context of the
framework for research question 2: school design and math program design.
Land High School demonstrated effective and unique practice in this area as
demonstrated by the following findings:
1. Land High Principal Grey and almost all Assistant Principals at Land
High School agree that accountability measures and policies such as
NCLB, AYP, API, CAHSEE and HQT have greatly influenced their
focus on increased student achievement. In addition 89% of math
teachers report that the CAHSEE, in particular, has contributed to the
school’s efforts to improve math achievement.
Math teachers at Land High worked diligently to promote a positive school
culture that emphasized and supported student achievement in math. Math teachers
devoted a considerable amount of attention to student assessments and leveraged this
to change the school culture as it relates to standardized testing. Land High
implemented a teacher and student motivation strategy by engaging students in goal
setting and by giving the students a sense of control over their achievement
outcomes.
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Land High leaders also held teachers accountable for helping students
achieve. For example, Land High implemented standards-based instructional
practices and assessments and the teachers provided additional support to struggling
students by changing basic math classes to two-hour class blocks to help students
catch up.
Math Department Chair, Castillo, reported that data-driven decision making
that includes the use of grades from classroom instruction in addition to outcomes
form standards-based tests, were critical to improved math performance. Department
Chair, Castillo noted that the math teachers routinely examined student grades using
the, in-class performance and math test data to determine how best to support
students who were underperforming. Castillo notes the data-driven decision making
process was effective because the math teachers have the most instructional time
with the students and are keenly aware of the students’ instructional needs.
In terms of curriculum and instruction, no other factor was more important to
the school’s success than the implementation of a communication and motivation
strategy involving standards-based testing. Assistant Principal, Mehia emphasized
that school administrators and math teachers adopted a testing
awareness/communication strategy that had been successfully used by another school
in the Orange District.
Principal Grey, Math Department Chair, Castillo and the other Assistant
Principals, made concerted effort to create a STAR-program communication strategy
that resulted in increased student awareness and motivation. First, they developed a
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script to support the strategy. The script consisted of three key elements: (1) general
steps, (2) class presentation/talking points, and (3) individual [student/teacher]
meetings). The SCRIPT outlined the process for how best to increase student
awareness, motivation, and accountability when presenting the STAR program
information. Involving the students and the parents in the accountability process was
one of the main reasons given for increased student achievement.
There were two important classroom practices that Math Department Chair
Castillo, believes contributed to increased student achievement. The two important
classroom practices were: teacher collaboration/mentoring and prescriptive learning.
In addition, “The math teachers closely collaborated to make sure they used similar
instructional practices.” Math Department Chair, Castillo, noted that the teachers
were in favor of this level of accountability because it ensured continuity of
instructional content and instructional methods.
Among the most critical findings in this case study are the teacher
perceptions regarding standards-based instruction. This perception is evidenced from
math-teacher questionnaire responses. First, all math teachers agree that they teach
standards-based lessons. Second, a full 78% agree that assessments were linked to
standards. Finally, 88% agree that student achievement data was used to drive
instruction.
Research Question 3: 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 findings for this research question are discussed
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from the framework of Bolman and Deal’s Four Frames of Leadership. The Four
Frames of Leadership provide “lenses” from which to view the organization in the
context of the change process. Therefore, the findings for research question 3 are
presented according to the four frames.
Research question 3 asked, “What change process did the school use to
enhance its math program and strategies to assist students in math?” The study used
Bolman and Deal’s four frames to analyze the data collected and make sense of the
change process.
The Human Resources Frame. One of the key findings in this study was that
the human resources frame was connected to a supportive teacher environment that
called for increased levels of student achievement. An important finding in this
study was the role that the math teachers played in promoting improved student
achievement in math. The principal and Math Department Chair both agree that
dedicated math teachers were crucial elements for increased student achievement.
The Structural Frame. The structural design of the site administrative team
supported improved student achievement in several ways:
1. Assistant Principal Nara Dim was the administrative team member
assigned to the math department. His role was to work with the Math
Department Chair to ensure that “teachers have what they need” and
to support teachers with the math achievement process.
