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Improving and sustaining math achievement in urban high schools: a case study of a southern California high school

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Improving and sustaining math achievement in urban high schools: a case study of a southern California high school

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IMPROVING AND SUSTAINING MATH ACHIEVEMENT
IN URBAN HIGH SCHOOLS
A CASE STUDY OF A SOUTHERN CALIFORNIA HIGH SCHOOL

by

Sergio Flores

___________________________________________________________

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

December 2007

Copyright 2007 Sergio Flores
ii
DEDICATION

For looking beyond my flaws as a husband and father and always blessing me
with unconditional love, I dedicate this work to my wife Liliana and my children
Alyssa, Erica and Estevan.
iii
ACKNOWLEDGMENTS

The experience I labored through in completing this dissertation has helped
me reach a new scholarly level that will impact my professional life and help me
redefine my role in society. I would like to acknowledge the following people for
the information they provided me with, the experiences they shared and the support
they afforded that made this endeavor possible:
Dr. David Marsh who has modeled strong scholarly work, challenged me to analyze
and question at a whole new level, and who skillfully guided me through this
process.
Tina Tsai for keeping the thematic group informed and organized through this
process.
Dr. Carlye Olse and Dr. Sylvia Rousseau for their participation and valuable
feedback.
The administration and math department at Whittier High School for sharing their
successful experiences.
The members of this thematic dissertation group for their collegial support.
The numerous mentors, teachers and students who have inspired me to achieve at
higher levels.
iv
TABLE OF CONTENTS

DEDICATION ....................................................................................... ii

ACKNOWLEDGMENTS .................................................................... iii

LIST OF TABLES ................................................................................. v

LIST OF FIGURES ............................................................................... vi

ABSTRACT .......................................................................................... vi

CHAPTER 1: INTRODUCTION ...........................................................1

CHAPTER 2: LITERATURE REVIEW ............................................... 23

CHAPTER 3: METHODOLOGY ........................................................ 76

CHAPTER 4: ANALYSIS AND FINDINGS....................................... 104

CHAPTER 5: SUMMARY, CONCLUSIONS AND
IMPLICATIONS ................................................................................. 182

REFERENCES ..................................................................................... 213
v
LIST OF TABLES

Table 2.1 Overview of the Four-Frame Model ........................................... 66

Table 3.1 Academic Performance Index and Algebra Proficiency
Bailey High School ...................................................................................... 83

Table 3.2 Performance Band Changes from 2003 – 2005 .......................... 84

Table 3.3 Teacher Questionnaire ................................................................. 89
Table 3.4 Boleman and Deal’s Four Frames .............................................. 93

Table 3.5 Instructional Leadership Framework ........................................... 97

Table 4.1 School Wide Algebra Performance ........................................... 113
Table 4.2 SAT Results ............................................................................... 114

Table 4.3 Advanced Placement Passing Rates .......................................... 114

vi
LIST OF FIGURES

Figure 1. School Design ..................................................................... 90

Figure 2. Effective Math Programs .................................................... 95

Figure 3. Assessment of Principal’s Expertise in Math ...................... 99

Figure 4. Economically Disadvantaged Subgroup ........................... 109

Figure 5. English Learner Subgroup ................................................. 110
Figure 6. Hispanic/Latino Subgroup .................................................. 111

vii
ABSTRACT
Various forces are compelling American high schools to increase
student achievement in math, science and other content areas. Local schools
and school districts are responding to state and federal accountability
measures that are prompted by reports such as the Third International
Mathematics and Science Study (TIMSS) that creates a sense of urgency in
improving education particularly since the findings in this study convey that
American students rank far below even developing countries in science and
mathematics.
The purpose of this study is to examine the leadership constructs at a
high performing urban high school in order to determine the relationships,
patterns and practices that lead to high achievement in math. In addition, the
study examines how instructional leaders at the school site responded to
providing leadership for the mathematics program without content expertise
in this area. Qualitative case study research methods were used to perform
and in-depth analysis on a Southern California High School characterized as
a large urban high school. Bailey High School was selected based on its
pattern of sustained math improvement for all students including English
learners, economically disadvantaged and Hispanic/Latino which are the
schools most significant subgroups. The pattern of increased student
achievement in math has been sustained for the past four years.
viii
The analysis of findings credits several factors that led to a shift from
a school identified as “program improvement” to one that was meeting and
exceeding all the No Child Left Behind targets in mathematics. Three salient
themes emerged in the study that focused on the relationships, patterns and
practices within the school’s math department: (1) political demands
triggered a need for change at Bailey High School. These demands resulted
in a series of other changes that relate to policies and practices within the
math department; (2) sustained change occurred through ongoing teacher
collaboration that focused on identifying and eliminating barriers to the
teaching and learning process; (3) instructional leadership, provided primarily
by the department chair, led to systemic processes that promoted student
achievement.
1
CHAPTER ONE

INTRODUCTION

Background of the Problem

Math student achievement in American High Schools is not where one would
expect from an industrialized country. The Third International Mathematics and
Science Study (TIMSS), initially conducted during 1994-95, collected student math
and science performance data from 40 countries. The study was conducted at five
grade levels (the third, fourth, seventh, and eighth grades, and the final year of
secondary school). The United States performed below the international average,
ranking far below many underdeveloped countries. The study also presented results
for 16 countries participating in the assessment of students having taken advanced
mathematics courses. Again, the United States was among the lowest performers
accompanied by the Czech Republic, Germany and Austria.
While the global economy demands more skilled labor that requires
particular competence in the areas of math and science, current research suggests that
students in the United States are likely to continue ranking at lower levels of
performance in these subject areas. Presently, and substantiated by results from
TIMMS and other international tests, the quality of domestic graduate students
compared to their international counterparts have resulted in a reduction of the
student pool for engineering and science programs in the United States due to lower
math and science achievement (Chellaraj, Maskus & Mattoo, 2005). One reason this
trend may sustain is the current nationalization of educational policy and its aim at
2
increasing the number of students who meet only minimum levels of proficiency in
math and English Language Arts (Elmore, 2003). One reason these downwards
trends may have been sustained, is ironically due to well-intentioned programs, that
have drawn the attention of educators to solving immediate and discrete problems,
rather than looking towards more long term goals and the future. The No Child Left
Behind Act (NCLB) burdens states that have already, by and large, shifted their
resources and time to meeting minimum content standards set by the federal
government. Schools search for short-term solutions—test preparation, for
example—rather than more powerful and long-term solutions, such as curriculum
focused professional development (Elmore, 2003). As a result of focusing on
meeting these targets, teachers and school leaders lose sight of the national goal of
increasing the capacity of schools and students to meet rigorous standards in science
and math, so students in the United States can compete globally.
Within its own borders many American students struggle to compete with
peers on high stakes tests, college entrance exams, and even the likelihood for
graduating from high school. Numerous studies report that students who do not
graduate from high school have a high chance of facing economic challenges later in
life. High school students who do not graduate earn less and are more likely to strain
economically. Students who fail to graduate from high school are also significantly
more likely to become single parents and have children while young themselves
(Greene, 2002). In his 2002 report regarding high school graduation rates, Greene
(2002) reports the national graduation rate for the class of 1998 was 71%. For white
3
students the rate was 78%, while it was 56% for African American students and 54%
for Latino students. It is because of such pervasive disparities in the American
school system that The National Commission on Excellence in Education was
formed and produced the report A Nation at Risk (1983). This report examined the
state of American schools, in search for answers to question such as why the
percentage of 17-year-olds that were illiterate was on the rise, particularly among
minorities. The report also noted that performance on SAT exams continued to
decline while the number of remedial math courses in public 4-year colleges
increased by 72 percent (A Nation at Risk, 1983, p.8). Poor student performance
began to have an even closer economic impact on various segments of society as
business and even military leaders had to spend millions of dollars to re-train on
basic reading, writing and math skills. More than twenty years later these trends in
declining student performance continue, and although some progress has been made,
the performance gap between majority and minority students remain unwavering.
The achievement gap among students in the United States is not only
manifested at the international level, when our students are compared to their peers
in other countries. The achievement gap further manifests itself within our borders
among low socio economic populations, with underprivelaged students of color, with
students who speak a language other than English and with those that have learning
difficulties. In 2003, U.S. eighth-graders in U.S. public schools with the highest
poverty levels had lower average mathematics and science scores compared to their
counterparts in public schools with lower poverty levels (NCES, 2003). In
4
California, only 20% of tenth graders receiving special education services, 31% of
English learners, 46% of African American students and 51% of Hispanic students
passed both parts of the California High School Exit Exam (Human Resources
Research Organization, 2005). Schools where there were high concentrations of
minority and disadvantaged students had lower CAHSEE passing rates then their
counterparts at other schools (Human Resources Research Organization, 2005). This
result highlights a problem within student achievement that is especially important
where significant populations of minority students attend urban schools. Failure to
pass exit exams such as the CAHSEE will only intensify the existing adversity that
faces poor students of color. The research continues to reveal that graduation rates
are shockingly low for African-American and Latino students nationwide (Greene,
2002), and without a change in current policy and instructional practice, this problem
will only be exacerbated.
In order for urban youth to achieve at higher levels in math, they not only
need access to their more successful student counterparts, but they need real
opportunities for universal success in challenging math content. If relegated to
remedial math courses only, students will never have the opportunity to tackle higher
level mathematic applications. The College Board (2005) reports that once students
are enrolled in advanced placement (AP) courses, they frequently find themselves
developing new confidence in their academic abilities, discovering previously
unknown potential to go to college and to succeed once there. It is hoped that
breaking the cycle of low level math content for urban youth will also lead to success
5
at the post-secondary level. College students are more likely to receive a bachelor’s
degree if they took a college preparatory curriculum in high school math (Watson,
Cabrera, Lee & Williams, 2000). However, very few states have made substantial
progress in offering college preparatory courses to minority students. In 2004,
64.5% of total nation-wide Advanced Placement exams were taken by White
students (Collegeboard, 2005). Reform efforts, such as the standard-based
movement and a more concerted effort to provide equity for all students, are
essential in providing all students the opportunity for academic success.
The vehicle for most elements of school reform has been the movement
towards a standards based academic curriculum. The adoption of standards has
affected the content of textbooks, school plans, teacher instruction and professional
development programs. A common set of standards levels the playing field to some
degree by establishing a minimal set of expectations for all students. The Thomas B.
Fordham Foundation published its second report in 2002 (Fordham II) that evaluated
the math standards of 49 states in the United States based on an evaluation criteria
that consisted of measures that included clarity, content, reason as well as the
negative qualities of the states’ standards. Only three states were assigned “A”
grades or marks of excellence: California, Indiana, and Massachusetts. Although a
good standard has many elements, content is what matters most in state standards;
clear but insubstantial expectations are insufficient (Klein, 2005).
Just as practitioners and researchers argued in the early 90’s over the value of
whole language versus a reading skills-based curriculum, states vary in the
6
performance of their students and state standards that are related to math. Some state
standards emphasize the use of calculators and manipulatives and are heavy in
estimation and the identification of patterns. Klein (2005) argues that students
should have a solid understanding of standard algorithms and the arithmetic of
rational functions. Challenging math standards that help students develop their
conceptual and procedural knowledge lead to a higher level of success in advanced
math courses. The disparity in opinions, instructional practices and state policies
further magnifies the question of equity. Whose standards are more rigorous? What
policies lead to higher levels of learning?
Even with excellent math standards in the state of California, high school
math teachers’ chief complaints continue to be students’ lack of proficiency in
multiplication, division, and ability to work with fractions. Students need to
memorize the basic number facts because doing so frees up working memory
required to master the arithmetic algorithms and tackle mathematical applications
(Klein, 2005). This task cannot be left to high school math teachers alone. The
responsibility lies with all teachers in the K-12 system.
Textbooks have been redesigned so that they are aligned with new rigorous
math standards and all students are expected to not only access the core math
curriculum, but to be proficient in the standards. However, students cannot be
expected to meet rigorous math standards without exposure to good instruction.
Teachers, both new and experienced, need to be familiar with the standards and the
textbooks designed as the principle tool to deliver the curriculum.
7
In many cases, teachers are not effective because they have not received
adequate training in the current best practices. Veteran teachers who began their
teaching careers far before standards were implemented need training and coaching
in their classrooms with their own students. Many math programs and professional
development opportunities are available to teachers. However, not all professional
development programs are closely tied to standards, the curriculum and the specific
needs of students (Elmore, 2002).
While training is available, it is also imperative that teachers are proficient in
the content they teach. Studies indicate that students taught by teachers with
backgrounds and credentials in mathematics outperform students taught by teachers
with certificates in other areas (Felter, 1999). Felter also investigated the
relationship between measures of mathematics teacher skill and student achievement
in California high schools and found that students of teachers who rated themselves
as knowledgeable or very knowledgeable about the curriculum and evaluation
standards scored higher than students whose teachers reported little or no knowledge
of the standards.
Changes in math curriculum alone may not bring about expected
improvements in student performance. Many high schools continue to operate with
outdated designs that do not offer students the chance to accelerate their learning in
order to become proficient in math. While national and international results show
that American students are deficient in math, the High School Survey of Student
Engagement (2004) results show that students continue to take fewer math courses
8
their senior year than they took in earlier grades. When students’ transcripts were
examined, only 36% of public high school graduates in the United States had taken
courses necessary to prepare them for college (Plucker, Zapf & Spradlin, 2004). It is
safe to assume that these startling course completion rates will result in lower
college-going rates and a higher number of college freshmen in remedial math
courses once in college.
New school designs that focus on math achievement and related school
features have surfaced in order to bring about improvements. Reform and redesign
initiatives such as secondary curricular realignment, Small Learning Communities
(SLC’s), career and technical education and competency-based promotion are being
implemented in schools throughout the United States. But even though schools have
completely restructured into smaller learning communities (i.e. houses, academies,
pathways, etc.), many find that student achievement has not increased
correspondingly. This is due largely to the fact that time and energy is given to
program and process improvement that incorporate only partial theories without a
strategic comprehensive curricular realignment (Fullan & Miles, 1992).
A struggling math student cannot be expected to advance if a school
restructures by simply breaking up into smaller learning communities. Progressing
through high school taking only lower-level courses in mathematics may not only
hinder students in the long run, but may also deny them the opportunity to be
challenged academically and rise to meet those challenges (Plucker, Zapf &
Spradlin, 2004). Students who entered high school with standardized test scores in
9
the lowest quartile, and who enrolled in college-preparatory courses, showed better
performance on subsequent standardized tests than their peers enrolled in vocational
courses (National Center for Educational Statistics, 1999). Redesigning schools for
universal success must include all students taking high level college-preparatory
courses in math and other subjects.
While schools are restructured and curricula are redesigned, accountability
measures and educational policies need to be reconsidered. Critics of test-based
accountability often argue that its primary impact is to increase the time spent on
test-preparation activities, thus improving test-specific skills at the expense of more
general skills (Jacob, 2002). Educators have reacted to current accountability
policies by equipping students with the skills necessary to pass high stake tests.
While the Advanced Placement Report to the Nation (2005) identifies student
success in the most challenging high school courses available as the most important
factor in college admissions, most educational policies continue to center on a
minimal set of standards and a corresponding test to prove mastery of those
standards. In the advanced mathematics section of the Third International
Mathematics and Science Study (TIMSS, 1995) those countries whose students
performed at the highest levels also had the highest percentage of students taking
higher level math courses. Most school systems continue to invest time in preparing
students for high stakes tests through remedial math courses. However, policies that
ensure higher level math course participation for all students are non-existent.

10
Leadership
John C. Maxwell (2005) affirms that leadership does not necessarily have to
originate with the highest person on the organizational chart. In education, without
the principal’s leadership, efforts to raise student achievement will generate limited
results. The top priority for the principalship must be leadership for learning
(Institute for Educational Leadership, 2001). Just as the standards movement has
reshaped the role of the teacher, school leadership, and principals in particular, need
to adapt to the new demands of the curriculum. They must know academic content
and pedagogical techniques. They must collect, analyze and use data in ways that
fuel excellence (Institute for Educational Leadership, 2001). Along with these
important tasks that help define instructional leadership, principals must not forget
the importance of developing a culture of spirit and excitement with students,
teachers, parents and local businesses.
The Institute for Educational Leadership (2001) defines an effective principal
of the 21
st
century as “One that carries out instructional leadership, community
leadership and visionary leadership. The instructional leader focuses on
strengthening teaching and learning, professional development, data-driven decision-
making and accountability. The community leader provides a big picture awareness
of the schools’ role in society and the market place. He builds and nurtures
relationships with parents and businesses and builds the school’s capacity as an
advocate and by soliciting additional resources. The visionary leader believes that
11
all students can learn and inspires all stakeholders to reach the goal of all students
achieving at high levels” (p. 4).
This type of leader, despite the numerous challenges in reaching this level of
leadership, needs to exist in an urban school setting where efficacious leaders are
desperately needed. Given the daily responsibilities a principal has, many report
spending more time on management, paperwork and meetings than on instructional
leadership because that is what they perceive to be the district’s priorities (Cudeiro,
2005). In addition to the demands of an inner city high school and the added stress
from district management, principals are bogged down by paperwork and procedures
from state and federal educational departments and slowed down by the red tape and
restrictive beauracratic system. Instead of devoting time to building instructional
capacity in the classroom, principals are often found in their offices meeting report
deadlines and working on duties assigned by educational policy makers. Today’s
high school principal and co-administrators act as key players and need to work with
a team of dedicated classroom teachers (Marzano, 2003).
School leaders are not just limited to school site administrators. Many
skilled, committed and passionate teachers provide leadership in their own
departments and even school-wide as they build the capacity of their school and
work towards a common goal and for a collective purpose (Fullan, Bertini & Quinn,
2004). Principals can delegate and empower others to help carry out the goals of the
school and still accomplish management tasks that must be carried out. The
leadership structure, with respect to teacher leaders within a school, therefore
12
becomes horizontal. The capacity of a school improves when teachers support their
colleagues and make important instructional decisions without the physical presence
of the principal.
Another segment of school administration that is often overlooked is district
level administration. Often, district level administration, generally made up of
highly educated and skilled people, is also engrossed in managerial and compliance
tasks that offer little to no support in helping schools meet their instructional
objectives. District administration, rather than simply monitoring and supervising
policies and procedures, need to be active participants in the school improvement
process. MacIver & Farley (2003) suggest that district personnel assist schools in
the decision-making about curriculum and instruction, support good instructional
practice through professional development and evaluate student achievement results.
The background, training and expertise of central office personnel is in great need at
the classroom level, not at a distant building that is far removed from students and
teachers.
In an era of accountability, principals and school leaders can no longer devote
their time and energy to what they feel comfortable with. The leadership, especially
in urban settings, must exercise instructional leadership, otherwise, student
performance results will not improve. School leaders need to be closer to where
learning actually takes place.

13
Statement of the Problem

Urban high school students continue to perform poorly in math. Success in
math is not only an imperative part of a quality high school education, but also a
strong indicator of how well a student will perform in college and later in the much
needed fields and careers related to science and math. The research reviewed in the
subsequent chapter points to rigorous coursework and curriculum that is aligned to
content standards as the remedy to help eliminate the achievement gap in math and
the lack of preparedness in higher level math for those students who otherwise meet
the requirements for college.
In addition to math programs that include rigor in their curriculum, students
who perform well in math are exposed to sound instructional and best practices that
include collaboration and focus on the understanding of concepts over the need for
understanding the procedures for solving math equations. For those students who
struggle with higher level math, support programs are also necessary in order for
those students to accelerate their learning and keep from increasing the gap in their
current level of performance and high achieving goals related to rigorous academic
standards.
Many urban high schools are not designed to provide a rigorous math
curriculum to all students and do not have the support structures in place to help all
students succeed in math. In addition to problems with design, urban high schools
must understand the complexities of the change process so that teachers and school
leaders believe that all students can achieve in a rigorous math curriculum and so the
14
entire high school culture can shift to an environment in which all students are
provided the resources for math achievement.
It is therefore important to learn what the components of an effective
program are and what reform initiatives produced higher math achievement for all
students, including those students that generally do not perform well in Algebra and
other math courses. In addition to investigating the effective elements of a math
program in an urban high school, it is important to identify the leadership structures
for the school and how the principal and other school leaders put together resources
to produce increased and sustained results in math. When high school principals do
not have experience and background in math, it is imperative to study how school
leaders responded to the challenges of improving performance in a content area in
which they themselves are not experts.

Purpose of the Study

The purpose of this study is to examine the leadership constructs at a high
performing urban high school in order to determine the relationships, patterns and
practices that lead to high achievement in math. In addition to the leadership roles,
the study will examine the policies, curriculum and instructional practices that have
lead to math proficiency in students who generally perform poorly. Other indicators
such as teacher attitude, change process and any other factor leading to improved
student performance in math will also be investigated.

15
Research Questions

The following research questions paramatized and guided this study:

1. What was the pattern of math achievement for various students at
the school?
2. What policy initiatives as well as curriculum, instruction/and
related conditions 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 instructional leaders respond in academic areas in which
they were not experts?
The research questions will also guide data collection for eventual analysis and
discussion. Each of the questions will also be addressed in the conclusions and
recommendations section of this study.

Importance of the Study

International data reveals that American students perform at significantly
lower levels in math and science than their counterparts in other countries.
Nationally, an achievement gap exists for the various subgroups present in our
16
schools. Educational leaders at every level have examined various math programs in
an effort to improve student achievement, yet the results of the interventions they
have designed continue to produce the same and limited results. This study provides
an opportunity to examine those math programs that provide an optimistic context
which would allow all students can achieve at high levels.
Not all educational leaders have a background in math. Principals with
limited background and experience in mathematics will find this study particularly
important. Even with excellent leadership skills, principals find that successful
implementation of a program does not necessarily lead to high math achievement.
This study will inform principals on successful practices in identifying a sound math
program and how to avoid challenges for effective implementation. Principals and
other instructional leaders will also learn of the impediments that one might
encounter during a change process and strategies to overcome them.
Finally, educators could use this study to develop a programmatic map that
could lead to increased math achievement, higher graduation rates, and increased
college acceptance rates. This study could enable the groundwork necessary to
restructure how math is taught and learned in American classrooms. As teachers
increase their understanding of how students learn math, more students will reach
proficiency leading to more coherent teaching and a deeper understanding of math
for students.