2. The math program was structured to allow the ongoing assessment of
students to enable teachers to make data-driven decisions. The
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teachers used information from classroom performance and math tests
to determine if students needed additional instructional support. If a
need was identified, the student’s class schedule was adjusted to
accommodate a two-period math class.
3. The math department was structured to offer intervention math
courses, such as Math Studies and Pre-Algebra, for students who
entered ninth grade lacking basic math skills. In addition, the Algebra
1 course was divided into Algebra 1A and Algebra 1B for students
whose pre-enrollment assessment data indicated a need for additional
math support before enrolling in Algebra 2.
The Political Frame. The political frame of the site was used to identify the
practices that lead to increased student achievement in math. A key finding was that
the math teachers at Land High took on the role of teacher leader in their efforts to
improve math achievement. Although the school leaders initiated the standards-test
awareness campaign, the math teachers were the primary drivers of standards-based
instruction, assessment and reform.
The Symbolic Frame. Site Leadership at Land High made little use of
ceremonies and symbolism to support increased student achievement in Math. This
is reportedly due to budget issues. Math Department Chair, Castillo noted that many
teachers used their personal resources and conference time to support and encourage
students.
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The symbolism associated with the school’s mascot, is very important to the
students and faculty. The Saxon, appeared throughout the entire school and the
schools web site with the caption: “Saxon Pride.” Observations noted that Saxons
were displayed in the school yard, the library, the student and teacher newsletters and
the school’s front office area to gain the attention of visitors, teachers, students and
administrators as they entered the school’s front office
Research Question 4: Instructional Leadership
The fourth research question asked, “How was instructional leadership important in
improving a) the math programs/strategies and b) math achievement among
students?” The framework used to analyze data for this research question
emphasized six discreet areas and the findings presented have been aligned to those
areas. Land High teachers and leaders were effective in these areas as evidenced by:
1. More than 50% of the math teachers expressed a shared vision for
learning.
2. The “catch up” courses are directly responsible for reducing the number
of students scoring basic and below basic during the timeframe of this
study.
3. Principal Grey uses the Beginning Teacher Support and Assessment
(BTSA) program to support and develop new teachers and to monitor the
teacher’s progress.
4. Struggling students were immediately reassigned to a class that was
designed to help the student catch up with his peers. These same students
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were also assessed on an ongoing basis and provided additional resources,
such as classes that extended over a two-hour block of time.
Research Question 5: Strategies to Overcome Lack of Subject Matter Expertise
The fifth research question asked, “How did instructional leaders respond in
academic areas in which they were not experts?” The framework for this research
question consisted of two distinct components. The first component was a three-step
flow chart used to assess a principal’s knowledge domain in math. Principal Grey
reportedly had limited experience and training in math instruction. Therefore his
level of expertise in math was identified as “low.”
The second component of the framework for research question 5 is based on
the research related to strategies for school improvement. These include strategies
that the instructional leader employs to achieve improved math. These include the:
1. Delegation Approach. Principal Grey delegated leadership to assist the
math department chair and math teachers in their efforts to increase
student achievement. Principal Grey primarily relied on Assistant
Principal Dim to work with the Math Department Chair to make sure the
teachers had what they needed to do their jobs.
2. Emphasized Raised Expectations. Math Department Chair Castillo,
worked with Assistant Principal Dim to support the communication and
awareness strategy for the standardized testing program in order to
actively involve teachers, students, and parents in the goal-setting process
for increased achievement.
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3. Empowered Department Chair. The math department chair worked
closely with teachers and school leaders to support the ongoing student
assessment process. The math department chair encouraged the math
teachers to actively monitor student data in order to help increase math
achievement. The Math teachers used classroom performance data,
periodic assessment data, and standards test data to “informally” track
student achievement and to engage in data-driven decision making for
instructional practices
4. Emphasized Inquiry and Problem Solving. Math teachers engaged in
practices of inquiry and problem solving by consistently reviewing
student achievement data. This included consistent teacher collaboration
for data analysis, goal setting, and adjustment of instructional practices.
5. Revised Instructional scope and sequence. Classes such as Pre-Algebra,
Algebra 1A and 1B, all attributed to decreasing the number of students
scoring basic, below basic and far below basic. Math Department Chair,
Castillo believes these classes were critical to helping students “catch up”
and transition to the Algebra 2 class. With careful monitoring, students
were moved to the appropriate classes
Implications for Practice
The findings and conclusions of this study have led to the following
implications for those implementing instructional reform:
As data was collected and analyzed, further research was indicated in several areas:
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1. This study focused on identifying policies and practices related to increased
student achievement in math. The study was limited to the content area of
math. Additional studies are needed to examine effective practices for
increasing student achievement in English/Language Arts and Science.
2. The site selected for this study was chosen using a purposeful sample based
on overall gains made on Algebra I CST scores. The role of student
motivation and feedback was not examined in the study. It may be beneficial
to obtain the perceptions of students related to improved math performance.
While the current methodology fully supported this study well, it is probable
that additional insight can be gained from the students. Therefore, further
research is needed to fully identify the various perceptions related to student
gains.
3. A key finding in this study revealed a strategy involving organizational
communication and goal setting to support student motivation and
achievement for standards-based practices. However, many students often
lack the ability to self-regulate learning and make adjustments based on
classroom assessments and achievement outcomes. Of interest would be
presenting strategies to students to help them learn to fully engage in learning
and self-regulation of learning. Presenting students with these strategies may
provide additional insight into the role of student motivation and increased
student achievement in other content areas and in the context of high school
reform.
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4. The study examined the change process the school used to enhance its math
program and the strategies used to assist students in math. Overall, the
findings revealed that the change process included modification of the
structure of the math courses, but very little was revealed about the change in
instructional practices and student learning. With the “catch up” courses
being removed from the 2007/2008 academic program, further research is
needed to identify best practices related to math instruction and the effective
diagnosis and assessment of math learning that yields increased conceptual
understanding of math operations. This includes examination of the role of
math coaches, professional communities of learning for math teachers, and
student-centered math curriculum reform
This study has also yielded findings and conclusions that may serve to
provide important insights to those educators charged with the responsibility of
improving the achievement of their students. The implications listed below are
presented by general areas of responsibility, and include implications for school
boards and key district leaders, site administrators and teacher leaders as well.
District Boards and Key District Leaders
1. The ongoing implementation of Standards-Based Instruction and
Assessments linked with classroom instructional and assessment practices
was a key finding in this study and as such, School Boards and key district
leaders need to promote and support standards-based instructional and
assessment practices at the site.
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2. One of the key findings in this study was the importance of taking the time to
effectively communicate the importance of doing well on standardized tests
and linking the outcome to preparation for the CAHSEE. This provides the
students with a means to gather knowledge, set a goal, and make an effort to
reach the goal. This also provides a student with a sense of control over what
he has to do to achieve a better result. Thus, in order to help students sustain
their motivation and to share accountability for learning freely in this regard,
School Boards and key district leaders need to train instructional leaders in
student goal setting and motivation and provide this training in the context of
standards-based assessments.
Site Administrators
1. In the context of school reform, the instructional leader’s support of teachers
must be explicit. And if another member of the leadership team is aligned
with a specific department to support school reform, ensure the teachers,
department chair, and other administrators are fully aware that the directive
for this alignment is from the principal. At Land High, it appeared that the
teachers were not fully aware that Principal Grey was providing instructional
support to them through “delegation.”
2. If students are assigned to a two-block class period. Base the class
assignment and instructional practices on assessment and performance data as
well as student observations. The math teachers at Land High teamed with
one another to teach classes in order to identify the instructional needs of
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students and to provide the instructional support and classes that were needed
to help students close learning gaps.
3. Using a data-driven approach helps teachers provide a more prescriptive
instructional support to struggling students. In addition, the use of
performance data allows teachers to target the instruction to the needs of the
student. The math teachers and math department chair at Land High were
very deliberate in their efforts to provide instructional support to student and
designated classes and revised the instructional scope based on assessment
data and other student performance data.