17

Limitations
Primarily due to time constraints, this study is limited to southern California,
and more specifically, Los Angeles County and surrounding areas. Also due to time
limitations, the study examines the effectiveness of a high school based on short-
term data and on the accounts and descriptions of teachers and administrators.
In California, accountability has restricted all public high schools to a
minimum set of standards. To ensure that mastery of the adopted standards is the
objective of instruction in every classroom, the California Department of Education
has approved a number of textbooks that schools and school boards can choose from.
These requirements limit how this study measures successful schools based on a
minimum set of standards and the assessments that evaluate how much students have
achieved. Indicators that identified schools whose students excel in math were
limited to standards-based assessment data that neglects other indicators that may
illustrate high student achievement in math.

Delimitations
This study analyzes math programs and math student achievement that may
not relate to achievement in any other content area. When measuring student
achievement and school success by analyzing data alone, the process for how the
results were attained is ignored. Therefore, this case study looks at policies,
practices and the interaction between staff and students to better understand math
18
results. Because the culture and structure varies significantly from school to school
and one department to another, the generalizability of this study’s conclusion is
limited.
Many school leaders have limited backgrounds in mathematics. This study
was designed to examine a school whose leaders had limited or no background in
mathematics. The high school studied was also selected based on the demographics
including, socio-economics, total student population, percent of English learners and
other features that make it an urban school setting.

Assumptions
Not all teachers have the same level of skills and experiences. This study
assumes that all teachers are highly qualified and prepared to teach to the California
content standards. Although student achievement data will be analyzed, the study
relies on interviews and questionnaires that are presumed to yield credible data. The
study also assumes that California standards, curriculum and conventional pedagogy
is acceptable for evaluating the success of a quality math program.

Definition of Terms

For the purpose of this study, the following terms were operationally defined
below.

19
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)
1
.
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: The difference in academic achievement between
different ethnic groups (U.S. Department of Education).
Advanced Placement (AP): The College Board partners with colleges and
universities to create assessments of college-level learning in 34 subject
areas. AP exams assess student skills and knowledge of high academic
intensity and provide a reliable indicator of future success in college
completion.
Assessment: The processes used to collect information about student
progress toward educational goals. The form varies with what is being
assessed and the purposes for which the results will be used. Secondary
Periodic Assessments measure student proficiency toward California

20
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 technique or methodology that, through experience and
research, has proven to reliably lead to a desired result.
California High School Exit Examination (CAHSEE): A graduation
requirement, authorized by state law in 1999, that requires California public
students, beginning with the graduating class of 2006, to pass the CAHSEE
in order to receive a high school diploma. The CAHSEE will cover the
curricular areas of reading, writing, and mathematics and will be aligned
with the state content standards adopted by the State Board of Education
(California Department of Education, 2001).
California Standards Test (CST): A standards-based assessment given to all
second through eleventh graders in math, English, science and social
science.
California Basic Education Data System (CBEDS): An annual collection of
basic student and staff data; includes student enrollment, graduates,
dropouts, course enrollment, enrollment in alternative education, gifted and
talented education, and more.
21
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).
Data-driven decision making: The process of making decisions about
curriculum and instruction based on the analysis of classroom data and
standardized test data. Data-driven decision making used data on
operational functions, the quantity and quality of inputs, and how students
learn to suggest educational solutions (Massell, 2000).
Highly Qualified Teacher: Teachers who have appropriate certification,
training and subject matter competency to teach at specific grade levels
and/or subject areas
Instructional Leadership: An influence that guided the activities designed to
impart knowledge or skills to students (Olsen, 2005).
School Accountability Report Card (SARC): California public schools
annually provide information about themselves to the community allowing
the public to evaluate and compare schools for student achievement,
environment, resources and demographics.
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
22
U.S. Department of Education. One NAEP component provides states with
a measure of their students’ academic performance over time and a
comparison to the results of other states and students nationwide (California
Department of Education, 2001).
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).
23

CHAPTER TWO

LITERATURE REVIEW

Introduction
The review of literature consists of research that includes current and past
student achievement in math; how American students compare to their counterparts
in other countries; the disparity in achievement nationally; current efforts to improve
math instruction; and the leadership practices that lead to increased math results for
students in urban high schools. The theories and best practices drawn together in this
review offer possible themes, ideas and solutions to the problem of low math
performance in the United States that is the subject of this dissertation.

The Academic Performance of American High School Students
There are many indicators that American students are performing poorly in
school, particularly in the area of math. International test results also show that
American elementary and secondary students are performing far below other
industrial countries in both science and math (TIMMS, 1995). This is cause for
alarm as American society, business, industry and the economy demand a great deal
from our educational system now, and undoubtedly, will demand even more in the
future.
Indicators of student performance are disaggregated into state-wide
performance and show similar results across most states. When compared to
24
performance levels from more than three decades ago, California students are
performing lower now on the SAT than their counterparts did in 1972
(CollegeBoard, 2005). The SAT Reasoning Test assesses student reasoning based on
knowledge and skills developed by the students in their coursework. The SAT
Subject Tests are a series of one-hour, mostly multiple-choice tests that measure how
much students know about a particular academic subject and how well they can
apply that knowledge (CollegeBoard, 2005). In 1972 the mean verbal scores on the
SAT for both male and female California students were 530. In the year 2005, the
mean verbal scores were 508. Math presents the reverse; the mean math score for
both male and female students was 509 in 1972 and 520 in 2005. These differences
are attributed not to a dramatic difference in instruction, but to a difference in the
kind of student that is present in our classrooms. Over one million school children
who are not proficient in English attend California schools, constituting one-quarter
of the state’s elementary and secondary school population. Most of these students
speak Spanish, but over 50 other languages have been identified in California
schools (Jepsen & Alth, 2005). The highest minority group represented in the SAT
report is Asian American. Asian students are the highest performing group in math,
far outperforming any other ethnic group in the country.
A dramatic shift in the demographics of our students is not the only change
that American educators, and California in particular, have experienced. The type of
student, and how they perceive the world they live in now in the 21
st
century is the
second and most challenging shift. Already students think and operate in the context
25
of a digital society that is much different from the more than 100 years ago when our
current educational system was designed. Daggett & McNulty (2005) studied the
trends in scientific advancement and suggest that more extensive scientific and
technological advances will occur in the next few years than have happened in the
last two centuries. Dealing with these advances requires a different educational
system from the one in which we were educated (Daggett & McNulty, 2005).

International Comparison
The Third International Mathematics and Science Study (TIMMS) is one of
the most comprehensive studies that includes the performance level of students in
more than 40 countries and collected the data in more than 30 different languages.
The difference across countries in how education systems are organized, how
students proceed through the upper secondary system, and when students leave
school posed a challenge in defining the target populations to be tested in each
country and also in interpreting the results (NCEA, 1998). Nevertheless, the United
States’ mean achievement in mathematics and science literacy, when compared to 20
other nations, was significantly lower than thirteen nations and only significantly
higher than Cyprus and South Africa. When the results were looked at separately for
mathematics, the top-performing countries were Singapore, the Netherlands,
Sweden, and Switzerland (NCEA, 1998).
How American students perform against their counterparts in other nations
has to do with several factors. One aspect is how American schools organize their
26
curriculum and teach students here in America. Among many of the conclusions
from the TIMMS study is that U.S. schools cover far too much content and expect
students to master it in a short period of time. For example, U.S. fourth and eighth
grade mathematics textbooks cover between 30 and 35 topics, whereas textbooks in
Germany and Japan cover 20 and 10 topics respectively (Marzano, 2003).
Other studies have identified a variety of factors that have resulted in higher
math achievement in the participating countries (TIMMS, 1995). Martin, Mullis,
Gregory, Hoyle and Shen (2000) studied the various factors that led to the
effectiveness of TIMMS schools in science and mathematics and found that
mathematics class size and an orderly classroom environment were commonalities
for high achieving TIMMS schools. According to the findings of the study, an
efficacious classroom environment was dependent on three aspects of student
behavior in their mathematics class: students are orderly and quiet during lessons;
students do as the teacher says; and students rarely neglect their work. Class size
was positively related to an adjusted school achievement, meaning that higher
mathematics achievement was associated with larger class sizes. This may be due to
a tendency for schools to assign weaker students to smaller classes (Martin, Mullis,
Gregory, Hoyle and Shen, 2000).
National Objective Standards
The U.S. Department of Education’s landmark 1999 study of Answers in the
Toolbox found that a high school curriculum of “academic intensity and quality”
such as that found in AP courses is far and away the most powerful predictor of
27
bachelor’s degree completion, much more accurate than GPA or test scores
(Collegeboard, 2005). Throughout the nation, by and large, it is accepted that a
rigorous curriculum leads to better performance in high standards for mathematics.
Using national Advanced Placement Data (Collegeboard, 2005) some states have
made much progress in increasing the percentage of students demonstrating college-
level mastery than others. States such as New York, Maryland and Utah had
approximately 20% of their 2004 students demonstrating mastery of rigorous
standards as measured by their enrollment in at least one AP course in high school
(Collegeboard, 2005). California had 18.7% of their high school students in AP
courses in 2004 and only had a 3.7% increase in AP enrollment from 2000 to 2004.
The number of high school students that enroll and complete Advanced
Placement courses, however, is dreadfully low. Therefore, the challenge is to
provide a set of high academic standards, such as in the AP program, and support
them with a sound curriculum and instructional practices so that all students, nation-
wide, achieve at higher levels in math (and other content areas).
Signed into law in 2002, the No Child Left Behind (NCLB) act set a national
educational policy that mandated accountability for results achieved, gave more
freedom to states and communities to initiate their own educational reforms,
encouraged the use of proven educational methods and created more choices for
parents and students. It is the single largest nationalization of education policy in the
history of the United States, promoted paradoxically by a conservative
administration with the docile cooperation of congressional liberals (Elmore, 2003).
28
Under the act’s accountability provisions, states must describe how they will close
the achievement gap and make sure all students, including those who are
disadvantaged, achieve academic proficiency (California Department of Education).
The NCLB legislation also requires state governments to report progress to parents
and communities and to provide supplemental services as part of a series of sanctions
if and when a significant percentage of students are not making minimal progress.
According to Marzano and Kendall (1996), many educators consider the
publication of A Nation at Risk (National Commission on Excellence in Education,
1983) as the initiating event of the modern standards movement. Preceded by A
Nation at Risk, NCLB required states to develop a set of standards stating what
students should know and be able to do at individual grade levels. The California
Department of Education states that its content standards were designed to encourage
the highest achievement of every student, by defining the knowledge, concepts, and
skills that students should acquire at each grade level. Content standards are what
students are expected to master and not how they are expected to reach the level of
mastery. Developing and adopting standards is the foundation, adopting a
curriculum that is aligned to state standards is subsequent and has presented a
challenge to many states.
Academic Performance for California Students in Math
The STAR program was authorized by Senate Bill (SB) 376 in October 1997.
California’s STAR program began by designating the Stanford 9 (SAT 9) as the test
and was first administered in 1998. From 1998 to 2000 the SAT 9 test, a nationally
29
norm-reference standardized test, was used as the primary tool to assess California
student achievement in math and English language arts. In 1999 California
introduced the California Standards Test (CST). The CST is a criterion referenced
exam based on California state content standards. Results from both the CST and the
SAT 9 were used in the calculation of the Academic Performance Index (API) used
to measure the success of California schools’ academic programs. California
abandoned the use of SAT 9 and replaced it with the California Achievement Test,
Version 6 (CAT 6) which is currently administered at two grade levels in elementary
and middle school only.
Since the inception of the STAR program, California has had the capacity to
measure student performance in math and other content areas. Various reports are
available and schools have the ability to measure their own progress and how they
compare with like schools. In 2005, 45 percent of all second through eleventh grade
students in California were proficient in the math section of the California Standards
Test (CST). Among the lowest performing subgroups are Latino and African
American students with 32 percent and 27 percent, respectively, reached proficiency
in math standards as measured by the CST (California Department of Education).
After determining that local proficiency standards were generally set below a
high school level and were not consistent with the state's content standards, the
California Legislature indicated its intent to set higher standards for high school
graduation. In proposing the California High School Exit Exam (CAHSEE), the
Legislature's primary goal was to "...significantly improve pupil achievement in high
30
school and to ensure that pupils who graduate from high school can demonstrate
grade level competency in reading, writing, and mathematics"
(http://www.cde.ca.gov/ta/tg/hs/overview.asp). The CAHSEE was offered for the
first time in 2001 and was ultimately mandatory that the graduating class of 2006
pass both the math and English sections of the exam as a prerequisite for issuing a
high school diploma.
The California High School Exit Exam measures students' math skills in
numbers sense; statistics, data analysis and probability; measurement and geometry;
algebra and functions; algebra 1 and mathematical reasoning. In 2005 state-wide
results include 63 percent of all students passing the math section with a scaled score
of at least 350. Only 50 percent of socio-economically disadvantaged students met
minimum requirements for CAHSEE math (California Department of Education).
California’s STAR program is designed to meet the minimal target that schools
must meet, that combined with federal NCLB requirements, keeps a school out of
program improvement status. While many schools and school districts in the state of
California are making steady increases and meeting increasingly higher achievement
targets, there are very few schools making progress in more challenging coursework
that leads to increased performance on more rigorous assessments such as the
Advanced Placement (AP) test.
One of the chief purposes of the College Board’s Report to the Nation (2005)
is to provide state departments of education with new data to gauge success and
identify current challenges in providing equitable educational opportunities. States
31
and school systems can then identify gaps in their own students’ performance and
develop goals and a plan to close achievement and equity gaps. It also identifies
schools currently leading the world in Advanced Placement (AP) participation and
performance.
Only two College Board Advanced Placement courses and exams are offered
to high school students: Calculus and Statistics. Nationally, only 60 percent of
students who enroll in AP calculus and statistics courses pass the corresponding AP
exam with a 3 or higher on the AP rubric. Although both Polytechnic High School
(Pasadena, CA) and Diamond Bar High School (Diamond Bar, CA) are recognized
as schools with Exemplary AP Calculus AB programs, no schools in California are
recognized for having a significant percentage of African American or Latino
students passing the AP calculus exam with a 3 or higher (Collegeboard, 2005).
Only one high school, Mission San Jose High School (Freemont, CA) was
recognized as having an exemplary AP Statistics Program.
The Achievement Gap in Student Performance
Katie Haycock (2005), educational consultant and researcher with Education
trust maintains that in order to increase the achievement levels of minority and low-
income students, we need to focus on what really matters: high standards, a
challenging curriculum, and good teachers. Results from most any national and state
level assessment continue to show a significant gap in student achievement with
regard to race and ethnicity. Numerous studies identify a clear gap and attribute it to
32
a list of factors that include, school conditions, segregation, untrained teachers and
socioeconomic and family conditions to name a few.
Educators have been conscious for several decades that a wide gap exists
between low-income minority students and other young Americans. Concerted
efforts in narrowing or closing the gap have resulted in some gains. Between 1970
and 1988 the achievement gap separating Latinos and whites declined by one third
(Haycock, 2005). However, since then, the progress on narrowing the gap has
slowed and indeed widened. The wavering results from non-White students indicate
that curriculum and instruction in fact produces varied outcomes in student
achievement. Although students of color seem to perform better on assessments that
measure basic skills, it does not necessarily purport that they benefit from a basic
skill level curriculum as opposed to a curriculum and assessment program that
emphasizes higher order thinking.
In the past several decades, the emphasis on how student achievement is
measured has varied from assessing students on their basic skills and knowledge or
on higher learning standards that measure higher order thinking skills. Low-
performing students gained more than high performing students when minimum
competency was emphasized during the late 1970’s and early 1980’s, but the
opposite is true as we move to the period of higher learning standards during the lat
1980’s and 1990’s.
Jaekyung Lee (2002) studied Black-White and Hispanic-White achievement
gap trends over the past 30 years and found that despite the many challenges to
33
improve racial and ethnic equity in learning outcomes, substantial success in
narrowing the Black White achievement gap has been realized since the 1960’s.
Despite the success during the 1960’s, however, Lee (2002) found that earlier
progress in closing the achievement gap had been reversed during the 1980’s and
continued to show setbacks during the 1990’s according to National Assessment of
Educational Progress (NAEP) and SAT results.
The number of White students who took the SAT Reasoning test in 2005 was
66,274 while the number of Black students was a meager 12,084 (CollegeBoard,
2005). Students from successful high schools (top tenth in high school rank)
represented 32% of all test takers on the SAT in 2005 (CollegeBoard, 2005) and had
a mean math score that was 162 points higher than their counterparts in the least
effective schools (fifth on school rank). Both Black-White and Hispanic-White SAT
score gaps narrowed in the verbal and mathematics areas significantly by the late
1980’s but then stabilized and even widened during the 1990’s when White students
gained most and the size of the gains was greater at the higher performance level
(Lee, 2002).
While SAT results show inconsistent gains, the Advanced Placement
program has more promising results. Although African American, Latino and Native
American students have been significantly underrepresented in AP classrooms
nationwide, much progress has been made over the past five years (Collegeboard,
2005). Several states have closed the equity gap with respect to the percent of
students enrolled in AP courses and who have taken the corresponding exam.
34
Seventeen states have closed the equity gap for Latino students and only two states
have closed the AP equity gap for African American students. California continues
to lag behind many states with respect to the equity gap. College Board’s Report to
the Nation (2005) reveals minimal changes in the equity gap for California students,
particularly African Americans. In 2000, African Americans represented 7.3% of
the student population and only 3.0% of AP test takers. Four years later in 2004,
African American students were again 7.3% of the student population and rose only
.3% to 3.3% of AP test takers.
The Importance of Mathematics
The Role of Mathematics Achievement in College Success
National efforts and demands from the business community are joined by
pleas from postsecondary institutions to increase the mathematics and science
achievement at the secondary level. If student achievement in mathematics and
science does not noticeably improve, today’s high school students may enter college
or the workforce with limited mathematics or science-related skills. As a result, their
chances of success in college coursework or in the world of work, as well as their
contributions to the U.S. labor market might also be limited (www.act.org/research).
To examine the relationship between course-taking patterns and achievement
in Illinois schools, the Illinois State University researchers analyzed student and
school characteristics and the results of the Prairie State Achievement Examination
(PSAE) for 2002 eleventh graders. The researchers examined PSAE mathematics
scores and the “math ladder” while controlling for differences related to gender,
35
ethnicity, and family income. They found that the math ladder is the strongest
predictor that a student will meet or exceed standards. As a predictor, math
achievement exceeded all other single predictors, even including parents’
educational attainment and socioeconomic status (Center for the Study of Education
Policy, Illinois State University, 2005).
Other studies have shown a relationship between math course taking and the
type of college attended. The College Board (2005) has collected numerous data that
shows that students who take rigorous and high-quality coursework, such as AP, are
more likely to complete a bachelor's degree in four years or less. Similar studies
show that students who took high levels of math such as calculus were more likely to
attend graduate level programs and doctoral universities, while students who took
only algebra attended community colleges.
When students are familiar with higher level math content, they are better
prepared to succeed in mastering college-level math, even if they are majoring in
field outside of mathematics. Currently, 40 percent of students entering four-year
colleges and universities are requiring some remedial education (Collegeboard,
2005) which negatively influences the likelihood that a student will obtain a four
year college degree.
Advance Placement Report to the Nation (2005) estimates that 56.8 percent
of the nations 2005 seniors enrolled in any postsecondary institution while only 13.2
percent were equipped with the rigorous experience of an advanced placement
course. The results for California are 57.6 percent of students progressing to
36
postsecondary learning with only 18.7 percent demonstrating college-level mastery
of an AP course in high school.
Although nearly 60 percent of U.S. high schools participate in the AP
program (www.colleboard.com), not all college-going students took AP courses in
math. Plucker, Zapf and Spradin (2004) investigated high school reform efforts in
Indiana and other states in order to better prepare students for post-secondary
success. When students’ transcripts were examined, only 36 percent of public high
school graduates in the United States had taken courses necessary to prepare them
for success in college.
However, the prerequisite for college success in math is not the Advanced
Placement Program. What students need is exposure and support in any rigorous and
advanced math program. If students express a desire to attend college, or if any
particular high school’s goal is to increase the number of students who are accepted
into a four-year university, the role of the counselor becomes crucial in reaching that
aim. This is especially true in California. Rogers, Terriquez, Valladares and Oakes
(2006) report that California students face significant roadblocks on their pathway to
college. These roadblocks help explain why California sends fewer students to four-
year colleges than most other states in the country. Among others, a significant
roadblock is the extremely high ratio of school counselors to students. This is
especially important when California counselors are responsible for more students
than high school counselors in any other state.