4. Make a culture of teaching and learning the priority of the school and build a
consistent and clear communication strategy to support it. In addition link all
student learning initiatives to standards and policies that have relevance and
utility value for the students. In other words, help teachers and students
develop learning and performance goals that are aligned with outcomes that
are significant to the student. These outcomes include passing the CAHSEE,
preparation for college entrance exams, or workplace readiness. Land High
effectively communicated to students the critical link between the student’s
classroom performance, performance on standardized tests, and performance
outcomes on the CAHSEE and college entrance exams.
Teachers
1. One of the key finding in this study is the importance of teachers and
administrators helping students understand the importance of focused effort
190
in the context of a supportive learning environment. The leadership at Land
High was very skillful in helping teachers work with students to establish
learning and performance goals that were student-centered.
2. A key finding in the study is the importance of linking performance
assessments to standards-based instruction. The math teachers at Land High
engaged in consistent teacher collaboration and team teaching to support
student achievement. More importantly, the teachers at Land High effectively
used student achievement and assessment data to drive instruction.
Recommended Future Research
Based on the findings of this study, the following recommendations are made
regarding future research in this area:
1. One of the findings from the study revealed that students were not aware
of how standardized test were scored and indicated they would have
exerted more effort had they known the importance of just one additional
correct answer. Although mastery learning is the goal of instruction,
student performance outcomes are also important. Especially, in the
context of standards-based testing and school reform. Given the
importance of assessment outcomes, more research is needed to examine
if secondary students fully understand how standardized test are scored
and aggregated, and to determine if more understanding leads to
increased student effort and achievement.
191
2. Although the instructional leaders implemented the STAR
communication strategy, the math teachers played a central role in
participating in goal setting sessions with students and in making efforts
to increase student awareness and motivation for standards-based tests.
More research is needed to fully identify the impact of the
communication strategy and the perceptions of the leaders, teachers and
students about the efficacy of the strategy. It is unclear if the
communication strategy was effective because of the goal setting process
or because of the alignment of the school leaders, teachers and students
on a single performance outcome.
3. The math department chair credit the “catch up” courses with reducing
the number of students scoring below basic and far below basic during
the timeframe of this study. She noted that the District has decided to
remove these “catch up” courses from the 2007/2008 High School
curriculum. More research is need to 1) fully identify the best
instructional design for “catch up” and the most cost effective way to
structure the courses with the teacher and student schedules. In addition,
the study did not fully examine the instructional practices that comprised
the two-hour block of time for some of the “catch up” courses. More
research is needed to determine if longer class time is the most effective
strategy to use to support student learning.
192
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APPENDICES
202
Appendix A
School Profile Data: Sampling Criteria (Land High)
Criteria Case Study: School Profile Data
Algebra 1 Advanced Proficient Basic
Below
Basic
Far
Below
Basic
2005 1% 25% 46% 23% 4%
2004 1% 15% 41% 38% 5%
1. Improvement in
math achievement as
evidenced by results
on the California
Standards Test
(CST) in Algebra I.
2003 0% 15% 44% 32% 8%
Ethnicity School Studied State Average
Hispanic or Latino 61% 48%
White, not Hispanic 22% 30%
Asian 9% 8%
Filipino 3% 3%
African American, not
Hispanic
2% 8%
Pacific Islander 2% <1%
2. Student diversity as
defined by a student
population of at least
50% from
traditionally ethnic
minority groups.
American Indian or
Alaska Native
<1% <1%
3. Public high school
in the Southern
California region of
at least 1200
students.
Student Population - 2,577
4. An Academic
Performance Index
Score of at Least
600
Academic Performance Index - 680
5. A State Wide Rank
of 5 or higher.
Statewide rank - 7
6. Leadership stability
as defined by a
Principal being at
the school for at
least two years
The Principle has been at the school for 2 years.
Teachers This School State Average
Full credential 94% 94%
7. Teacher Credentials
(not a criteria)
Emergency credential 1% 3%
203
Appendix B
School Selection Criteria: California Department of Education:
California Standards Test Data
*Selected
for Case
Study Algebra 1 Advanced Proficient Basic
Below
Basic
Far
Below
Basic
*School
#1 2005 1% 25% 46% 23% 4%
2004 1% 15% 41% 38% 5%
2003 0% 15% 44% 32% 8%
Algebra 2 Advanced Proficient Basic
Below
Basic
Far
Below
Basic
2005 5% 22% 30% 30% 13%
2004 6% 17% 33% 34% 9%
2003 4% 22% 32% 36% 7%
Algebra 1 Advanced Proficient Basic
Below
Basic
Far
Below
Basic
School #2 2005 2% 34% 43% 18% 4%
2004 2% 14% 43% 38% 3%
2003 2% 13% 37% 37% 11%
Algebra 2 Advanced Proficient Basic
Below
Basic
Far
Below
Basic
2005 5% 31% 37% 25% 2%
2004 4% 27% 47% 20% 3%
2003 2% 27% 38% 27% 6%
Algebra 1 Advanced Proficient Basic
Below
Basic
Far
Below
Basic
School #3 2005 0% 3% 25% 52% 20%
2004 0% 8% 24% 53% 16%
2003 0% 13% 43% 33% 11%
Algebra 2 Advanced Proficient Basic
Below
Basic
Far
Below
Basic
2005 3% 22% 32% 32% 12%
2004 0% 0% 0% 0% 0%
2003 2% 15% 38% 38% 7%
204
Appendix B (continued)
School Selection Criteria: California Department of Education:
California Standards Test Data
Algebra 1 Advanced Proficient Basic
Below
Basic
Far
Below
Basic
School #4 2005 0% 7% 34% 43% 16%
2004 1% 9% 22% 49% 19%
2003 1% 18% 31% 35% 15%
Algebra 2 Advanced Proficient Basic
Below
Basic
Far
Below
Basic
2005 11% 34% 32% 18% 5%
2004 6% 25% 35% 25% 9%
2003 25% 30% 28% 14% 3%
Algebra 1 Advanced Proficient Basic
Below
Basic
Far
Below
Basic
School #5 2005 0% 8% 32% 45% 16%
2004 0% 11% 28% 47% 14%
2003 0% 18% 38% 34% 9%
Algebra 2 Advanced Proficient Basic
Below
Basic
Far
Below
Basic
2005 3% 20% 36% 31% 10%
2004 4% 18% 38% 34% 7%
2003 0% 0% 0% 0% 0%
Algebra 1 Advanced Proficient Basic
Below
Basic
Far
Below
Basic
School #6 2005 2% 13% 37% 37% 11%
2004 3% 16% 32% 41% 8%
2003 1% 19% 37% 32% 11%
Algebra 2 Advanced Proficient Basic
Below
Basic
Far
Below
Basic
2005 10% 28% 33% 20% 9%
2004 6% 26% 37% 21% 8%
2003 21% 32% 23% 19% 5%
205
Appendix B (continued)
School Selection Criteria: California Department of Education:
California Standards Test Data
Algebra 1 Advanced Proficient Basic
Below
Basic
Far
Below
Basic
School #7 2005 2% 18% 26% 37% 17%
2004 3% 19% 38% 31% 9%
2003 4% 33% 38% 20% 4%
Algebra 2 Advanced Proficient Basic
Below
Basic
Far
Below
Basic
2005 41% 34% 17% 6% 2%
2004 42% 34% 18% 5% 1%
2003 75% 23% 1% 0% 0%
Algebra 1 Advanced Proficient Basic
Below
Basic
Far
Below
Basic
School #8 2005 1% 13% 51% 32% 3%
2004 2% 24% 42% 27% 6%
2003 6% 38% 33% 18% 5%
Algebra 2 Advanced Proficient Basic
Below
Basic
Far
Below
Basic
2005 7% 30% 36% 21% 7%
2004 7% 29% 36% 24% 4%
2003 13% 28% 35% 17% 7%
Algebra 1 Advanced Proficient Basic
Below
Basic
Far
Below
Basic
School #9 2005 9% 26% 38% 21% 6%
2004 5% 34% 37% 20% 5%
2003 13% 42% 33% 10% 1%
Algebra 2 Advanced Proficient Basic
Below
Basic
Far
Below
Basic
2005 10% 36% 34% 17% 3%
2004 7% 40% 36% 17% 1%
2003 17% 33% 31% 15% 4%
206
Appendix B (continued)
School Selection Criteria: California Department of Education:
California Standards Test Data
Algebra 1 Advanced Proficient Basic
Below
Basic
Far Below
Basic
School
#10 2005 9% 26% 38% 21% 6%
2004 5% 34% 37% 20% 5%
2003 13% 42% 33% 10% 1%
Algebra 2 Advanced Proficient Basic
Below
Basic
Far Below
Basic
2005 10% 36% 34% 17% 3%
2004 7% 40% 36% 17% 1%
2003 17% 33% 31% 15% 4%
207
Appendix C - 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?