37
The Impact of Math on Economics
“Mathematics is the language of technology. It is used to formulate, interpret, and
solve problems in fields as diverse as engineering, economics, communication,
seismology, and ecology. Mathematics provides us with powerful theoretical and
computational techniques to advance our understanding of the modern world,
societal problems, and to develop and manage the technology industries that are the
backbone of our economy”.
-- Dr. Leon H. Seitelman, University of Connecticut
The results of TIMMS represents a cause for concern to the United States,
especially if it wants to maintain its status as a global leader. The intent of countries
participating in TIMMS was to determine what skills and knowledge students with
special preparation in mathematics had as they left school, as a way of determining
their country’s future potential in the global economy. Countries are aware that
many of the mathematicians, scientists, engineers, medical practitioners, and
business leaders of the future will be drawn from this group (NCES, 1998). In the
case of the United States, the demand for professionals with mathematics
backgrounds has already surpassed the supply and consequently it has become
common to import math professionals from other countries or outsource work
altogether.
Levy & Murnane (2004), with respect to the changing job market, assert that
the dramatic changes taking place in the U.S. economy jeopardize the economic
future of students who leave high school without the problem-solving and
communication skills essential to success in postsecondary education and in the
growing number of high paying jobs in the economy. Getting students to
successfully progress through a rigorous math program in high school is the
38
groundwork for improving the national quandary with respect to mathematics and
related fields.
Improving Math Achievement
National Efforts to Improve Math Achievement
More than two decades ago, when A Nation at Risk (1983) was published, the
goal was to reform education in such a way that students would undergo an
educational experience as rigorous and even superior to their predecessor’s the
generation before them. The National Commission on Excellence in Education was
formed by T. H. Bell, Secretary of Education under Ronald Reagan’s
Administration, as a result of his concern that “the widespread public perception that
something is seriously remiss in our antiquated educational system. The world was
rapidly changing, and many countries were changing along with it while American
students began to fall behind” (1983, p.1). The commission indeed discovered
weaknesses embedded throughout the American educational system in terms of
content, expectations, time, and teaching practices. What worked for past generations
was no longer applicable for a new age of youngsters that faced different economic,
political and societal challenges. The demands on the educational system, however,
were to provide solutions for these challenges using what was clearly an antiquated
educational system.
Student achievement was compared between several industrialized nations
and American students were never first or even second. The percentage of 17-year-
olds that were illiterate increased, particularly among minorities. Declines in
39
performance on SAT exams became consistent while the number of remedial math
courses in public 4-year colleges increased by 72 percent (A Nation at Risk, 1983,
p.8). Poor student performance began to have an even closer economic impact as
business and military leaders had to spend millions of dollars to retrain on basic
reading, writing and math skills.
Well into the 21
st
century, and nearly a quarter century later, the findings of A
Nation at Risk (1983) still haunt American schools. Although progress has been
made on many of the recommendations made by the report, some are still far from
being attained. Increased expectations by way of the development of content
standards are one of the major improvements the educational system has seen.
Graduation requirements have been strengthened and curriculum is becoming more
aligned to what students are expected to learn. Schools have been good at
implementing procedural recommendations, and for some states, even setting higher
content and performance standards.
What have not been as successful are the instructional and leadership efforts.
School leaders at the local and state level have been unsuccessful changing the
structure of the school day and school year and to make the teaching profession a
more professionally competitive, market-sensitive, and performance-based option for
high quality college graduates (A Nation at Risk, 1983). Although public officials
often assert that education is at the top of their agenda, the resources for education
continue to be deficient. One of the recommendations from A Nation at Risk (1983,
p.6) was that State and local officials, including school board members, governors,
40
and legislators, have the primary responsibility for financing and governing the
schools, and should incorporate the reforms we propose in their educational policies
and fiscal planning. With the exception of some states that have some strong
policies, the need for strong leadership persists.
Along with strong leadership, which will be discussed in more detail later in
this review, there is an obvious need for stronger instruction that is research-based
and delivered by highly qualified teachers. The No Child Left Behind Act includes a
provision that requires school districts to employ only highly qualified teachers
(HQT). Given that students in high-poverty schools are more likely than other
students to be taught by teachers without even a minor in the subjects they teach
(Haycock, 2002), the federal government was attempting to eliminate the practice of
having teachers who had limited or no content knowledge in their instructional areas
from being hired by school districts. In addition to having subject matter
competency, the federal government wanted to ensure that every classroom in
America had a teacher with full certification or state licensure.
Being deemed highly qualified by state and federal standards is often
misunderstood by many teachers. A highly qualified certificate implies that a
teacher has, at minimum, the content knowledge and pedagogical skills to teach
students in a public classroom. High school math teachers, particularly those
teaching higher-level coursework, need to meet at least minimum requirements to
teach those subjects. But content knowledge alone will not suffice for those students
struggling through a rigorous math content. The most effective teachers with strong
41
pedagogical skills and equipped with multiple instructional strategies are the
professionals that need to be assigned to work with students performing at the lowest
levels.
The single factor that makes the most impact on student achievement is the
teacher. Marzano (2003) reports that 20 percent of the variance on student
achievement is credited to schooling while 67 percent of the effect is due to the
individual teacher. Similar studies, when looking at characteristics of an effective
teacher, reveal that the distribution of effective teachers is normally expressed as a
bell curve. If schools are willing to invest in improving the capacity of all teachers
through professional development and effective evaluation procedures, then the
highly qualified teaching staff can have dramatic effects on student achievement.
Teachers and administrators alike, when part of a professional learning
community (PLC), learn continuously in order to better lead their schools and
become increasingly effective in meeting the needs of a dynamic student body. Fink
and Resnick (2001) over an eleven year period, studied Community School District
Two in New York City. District Two has experienced an increase in test scores and
a remarkable professional spirit among teachers and other staff. There is a culture of
learning and mutual dependency among staff at all levels. The design of this school
district goes beyond hiring the most qualified teachers. District Two’s design of
nested learning communities requires schools to be learning organizations that, under
its principal’s leadership, is continuously improving its capacity to teach children.

42
State Efforts to Improve Math Achievement
Many attempts at reforming the educational system and specifically,
mathematics, have been made in California and in other states. Cohen and Hill
(1998) used data from 1994 California Learning Assessment System (CLAS) to
examine the influence of assessment, curriculum, and professional development on
teacher practice and student achievement. At the time, more than a decade ago,
educational reformers in California sought to manipulate policy regarding curriculum
and assessment in order to improve instruction. California educational policymakers
took a momentous step in 1985 when they published the new Mathematics
Framework. The new framework called for much more intellectually ambitions
instruction, for more mathematically engaging work for students, and for the teachers
to help students understand math rather than just memorizing facts and operations
(Cohen & Hill, 1998, p2).
Following the launch of the framework, the California Department of
Education began experimenting with the textbook adoption process. Although the
process was not entirely successful during its initial attempts, it marked the
beginning of the state department of education’s direct impact on the development of
curriculum materials. Alignment between the framework, the structure of what was
taught, and the curriculum began to take shape. Both the effectiveness of the
instruction and what was being taught needed to be measured. The California
Department of Education used its student assessment system as another means to
change teaching (Cohen & Hill, 1998). Revisions to the curriculum and the
43
California Learning Assessment test continued in an effort to create more alignment
with the framework. Political interests and concerns over the subjectivity of the
testing system eventually led to a 1994 cancellation of the assessment program.
However, the initiative for teachers to improve their instructional practice based on
state policies continued to grow.
In their study, Cohen and Hill (1998) surveyed teachers and asked them the
ways in which the California Learning Assessment System affected how and what
they taught. Specifically teachers were asked “how CLAS has prompted me to
change some of my teaching practices” and “learning new forms of assessment has
been valuable for my teaching”. In both cases their responses where positive with
71% and 64%, respectively, agreeing that the CLAS affected their teaching practices.
Based on findings that assessment and accountability had indeed affected
teaching practices, states began to develop policies for holding schools accountable
for improving student outcomes. In 1999, the California legislature approved the
Public Schools Accountability Act (PSAA). The act had three components that
consisted of the Academic Performance Index (API), the Immediate
Intervention/Underperforming Schools Program (II/USP), and the High
Performing/Improving Schools Program which rewarded schools for making
sizeable improvements in student learning (California Department of Education).
The PSAA later added the High Priority Schools Grant Program (HPSGP) and made
some modifications to the Act’s components in order to meet the requirements of the
federal NCLB Act.
44
State-wide data shows that some II/USP and HPSGP schools have made
some progress (Dataquest, 2002). The impact of these programs however, has
dissipated at many schools after the completion of the program’s term. With
performance targets from both the federal and state programs, it could be that
schools aim at meeting the demands of one program over the other. However, expert
researchers like Pedro Noguera (2002) note that the state’s Academic Performance
Index (API) rankings reveal that poor academic performance is most common in
school districts serving low-income populations, particularly in racially isolated
urban areas where poverty tend to be concentrated. Noguera purports that
approaches at improvement in student achievement by way of accountability alone,
such as the PSAA in California, does not work in high-poverty areas. In order to
transform inner city schools, Noguera and other social scientists draw up the concept
of social capital: a concept related to social relationships and networks that affect the
quality of civic life.
As discussed in previous sections of this review, the standards-based
movement surfaced because of declines in student achievement throughout the
United States, and in particular, the gap in performance between White students and
students of color. Even if the learning gap is attributed to social relationships and
networks, it is still important to have established standards by which to measure any
progress toward closing the gap. Clear and public standards for what students should
learn at benchmark grade levels are a crucial part of solving the problem. Standards
are a guide for teachers, administrators, parents and students themselves to what
45
knowledge and skills students must master (Haycock, 2002). Once content
standards were established in California, the natural next step was to improve the
curriculum and to ensure that it was aligned to what all students were expected to
learn.
One cannot expect an increase in student achievement in math if student do
not have access to a rigorous math curriculum. Robert Marzano (2003) attributes a
guaranteed and viable curriculum as the factor having the most impact on student
achievement. A guaranteed and viable curriculum is a combination of an
“opportunity to learn” and “time” (Marzano, 2001). Therefore, if given the
opportunity and time, any student can master rigorous math content. Students who
entered high school with standardized test scores in the lowest quartile, and who
enrolled in college-preparatory courses, showed better performance on subsequent
standardized tests than their peers enrolled in vocational courses (National Center of
Education Statistics, 1999). How much time students have to learn and what courses
are available can be easily analyzed from a school’s master schedule and bell
schedule.
A cursory review of any high school’s master schedule will reveal the
school’s commitment to providing a challenging and rigorous math curriculum. Kati
Haycock (2002), director of Educational Trust has examined many high school’s
course offerings and curriculum and found that students continue to be taught a low-
level curriculum that is aligned with jobs that no longer exist. Consistent with
reports from Collegeboard (2005), Haycock (2002) found that current patterns are
46
clearest in high schools where students who take more-rigorous coursework learn
more and perform better on tests. The more rigorous the courses they take, the better
they perform on exams.

New School Design
If student outcomes become the focus for schools that are committed to
improving student achievement, then all resources and time need to be dedicated to
instruction and the monitoring of student learning. Although the goal is for all
students to achieve at high levels, the strategies for achieving the goal will vary from
time to time. The design and objective for the school thus becomes dynamic and
non-standard. To address these issues, educators across the country have been
rethinking the traditional structure of secondary schools and restructuring their
buildings and curricula to better prepare students for the future (Plucker, Zapf,
Spradin, 2004).
Rethinking how schools are designed begins by understanding that today’s
high schools are failing primarily because they no longer meet the needs of the
modern student. Ark (2002) further underscores the problem with obsolete high
schools and how they “foster anonymity and stifle learning by systemically
inhibiting those things that are most important: powerful sustained relationships:
students’ ability to address complex problems individually and as members of a team
and to communicate in various ways; and the ability of teachers and administrators to
take on increasing responsibility” (p. 56). Some high schools throughout the country
47
have taken these elements and implemented them into their new school design and
found marked success in student achievement.
High Schools that Work (HSTW), sponsored by Southern Regional
Educational Board (SREB), is an effort based school improvement initiative that is
committed to providing students with rigorous academic and career/technical studies
and a learning environment that motivates students to succeed. Their study
examined how schools adopted key practices for raising student achievement.
Schools that are both raising academic achievement and improving graduation rates
use these key actions for raising student achievement and improving graduation
rates:
∞ Raise standards and provide and opportunity for student to learn a rigorous
and relevant curriculum of academic and career/technical studies.
∞ Help students set challenging goals, give feedback on their status in
achieving these goals and provide support needed to achieve the goals.
∞ Use instructional strategies that actively engage students in learning
challenging content.
∞ Involve teacher in continuous school improvement initiative.
Schools in this study reported having eliminated many sections of low-level courses
from the core areas of English, mathematics, science and social studies so that more
students are taught at a college-preparatory level (Bottoms & Anthony, 2005).
In their study of high-performing, high-poverty schools in Kentucky,
Kannapel and Clements (2005) found a set of common characteristics in schools
48
with an achievement gap of fewer than 15 points between low and middle income
students. High-performing schools that served low-income students all had high
expectations for their students, collegial and professional relationships among adults
and students, a focus on instruction and academics, a system for regularly assessing
student progress, a collaborative decision-making process, a strong faculty work
ethic, and a careful and intentional process for recruiting and hiring teachers.
The designs and practices in the various studies transcend barriers that are
commonly used as justifications for low achievement such as ethnicity, language,
socio-economics and regional practices and policies. Darling-Hammond, Ancess
and Ort (2002) performed a seven year study of the Coalition Campus School Project
in New York City in which they documented the process for new small schools that
were created as part of state-wide network of reform oriented schools. Darling-
Hammond et al found that the five new schools that replaced failing comprehensive
high schools produced better attendance rates, lower incident rates, better
performance on reading and writing assessments, higher graduation rates, and higher
college-going rates than the previous schools did.
The design feature found in these schools included restructuring so that
education became more personalized. Students had a smaller number of teachers
throughout the course of their high school experience. More personalized units
allowed for teachers to work together and to deliver higher quality of instruction.
Students were also organized around a common core of principles, common
49
academic standards supported by performance-based assessment and an
interdisciplinary “less is more” curriculum focused on inquiry and intellectual skills.
Schools designed with a focus on student performance are likely to achieve
improved results. As teachers and school leaders center their discussions on
improving student performance, they measure their progress using student data and
explore strategies to reach their objectives. Often this leads to the identification of
gaps not only in student learning, but in teachers’ skills and ability to meet the
learning needs of the students.
How teachers solve complex learning problems requires targeted professional
development. “High schools should be organizing themselves to support this
concept of professional development as an integral part of their strategy for getting
all students to standards (Marsh & Codding, 1999). The emphasis of providing high-
quality professional development is not only essential in new high school design, but
a central focus on improving the efficacy of teachers. Hiebert, Gallimore & Stigler
(2002) convey that professional development yields the best results when it is long-
term, school-based, collaborative, focused on students’ learning, and linked to the
curriculum. As teachers improve their own skills, they become better equipped in
increasing the level of learning in their students leading to successful programs and
effective schools.

50
Successful Mathematics Programs
Successful programs are not common off-the-shelf programs with a formula
for making every student successful in math. Effective schools with successful math
programs are those that have created the conditions that will make it possible for all
students to reach the college-ready standard (Tucker, 2003). The expectations
remain high for all students and the content and sequence of each course, along with
support and safety net programs, lead to all students entering into upper division
math and ultimately reaching graduation and college readiness. The challenge,
obviously, is not to lead highly skilled and highly motivated students to successfully
master rigorous math standards, but to get those students who traditionally fail in
math to reach the same high standard as their more flourishing counterparts.
By the time students reach high school, many have given up on succeeding in
math, therefore, a program that encompass options for varying student interests
needs to be developed. Marsh and Codding (1999) discuss the need for a program
around an occupational and industrial theme that interests the student and motivates
that student to stay in school and to eventually meet rigorous standards in math and
other content areas. Such a program avails an alternative route to the same goal.
The aim here is not vocational training per se, but rather to design a program around
occupational or industrial theme that interests the student and motivates that student
to stay in school and continue his or her education (Marsh and Codding, 1999).
Designing a successful math program, therefore, requires many elements
including high standards, a sound curriculum and learning activities that motivate
51
students as well as challenge them to think. However, since the launch of NCLB,
schools and school leaders have been attracted by those programs that build basic
math skills high enough to increase test scores and turnaround their schools. Many
so called “turnaround schools” are, in fact, functioning only at the minimal level
required to keep them from returning to failing status (Elmore, 2002). In such cases,
a school may be consistently increasing its scores and remaining just in front of
minimal federal and state requirements; it does not mean the school is effective in
meeting the needs of all students and challenging them in higher level math courses.
Deiger, LaForce & Feranchak (2004) analyzed course taking patterns and
passing rates for more than 58,000 students in Chicago public schools from 2000 to
2002. Most students followed the same sequence of algebra in ninth grade, geometry
in 10
th
grade and advanced algebra and trigonometry in 11
th
grade. Only percent of
all students continued beyond the three courses required for graduation by Chicago
public schools. In 2001, 54% of the ninth grade students failed algebra and took
geometry the following year, while only 8% retook algebra. Many students did not
take advantage of summer school offerings and were therefore simultaneously
enrolled in both algebra and geometry their 10
th
grade year. Promoting students,
despite failing grades, is a common practice not only in Chicago schools, but until
recently, in many high schools in California.
An important finding in the Deiger et al (2004) study was the number of
failing ninth grade algebra students who did not have data the following year.
Thirty-five percent of all students who failed algebra in ninth grade did not take
52
summer school and did not enroll in school the following year. This suggests that
these students may have dropped out or transferred. A more promising finding is the
percent of students who passed algebra their ninth grade year and also passed
geometry their following year. The implications of this study and many others in
this review indicate that the ninth grade algebra course is not only critical in
developing basic algebraic understanding, but essential in successfully passing
subsequent courses. Both the design of the math course sequence and the instruction
in algebra courses, therefore, becomes crucial in the success of any high school’s
math program.
If evidence exists that success in algebra is critical to future student success in
math, then a quality math program will give particular attention to ninth graders by
providing them with a well planned course and support system. Although a common
practice has been to assign the strongest teachers to the higher level math courses, a
good foundation for successful math programs would be to assign all ninth grade
algebra courses to the most effective teachers that posses both content knowledge
and strong pedagogy. A second step would be to identify the most essential
standards and make those standards the focal point of the curriculum. Marzano
(2003) cautions that any math program that expects students to master a sizeable
amount of standards is likely to get limited results and has a straightforward answer
for getting students to master all math content standards: schools should drastically
reduce the amount of content standards teachers are required to address in a class.
53
Establishing the curriculum, however, has become less of a teacher and school
function and controlled more by external sources.
What students learn and the materials used to teach the content has become
increasingly rigid and established mainly by the state’s department of education.
Most high school math programs consist of a sequence of courses beginning with
algebra though higher levels of math such as calculus. Teachers are highly
dependent on the textbook and in many cases, follow a pacing guide or instructional
calendar that leads them through the standards of the corresponding course. Students
who struggle with math content are frequently placed in parallel or shadow math
courses in order to have extended instructional time in math and to improve skills
that were not mastered in past math classes.
Despite the design of the math program, the research on effective schools and
effective instructional programs consistently points at quality instruction based on
high standards for teaching and learning and a system for regularly assessing student
progress. In addition to high standards and good instruction, a successful school and
math program will include teachers who improve student achievement by
understanding what students bring to the classroom (Elmore, 2002). Teachers should
not only understand the process in which students learn, but also understand what
each students brings to the learning in order for there to be meaningful interaction
between teacher and student around math content.
The interactions that take place between teacher and student, particularly in
cases where students of color interact with a White teacher, are especially important.
54
Ronald Ferguson (2002) analyzed the responses on a survey given to more than
30,000 seventh through eleventh grade students from ten states. The survey was
concerning racial and ethnic disparities in places where schools are reputedly
excellent. The most obvious finding was that minority students were performing far
below their White and Asian peers in math and English, even when they belonged to
the same socio-economic class. Other significant findings included the teachers’
demeanor and behavior and how minority students interpreted it. Black and Latino
students favored teachers who encouraged hard work and reacted adversely when
teachers demanded it. Students of color further explained that they appreciated full
explanations from their teachers when trying to understand difficult concepts instead
of short ‘yes’ and ‘no’ answers. Based on these and other anecdotal observations,
Ferguson found that encouragement seems to entail assurances from teachers that
students have the ability to succeed and teacher behaviors that provide active support
for success (Ferguson, 2002).
The teacher behaviors that are common in a department or program make up
the culture and norms that students are exposed to. In some cases, programs in
schools fail because they systemically inhibit those things that are most important
such as powerful sustained relationships between teachers and students (Ark, 2002).
Mathematics as a content area can be tedious and unexciting as a teacher jumps from
problem to problem reviewing the process for solving an equation. Successful math
programs include teachers and school leaders who recognize that learning is
influenced by social interactions, interpersonal relations, and communication with
55
others (McCombs, 2001). When the setting for socialized learning is developed,
students can begin learning what the National Council of Teacher of Mathematics
(NCTM) recommend as a 21
st
century high school math program characterized by a
decreased emphasis on routine procedural skills and an increased emphasis on real-
world uses of mathematics and multi-step problem solving.
As stated earlier, no one specific math program provides a flawless solution
to students who have repeatedly struggled with math. Instead, successful math
programs offer a wide scope in terms of content, instructional strategies and support
for struggling students. The University of Chicago School Mathematics Project
(UCSMP) was developed in 1983 prior to the NCTM standards and later developed
based on influences from the standards movement. Later changes were also
influenced by advances in technology, particularly the availability of graphing
calculators, theories on the advantages of writing mathematics and by the benefits of
working in small groups (Thompson & Senk, 2001). The materials used by UCSMP
include reading and problem solving, realistic applications, technology, a
multidimensional approach to understanding, and instructional format featuring
continual review combined with a modified mastery-learning strategy (Thompson &
Senk, 2001).
Thompson & Senk, 2001 examined the effects of student performance in
eight pairs of algebra classes in five schools. Teachers in these schools used either
UCSMP materials or comparison materials to instruct their students in math.
Students in programs using UCSMP materials outperformed comparison students at
56
two sites, on both traditional content and applications, and comparison students
outperformed UCSMP students at one site. Performance also varied when assessing
specific skill areas such as graphing technologies, procedural skills, rational
expressions, polynomial factoring and problem solving. Teachers did not always
follow what was emphasized in the textbooks and often supplemented these with
additional content or other pedagogical strategies they felt would assist their
students.
Along with many others, this study offers strengths and weaknesses of using
any one math program over another. Where some programs fail, others excel. And
yet other program weaknesses are enhanced by teachers supplementing with
additional content or other strategies they have found to be effective. Despite the
program that is used, studies also show that the complexity of a successful school
math program requires strong leadership and teacher knowledge with respect to
standards, curriculum, assessment and the process for learning. Math teachers also
need to understand their students in a social-cultural context in order to better
understand what their learning needs are. Along with redesigning a math program
that yields higher student achievement, teachers need the training in order to deliver
effective instruction that generates the achievement that was intended by the
curriculum design.
When designing the “new high school” professional development was
identified as one of the key elements to an effective school model. Elmore (2002)
describes how professional development becomes even more focused on certain
57
elements of a program such as inferential and problem-solving skills in algebra. In
this case, professional development is to be focused on student learning and tailored
to address the difficulties encountered by real students in real classrooms as well as
broader program objective. For a school, professional development is provided in
order to meet school-wide goals and objectives. When addressing specific needs
within a department or program, training for teachers needs to be aligned to their
disciplines. Training for math teachers should include having students use
technology and work in groups to solve real-world problem, use hands-on materials
and other research-based strategies that advance their mathematics achievement
(Bottoms & Anthony, 2005).
As stated frequently in this review, overcoming the barriers that keep all
students from achieving at high levels in math will require strong leadership. The
success of the school’s math program will depend greatly on the leadership that
supports the program and sustains its success by closely working with teachers and
helping them develop as professional math teachers. In order to do this, the principal
is expected to be an instructional leader and understand the instructional programs
that the school has adopted well enough to actively guide teachers in its
implementation (Fink & Resnick, 2001).