208
Appendix C - Key Leader Interview Guide (Continued)
CHANGE PROCESS
Research Question 3: What change process did the school use to enhance its math
program and strategies to assist students in math?
“Let’s turn our attention to how you handled the change process related to your
efforts to improve student achievement in math. Specifically, I will be asking you
about different aspects of the change process as described in Bolman and Deal’s
Four frames, as well as the Concerns Based Adoption Model (CBAM). In case you
are not familiar with either of these models, Here is a copy of the frameworks for
your reference and clarification. (give the frameworks to the interviewee). OK, so I
will be asking you about”:
Structural changes (school design, leadership, use of facilities, etc. )
HR – Key Personal Changes
o Teacher assignments and master schedule
Political issues related to the changes made at your schools
o How did you negotiate the political aspects associated with you
change process
Symbolic Methods used to add meaning and importance to your initiatives
such as:
o Vision/mission
o Culture/climate
o Ceremonies/ awards/recognition
CBAM
o Ask to describe where their staff is and how they got there
1. What structural changes have you made that you feel have contributed to
improved math achievement?
o School design
o Leadership
o Facilities
o CSR
2. What personnel changes have been implemented that has positively influenced the
math achievement?
o Teacher assignments
o Leadership roles
209
Appendix C - Key Leader Interview Guide (Continued)
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
o Culture climate
o Ceremonial/awards
5. Where do you view your staff on the CBAM continuum (Concerns Based
Adoption Model)? And, how did they get there?
Leadership Instrument RQ 4
Research Question 4: To what extent was strong instructional leadership important in
improving (a) the math programs/strategies and (b) math achievement among
students?
“I would now like to ask you about issues specifically related to the role of
instructional leadership in your efforts to improve student achievement in math.
Specifically, I will be asking about the roles leaders played and issued related to the
development of a professional learning community on your campus.”
1. Who were the leaders on your campus who helped bring about the improved
achievement in math?
a. What were their 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?
210
Appendix C - Key Leader Interview Guide (Continued)
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 resolve dilemmas about
instructional leadership?
“Now let’s talk a little about how the site leadership went about overcoming any
obstacles you may have faced as you worked to improve student achievement in
math.” You may find it useful to refer to the frameworks on change that I provided
to you earlier.
1. What particular obstacles did you school face in the implementation of you changes
related to improved achievement in math?
2. How did the site leadership work to overcome these obstacles?
a. Structural Changes / Solutions
b. Human Resource Changes / Solutions
c. Political Changes / Solutions
d. Symbolic Changes / Solutions
211
Appendix D –Math Teacher Questionnaire
Thank you for taking the time to complete this survey. It is hoped that the results
will serve as a rich source of data that may serve to better inform schools seeking to
improve in math achievement. Please return the survey to the principal’s secretary
by October 15, 2006. 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
1 2 3 4 5
212
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.
12 such as NCLB regulations and
the CAHSEE requirement.
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
213
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
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.
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.
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
1 2 3 4 5
214
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
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.
22. Professional Development
has played a key role in
increasing student
achievement in math
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.
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
1 2 3 4 5
215
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
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.
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.
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
216
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
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.
39. I received coaching and
mentoring from instructional
leaders or peer coaches.
41. The district personnel, school
leaders and teachers all have a
shared vision for increased math
achievement.
42. My district and school leaders
seem knowledgeable about
instructionally effective math
practices and assessment strategies
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
217
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
43. The Math Department Chair has been entrusted with and is empowered to make
important curricular decisions.
1 2 3 4 5
44. Outside experts have been used to promote greater capacity in the area of math
instruction.
1 2 3 4 5
45. The school’s leaders emphasize the importance of quality instruction as a
primary mission of the school.
1 2 3 4 5
46. 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
47. Site leaders emphasize having high expectations for student achievement in
math.
1 2 3 4 5
48. Quality interventions in math have been implemented on our site to help
students at risk of failing academically.
1 2 3 4 5
49. Our site leaders emphasize a culture of collaboration as a means of improving
instruction at our site.
1 2 3 4 5
218
50. Teacher assignments in the math department are made strategically and with
student need in mind.
1 2 3 4 5
219
Appendix E- Math 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,
and 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 F – 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 to the principal’s secretary
by October 15, 2006. 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.
5. Teachers at our school teach
standards-based lessons.
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
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
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
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
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
.
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
17. The principal works to gain
the support of the community
for the school’s academic
efforts
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 pincipal 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.
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
24. Outside experts have been used to promote greater capacity in the area of
instruction.
1 2 3 4 5
25. Site leadership fosters a culture of inquiry and collaborative problem solving.
1 2 3 4 5
26. The school’s leaders emphasize the importance of
quality instruction as a primary mission of the school.
1 2 3 4 5
27. Site leaders emphasize having high expectations for student achievement.
1 2 3 4 5
28. Quality interventions have been implemented on our site to help students at risk
of failing academically.
1 2 3 4 5
29. Professional Development has been a key tool used by site leaders in our effort
to improve instruction on our campus.
1 2 3 4 5
30. Teacher assignments are made strategically and with student need in mind.
1 2 3 4 5
Abstract (if available)
Abstract
The purpose of this study was to identify how high school leaders in urban schools successfully integrate policy initiatives and best practices to improve math performance in their schools. The study investigated how school leaders, who may not have strong pedagogical content knowledge in mathematics, garner the resources to improve student achievement and sustain academic growth. Moreover, the study examined how the school leaders, in the absence of instructional expertise in mathematics, carried out functions related to fiscal management, personnel management, change management, organizational leadership, and data collection and analyses to successfully bring about increased math achievement outcomes.
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Asset Metadata
Creator
DeLoach-Langford, Beverly Ann
(author)
Core Title
The effective implementation of reform strategies, instructional conditions, and best practices to improve student achievement in math: a case study of practices at Land High School
School
Rossier School of Education
Degree
Doctor of Education
Degree Program
Education (Psychology)
Publication Date
08/07/2009
Defense Date
06/28/2007
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
best practices,high school reform,instructional quality,math reform,OAI-PMH Harvest,reform strategies,secondary education reform
Place Name
California
(states),
USA
(countries)
Language
English
Advisor
Marsh, David D. (
committee chair
), Olsen, Carlye (
committee member
), Rousseau, Sylvia G. (
committee member
)
Creator Email
langfordmb@verizon.net
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-m742
Unique identifier
UC1324319
Identifier
etd-DeLoachLangford-20070807 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-545893 (legacy record id),usctheses-m742 (legacy record id)
Legacy Identifier
etd-DeLoachLangford-20070807.pdf
Dmrecord
545893
Document Type
Dissertation
Rights
DeLoach-Langford, Beverly Ann
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
Tags
best practices
high school reform
instructional quality
math reform
reform strategies
secondary education reform