The High School Principal
The role of the high school principal and the conditions they work in have
become increasingly demanding (Shen, 2003). Compared to a few decades ago, the
58
role of the high school principal has changed considerably. It was common to see
mostly white male principals with expertise in traditional comprehensive high
schools performing mostly managerial duties such as sorting out human resource
issues and maintaining the physical security of the campus. In today’s high school
the role of the high school principal has become more multifaceted and conflict laden
(Shen, 2003).
Overwhelmingly the research shows that the role of the principal is important
and that having a strong principal results in a well performing school. Effective
principals today, however, no longer play the role of the headmaster making all the
decisions. Nor do they delegate essential responsibilities, such as curriculum and
instruction, to assistant principals. Today’s high school principal and co-
administrators act as key players and work with a team of dedicated classroom
teachers (Marzano, 2003).
Current high school principals’ responsibilities, like their preceding
colleagues, still contend with management responsibilities and activities from past
years such as athletic programs, interacting with the public and managing human
resources. In a survey conducted by the National Center for Educational Statistics
(NCES, 2000), a sample of high school principals reported that additional
responsibilities supplement their traditional roles, and that although instructional
leadership is the focus, management tasks still occupy more time than leadership
initiatives. Despite this, high school principals today, particularly in urban high
schools, are also expected to be instructional leaders.
59
Principals in countries such as Denmark have an advantage over American
principals. American high school principals, especially those in urban zones, are
often absorbed in dealing with dilemmas that are not necessarily related to the
academic teaching and learning process. Not only does the school system in
Denmark do a better job educating students in the first nine years of a child’s
education, their high schools and class sizes are smaller and interscholastic sports
programs are organized and managed by their municipalities, not the school systems
(Tucker, 2003). Nevertheless, many of the management tasks that high school
principals are responsible for are important and cannot be neglected. High school
principals’ days are filled with an abundance of management activities. They attend
meetings, handle crisis situations, interact with parents and community members and
problem solve the multitude of typical situations that arise in any high school, many
of which are related to athletics, school security, employee associations and other
non-academic issues that don’t have a direct impact on students. Most principals
spend relatively little time in classrooms and even less analyzing data and
instructional practices with teachers (Fink & Resnick, 2001).
Almost certainly the most important element of public K-12 school is
teaching and learning, yet this function in schools is often the most unsupervised.
Even those schools that have devoted time and energy into developing a rigorous
curriculum find there is a difference between the intended curriculum, the
implemented curriculum, and the attained curriculum (Marzano, 2003). The state
and school expect a curriculum to be delivered, however, at the classroom level, the
60
teacher delivers a curriculum of her own. Marzano (2003) defines the attained
curriculum as what the student actually learns.
Marzano’s model of intended curriculum versus attained curriculum
intensifies the need for secondary principals to supervise every step of the teaching
and learning process. Alexander Wiseman (2002) used a meta-analysis for his study
on whether or not the principal’s instructional management activity influenced
school effectiveness, namely student achievement. Although experts in the field of
instructional leadership and educational policy suggest that there is a positive
relationship between the activity of the principal and student performance,
Wiseman’s (2002) findings conclude that principal activity and school effectiveness
are not positively related.
The idea that a principal’s management and leadership style has influence on
a school community has little bearing on how students perform academically is
supported by ideologies such as that of the 1966 Coleman’s report. As Wiseman
(2002) discovered, bias sample selection was not randomized or systemic and may
have sampled on the dependent variable, student achievement. In this case, much
like a teacher in a classroom full of high-achieving students, it is prudent to assume
that students in a high-achieving, middle-class high school will likely perform well
in math or other subjects despite the behavior or leadership style of the principal.
When searching for successful school leaders, one must control for this factor and
look at situations in which strong instructional leadership makes a difference in
schools that have traditionally performed poorly.
61
Kannapel & Stephen (2005) in their research on high performing, high-
poverty schools found that for the most part, high poverty schools did not have
flashy, publicity-seeking principals, but devoted individuals who cared deeply about
the community and about establishing a culture of high expectations, high
performance, collaboration, and mutual respect. These behaviors are not only sound
leadership attributes, but support and reinforce the goals of the instructional program.
Fullan (2002) adds that “charismatic leaders are actually a liability for sustained
improvements” (p. 20). Successful leaders make sustained gains by building
enduring and systemic success and not by becoming high-profile flashy performers
themselves.
If instruction is the focal point of any successful leader, it can be presumed
that high school principals have generally been English teachers, math teachers, and
literacy coaches. Based on anecdotal data, Fullen, Rolheiser, Mascall & Edge (2001)
hypothesize that experienced literacy coordinators are becoming the leading
candidates for principalships. If these types of leaders get promoted in numbers,
they will in turn develop the capacity of teacher leaders in their schools at a much
greater rate than their principals did with them. In addition to the differences in
background and experience, the profession of secondary principals has also made
some progress in terms of racial and ethnic diversity and has doubled the number of
women in secondary principal roles in the past 12 years (Shen, 2003).
As a group of professionals, the image of the high school principal is shifting
not only because of accountability and societal demands, but as Shen (2003) reports,
62
NCES survey data shows that approximately one half of all high school principals
currently on the job plan on retiring in the next ten years. Those principals who
recently entered the ranks of school administration are likely to have been trained in
a standard-based, accountability system and therefore understand the elements of
what a modern high school should be like. Those who transitioned from past
structures and practices need to develop the right philosophy and skills in order to
experience success in modern high schools. Accountability, as designed both by
NCLB and California’s PSAA, places the onus of all students meeting minimum
proficiency standards mostly on the principal. With this in mind, the principal not
only warrants the authority to provide overall direction for instruction, but needs to
be given considerable latitude in defining how resources are spent to achieve the
desired results within their schools (Marsh and Codding, 1990). This shift of
authority in designing programs and innovations at the school level also requires
resources that are readily available for discretionary use by the principal and the
instructional team. Marsh and Codding (1990) assert that the arrangement of having
a principal with authority and fiscal support often makes teachers feel more
empowered as the principal has the ability to approve important proposals locally at
the school site.
Fink and Resnick (2001) describe how District Two in New York City keeps
principals focused on instructional leadership through the use of a system of
principals’ conferences, along with specialized training institutes to ensure that
school leaders share a common view of the kind of learning environments and
63
opportunities its school should be providing to their diverse student body. Having a
well trained principal with support from central office management will likely lead
to longer more sustained improvements in student achievement.
A challenge for school systems throughout the country, however, is principal
tenure. How can high school reform plans be sustainable when many principals are
not present long enough to see plans through? Borman, Katzenmeyer, Barber and
Moriarty (2002) found that principals at 46 schools they were studying in Chicago,
El Paso, Memphis and Miami averaged less than 10 years at their assigned high
schools. Chicago principals had the longest length of average experience with 9.5
years. El Paso had only 5.3 years of average experience. Same-school tenure was
even lower in these states as many principals moved from school to school within the
school district. The highest same-school experience tenure was in Memphis schools
with an average of 7.6 years and the lowest was 4.4 years of experience for El Paso
principals.
Recent accountability programs, such as the PSAA in California, include
sanctions that further exacerbate the problem of principal tenure. Low-performing
California schools in high-poverty areas have average principal tenure of less than
five years (DataQuest, 2004). With the high responsibility and lack of support, more
than half of the superintendents surveyed reported a shortage of K-12 principals in a
1999 California study conducted by the National Association of Secondary School
Principals (NASSP). The top three discouraging factors cited by nationally-surveyed
64
superintendents were: compensation insufficient compared to responsibilities (58%),
too much time required (25%), and job too stressful (23%).
Conversely, low-achieving schools that lose their instructional leader may be
presented with new and promising opportunities when new leadership is acquired. In
spite of this, what can educational institutions do when they are on a successful path
toward reform and their principal leaves? Steven J. Gross (2002) followed a
mentoring program at a reforming high school during the 1999–2000 school year
observing interviews and artifacts from a mentoring program. Gross (2002),
operating under the finding that effective leadership is a common attribute of
successful schools, asked the following question: What happens to the agenda of
curriculum, instruction, and assessment reform at sites when a new leader is put into
place? The first and most essential prerequisite was for Gross to find a mentor and
mentee that were willing to participate in the study as was well as a compatible pair
that is open to working together. Gross (2002) then investigated the mentoring
process in search for patterns that focused on sustaining curricular, instructional and
assessment renewal. Beyond coaching through the typical challenges that a school
principal faces, the mentor-protégé relationship included several scheduled meetings
dealing with many facets of the job including, gathering and organizing information
related to complex problems, working with academic council (site-based
management), discussing the human relations side of problems, and even coping
with the “loneliness” of the job as principal. The content of the regular meetings had
a clear and sustained connection to the curriculum and instructional reform at the
65
school. Beyond the favorable benefits to the new principal of this particular mentor-
protégé relationship, Gross suggests that mentoring of new principals might be an
important alternative to the dilemma of finding sustainable effective school
leadership.
As the role of high school principal continues to shift and becomes gradually
more complex, new and existing school leaders in urban high schools must
understand how to remain focused on improving student achievement in math and
other content areas. Programs like the mentor –protégé program not only support
new or struggling principals, but they aide in getting principals to recognize the often
obscured influence that keep principals from leading their schools toward
successfully meeting their goals.
Boleman and Deal (2003) organize the ideas, concepts and pressures that
leaders face into four frames. The frames function as a set of metaphoric windows
which a leader looks through to make sense of a challenge they encounter. Having a
framework helps a leader navigate through the complexities of leadership and
provides a tool to better understand the organization in order to transform it. Table
2.1 below describes the four frames: structural, human resource, political, and
symbolic.

66

Table 2.1 Overview of the Four-Frame Model
Frame Structural Human
Resource
Political Symbolic
Central
Concepts
Rules, roles,
goals,
policies,
technology,
environment
Needs, skills,
relationships
Power,
conflict,
competition,
organizational
politics
Culture,
meaning,
metaphor,
ritual,
ceremony,
stories,
heroes
Boleman & Deal, 2003
Finding the appropriate frame for a corresponding challenge involves analysis,
intuition and artistry (Boleman and Deal, 2003). Boleman and Deal explain that
technical questions and matters require rationality and logical procedures and are
therefore viewed through the structural frame. When a decision must be acceptable
to major constituents, the human resource, political, or symbolic frames become
more significant.
Principals frequently deal with conflict amongst staff, and in some cases,
conflict between teachers and administration. In such cases, human resource logic
fits best in situations seeking to establish collaboration in order to unify the staff and
school. In cases where a principal is building a program and needs a power base for
support, the political frame will become essential in the approval and implementation
process.
Particularly for a new principal, there are many instances where uncertainty is
prevalent. Not sure of the principal’s agenda, leadership style, or special interests,
67
stakeholders look for symbols that help clarify or bring meaning to any situation. As
ambiguity increases, Boleman and Deal affirm that symbolic frames become more
relevant. While all school leaders face incredible challenges in providing students
with quality learning experiences, the high school principal is currently in the
spotlight. In California, elementary and middle schools have done a fairly good job
in sustaining growth as determined by current accountability measures. High
schools, despite the numerous programs and complexities, must change their current
structures in order to build on the progress their elementary and middle school
counterparts have made. For a high school principal to change instructional practice
in a school that leads to improved student achievement, he or she needs to build in
the staff both an interdependent culture of learning and increasing levels of skill in
specific instructional practices (Fink & Resnick, (2001).

Instructional Leadership
Only when schools improve their student performance are instructional
leadership efforts noticed. When looking at improved math scores over time, is it
possible for a principal to boost student achievement in math when his experience
and background in math is limited? In the 1990’s a different form of leadership
emerged that emphasized transformational leadership and organizational learning
and was grounded more firmly in the empirical study of organizations (Wiseman,
2002). This view places the principal’s main objective on facilitating and guiding
student learning, instruction and curriculum development rather than taking the
68
primary role as instructional leader and supervisor. A transformational leader
inspires others and provides them the resources and tools necessary for both students
and teachers to develop.
Boleman and Deal (2003) elaborate on inspirational leadership and put it into
the context of symbolic leadership. “Symbolic leaders demonstrate their
commitment and courage by plunging into the fray. They take risks and hold
nothing back, they reassure and inspire others” (Boleman & Deal, 2003, p. 361.) In
earlier sections of this review, the capacity of a school has been referred to in several
studies and by several theorists. A primary responsibility for a high school principal
is to build the school’s capacity by not only inspiring teachers and other staff, but by
providing feedback and allowing teachers to develop professionally. As the capacity
of the school is developed, teacher leaders surface and add to the instructional
leadership team’s overall competence.
Fullen et al (2001) describes a process that instructional leaders and
leadership teams follow in order to improve the instructional program. The process
includes reaching a level of awareness, planning, implementation, and reflection. As
the instructional leader or leadership team increases their knowledge and awareness,
the capacity to improve increases. New ideas begin to emerge and instructional
practice begins to refine itself so that both efficacy and talent develop. But the
sharing of new ideas should not only be confined to a single school or district. Other
strategies include inter-visitation (teams of principals visiting schools to examine
implementation of initiatives), monthly principal support groups, peer coaching,
69
study groups, institutes, and the like (Fullen, Rolheiser, Mascall & Edge, 2001).
This type of learning activity contextualizes learning in a way that principals are
members of a team that examine and find solutions to real problems in schools
(Fullan, 2002).
Fullen, Rolheiser, Mascall & Edge (2001) explain the process not only for
individual principals, but for an entire school system that is going through reform. In
year one people experience the difficulties of getting started. In year two people
begin to talk about initial success. By year three people can see that their own skills,
especially the collective skills of teachers and principals together, have developed.
Having a strong leadership team focused on student achievement can have
desirable effects on the overall performance of a high school. But parent and
community participation in school governance, along with pressures for teachers’
professional autonomy, is often perceived by principals to severely limit the space
within their professional leadership (Fink & Resnick, 2001). The principal must then
manage the autonomy of the group and maintain control both of the direction and the
power that the group exercises. Again referencing Boleman and Deal’s (2003) four
frames in the context of managing conflict, the principal must decide which frame to
utilize in order to resolve the problem with the team’s dynamic and ensure that they
remain focused on student achievement.
One of the principal’s most valuable assets is the department head.
Particularly when the principal has limited content knowledge in math, the
department head can provide the instructional leadership necessary to insure that
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math teachers receive support and guidance in delivering effective math instruction
via a rigorous math curriculum. Carter and Ferrucci surveyed twelve department
heads of secondary schools from Singapore and twelve from the United States
exploring possible patterns and relationships from results of the TIMSS study and its
follow up study, TIMSS-R. Specifically, the study assessed the perceptions of
department heads and their department culture and the influence it had on student’s
performance on measures of achievement. Singapore heads of departments
(HoD’s), reported the amount of mathematics classroom time per week ranging from
180 to about 300 minutes. American HoD’s reported the range of mathematics
classroom time per week ranging from 225 to 350 minutes. A significant difference
also transpired in the amount of time HoD’s spent working on departmental issues
outside of their normal workday. Singapore HoD’s spent an average of 18.1 hours
working on department-related issues per week, while American HoD’s spent only
12.7.
Corresponding results based on the TIMSS findings showed that 60% of the
Singapore teachers and 32% of the American teachers reported that they spent more
than 21 hours per week outside the school day preparing for classes or grading
exams (Ferruci & Carter). When asked what humanistic activities they should
undertake to influence the quality of learning in the department, Singapore HoD’s
emphasized the need to be a role model, and expert in the field, and a catalyst for
transforming the department into a caring, professional learning community.
American HoD’s, when asked the same question, also acknowledged their
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responsibility in transforming their departments, but focused their interests on
holding administrators accountable for being educated on current reform issues in
mathematics.
Another disparity that highlights the differences between both countries
culture of teaching and learning relates to the degree that teachers work as a
professional learning community. Singapore teacher leaders implemented
professional learning sessions, tracked student performance, developed departmental
lesson plans and mentored new or weak teachers. United States teacher leaders
preserved individual teacher autonomy and made no mention of shared planning or
use of departmental lesson plans.
Although teacher observation, coaching and modeling in the classroom are all
effective practices, teachers still need time to collaborate in a formal setting with one
another. Despite compelling evidence indicating that working collaboratively
represents best practice, teachers in many U.S. high schools continue to work in
isolation (DuFour, 2004). The goal is for teachers to use their planning time and
even voluntarily outside of their contractual time discussing student learning rather
than brainstorm on why students cannot learn. Each individual teacher and
department contributes to instructional leadership when they take on the
responsibility of improving teaching and learning and engage in activities that relate
directly to improved student learning.

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Summary

Numerous sources clearly convey that math student achievement in U.S. high
schools is unacceptably low. Furthermore, the increased expectations placed on
students do not conform with the design of most American high schools. Modern
high school design must have a curriculum and central theme or focus that is relevant
to student interests and current issues. Ark (2002) suggests that high schools be a
place where students address complex issues such as globalization, environmental
degradation, terrorism and implications of new technologies.
For those students in high-poverty urban schools, the problem of low
achievement and math performance is even greater. When studying the impact that
schools and teachers have on student achievement, Marzano (2000) found that
schools and teachers combined only have 20 percent of the variance in student
achievement. The remaining 80 percent of the variance in student achievement was
attributed to the student. Despite the limited extent of variance schools and teachers
may have on student achievement, Marzano also points out that a school can still
control how a student performs in any academic content area when looking at factors
that a school can control such as instruction, curriculum, school culture and parental
involvement.
An average student who spends two years in the same math classroom with
the same math teacher is likely to maintain their average rank. When placed in an
effective classroom with well-designed curriculum and effective teaching practices,
that same student may climb to proficient or advanced levels. Because schools can
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have such a significant impact on student achievement, it is critical that they put into
effect policies and practices that support student learning (Miller, 2003).
While expectations for all math students should remain high, creating a
curriculum that is feasible for students to succeed in becomes imperative. Due to the
extensiveness of math standards that students are expected to master, it is important
the states, and definitely schools, distill their current standards and benchmarks into
a core set of essential standards and eliminate those standards that are not essential
for students to learn. Anyone can argue that all math standards are important, but
given the time teachers and students have for teaching and learning, it is critical that
essential standards are identified and prioritized for learning. When identifying
essential content, it is also important to consider what knowledge and skills students
will be held accountable for school-level and state assessments (Miller, 2003).
Students can only achieve high levels of success when their teachers deliver
effective instruction. To positively influence teacher effectiveness in the classroom,
schools need to implement coherent, meaningful professional development programs
that ensure that teachers are given adequate time and support to put what they have
learned into practice (Miller, 2003). In addition to time, teacher capacity develops as
teachers collaborate in professional learning communities (DuFour, 2004) and share
solutions to common teaching and learning problems. Teachers also need time and
targeted training in areas in which they struggle in order to bring about considerable
student learning.
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Along with recruiting and developing effective teachers, the implementation,
curriculum, resources and design of any math program should be led by the
principal. Thus, a school leader, in order to have a direct impact, would greatly
benefit by having some expertise in the field of math. A random search of the
credentials held by many of the principals in Southern California yields very few
results of high school principals having any background in mathematics. In spite of
this, principals need core content knowledge, as well as management skills, to inform
and lead change (Miller, 2003).
Instructional leadership need not be provided solely from the principal.
Informal leadership roles can play a central emphasis of school activity more directly
onto instructional improvements that lead to enhanced learning and performance
(Supovitz & Poglinco, 2001). In successful urban high schools that have built
capacity within their schools, Fullan (2002) has found “principals focused on the
development of teachers’ knowledge and skills, professional community, program
coherence, and technical resources” (p. 16). The principal, however, should be the
chief instructional leader who not only implements a successful math program, but
monitors its progress and success based on the rate and level of student success.
Anecdotal data gathered from an America’s Choice study (2000) suggests
three themes that emerged as crucial elements for successful instructional leadership.
First, principals nominated as instructional leaders by their peers organized their
schools around an emphasis on instructional improvement supported by a distinct
vision of instructional quality. Second, leaders cultivated a professional learning
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community of instructional practice in their schools, creating environments for
teachers to engage in their work and drawing upon a wide network of individuals to
deepen their work. Third, instructional leaders restructured their own professional
practices, priorities, and time to support instructional improvement. Successfully
implementing these themes and monitoring the development of a professional
learning community will result in increased student achievement in math and other
content areas.
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CHAPTER THREE

METHODOLOGY

Introduction

This chapter begins with an overview of the school that was the subject of
this study and the instrumentation, data collection, and data analysis processes. This
study investigates the best practices, organizational structure and leadership in an
urban high school that has produced high student achievement results in math for
three consecutive years or more. The study also explores specific programs,
curriculum and any policies that contributed to the improved math results. Of
particular importance is how leaders in the school resolved dilemmas about
instructional leadership. A Southern California High School was selected for study
using a school profile instrument that identified schools based on a set criteria. Data
from student achievement, teacher and administrator questionnaires, observations
and interviews were used to answer 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 at the school?
3. What change process did the school use to enhance the math
program and strategies to assist students in math?

77
4. To what extent was strong instructional leadership important in
improving A) the math programs/strategies and B) math
achievement among students?
5. How did instructional leaders respond in academic areas in which
they were not experts?
The methods used in this research study are qualitative and descriptive-
analytic. These methods led to a concerted study and analysis of a high school that
has demonstrated success in improving and sustaining student achievement in math.
The instruments used included observations, open-ended interview questions and
itemized questionnaires designed to capture the philosophies, practices and behaviors
of teachers, students, administrators and support staff. A case study approach was
employed in order for the researcher to capture, in-depth the practices, events and
themes that take place in a natural setting (Creswell, 2003).
Through observation, interviews and teacher surveys, the researcher analyzed
descriptive data that was gathered during five visits to the research site. The themes
that surfaced in the data analysis process were evaluated on five conceptual models
that served as a guide in measuring the school’s practices and their feasibility of
being generalized or replicated in other settings. The conceptual frameworks used in
this study were developed by the research team and based on research-based models
that serve as a valid tool to gather and report reliable findings.

78

Sampling Criteria and Process
A purposeful sampling process was used in order to provide an opportunity to
conduct a thorough investigation and to explore more deeply the processes related to
the research questions of this study. The school selected for the study was chosen
consistent with the following criteria:
1. Improvement in math achievement as evidenced by results on the California
Standards Test (CST) in Algebra I.
2. Student diversity as defined by a student population of at least 50% from
traditionally ethnic minority groups.
3. Public high school in the Southern California region of at least 1200 students.
4. An Academic Performance Index Score of at Least 600
5. A State Wide Rank of 5 or higher
6. Leadership stability as defined by a Principal being at the school for at least
three years during the time the improvement was made.
The eleven members in the cohort group led by Dr. David Marsh, at the
Rossier School of Education in the University of Southern California, 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.
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2. The data file was exported into Microsoft Excel to create a spreadsheet that
was used to analyze and filter the available data in an effort to identify
schools fitting the profile.
3. Knowing that the group would need to research improvement in CST in
Algebra in a later step and that many schools would not have demonstrated
improvement, the group set a goal of a sample size of no less than 100
schools in the southern California region.
4. Preliminary efforts to use more stringent requirements did not yield a
sufficient sample so adjustments had to be made. For example, when the
student enrollment parameter was set to 1500; the percentage of minority
students was set at 65%; the statewide rank set at 6 or higher, the sample was
limited to only 28 schools in southern California.
5. The second iteration included adjusting the parameters to an enrollment of no
less than 1200; a minority population of 50% or more and a statewide rank of
5 or higher. The sample population then rose to a satisfactory level of 110
schools in the southern California region.
6. Students in the group were then assigned to research 10 schools each by
looking up and recording CST scores in Algebra I for the years 2003, 2004
and 2005 onto a common spreadsheet which one person in the group
compiled.
7. The group then assigned an absolute value to the improvement made in two
areas. First, decreasing the number of students scoring in the bottom two
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performance bands; and second, increasing the number of students scoring in
the top two performance ands. These totals were added to indicate an overall
level of improvement. For example, if a school decreased the numbers of
students scoring in the bottom two performance bands by 3% and increased
the number of students scoring in the top two performance bands by 5%, the
school would have an overall improvement score of 8%.
8. The group then reviewed the scores of all schools in the sample and
eliminated any school that:
a. Evidenced a decrease in the number of students scoring in the top two
performance bands from 2003 - 2005.
b. Evidenced an increase in the number of students who scored in the
bottom two performance bands.
c. Failed to evidence an overall improvement score as calculated in the
example detailed in number 7 above.
9. Using this process resulted in 44 schools qualifying for the study.
10. A geographic map was then developed of the qualifying schools to help
cohort members select a school for their study based on geographic proximity
and other relevant factors.
Bailey High School’s principal and central office leadership in the Bailey Unified
School District accepted the request to participate in this study and became the focus
of for this individual research study. Other members of the research team followed a
similar process in identifying their research sites. The research team began meeting
81
in a collaborative cohort model in January of 2006. At that time, research questions
and relative research was discussed in preparation of this 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 chosen sites.
A flyer was distributed to all potential participants of this study. The flyer
included a detailed description of the research procedures, purpose, and objective of
the study and also indicated that participation in the study would remain anonymous
and was 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. The recruitment letter for teachers was
placed in their individual mailboxes, and again, clearly stated that participation in the
study was completely voluntary. Teachers read the letter and were asked to
participate in the study by completing and returning a questionnaire. Returning the
completed questionnaire without any involvement from their principal or any other
superior, denoted agreement to participate, thus, no further consent letters were
necessary.
The subjects involved in this study were limited to teachers and administrators.
Students were not part of the study. 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 subjects consisted of all teachers, math teachers and other
personnel who appeared to have a leadership role at the school. As the research
82
progressed, other education professionals within the school were identified and were
asked to participate in the study. If and when the educational professional agreed, he
or she was provided with a recruitment letter specifying the purpose and process for
the study.
All administrators at the research site were recruited in the same manner as
teachers. In some cases, district level administration or other school district support
personnel were directly involved with the math program at the school. In such
cases, the administrator or central office support professional was asked to
participate in the study. He or she was provided with a recruitment letter specifying
the purpose and process for the study.
The Principal Investigator and Co-Investigators working on this study visited
research sites between 4 – 10 times consisting of approximately three to seven hours
per visit from September 2006 until January 2007. The visits included observation,
interview and other research activities related to this study. The Principal
Investigator, Co-Investigators and Graduate Student Research Assistant met to
evaluate and discuss research findings gathered at individual research sites. Ongoing
meetings and electronic mail discussions also took place between the Principal
Investigator and Co-Investigators to insure that deadlines were met while 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.

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Overview of the School

Bailey High School is a comprehensive 9 – 12
th
grade high school located in
the city of Bailey and part of the Bailey Union School District. This district serves
13,231 students and has a total of 5 comprehensive high schools, 1 alternative high
school and 1 continuation high school. Bailey Union High School District is located
approximately 10 miles southeast of downtown Los Angeles. It comprises
approximately 41.65 square miles. Bailey High School located in a residential area
in the city of Bailey, has been serving students and their families since 1900. The
current enrollment of 2338 includes students who live in one of five cities and some
unincorporated areas of southeast Los Angeles County. Bailey High School has
made steady increases both in their Academic Performance Index (API) and in their
Algebra 1 California Standards Test Scores (CST). API scores went from 616 in
2003 to 682 in 2005. The API score for 2004 went down 7 points to 609 but then
improved by 73 points the following year elevating its state rank to fifth.

Table 3.1 Academic Performance Index and Algebra Proficiency – Bailey High
School
2003 2004 2005
API 616 609 682
Increase in CST
Algebra
% Proficient
4% 9% 8%

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Since the 2003-2004 school year, Bailey High School has increased the
number of students in its two performance bands in CST Algebra scores by 4% and
decreased the number of students in the bottom two performance bands by 16% with
an overall improvement of 20% in the past three years. For the 2004-2005 school
year, Bailey High School met school-wide and comparable improvement API targets
for all subgroups and also met all federal annual yearly progress (AYP) requirements
under the No Child Left Behind Act.
Table 3.2 Performance Band Changes from 2003 – 2005

Increase in Top Two Quintiles 4%
Decrease in Bottom Two Quintiles -16%
Algebra I Total Gains 20%

Demographics

The total population of students at Bailey high school for the 2005-2006
school year was 2,330 students.
∞ 13% English Learners (mostly Spanish-speaking)
∞ 1% African American
∞ 1% Asian American/Pacific Islander
∞ 84% Latino
∞ 13% White/European American
∞ 53% Low-Income
∞ 49% Parents with some college
∞ 16% Parents with college degree

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School Principal

The principal at Bailey High School has 14 years of experience as a school
administrator and has been the principal at Bailey High School for the past four
years.
Teachers
∞ 26 Average class size in English
∞ 34 Average class size in history
∞ 28 Average class size in math
∞ 32 Average class size in science
∞ 83% Fully credentialed
∞ 10% Currently in teacher credential training programs
∞ 7% Emergency permit waiver
∞ 10 years of average teaching experience
∞ All math courses are taught by a teacher with appropriate subject
matter authorization as defined by NCLB

Selected Participants

Six teacher participants were selected for formal interviews that lasted
approximately 30 minutes each. Three interviews were conducted with those
recognized as key leaders at the school. Key leaders included the principal, the
assistant principal assigned to curriculum and instruction and the math department
chair. In some cases, teachers that participated in interviews also had leadership
roles and gave input and information related to leadership in the math department
that contributed to increased math achievement.
All teachers in the math department and all other non-math teachers were
asked to complete a questionnaire. All math teachers responded to the math teacher
questionnaire and 58% of non-math teachers responded to the non-math teacher
questionnaire. Teachers new to Bailey High School were excluded from the
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questionnaire and interview process given that a large proportion of the questions
were related to improvement and the change process over a four year period of time.

Instrumentation

Various data collection instruments and conceptual frameworks were
developed in order to gather the data necessary to answer the research questions
stated above. Eleven doctoral students that formed the parallel dissertation group
were divided into groups in order to develop the instrument tools. Members of the
dissertation group then agreed on the final instruments based on the relevant
literature related to math achievement and successful leadership in schools. Each of
the instruments were designed to elicit information and data that that would later be
examined and studied. The group then shared the various literature on school reform
and formed a structure that would enable each of the researchers to have a
framework that would guide the data collection and analysis process of this study.
After careful review and several revisions, five conceptual frameworks were
developed.
Data Collection Instruments
Four data collection instruments were developed by the research team in
order to collect data and to interpret it by way of the conceptual frameworks. The
school profile, teacher interview guide, key leader interview guide and teacher
questionnaire were the research tools employed to gather the data.

87
School Profile
The school profile, gathered most of the demographic and student
performance data that lead to the final selection of the research sites. The first
section of the school profile centers on demographic indicators such as school size,
ethnic breakdown, percentage of students receiving free or reduced lunch and other
subgroup data as defined by AYP. The sources used to find this data were mostly
the California Basic Education Data System (CBEDS), and the School
Accountability Report Card (SARC).
The second part of the school profile focused on the human resources
available at the school. This section provides valuable information on the average
years of experience of the teaching staff, compliance with NCLB highly qualified
teacher standards and the number of years each teacher has been employed by the
school. Administrator data is also part of the school profile and centers on the
number of years the leader has been a school site administrator, the number of years
at the high school, and background experience in math.
Data on student performance makes up the final section of the school profile.
Much of the data was located on the California Department of Education’s Website,
College Board reports, SARC, and the school’s master schedule. Student
performance data includes graduation rates, percentage of students scoring proficient
in math, percentage of students taking the College Board SAT exam, percentage of
students meeting A-G college entrance requirements and other student achievement
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data. The data collected in the school profile is all relevant to the literature related to
school reform and effective math programs.
Teacher Interview
All the math teachers at Bailey High School were interviewed using a teacher
interview guide, developed by the research team. Three teachers in the math
department were new to Bailey High School and were not interviewed. This
instrument consisted of seven questions based on the literature reviewed for this
study and relate directly to the study’s research questions. Teachers were asked
about their own professional background and training, what they felt contributed to
improved student achievement in math, the teaching strategies they employed in
their math courses and the role of the school’s leadership in the development and
implementation of the math program.
Key Leader Interview
The literature on instructional leadership and effective math programs
identifies instructional leaders not just as school principals, but as other
administrators or teachers who emerge to take on the role of leading a successful
program. Therefore, the key leader interview guide, was used with school
administration and any other teacher, department head, or district-level personnel
taking on the role of instructional leader. The key leader interview guide consists of
five sections addressing each one of the research questions. The questions in this
guide focus on the leader’s motivation for making decisions that led to improved
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student performance in math and how the leader views the change process with
respect to Boleman and Deal’s (2003) Four Frame model.
Teacher Questionnaire
Two versions of the teacher questionnaire, were developed. Each tool
consisted of 48 questions using a five point likert scale. The first version of the
questionnaire was developed specifically for math teachers that were part of the math
department at the research site. Version two was designed for and distributed to all
other teachers who teach at least one course at the research site. Both questionnaires
are divided into four sections each addressing research questions two, three, four and
five. The questions in this instrumentation tool 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 3.3 Teacher Questionnaire
Data
Collection
Instruments
RQ1:
Patterns of
math
achievement
RQ2:
Policy
initiatives
RQ3:
Change
process
RQ4:
Instructional
leadership
RQ5:
School
leader
not
expert in
math
School
Profile
X X
Teacher
Interview
X X X X X
Key Leader
Interview
X X X X X
Teacher
Questionnaire
(one & two)
X X X
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Conceptual Frameworks

Conceptual Framework A – School Design

The School Design conceptual framework is made up of four areas:
curriculum, school culture, learning activities and student performance assessments.

School
Design
Curriculum Learning
Activities
Challenge
Students to
Think
Students
Solve
Problems
School
Culture
Based on
Enhanced
Learning
Meaningful
Staff-Student
Interactions
Ongoing
Professional
Development
Collaborative
School -to-Career
Applications
Constructivist
Knowledg e
Based on
Student
Outcomes
Student Performance
Assessments
Capture
Conce ptual
Understanding
Capture
Problem
Solving
Cap ture
Communication
Skills

In this framework, developed by Marsh and Codding (1999), high schools are
designed based on those elements that affect the teaching and learning process most.
It offers a broader view at how a school operates and those factors that impact how
and under what conditions students learn best. In the context of this study, a student
may achieve well in math due to circumstances other than a well-designed math
Figure 1. School Design

91
program. Other cultural factors such as meaningful staff-student interactions could
have been the cause for higher achievement in math and other content areas.
The school design framework assumes that a well designed curriculum based
on student outcomes can result in higher levels of learning. The curriculum is
closely connected to student performance assessments given that how students
perform on assessments that focus on the students’ understanding of the content,
their problem solving skills and communication skills dictates what the curriculum
will look like. Learning activities that students engage in, are also part of this
framework. Judith A. Langer conceptualizes student learning as occurring in an
environment in which students and the teacher participate in thoughtful examination
and discourse about the content being learned. After the content has been taught and
the learning has been assessed, teacher and school leaders can then analyze results
and target professional development activities if necessary. High schools should be
organizing themselves to support this concept of professional development as an
integral part of their strategy for getting all students to standards (Marsh & Codding,
1999).
Many high schools have redesigned themselves into smaller learning
communities. In such cases, a student may be part of a program that has an
industrial or occupational theme that is of high interest to the student. Marsh and
Codding (1999) purport that these kinds of programs may provide the motivation
needed for the student to be in school and to eventually meet rigorous standards in
math and other content areas. Having these alternative routes that are more
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appealing to students can lead to the same goal that educators and students often find
difficult to reach.
The design of a school, including curriculum, assessment, learning activities
and school culture has an impact on the degree of learning that takes place in every
classroom. Particularly in urban high schools, it is challenging to reach a stage in
which all students perform at high levels in math and other content areas. For those
urban high schools that have accomplished this goal, the struggle is to sustain the
success, but for those that have not yet reached the objective of all students reaching
proficiency in algebra, changing the system and how math instruction is delivered is
the challenge.
Conceptual Framework B – Change Process
Change requires frameworks and tools that help a leader navigate through the
complexities of leadership and to better understand the dynamics of the organization.
Boleman and Deal (2003) offer a framework that is widely used in corporations and
other organizations. The framework includes four frames; structural, human
resources, political and symbolic. The value of this framework is in the multiple
dimensions it presents. (See table on following page):

93
Table 3.4 Boleman and Deal’s Four Frames
Structural Human Resources Political Symbolic
Top Down
Hierarchies
Employees as
Partners & Family
Power Vision
Rules, Policies,
Procedures
People of the
Organization
Bargaining Belief and Faith
Specialized Tasks Productivity
through Group
Effort
Compete for
Limited Resources
Stories
Goals &
Objectives
Self-actualization Negotiations Culture

High schools can make the change process very difficult by being resistant to
meaningful change. On an organizational level, high schools include multifaceted,
sometimes irrational systems that have multiple goals and layers of complicated
political arrangements. To gain approval for change within such a complex
organizational structure as a high school, can be a struggle for principals and other
school leaders. In many cases, change itself is accepted, but a leader may find it
impossible to implement the new strategies successfully. This can be due all or in
part to structural issues that may include poorly articulated goals and objectives or a
human resource issues in which employees (teachers) need additional training.
Boleman and Deal’s (2003) four frames give the leader a set of lenses to help
analyze and make sense of obstacles that inhibit change. The lenses start as tools for
analysis of a problem and then become a means for finding strategies to overcome
the hindrance as leaders find appropriate strategies once they have successfully
diagnosed the problem. It may seem clear that when attempting to increase math
results, the obvious solution is to develop a successful math program. However, to
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successfully implement any effective math program, a leader needs to be mindful of
other forces that may impede on the successful implementation of the program. To
assess the results of how the change process was carried out, one needs to measure
how long lasting effective practices are operationalized within the organization in
order to sustain improved results.
Conceptual Framework C – Math Education
The math education framework draws on multiple sources of research-based
models on effective math programs. Central to effective math programs are three
components: standards-based instruction, curriculum design, and effective classroom
practices. The key in developing effective math programs is that each of these
components needs to be fully implemented. Ball and Cohen (1996) caution that not
incorporating the right elements when designing a program or some initiative for
improvement will likely result in the efforts “misfiring”, for they leave out critical
features of the program such as instruction and instead devote resources, time and
energy to other areas such as recruitment and incentives. (See Figure 2 following
page):

95

Curriculum Design
∞ Student -centered curriculum
∞ Driven by learner outcomes
∞ Emphasizes Conceptual
∞ Focuses on problem -solving
∞ Incorporates current learning
theory
∞ Year -long scope & s equence is
supported by learning theory
Standards Based Instruction
ο Assessments aligned to
standards
ο Student achievement data
drives instruction and
decision
ο Common performance
rubrics through
collaboration
Effective
Math
Programs
Classroom Practices

ο Effective and cohe rent
lesson design
ο Promotes high levels
of student engagement
ο Makes use of prior
knowledge
ο Cultural relevance
ο Accelerated
Interventions

Figure 2: Effective Math Programs

The frameworks for both math education and school design have important
similarities. A student-centered approach is a feature in both designs. Just as the
various elements of a school should be designed and based on student outcomes, an
effective math program includes a curriculum that is driven by learner outcomes as
well. Students are therefore tested on standards-based assessments that measure
students’ conceptual understanding followed by curriculum, instruction and learning
activities designed to close the learning gaps identified in the assessment process.
96
As Ball and Cohen (1996) indicated, classroom practices, namely
instructional practices, are often neglected when designing a math program. If a
math curriculum is to be standards-based, then the instruction that students are
rendered given should complement the rigor of the content. Kinard (2000) defines
rigorous mathematical thinking as “the synthesis and utilization of mental operations
to perform critical examination, analysis, introspection, and ongoing monitoring of
the structures, operations, and processes” (p. 2). If high school students, particularly
those that have struggled with math for several years, are expected to think through
rigorous mathematics, the classroom practices that are part of this framework must
be employed. In some circumstances good instruction may be taking place.
However, in many urban mathematics classrooms sound research-based instructional
practices are absent. In these cases, the need for strong instructional leadership to
monitor instruction and to improve the capacity of math teachers is necessary.

Conceptual Framework D – Instructional Leader

The Laboratory for Student Success (LSS) at Temple University has
developed standards for school leadership practice. The standards center on the need
for principals and other school leaders to be instructional leaders who strengthen
teaching and learning, professional development, data-driven decision making and
accountability. In addition to instructional leadership, the LSS proposes that school
leaders be community leaders that advocate for school capacity building with various
community partners and to be visionary leaders that demonstrate energy,
97
commitment and entrepreneurial spirit toward the goal that all students will learn at
high levels.
Table 3.5 Instructional Leadership Framework
What an effective leader must have knowledge of…
Vision for Learning Supervision and
monitoring of
instruction
Community and
Political
Culture of
Teaching and
Learning
Data Driven
Decision Making
Analysis
1.0 - Facilitates the
development,
articulation,
implementation,
and stewardship of
a vision of learning
that is shared and
supported by the
school community.

A- Developing
vision
B- Communicating
the vision
C- Implement the
vision
D- Monitor and
evaluate the
vision
E- Addresses
obstacles to
vision
implementation
and realization

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

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

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

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

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

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

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

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

The framework for instructional leadership employs the LSS standards along
with other research-based models of instructional leadership. In this framework, a
vision for learning, supervision and monitoring of instruction, political and
98
communal contexts, culture of teaching and learning, and data driven decision
making are all focal themes in effective instructional leadership. Leaders whose
primary function is to guide the learning that takes place in their school will not only
understand, but practice the behaviors that are associated with these five themes.
When identifying causes for improved or sustained student achievement, the
causes may be related to instructional leadership. A visionary leader’s energy and
conviction may motivate an entire learning community resulting in higher student
achievement. In some cases, a leader can apply one theme very well and be less
effective in another. This framework will assist the researcher in identifying whether
instructional leadership influenced improved math achievement, and if so, what
elements of the leadership had the greatest impact.

Conceptual Framework E – Instructional Leader
It would be prudent to assume that many high school principals and other
educational leaders are not math majors and, with the exception of coursework in
college, have a limited mathematical background. The final framework was
designed by the research team in order to measure the level of math expertise for the
principal at each research site. (See Figure 3 following page):

99

The framework provides a flowchart that begins by assessing whether or not
the principal is deemed highly qualified (HQ) under federal NCLB requirements. If
the principal is HQ, then he or she possesses a credential to teach high school algebra
Figure 3. Assessment of Principal’s Expertise in Math
Level 1
Is the Principal
HQT Compliant?
Yes No
High
Expertise
Level 2
Does the
Principal have a
credential or
major in math?
Yes No
Medium
Expertise
Does the Principal
have a minor or
taught math?
Yes No
Medium
Expertise
Low
Expertise
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or higher and is a level 1 principal with high expertise in math. If the principal is not
highly qualified and is either a college math major or has taken the supplemental
coursework and state-level testing to be eligible for a California teaching credential
to teach high school algebra or higher, then the principal is deemed a level two with
medium expertise. The final level assesses whether the principal has a college minor
in math or has taught high school math at one point in his or her career. If the
principal has a minor in math or has taught at least one coarse they are considered to
have medium expertise. If the principal has never taught high school math and does
not posses at least a minor in math then they have low expertise.
This framework addresses research question five and seeks to understand
how the school leader resolves dilemmas about instructional leadership related to
math. With high expertise, the school leader is likely to approach dilemmas with the
math program differently from a principal with low expertise. If the principal is not
proficient in math and cannot closely participate in activities such as the delivery of
professional development and curricular design, the study seeks to find how the
principal or school leadership provided, if at all, the necessary leadership to guide the
learning process in math.

Data Collection

The data collection for this study was conducted between October 2006 and
December 2006. Over the course of the three months, five rounds of data collection
were made at the research site that consisted of four partial days and one full day.
101
One additional visit was made to conduct key leader interviews at times that were
convenient for the subject. Each of the five rounds of data collection included the
disbursement and gathering of completed teacher questionnaires, teacher interviews
and key leader interviews. During the various stages of the data collection process,
participants were informed and reminded that their participation was strictly
voluntary. The fact that participants are busy professionals working with students
was respected and every attempt was made at respecting instructional time, while
collecting valuable and reliable survey and interview data.
The school profile was the initial data collection tool used to identify the
research site and later to collect data regarding demographics of the school and
student achievement in algebra. Prior to contacting the principal at the research site,
most of the data collected in the school profile was gathered by way of Dataquest
and Ed-data , both tools are available on the California Department of Education’s
website (www.cde.ca.gov) and make their information available to the public. In the
first round of data collection at the research site, the remainder of the school profile
was completed when the school’s principal provided the school’s master schedule in
order to collect data on A – G offerings and other information such as the number of
parallel courses that support the algebra program at the school.
Prior to beginning the rounds for data collection at the school, the researcher
scheduled a meeting with the school principal to discuss the process for data
collection including a schedule for when the researcher would visit the school for
disbursement and collection of the teacher questionnaires and to conduct teacher and
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key leader interviews. It was at this time that the school principal provided the
researcher with a copy of the master schedule, bell schedule and a faculty and staff
directory. The researcher again explained the purpose and process for this study and
emphasized the need for teachers and other participants to voluntarily participate and
feel unbound from the need to participate due to any influences from the researcher
or other staff member.
The first round of data collection was an overview of the study to all teachers
and key leaders at the research site. The overview was a reiteration of the
information in the recruitment letter given to teachers in October 2006 which
described the nature of the study and the function of participating subjects if they
agreed to participate in the study. Participating subjects provided the researcher with
convenient dates and times for individual teacher and key leader interviews. Teacher
questionnaires and a cover letter were placed in participating subjects’ mailboxes
later that day.
Round two included the gathering of any teacher questionnaires that were not
returned to the researcher or to the school secretary during the first round of data
collection. Before any individual interview, the researcher reassured the study
participant that any and all the information provided would be kept confidential and
safely stored on a computer hard drive and recorder only accessible to the researcher.
The remaining rounds of data collection included teacher and key leader interviews
including an interview with the principal and other administrators at the research site.

103
Data Analysis
The purpose of this study was to investigate and understand the pattern of
math achievement and how instructional leaders sustained math improvement at the
selected research site. Specific attention was given to how instructional leaders
overcame dilemmas related to the change process and what programs and curriculum
were used to improve and sustain student achievement in math. The qualitative
research and data analysis methods were used in order to purposefully select both the
participants and the site that would best help the researcher obtain and understand the
data related to the research questions (Creswell, 2003).
Key leaders/teacher Questionnaires- Data from the questionnaires was entered in a
database and descriptive statistical analysis was conducted in order to determine
frequency and mean for each response item.
Qualitative Data- A total of 6 math teacher interviews and 3 key leader interviews
were taped, scripted and reviewed in order to find key/saleable points related to the
topic under study.
Summary
This chapter discussed the research methods used in the study, which
included a description of the research design, sample, conceptual frameworks, data
collection instruments, and an overview of the data collection process used to
analyze the data findings. These methods provided a sound basis for collecting,
analyzing and synthesizing the data that would result in the research findings and
corresponding analysis found in the following chapters.
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CHAPTER FOUR
ANALYSIS AND FINDINGS
The aim of this study was to investigate the patterns of math achievement at a
Southern California High School, and to identify the policies, programs, processes
and leadership strategies within the school, particularly in the school’s math
department. This chapter presents the data that was collected in the study, along
with an analysis of the findings.
The focus of this case study was to ascertain and analyze the relationship
between the math department’s characteristics and how those characteristics led to
sustained gains in algebra, geometry, algebra II and other math content areas.
Because the research site has had ongoing improvement in math after being
identified as a program improvement school, there was an additional focus on the
change process and how it relates to increased math achievement.
The data for this study was collected using the following instruments:
∞ Evidence-based interviews with six math teachers who teach various math
courses
∞ Evidence-based interviews with three key leaders at the research site
including the principal, assistant principal, and the math the department chair
∞ A likert scale questionnaire for all non math teachers at the research site
∞ A likert scale questionnaire for all math teachers at the research site
∞ A data collection grid that recorded math achievement results for each of the
school’s significant subgroups

The data collected for this study was analyzed using the conceptual frameworks
presented in the previous chapter. The frameworks were aligned to the research
105
questions that were developed to guide this study. The five research questions
developed for this study were:
1. What was the pattern of math achievement for various students at
the school?
2. What policy initiatives as well as curriculum, instruction/and
related conditions seem to be related to improved math
achievement 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 instructional leaders respond in academic areas in which
they were not experts?

Research Question One:
What was the pattern of math achievement for various students at the school?

Student Subgroups
There has been both change and growth at Bailey High School (BHS)
during the past ten years. Total enrollment in 1987 was nearly 650 students
lower than the current enrollment. The most significant subgroup, Latino
students, was 12% lower twenty years ago than in 2006. More recently, in the
106
past four years just after BHS was identified as a program improvement school,
the total enrollment for the 2002-2003 school year was 2,204 and grew to 2,467
for the 2005-2006 school year. The increase of just over 10 percent represented
not only a change in the total number of students, but also a change in the
demographics and makeup of the student body at Bailey High School.
Along with changes in enrollment numbers, BHS has had a change in the
percentage of students that speak a language other than English at home. The
school also experienced a shift in the ethnic taxonomy and the socioeconomics of
the community that is served. Like many other high schools in Southern
California, BHS’s percentage of students identified as English Learners has
increased during the past decade. Out of the 305 English Learners at BHS, 13%
are at lower levels of English development and 87% have been redesignated as
English proficient students. The dominant home language of English Learners is
Spanish. Other home languages represent only 1% of the English Learner
population.
Student ethnic background has also undergone a dramatic shift in the past
decades, and although the rate of the shift has slowed, the increase in the
Latino/Hispanic subgroup continues to grow. The largest ethnic subgroup is
Latino/Hispanic representing 85% of the student population. White/European
Americans represent 13% of the population followed by Asian American and
African American each representing only 1%. The family income of these
students is based on their participation in the federally funded free or reduced
107
lunch program. Fifty-three percent of BHS’s students are low-income based on
the free or reduced lunch indicator.
Thus it is clear to see, that Bailey High School has experienced
considerable changes in the students served over the past two decades. How the
staff at the school responded to those changes, coupled with a new system for
measuring student achievement, was perhaps the reason for the school eventually
being given a program improvement status. The designation of program
improvement status, as defined by the California Department of Education and
approved under the No Child Left Behind Act of 2001, is reached when for each
of two consecutive years, the school does not make Annual Yearly Progress
(AYP) in the same content area school-wide or for any numerically significant
subgroup. The school can also be identified as program improvement if it does
not meet its school-wide Academic Performance Index (API) or high school
graduation targets. The following section of this chapter examines patterns of
achievement after BHS was identified as program improvement and subsequent
sections will investigate how those patterns of growth were sustained throughout
the course of four years.
Patterns of Achievement
The No Child Left Behind Act defines a subgroup as significant when the
percentage of students in a specific group is at or exceeds 10% of the student
population or is comprised of more than 100 students. BHS’s significant
subgroups include Hispanic/Latino, Economically disadvantaged, English
108
Learners, Special Education, and White students. With the exception of the
White student subgroup, every one of these subgroups at BHS has performed low
in math and other subject areas prior to 2003. In the past four years, however,
each of the abovementioned subgroups has steadily increased their performance
in math as measured by state standards-based assessments.
The data that follows will show a pattern of growth for each of the
numerically significant subgroups at Bailey High School. The data will be
presented by subgroup in order to examine the pattern of growth for each and so
that it can subsequently be analyzed for specific strategies and program design
the school may have used to meet the needs of the specific subgroup. Not all the
data presented will show growth. It is important to include this data in order to
illustrate barriers that the school has faced in order to highlight those areas that
have yet to be addressed by Bailey High School. (See Figure 4):

109
Figure 4: Economically Disadvantaged Subgroup
Economically Disadvantaged
0
2
4
6
8
10
12
14
16
18
9th 10th 11th
Algebra 1 % Prof and Above
Grade
Percent Proficient
2003
2004
2005
2006

Figure 4 above shows the performance of the economically disadvantaged
subgroup from 2003 to 2006. An interesting finding is the dip in performance for
all subgroups at the tenth grade. While this steep decline in student performance
is a concern for BHS staff, this trend is consistent with state-wide 10
th
grade
student performance (www.cde.ca.gov). Twelfth grade students are not included
in the analysis because they are not tested by the state STAR testing system.
Economically disadvantaged students at BHS are performing significantly higher
in Algebra and other math content areas in 2006 than they were in 2003. In
2003, only 7% of all ninth graders in Algebra were at proficient or above.
Proficiency levels continued to rise in 2004 to16%, dipped 5% in 2005 and then
110
climbed to 13% in 2006. The same trend emerged in 10
th
grade. A more
impressive gain occurred with the economically disadvantaged subgroup taking
algebra at the 11
th
grade. As Deiger,LaForce & Feranchak (2004) found in their
Chicago Public School study measuring student achievement in algebra, students
who did not successfully pass algebra by their ninth grade year were less likely to
pass in subsequent attempts later in their high school career. Although these
findings were consistent with BHS10
th
graders taking algebra for the second
time, BHS 11
th
graders in the economically disadvantaged subgroup who
performed at proficient or higher rose from 3% in 2003 to 11% in 2006.
Figure 5: English Learner Subgroup
English Learners
0
2
4
6
8
10
12
14
16
18
9th 10th 11th
Algebra 1 % Prof and Above
Grade
Percent Proficient
2003
2004
2005
2006

111
The same trend surfaced for other subgroups taking Algebra 1. English
learners have an added challenge when taking the California Standards Test.
Even in the Algebra or other math subsections of the test, students have to
possess literacy skills and a high enough level of English proficiency to
understand word problems and directions explaining how to solve algebra
equations and problems on the test. Prior to 2005, English learners at BHS were
performing poorly and only few were reaching proficiency levels. In 2005 and
2006, 9
th
graders scoring at proficiency levels were 10% and 16% respectively.
By 2006, the math team at BHS was successful in getting a significant
percentage 10
th
and 11
th
grade English learners to perform at proficient levels.
Figure 6: Hispanic/Latino Subgroup
Hispanic/Latino
0
2
4
6
8
10
12
14
16
18
9th 10th 11th
Algebra 1 % Prof and Above
Grade
Percent Proficient
2003
2004
2005
2006

112
Hispanic/Latino students, the largest subgroup at BHS, had similar gains
in Algebra proficiency. The trends in algebra performance from 9
th
grade to 11
th

grade mirrored those of other significant subgroups. Again, 9
th
graders
outperformed their 10
th
and 11
th
grade peers but all show significant gains during
the course of the four year period. From 2003 to 2006, Hispanic/Latino students
gained 11 percentage points in the 9
th
grade, two percentage points in the 10
th

grade and 10 percentage points in the 11
th
grade. As was the case for all
subgroups, many of the 10
th
graders represented in this data set who did not meet
proficiency levels retook algebra based on the school’s retake policy which will
be described later in this chapter. As evidenced by Tables, 3.1, 3.2 and 3.3,
many of the students who did not reach proficiency levels as 10
th
graders
successfully reached proficiency later in their 11
th
grade year.
From 2003 to 2006, Bailey high school not only increased the number of
students reaching proficiency in algebra and other math content areas, but the
school also decreased the number of students performing at basic, below basic
and far below basic. When analyzing school-wide algebra performance, Bailey
High School increased the number of students at proficiency and advanced levels
by 9% and decreased the number of students at the two bottom quintiles by 12%.
Although many students at BHS have yet to reach proficiency in algebra, many
have moved into the basic level which better prepares them for subsequent math
courses. (See table on following page):

113
Table 4.1: School Wide Algebra Performance
School Wide Algebra & Algebra II Results
Algebra I Advanced Proficient Basic
Below
Basic
Far Below
Basic
2006 1% 12% 27% 40% 21%
2005

0%
8% 35% 41% 16%
2004 0% 9% 34% 43% 15%
2003 0% 4% 22% 45% 28%
Algebra II Advanced Proficient Basic
Below
Basic
Far Below
Basic
2006 7% 17% 31% 31% 15%
2005 0% 8% 33% 38% 20%
2004 1% 3% 19% 46% 31%
2003 2% 9% 28% 42% 19%

Higher Level Math Results
Primarily due to demands from state and federal accountability policies,
there has been a trend in education to reduce the number of students at below and
far below basic levels and to move them into levels of proficiency. This was the
case for BHS, particularly since they had been identified as a program
improvement school. There are, however, students who take course work
beyond algebra II and who are examined by another criteria related to more
rigorous course work such as Advanced Placement (Collegeboard) and tests such
as the SAT and ACT.
114
There are no clear trends in SAT and AP results for BHS. Although
there has been sustained growth for the past four years on CST math
assessments, higher level assessment results associated with students who are
college bound do not show the same results.
Table 4.2 SAT Results
School Year Percent Tested Math Average
2006 40.86 451
2005 45.28 448
2004 43.95 454

The calculus AP program at BHS has suffered. The Assistant Principal
over curriculum and instruction, attributes the problem to the teacher who had
been responsible for teaching the advanced math class. As is the case in many
high schools, usually one teacher is responsible for teaching all advanced math
students. In recent years, the enrollment in the calculus AP class dwindled and
the number of students who felt prepared to take the test also dropped each year.
BHS recently hired a new teacher who started with 70 students and currently has
59 in two sections.
Table 4.3 Advanced Placement Passing Rates
Year Number Tested Number Passed Percent Passed
2006 15 10 66%
2005 23 9 39%
2004 22 11 50%
2003 20 11 55%
2002 9 8 89%
115

The pattern of sustained math achievement in algebra, geometry and
algebra II courses beginning in 2003 for students at BHS was the result of
various planned strategies that took several years to accomplish. The teachers
and leadership at the school and district responded to the school being identified
as program improvement and had to do something about poor performance in
math and English, particularly for English Learners and students in special
education. Before the school was able to implement programs designed for
students who struggle with rigorous math content, the school and district’s
leadership had to reevaluate their program, policies and school level leadership to
carry out the math program in general.
The following sections will be guided by research questions two, three,
four and five and will investigate, by way of responses from the teacher
questionnaire and interview guides, how the school responded to low student
achievement. The key leaders interviewed for this study will be identified based
on their title and the teachers quoted will be referred to by letters in order to
illustrate various perspectives from different teachers and to preserve their
anonymity.

116
Research Question Two:
What policy initiatives as well as curriculum, instruction/and related
conditions seem to be related to improved math achievement at the school?

Federal, state and local policies
Prior to the pressures that derived from federal and state accountability
measures, Bailey High school did not have a sense of urgency in changing its
curriculum, instruction or any other element related to the math program. Because
there was no specific definition of a successful school or a mechanism for measuring
how effective a school was in meeting the needs of all its students, BHS staff was
complacent and there were no initiatives to make changes to the math program and
how instruction was delivered. Results from teacher questionnaires, teacher
interviews and key leader interviews conveyed that the federal and state
accountability programs generated the initial changes in the math program at Bailey
High followed by district and school level policies that transformed the math
department and the math program.
No Child Left Behind – Program Improvement Process
It is quite clear that the program improvement status was the driving force
that triggered the need to make changes in the math and English programs offered at
BHS. Survey results showed that 58% of math teachers and 53% of non-math
teachers at Bailey high school felt that the No Child Left Behind Legislation
promoted increased student achievement at their school. The school’s principal
explained the process that got the school into program improvement.
117
When we got to the school more than four years ago test scores
indicated that it was pretty clear that we really needed to work with a
certain segment of our population in order to get out of program
improvement. BHS was very traditional in the sense that a small
percentage of students, those that came from stable and well educated
families and who were motivated did well. These students were very
familiar with the system and they were very successful.” Although
NCLB was not a policy developed by Bailey High School or Bailey
Union High School District, it did force the school and district to
develop curriculum and instruction that would yield higher
achievement for all student groups (interview, 10.30.06).

Responding to a federal and state policy that sets a goal for all students to
achieve proficiency in math by 2014 was a challenge even for the principal who had
more than ten years experience as a high school administrator. The principal
explained that prior experiences in other high schools he had worked at were
different from what he encountered at Bailey High. For the principal, this particular
challenge was not in a matter of school design, but rather negotiating the differences
in the social and academic needs of the students. At his previous school, a very large
percentage (in excess of 80%) of the students were college bound. The previous
school had been ranked based on graduation rate, average on SAT scores and other
measures that highlighted the students at the top.
This was prior to NCLB and with these kinds of rankings we did not
have to care about those students who were not achieving success;
which is the same students who were having trouble here at BHS.
Those who were not from the affluent part of town were getting
hammered. They were irrelevant with that system of measurement. I
am not 100% happy and in favor with all the policies related to
NCLB, but it has forced us to look at and provide quality services to
all students (interview, 10.30.06).

118
The focus on pulling students up from the bottom quartiles of math
performance was new for BHS prior to the new principal’s arrival. The school was
in need of a new school design if it was going to create a culture in which all
students experienced success. Along with other leaders at the school, the principal
developed a program by redesigning how the school was structured that led to more
students reaching proficiency. Framework A: School Design provides four themes
that are essential to the effectiveness of a school and meeting the needs of all
students. Bailey High School, and particularly its math department, needed to
address all four areas of its school design. With virtually the same resources as they
had previously, BHS staff had to make fundamental changes to its math program
without affecting those that were already experiencing success in math. “I don’t feel
we have neglected upper-end students,” explained the principal, “as a matter of fact,
if nothing else, we are offering more AP courses now than we were four years ago.
NCLB has changed the mentality of even our AP level students in terms of the
support they feel they should have and of AP teachers with respect to how they teach
students. They no longer throw the material at students and expect them to
understand it. The level of support for AP students has improved as well (interview,
10.30.06).”
Also instrumental in the change process was the math the department chair
who had been deliberately placed at BHS by the district leaders. The department
chair also acknowledges that NCLB policy impressed on the school district the need
for change and prompted school officials to begin the reform process by creating a
119
team worthy of carrying out a very challenging task. “Because of NCLB, states the
department chair, “we have not been able to ignore the low end students, not that we
tried to in the past, but it was very apparent that we could no longer do it. We had
programs to help low students before, but now we had to create something that was
more systematic.” The department chair believes that the biggest impact NCLB has
had on BHS is that teachers today must posses a credential.
In the past were able to get some teachers with good people skills that
later developed some good teaching skills. Now we look first for the
credential, and sometimes end up with a teacher with minimal people
skills. Now we find, with the new group, that they need help in how
to deal with students, the curriculum and teaching skills in no longer
the issue. There is still a lot of growth that needs to happen. We
emphasize in the interview the need for teachers to want to grow as
professionals. Because most of them are math majors, the curriculum
is not an area they will need to grow in, it is classroom management,
student discipline that is the area most of our new teachers need to
grow in. I do think we miss some salespeople. We had some teachers
that were very good in selling math (interview, 10.20.06).

The federal No Child Left Behind Policy created a shift in how teachers were
selected at BHS and subsequently, the need for training and professional
development. The principal agrees with the department chair’s opinion on NCLB’s
impact on teacher preparedness for teaching math subject matter and limitations on
finding professionals who have the skills and ability to connect with students.
Technically speaking we have significantly increased the number of
teachers that are highly qualified here at BHS. Virtually every one of our
teachers here is currently highly qualified. I am not always as convinced
that the designation highly qualified means that they are really highly
qualified. I am sure there are situations when things have occurred such
as a football coach who took a few classes in high school and you got him
an emergency credential in algebra and geometry and he really did not
know what he was doing with respect to teaching math. When I first
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arrived here four years ago there was a teacher who had a strong
background in physics and unfortunately had some credentialing issues
and did not qualify under the law’s definition of highly qualified. We
ended up finding somebody with the right credentials and in this instance
the individual that met the designation was in essence a very poor teacher.
In some instances NCLB restricts us from finding good people that work
well with students (interview, 10.30.06).

Not all the leadership at BHS feels that NCLB’s limitations adversely
affected their hiring practices. While some feel that NCLB’s Highly Qualified
requirements limit school leaders to hire only based on credentials and content
knowledge and don’t allow any flexibility to hire those teachers who exhibit
characteristics that are appealing to students, others feel that strong content
knowledge is the basis for good math teachers. The assistant principal over
curriculum and instruction admits that hiring, at first, was difficult. He recalls that
prior to NCLB’s requirements, you could hire somebody to meet many needs even
though they were not necessarily credentialed in that area. In recent years, once
BHS administration got over the initial challenge of filling the numerous math
sections that were taught by teachers without appropriate credentials, finding
credentialed teachers who also possessed other desirable traits related to good
pedagogy was a lot easier. As a result, the assistant Principal feels that BHS now has
a staff that is much better prepared. They have the appropriate background and
subject matter competency. All of the math teachers at BHS are highly qualified,
only two are still in teacher preparation programs working on becoming fully
credentialed.
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Bailey High School teachers have a slightly different perspective on the
impact of NCLB on their practice as teachers. Teacher E, algebra teacher and the
department’s curriculum coordinator, attributes the fact that teachers are now more
accountable to NCLB legislation.
I am not a strong proponent of NCLB but for many years it was too
lax. Showing the data that we do in our departments holds us
accountable as teachers and forces us to see that we are not doing our
job, what are we doing with our students that they are doing so
poorly? So I think the NCLB act in a sense has been the Bunsen
burner under teachers and has inspired administrators to get after
teachers and I know they have to do it in a very diplomatic way
because of contractual reasons but I just think it has been a real good
impetus for us to be better teachers. Being a teacher for 29 years I
have heard, ‘you can teach an old dog new tricks’, well yes you can
(interview, 11.17.06).

Teacher D, algebra II teacher and algebra II course lead, sees that NCLB has
made an impact in some areas, but not others. He feels that NCLB and its annual
yearly progress (AYP) objectives are an unrealistic set of goals, “especially in math
and dealing with the kinds of students BHS has.” He finds that some students have
difficulty with basic arithmetic and need more time to successfully execute higher
levels of math. He does, however, see the federal legislation as having an impact in
that every student has to test and that BHS teachers are at least attempting for every
student to reach basic levels.
Common Assessments
Getting students to achieve at higher levels in math was not only prompted by
federal legislation. Administrators and teacher leaders understood that there were
other accountability measures from the state and their local district that they needed
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to meet as well. BHS was under close supervision from the California Department
of Education based on its program improvement status. The math department chair
remembers joining the BHS staff four years ago and being pressured by school
district officials to “do something”. The district was aiming for all schools to
implement the common assessment program as a method for monitoring progress.
This was a structural change (Framework B) that relates to a change in policies and
procedures for assessing students. The top down policy was also linked to
Framework A: School Design as it builds in an assessment component to the school
that captures students’ conceptual understanding. It was important for the Bailey
Unified School District to get out of program improvement status and to not wait for
the end-of-year test results to see how students were progressing in math and
English. BHS began working on the common assessment system four years before
the other schools in the district and now all schools in the district are being held
accountable for implementing the same system of common assessments.
Other departments at BHS are now implementing the common assessment
program and the analysis that goes with it. As the department chair put it, “common
assessments are nothing new for us.” The math department, based on survey data
and interviews, uses common assessment data to drive instruction. The fact that the
math department has reliable data showing that students have made steady progress
in math makes them believe that the common assessment program is working
effectively. Although 83% of non-math teachers surveyed either agree or strongly
agree that the school has successfully implemented the common assessment program
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to raise student achievement, the principal, in contrast, does not believe that all
departments have successfully implemented the assessment program and thus is
dealing with a broader leadership issue.
Speaking candidly is that math is going gangbusters, science is going
gangbusters, and ironically, foreign language is going gangbusters.
The departments we are struggling with now are English and social
science departments. There may be some validity to what they are
saying, but they feel that the math standards are so much more defined
and lend themselves to common assessments. Our social science
department does not believe, philosophically, in the entire common
assessment process, comparing results, etc. (interview, 10.30.07).

The common assessment policy developed as combined effort between BHS
and the Bailey Union High School District. The assistant principal reported that a
standards-based curriculum accompanied by a common assessment program being
the focus for the entire district has resulted in developing course binders, pacing
guides standards-alike curriculum and that these efforts have pushed BHS more
quickly in the direction of more students reaching proficiency in math.
Much of the push for us has been on the California High School Exit
Exam (CAHSEE)” reports the assistant principal, “there is a much
bigger emphasis on areas such as passing the CAHSEE.” Due to state
guidelines that require students to pass algebra and the CAHSEE in
order to receive a diploma, the BUHSD has eliminated essentially all
other lower level math classes. For those students who move into
their junior year and have not yet passed the CAHSEE, math
standards review courses are available. The district has also organized
some additional support such as very specific tutorial classes that may
already be in standards review classes but need some additional one to
one support during the day. This is a district structure, a district
policy that is organized and administered by the district (interview,
10.15.06).

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In addition to having local policies aimed at improving student achievement
in math, the BUHSD has provided BHS with resources targeted directly at
supporting students, such as tutorials, and other resources at assisting teachers with
the delivery of a viable curriculum. Course lead paid positions are provided for each
school and are assigned to each of the courses in math (i.e. algebra, algebra II,
geometry, etc.). Course leads are responsible for common assessments, pacing
guides and making sure that everybody is teaching to the standards and reteaching
material that is deemed necessary by the common assessment results.
Teacher C has taught at BHS for six years and teaches CAHSEE support
courses for the math department and economics for the social science department.
He sees the course lead position as very important. “This is a top down policy and
no longer a decision of the administration to determine if only the department chair
will manage the department’s courses. There are now course leads to assist.”
Course leads report to the department chair; this is a structure that the district has
created. Teacher C also stated that the value and effectiveness of course leads, as
does the common assessment program, vary from department to department. He can
clearly see this as he teaches in two different departments and is able to compare and
contrast. The assistant principal clarified that course leads are not evaluating
teachers; “they are facilitating the work that everybody is responsible for doing.
This was, at one time a department chair function, but course leads assist in this
process for all courses.”

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Recruitment of Key Staff
Bailey High School was going through demographic changes and was not meeting
the targets set by state and federal accountability programs prior to 2003. The school
district, upon BHS’s identification as a program improvement school, had to provide
the leadership and support the school needed in order to avoid future sanctions from
program improvement and so that students could experience more success at school
in general. The principal was one of the initial appointments from the school district.
I have been here now for four years. My original administrative team,
three quarters are the same. When the school went into joint
intervention agreement as a PI school, the district, to some extent,
cleaned house. They brought in a brand new administrative team and
a number of new department chairs; this is how the math department
chair got here. Some forced moves from other campuses took place
but I came here from another district voluntarily. It seemed like a
good time to come here to BHS. I asked to bring my assistant
principal from my former district and that was granted. They brought
in other assistant principals from other schools in the district that were
effective at those schools. They were not necessarily in favor, in fact
none requested the moves themselves, they were initiated by the
district. One of my original assistant principals was with us and is
now the principal at another high school in our district. Other than
that it has been a pretty stable administration (interview, 10.30.06).

The coordination of bringing the right people to this school was mostly
initiated by the district. The principal did not really know the assistant principals
prior to his relocation to BHS with the exception of the one assistant principal he
recruited from his former school and district. The movement of the department chair
and other department leaders and other changes including classified personnel were
all initiated by the district. Teachers and administration alike agree that the transfer
and recruitment of key people made an impact on the math department’s efficacy.
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This change has obvious connections to the human resource element of the change
process framework (Framework C). Teacher C emphasized how much the
department chair allows flexibility so that teachers can be as creative as one wants, at
the same time, he is still carefully managing the department.
I think every department needs quality management. He has given us
the direction that we need. He makes us want to work for him. I think
that is the difference between our department and others. You don’t
find many departments wanting to work for the department chair. He
has an expectation for us and we rise to it just like we expect our
students to. Now we hold each other accountable and we are
flourishing (interview, 11.17.07).
It is important to note that much of the change that resulted in higher student
achievement in math was accomplished with a new team of administrators and a new
the department chair. As the principal indicated, the changes in personnel were
initiated by the district that in effect assembled a team of leaders and put into effect
policies and resources to support the high expectations that had been set for them. )
Professional Development
Professional development, particularly when it is structured, aligned to the
department or school’s plan for increasing student achievement and genuinely
intended to increase the teacher’s instructional effectiveness will not only result in
increased achievement, but it can change the culture of the school or department
(Framework A: School Design). When the new administrative team took over BH,
they were immediately immersed in resolving various needs throughout the school.
Addressing the low achievement in math was among the many challenges that
needed attention. The BUHSD had some common district-wide workshops that were
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being offered to all BUHSD math teachers. Because one of BUHSD’s goals was to
offer all high school students a college preparatory math course, most teachers were
trained in College Preparatory Math (CPM). Despite his 29 years of teaching at
BHS, Teacher E, has been to only one training session related to his math teaching
position. He remembers attending a few other workshops as well, but cannot cite
any formal training that influenced his effectiveness as a math teacher.
Each of the teachers that were interviewed cited CPM as one of the required
trainings they had attended. Teacher B, geometry teacher at BHS, described CPM
training as one that encourages more use of manipulatives, investigation techniques
and problem solving. CPM offers course specific strategies that are aligned with the
textbook being used at BHS. Bailey High School now only uses CPM in Geometry
and has eliminated it in both Algebra and Algebra II for reasons not clear to BHS
math teachers. Teacher C and Teacher D were also CPM trained. Both agree that
there was some value to the training. Teacher C explained that all the training he has
had have helped in some measure and that the strategies that he has acquired via
trainings, including CPM, are shared with others during their regular department
collaboration time. Teacher E described the collaboration time not as a formal
training, but as a discussion among teachers. He underscored that sharing of
strategies and experiences together has been very helpful for every math teacher.
Teacher E described a typical collaboration session as time for sharing ideas,
concepts, approaches, use of worksheets and the challenges faced during
instructional time. The collaboration time has helped teachers become more
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effective professionals. Teacher E considers what he learns in collaboration on his
own campus surrounded by his colleagues as far more beneficial than the trainings
and workshops he has been part of off campus.

Collaboration Time
The math department team meets about twelve times throughout the year and
a few additional times for the team’s math day. After each common assessment, the
team meets to discuss the results of the assessment. The department chair leads the
meeting as teachers analyze the multiple choice problems collectively and the open
ended questions teachers do independently. The analysis and synthesis of student
test results leads to a group discussion and problems solving session along with some
acknowledgement of areas and specific classes that performed exceedingly well.
Teacher A recently completed her second year of teaching algebra and geometry at
BHS. She values collaboration time with her colleagues
The collaboration with the department chair and my colleagues is far
more valuable than any other professional development I have
received. The CPM training is very general. They point out very
general ideas of how the program is supposed to work. The
collaboration with my colleagues is very valuable to me. The teachers
in my department have a lot more experience than I do and they share
what has worked for them in the past. Talking to my colleagues and
hearing their advice helps speed up the process for me in terms of
using the right strategies and making fewer mistakes (interview,
11.17.07).

Collaboration time for the math department is multifaceted. Teachers not
only analyze student assessment results, but they analyze each other’s work and
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effectiveness in getting students to master the material they were taught.
Collaboration is an internal accountability structure in which teachers, in a very
transparent fashion, share results, ideas and concerns related to how their students
performed on common assessments. Those teachers whose students performed well
on course-a-like common assessments coach those whose students performed poorly.
All math teachers responded to the math teacher survey designed for this study and
92% agree or strongly agree that they received coaching and mentoring from
instructional leaders or peer coaches and 100% of math teachers feel supported by
the instructional leaders in their specific area of math instruction. As part of the
change process, teachers coached each other and developed not only into a
department of skilled teachers, but a cohesive group of professionals.
School administration and the department chair explained that getting the
math department to this level of collegiality and openness in sharing not only their
students’ performance, but their own successes and shortcomings as teachers was not
easy. The process of getting the team to this level of collaboration and cooperation
will be discussed later in this chapter, but nonetheless, the conditions created within
the math department led to higher assessment scores as measured by subsequent
local and state assessments. All math teachers agreed, according to the survey
results, that by watching and listening to each other discuss best practices, they learn
to become a more effective teacher. Every math teacher at BHS also agreed or
strongly agreed that the use of math coaches helps teachers become more reflective
about their own math instruction. Not all, however, feel that collaboration has been
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the key to increasing student achievement in math. Two teachers are neutral about
this statement and one strongly disagrees that collaboration has been the key to
increasing student achievement in math.
Creating the Conditions for Student Learning
How teachers see the teaching and learning process at Bailey High School
has been transformed in the past four years. The transformation has taken place for
various reasons, mostly related to strong leadership in the department and consistent
use of student performance data. As a result, after four years since BHS was deemed
a program improvement school due to its low performance in math and other content
areas, and after school district leadership replaced leadership personnel at the school,
every teacher now agrees or strongly agrees that math instruction is standards-based
and aligned to state assessments. They also agree that the master schedule, as it
relates to math, was developed strictly to meet the needs of students based on
assessment results. Due to structural changes in the master schedule and personnel
changes generated by the school district leadership, the conditions that students learn
in have changed, making more students successful each school year.
Increased numbers of students achieving proficiency in algebra, geometry
and algebra II are likely due to a higher level of instruction and interventions
designed for those students who do not meets standards the first time they are taught.
All math teachers agree or strongly agree that quality interventions in math have
been implemented at BHS to help students at risk of failing academically. However,
there is a difference of opinion among math teachers when asked if support classes
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have been included in the master schedule to improve student achievement in math.
Half of the math teachers disagree or strongly disagree that support classes are
included to meet the needs of students, 17% are neutral and 34% agree or strongly
agree that support classes exist to meet students’ math needs. Bailey High School’s
current master schedule provides eight support classes that are CAHSEE intervention
classes designed for students who are at risk of not passing CAHSEE before their
graduation date. These eight classes or 1.6 of a full time teacher are devoted to
students who struggle the most with grade level math content. Providing additional
support classes for those in geometry, algebra II or higher level math would
necessitate additional resources and funding that may not be budgeted or available to
the school. The assistant principal explains that the eight exit exam prep classes for
tenth graders are taught by the math department chair and other department teachers.
Students in these classes have demonstrated problems in Algebra and will be taking
the CAHSEE later this academic year. The idea is to get these students who are
having trouble in algebra ready for the CAHSEE.
With an obvious focus on intervening with those students who struggle most
in math, teachers interviewed explained how all students receive intervention and
support within the regular classroom to ensure that students do not fall behind.
Teacher A believed that the conditions that helped her and her students to increase
the degree of learning had to do with the continuity of common assessments,
teachers sharing each others review sheets, the type of material covered and how it
was presented to students over time.
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When teachers collaborate in this fashion, everyone is as successful as
the teacher with the most experience and who has the best teaching
practices. We all review our data together as a team and tackle the
weak areas together. We know where we need improvement and go
from there. We don’t focus on areas that we should not be focusing
on. We focus right on the areas where we need improvement. When
we are looking at data, I see the weaknesses as both instructional and
learning issues. What happens in the classroom goes back and forth
between students and teachers (interview, 11.17.06).

Teacher collaboration is a time when BHS teachers share their best practices,
ideas and challenges. As Teacher A stated, it makes everyone as successful as the
best teacher and keeps less experienced or struggling teachers from making mistakes
and failing to meet their instructional objectives. The department chair leads most of
the department-wide collaboration meetings and course leads take the same role
when the math department meets in subsets based on specific courses. The
department chair describes a typical collaboration meeting:
After every assessment we have a meeting to discuss the results of the
assessment. We look at the multiple choice problems collectively and
the open ended questions teachers do on their own. The grading
policy is standard for any open ended questions. Basically we follow
the Harvard Protocol. We talk about all the things we did right, what
needs improvement, which teachers did very well on specific
standards and ask them to share what they did. In some cases they are
big things and we ask why didn’t you share that earlier? Sometimes it
is not so obvious. We basically meet once every three weeks or just
after a test. The test is given and then collected, analyzed over the
weekend and input into a spreadsheet, printed out and then we meet
on Monday after school. Teachers get the results at the meeting.
Teachers are anxious to see the results so they all come to the meeting
(interview, 10.20.06).

As one may find in many schools, teachers at BHS don’t meet for the sake of
meeting. They have a very specific agenda item for every meeting: data. The
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procedures and cycles of instruction, assessments, analysis, and reteaching begin
with the standards that teachers teach and those that they know appear on state
assessments. BHS teachers then develop their own local tests to assess not only the
degree of student learning, but to asses their own effectiveness as instructors.
Developing reliable assessments to measure student learning takes some
knowledge of test design and should be comprised of test items that correlate with
the curriculum. The department chair was aware that developing tests internally
would be problematic and a tool for developing tests would be necessary. He
approached the assistant principal regarding a test generator program he had found.
The assistant principal granted the department chairs request and reported that the
nominal cost was well worth the benefit.
The school purchased the software for him. This program makes it
much easier, especially in math. The department chair creates a set of
problems based on one idea or concept; say factoring. All he has to
do is push a button and the program will go in and change all the
coefficients to an infinite number of possibilities. So you have many
problems in order to give students independent work or maybe a quiz.
The department chair is not rewriting or creating all these materials
because what students see looks different. This gives you options and
different versions for curriculum that you cannot necessarily replicate
in other content areas such as English (interview, 10.15.06).

The department chair or an assigned teacher develops the test. Regular
scantron forms are used for the test. The department chair described his
disappointment with other systems, “we have tried using other programs for this
purpose but they do not give us the data we want. The district has a web-based
program called IDMS, but it doesn’t work for us.” Therefore, the department relies
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on the test generator program where one writes in a test question such as X + 4 = 9.
Because the program is dynamic, it will write 5 or 9 more problems like it and it will
generate exactly what you asked it to produce. After several years of using this
software, the department chair estimates that there are hundreds of problems in their
test bank.
The tests that are developed by teachers and administered for students are
aligned to standards, chapters and units in the adopted texts, and carefully planned to
coincide with the school’s calendar.
We give about 13 common assessments during the year, six
assessments a semester. Each teacher is responsible for writing one,
only one a year. All other assessments are written for them. So when
we meet to analyze test results from a test, say test 2, on a Monday
after school, we will begin drafting test 3. We look at results from last
year’s test three and determine where the needs are based on the
results. So we go back to test two and identify the five questions that
most students had trouble with and add them to last year’s test three.
The teacher responsible for this particular test will type up a new draft
of test three for this year and have a review sheet made up for all the
teachers. The teacher will also draft a make-up test. Each teacher is
responsible for this process for just the one test they are in charge of
for the year. You have people critiquing their work. The first year we
did this I created the first test with another teacher and distributed it to
all the teachers. They ripped into that test really bad. I thought about
how I could address this and create a different structure. I also
reminded teachers that they need to act more professionally when
giving feedback. When the rest of the teachers went through the cycle
of writing their own tests they found that there were mistakes on
everybody’s. This made the process a lot easier. They pointed things
out, but did not ridicule. Because everybody is accountable at one
time, this has made it very important to do it right and to get the test
out on time according to the calendar. There is a very strong
accountability structure here. One interesting thing is that the writer
of the test usually did better than the other teachers on the student
performance results. Because they had the actual test earlier than the
others, they had more time to work with their students on the items
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that were on the test. This reinforced the need to have information on
where our students need the most help as early as possible; before the
CST’s. We need to know why we are delivering a lesson, re-teaching
and using particular strategies. How we measure growth is very
important. On our repeat questions, even those teachers that are not
on the high end, show growth in all questions that are repeated
(interview, 10.20.06).

After teacher collaboration and discussion that leads to a plan for addressing
the gaps in student learning, teachers move forward to implement the plan. The
strategies do not always include a modification or differentiation of instructional
strategies. Many times, there are structural changes that create the conditions for
struggling students to learn in. One math teacher stated that “dealing with the
weaker “F” students is the first priority. We put our failing students in one class and
teach them the main concepts, not everything in the curriculum.” At the end of the
semester, students in algebra were divided into two groups. One group consisted of
students who had failed the course or were at risk of failing. The other group was
comprised of those that had successfully mastered all or most of the content and
were passing the course. Teachers had the option of working with one group or the
other. There are benefits to working with both groups. One group is more proficient
in most or all first semester algebra standards and thus more likely to succeed with
second semester material. The second group has fewer students, usually less than 15
and the teacher can spend more time with individual students and slow down the
curriculum and cover less standards. Teacher A worked with the struggling algebra
students.
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We worked on the more general concepts and made sure they
understood them. That helped students get from “F’s” to at least D’s.
Half the students don’t like being in these classes and feel dumb. That
is when I work with them and help motivate them and give them hope.
I structure things so that they feel more successful. I make sure they
get ideas first before they move on to the next one. I do not tell them
they are in this class because they have failed, they know that, I try to
keep it positive. The other students, who are sometimes discipline
problems, say they like the class because of the small class size. They
say they like the attention and they can focus better (interview,
11.17.06).

After students are placed in appropriate courses that include various levels of
intervention, teachers relied on the instructional strategies that they learned mostly
from each other. Teacher B, after eight years at BHS uses student led work as
opposed to lecture and quiz. “Everything I do has somehow originated from the
department chair and my colleagues,” states teacher B. In her geometry classes she
gets students to pair, create, share, go around to stations and to engage in the material
they are attempting to learn. Teacher E does not use technology in his classroom as
an instructional tool mainly because he does not have the equipment. He does,
however use white boards as many of his colleagues do.
Whiteboards have been an integral part of my instruction because you
can do on the spot evaluation of how the students are doing and then
you can help those students that get the wrong answer. You can
actually work with students immediately and directly. This is so
much better than writing on a piece of paper, because then you have to
walk up and down the aisles, you have some students messing around
on the other side of the classroom. This way I receive immediate
feedback and give the right feedback. I tell students ‘yes, yes, and no’
and provide the help or ask others to help those that do not understand
the material. I even had a sub come in and he was amazed at what a
wonderful tool the whiteboards were for checking for understanding
(interview, 11.17.06).

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As BHS teachers continued to look for additional strategies and interventions
to assist students in mastering grade level math content, they looked toward a
strategy that other high schools in their district had implemented. The assistant
principal visited and investigated the use of tutorials and learned from other schools
that had utilized tutorial prior to BHS implementing them that, “structurally, tutorials
were not able to assist students because they had 14 or 15 students all needing help
with various subjects and various teachers. They were not able to successfully assist
them.” Based on this information from the assistant principal’s preliminary research,
BHS administration then made sure that their teachers kept their own students
needing tutorials for a twenty minute period that was built into the bell schedule.
This way, the students own content teachers would know exactly what they needed
help with. Adjustments to the master schedule and bell schedule allowed for a
tutorial period of twenty minutes where teachers helped struggling students in math
and other content areas.
The conditions that students learn in are more complex than simply
creating a physical and social learning environment that fosters student learning.
Teachers at BHS have created a system for sharing student achievement results
and their own experiences in delivering effective instruction. Contrary to what
Dufour (2004) found in many American High Schools, math teachers at BHS are
no longer working in isolation. The data that BHS math teachers share results in
a plan for re-teaching, a differentiation in instructional strategies, changes to the
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second semester’s master schedule, tutorials and other interventions that lead to
increased student achievement.
Other than state adopted textbooks and curriculum, BHS does not have a
packaged off the shelf program that is used for either proficient or struggling
learners. Algebra II teacher and course lead, Teacher D, describes the math program
as a group effort that everyone has bought into.
The program is a group of teachers that meet and discuss and try
everything until we find what works. This changes because our
students are different, but the program pretty much is the group effort.
We do whatever it takes to make sure we do well. This is not at all
what I experienced at my other school. There, administration and the
district were attempting to sell us on a program or idea that nobody
would by into. People were burning out because they were trying so
hard but they were not getting support from each other. Frustrations
would set in because so many of the teachers would not be doing
anything while a few were working hard. Here, everybody is working
hard and pushing in the same direction. This staff has a lot of good
veteran teachers that work well with new teachers sharing ideas.
Everyone now blends in and does well and moves ahead
(interview.11.17.06).
Because a method for sharing data, best practices and instructional issues is now
systemically in place in BHS’s math department, consistent teaching practices have
evolved throughout the math curriculum. In addition to uniformity of aims regarding
instruction, department-wide polices have also been established. Because the Bailey
Union High School District began to analyze and evaluate grading practices and used
the percentage of D and F marks assigned by school, department and teacher, BHS’s
math department implemented a strategy to reduce the number of D and F grades
assigned to students. They used their common assessments to predict those students
that would be failing and provided them with support, tutoring from students in
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business math and other interventions. If the students failed first semester of algebra
or geometry, those students were placed in classes with no more than 15 students in
order for the teacher to give each struggling student additional attention. Those
students who mastered the content were integrated into larger size classes in order to
maintain the reduced numbers in the struggling classes. Teacher E found these
interventions to be very successful for his students, “all these things are helping my
students. Last year my D and F rate at the quarter was 65% and this year it was only
30%, a big improvement”.
Teacher E also stated that the discussion of data helped him and his students
in many other ways.
We look at individual problems and discuss as to why, what were the
distracters and what was the reason behind the entire department
doing poorly on that question, did we not spend enough time? Then
we take four or five of those questions and put them on the next test in
order to tie up loose ends that were obviously there. That discussing
of the data has been very important in getting students to increase
their understanding in relation to teachers re-teaching. Some teachers
get a little apprehensive and even offended because our data has
everyone’s name listed. They are afraid because they don’t want
people to know that their classes are the ones that did really bad, but
you know what, we are all on this boat together and we are not all
going to have 100% scores with our students. You just need to accept
it and realize that if there are some shortcomings then you have to ask
yourself as a teacher -what did I not do with my students- because it
shows that they did not understand the material (interview, 11.17.06).

The BHS math team continued to look at ways to decrease their D and F rates
while maintaining the rigor of the standards-based course as they found that students
were losing motivation because they would work hard in class and not get any credit
for their work. Many of the teachers were assigning credit for homework, tests and
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quizzes, but not class work. The team agreed to start incorporating an end of the
grading period participation grade. Teacher E reported that the team realized that
students were not getting credit for the work they completed in class. “They were
getting credit for homework, but that is it. So if they were not doing their homework
and only doing class work then they were getting no credit and that did not seem fair.
We starting employing participation credit along with class work credit and that
helped a lot too,” explained Teacher E. He and the other teachers in the department
found that soon thereafter students were incrementally doing more in order to
improve their grades.
Because the team was experiencing so much success from collaboration
and supporting each other, the department chair approached the administration
asking for more student-free time to meet with his team. Both school and district
administration approved of additional time that the BHS math team refers to as
math day. Teacher C, one of the CAHSEE intervention teachers finds the math
day to be the most effective form of professional development.
First and foremost our math day makes an impact by giving us
time more time to collaborate. Students need a break from all the
work and it gives them time to catch up or review so it is not a
wasted day for them. Some may say that math days are wasted
days for students but if you go out and see what they are doing you
will see that they are actually working. The math instructors are
shuffled to supervise by the math content they teach, be it algebra,
geometry or whatever else and everyone gets a chance to meet.
This is the most important policy or program element for us
(interview, 11.17.06).

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The collaboration and collegiality among the math department is transmitted,
in some cases unwillingly, to the students. The department chair reports that there is
a competitiveness that has translated from teachers to the students. “You can ask a
class where they rank and they can tell you.” Students were told that how each
student performs in the classroom is important. The students scoring low were
encouraged to help the others; “you are a team.” The math team was inadvertently
replicating NCLB at the classroom level. Students and teachers understood that not
every student needs to know everything, but they need to know some things or
enough to help move the class up in ranking when compared to other classes. Every
teacher and every student soon wanted to be the best class. “We really encourage
classes to work as a team. I do, however, remind teachers that they need to share
their successes, their expertise and those strategies that work for them. Although we
compete during the year, we are still a team that needs to have high aggregate results
at the end of the year,” reports the department chair.
Despite the healthy competition that the department chair promotes both with
colleagues and students, he reported struggling with what he phrased as “low end
teachers” who consistently are at the bottom of the class rankings and not making
any changes. Although this is less of a problem than it was before, there is an
example of one teacher who is consistently at the bottom.
The good thing is that we know this. It is much better that we know we
have a person like this than to not know. If you don’t know that you are
not good than you do what has happened in education for years, you close
your door and hide in your classroom and continue doing what you have
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always done. But if you know, you could ask for help, observe others
that are more successful than you (interview, 11.15.06).

The process that the department chair described has helped teachers move
along the continuum of professional development and in becoming effective math
instructors. Teachers report that what they learn from each other in collaboration is
more effective training than anything they had received from workshops,
conferences or other external programs. This system, however, took time to
implement and enhance. Having individual teachers change, yet having the
department evolve cohesively was a challenge that took time and persistent effort.
Collaboration, therefore, is a central element in both research question two and three.
Collaboration relates to question two in how it has become part of the design of the
math program at BHS. In research question three, collaboration has been a vehicle
for the change process that led to an enhanced math program. The initial efforts
related to an improved math program design (Conceptual Framework A, School
Design) resulted from teacher collaboration and problem solving. Later, as both the
program and the math team developed, collaboration again played a crucial role in
the change process (Conceptual Framework B) that led to specific changes and
policies that became systematic within the department.
Research Question Three:
What change process did the school use to enhance the math program and
strategies to assist students in math?

Bailey High School’s achievement was not immediate. The catalyst for the
process was primarily political provocation, namely NCLB and PSAA and was
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followed by some district level accountability measures. District leadership then
looked further through the human resource lens related to the change process
(Conceptual Framework B) to identify the most appropriate leaders to carry out
structural changes that ultimately led to improved math results and exceeding targets
set out by NCLB and PSAA.
Initially, the department chair confronted many challenges in getting
teachers to become standards-based and data driven. There were structural changes,
human resource dilemmas, and some politics involved in meeting the vision of
getting all students to proficiency. Boleman and Deals (2003) Four Frames,
Framework B, serves as model to better understand how BHS’s math program
achieved success. In the course of the four years after being identified program
improvement, BHS and district office leaders had to make some changes in
personnel, allocate resources, develop policies in order to develop a culture of
continued improvement and to meet state, federal and local goals and objectives.
More than 50% of teachers and the leadership at BHS agreed that politics,
namely the pressures of the State’s Public Schools Accountability Act and the No
Child Left Behind Legislation were the catalysts that generated the changes at BHS.
The department chair recognized that BHS was “under CDE rule” and that its
participation in program improvement meant that some immediate changes were
needed. The department chair also added, “we could no longer ignore the low end
students and we needed to develop systems for helping them.” The Change Process
Framework (Framework B) does not suggest that any one frame precedes another,
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nor does it propose that all of the frames are present when executing a change. In the
case of BHS, the initiation of the change process came as a result of program
improvement identification followed by some changes in the human resource frame
prompted by school district leadership. The new administrative team did not need to
bargain, negotiate, nor impart political pressure because the politics that had incited
and necessitated the change had already taken place through NCLB and PSAA. The
principal confirmed that they did not run into any political opposition or any other
kinds of obstacles at all because the goals they had for the school were aligned with
those that were supported by the district. “The district has been phenomenally
supportive; we have had no political problems at all,” reported the principal.
The principal was asked to take over a school that was now in program
improvement and that had lacked leadership for several years. The principal
recounted his first few days and his examination of the school’s systems, culture and
values. He did not find any systemic structures or goals in place that would guide
the school, nor could he discern any sense of direction or identify the school’s
objectives. There seemed to be a focus on the “day to day managerial things that I
learned throughout my experience as an administrator that in my opinion, were not
effective,” reported the principal. Thus he discovered that there were some obvious
impediments that had become a part of the school’s culture that were having an
overall effect on how the school operated. As the principal analyzed these
impediments, he was in fact looking through the various lenses of the four frames.
Making sense of why systems that supported student achievement were not in place
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necessitated a framework for understanding the complexities of the problems at
BHS.
I can remember my first day going out to the front lawn. I don’t think
many of the past administrators had done even those basic things
before. Seeing students in the tunnel crossing under the street from
one part of the campus to the other, total gridlock, it dawned on me,
this must have been a problem for some time because Bailey high
school had not grown that much. It was an awful situation. I don’t
care what happens but we have to open up the gate and use the
crosswalk and if the cross guards are not out there then we use campus
security and do what needs to happen to make sure those students
cross the street safely, but this needs to be changed. Something as
fundamental as that, created a situation that was much better in terms
of daily management. Organizing campus security so that they have
specific duties and responsibilities so that how campus security is
handled is more structured. Changing the ways in which office
referrals are handled and how discipline is handled. We did a lot of
walkthroughs of classrooms. We kept things positive and upbeat, we
were sending notes to teachers after walkthroughs and identified the
things, mostly instructional that we wanted to keep seeing, just
keeping it all positive. We wanted the teachers and students to see us.
So much of the first year was just basic management style which I
think helped gain some confidence (interview, 10.30.06).

The changes that began to unfold at BHS were mostly structural at the
beginning. These structural changes also impacted the culture of the school and were
therefore part of the symbolic frame. Opening the gates so that students could safely
and more rapidly cross from one segment to the other not only got students to their
next class on time, but it sent a symbolic message that changes were being
implemented in order to facilitate a student’s transit from class to class. The
principal also emphasized the need to acknowledge what was positive at the school
and recognized those teachers that were doing well either by way of a brief note in
the teacher’s mailbox or by publicly broadcasting it to the teachers and the student
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body. Within a short time, people began to see changes in how the school was being
restructured and what was being acknowledged by administration and deemed as
important. As would be the case in the years to come, this was the beginning of a
new period when faith and belief was being restored amongst students and staff at
Bailey High.
After 29 years at BHS and as part of a math department that had been
experiencing frustration with their math performance results, Teacher E commented
on the administration’s approach and the direction in which they were taking the
school.
It is a much more positive feeling. This school had a very negative
feeling that began about ten years ago. It started when this school was
a pilot school for houses. It resulted in the have’s and the have not’s.
Those that were in houses got everything and those that were not were
cast aside and were not important anymore. This was very obvious in
the school. People were teaching out of their subject areas and this
did not work. This created a lot of apprehension. The administration
was not strong and was not a cohesive agent for the school. Now it is
not like that. Everyone is working together, departments are sharing
with other departments. Departments are having time to collaborate
and even getting together outside of school time. It is an enjoyment to
work here. The structure is very different (interview, 11.17.06).

Professional Development – Self Actualization
Throughout their first year and into the second, the principal and his team
continued to implement changes mostly within the structural and symbolic frames.
Changes to the master schedule; changes in rules, responsibilities and policies;
revision of goals and objectives; and an overall re-culturation of the school changed
how the school operated and began to concretize the belief that the school’s aims to
be able to exit program improvement and raise student achievement results was in
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fact achievable. The scope of these structural changes, however, inevitably reached
their limit and the administrative team realized that changes in teaching and learning
needed to take place. These changes were related to two elements of the change
process conceptual framework: productivity through group effort and self
actualization. At BHS these framework elements translated to collaboration and
professional development.
What teachers needed to be trained in was not just up to the principal and his
administrative staff. During the initial year of his principalship, the principal was
also taking recommendations from an external consultant due to BHS’s program
improvement status. One of the areas the external consultant recommended be
addressed immediately was student engagement activities in every classroom.
Framework C, Effective Math Programs, includes high levels of student engagement
as one of the elements of successful classroom practices. Both the principal and the
external consultant would go into classrooms and witnessed that students were just
not being engaged at appropriate levels. Consequently, teachers were told that
students were expected to be engaged in standards-based, grade level work during
every period of the day. The principal developed a classroom visitation schedule for
his administrators and they began their visits. Along with student engagement, the
team was looking for elements found in Framework C related to standards-based
instruction, student-centered curriculum design and other effective classroom
practices.

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Initially, there were some improvements observed during these administrative
classroom visits. However, it was evident that the overall capacity of the math team
was low. Since the administration was attempting to increase the effectiveness and
capacity of all departments at the time, they were too overwhelmed to give
additional, if necessary, attention to any single department including the math team.
The team was missing most or all of the elements of an effective math program
(Framework C) including accountability and leadership. The school district had
already considered that the administrative team’s time and energy would be
exhausted with so many challenges and had transferred the department chair Duran
to BHS to act as the math department chair.
Principal reflects on how crucial the decision to transfer the department chair
to BHS was.
The department chair comes along and starts talking and working with
teachers. This is where we sort of get lucky, I mean The department
chair is such as strong personality and does such a wonderful job, and
this is where department leadership becomes so vital. He comes in
and gets his team to buy into common assessments, organizes them.
He is one of those guys who is an absolute master at being direct with
people, making decisions but not doing so in such a way that he
forgoes the cohesiveness of his team. They end up agreeing,
supporting and they saw some immediate results. You look at our
CAHSEE scores jump dramatically and if you look at our standards
test results, they jump dramatically. Teachers begin to say these kids
are learning a little bit more, I can see why we are doing this now.
This has helped us and the math team get some momentum. Just after
a year we take a teacher from the math department who believes in
this process wholeheartedly and put him in science as the department
chair and he gets this kicked off in science (interview, 10.30.06).

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With the decision to employ the human resource frame to bring about the
leadership that would create a sense of belief and partnership amongst the math
team, the department began to see a change in their own branch within BHS. The
success that the math department began to experience was not reflected in any of the
other departments on campus, at least not nearly to the same degree. Despite the
immediate changes and successes the math department may have experienced, the
department chair’s leadership was not an immediate success. He needed a way to get
teachers to modify their instructional practices and a method for monitoring student
achievement. After giving the first assessment, he was faced with criticism on his
test design and on the validity of the results. To address this problem, the
department chair decided to create a schedule in which teachers would rotate, each
taking responsibility for creating a test that corresponded with the chapter they were
on. The designated teacher then proceeded to gather the results, publish them and
distribute them to the teachers for analysis and discussion during their collaboration
time. As a result, each math teacher developed a sense of appreciation and respect
for each other as they understood the complexity and difficulty of creating and
coordinating a test and its administration. The teachers’ criticism of the tests and the
common assessment program rapidly transformed into support and collaboration as
they attempted to enhance the assessment program and the desired outcome which
was to increase student achievement in algebra, geometry and algebra II.
The common assessment program went through some changes of its own.
Most of those changes were structural and were not all produced by the department
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chair, but as a collaborative effort of the entire math department. The department
decided to put the teachers names on the common assessment results, not just
numbers. None of the teachers objected.
The department chair did not take on the entire math department at one time.
He decided to divide his efforts and began working with teachers assigned to one
course at a time.
This entire process that we use of assessment and analysis began with
Algebra and we had success. We did it the following year with
geometry and again experienced phenomenal success. The Algebra II
teachers were reluctant and did not want use the system at first. We
implemented it anyway and had great success. We use this same
strategy now with higher-performing students, like being able to re-
take tests and you get more success. Our Algebra II results are the
same as our higher performing high schools in the district (interview,
10.20.06).

The math department continued its transformation. They were leaving
behind the practice of working as an isolated group of teachers who did not
collaborate, share their successes and frustrations and as a result, failed to meet the
needs of students. Not yet satisfied with the level of success of his department, the
department chair looked for additional ways to improve the department even further.
By his second year he had recognized that he had the advantage of teacher retention.
His math teachers were not leaving the school as they had in previous years. This
group of teachers was becoming very dedicated and loyal to BHS.
We have had one teacher leave and we let one teacher go. We hired
two or three more because of growth. We have been successful in
keeping our teachers. Math teachers, especially these days, can shop
around and go pretty much anywhere they want to go. This is exciting
for us; the fact that they want to stay. We treat them well. I don’t
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think you are going to get a math department that works as well as we
do (interview, 10.20.06).

The assistant principal over curriculum and instruction observed the same
patterns. He observed that in the three and a half years that the team had been
working at BHS there had been a fair amount of turnover. However the math
team has really remained consistent and improved. The math team, according
to the assistant principal, had always had some good levels of expertise, but
was just lying dormant.
Now with a more dependable and consistent team, the department chair
brainstormed ideas with his math teachers on how they could reach an even higher
level of success. The feedback he received centered on how valuable the
collaboration time was to nearly every teacher. The collaboration time had become
the driving force of their standards-based program as it was based on student
performance data and was creating commonalities in effective instruction throughout
the department. This change in the department is encompassed in Framework C:
Effective Math Programs and the element related to standards-based instruction. To
augment the limited time they were spending during collaboration time, the
department chair approached the principal and requested the opportunity to have
what the team calls a math day. Math day, which has now grown to 7 math days
each academic year, is a student free day for math teachers that is used to collaborate
and plan upcoming lessons and the curriculum to deliver them. On those days,
instead of coming to class, students go to the school’s auditorium. Some sit in the
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balcony and work on worksheets, others, mostly freshmen, sit in the foyer and work
on review. The work students do is carefully planned and monitored to ensure that
students don’t forego valuable instructional time. Teachers rotate and supervise the
students by subsection throughout the entire day. All the other teachers meet in the
department chair’s room. The cost for math days is minimal since substitute teachers
are not contracted and the training and professional development is internal within
the department. The department chair divides up his time for two hours with all the
algebra teachers, then with geometry, algebra II and so on. The last two hours of the
day are for the entire department.
Our assistant principal of instruction is very supportive and
generous. He buys us all food and that’s about it in costs. It costs
about $200 to pull out 21 teachers for the entire day. We provide
breakfast, lunch and snacks all day. The teachers like this because
food is very important in a meeting. Teachers feel valued. The
work that the teachers do is incredible and very valuable. Nobody
leaves early. We start at 7:30 and work through the entire day. The
English department now does this for 14 days and they say they get
an amazing amount of work done (interview, 10.20.06).

Time for collaboration helped BHS’s math teachers solve teaching and
learning problems and is playing an important role in closing the achievement gap in
math for students at BHS. Starting with The department chair’s leadership and later
as a result of the math team’s efforts, the math department has discovered ways to
increase their time for professional collaboration. Unlike Dufours (2004) finding
that many U.S. high school teachers continue to work in isolation, 85% of BHS math
teachers agree somewhat or strongly agree that the math department’s success has
been due to its collaborative effort.
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The only real obstacle has been time and developing a system where
teachers do not just close their doors and do their own thing. Time
allowed for the development of a system that holds teachers
accountable to themselves and to each other on how their students are
performing. It is not about saying you have a 60% D and F rate and a
teacher saying, well I put the material out there and students are just
not getting it. There has been a fundamental change in how teachers
work as a department and now how they think. Teachers are beyond
their old conception of how things should be done in the math
department. This was an obstacle for the department chair at first, but
working through this and a few minor personality issues, the team
now works pretty darn well together. The team is a real model
(interview, 11.17.06).

How math teachers interacted with each other and viewed their relationship
to one another to form a cohesive and productive internal organization changed at
BHS. Moving beyond teacher to teacher relationship, it is impossible to separate the
Change Process (Framework B) and its effect and relationship to the Effective Math
Program Framework (Framework C). Although BHS math teachers changed their
behavior with respect to working as a team, the critical behavior occurred in the
classroom regarding teacher interactions with students. What teachers gathered
during collaboration time is of no value unless it is successfully executed with
students daily during the teaching and learning time.
Effective math programs (Framework C) include effective lesson design,
high levels of student engagement, tapping into students’ prior knowledge and timely
and accelerated interventions, all effective classroom practices. These elements have
become systematic for math teachers at BHS. Not only are lessons designed for
daily delivery of instruction, but teachers now have multiple years of data available
and they know which students are likely to stumble based on past years’ assessment
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results. Lessons are designed based on current student needs and in anticipation of
what might happen based on learner or teacher error from prior years.
Teacher D, algebra II teacher has been at BHS for more than three years and
has seen a transformation in instructional practice.
Before we had a lot of good teachers who could not see why their
students were not scoring well on assessments. We could not get them to
see why, just because you teach something and they get it that day, does
not mean that they really get it. Sure, they can do twenty problems for
you that day, but how about tomorrow or the next day. You have to spiral
the concepts and your instruction daily. If you don’t spiral, then two
weeks later they cannot do different problems and in a different order.
The data analysis got teachers to see the need for spiraling (interview,
11.17.06).
Re-teaching and presenting material using various modalities was not only
visible by way of the administration’s classroom visits and the department chair’s
observations’ it was manifested in teachers’ accounts during collaboration that
clearly revealed changes in instructional delivery in the classroom. Because the
department was now standards-based and aware of exactly what was being assessed
on CAHSEE, CST and their own common assessments, the team became less book-
driven. Teaching a CAHSEE intervention class, Teacher C knows that his students
have some knowledge gaps in algebra and he attempts to fill them in any way
possible. “I integrate internet and use technology such as power point. Our whole
team looks carefully at standards and release questions. There is not one thing in
particular that we are dependent on. I just think we do a good job using multiple
resources and what works best for students,” stated teacher C. Since the team knows
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what needs to be taught, they begin to focus more on how it is taught and how much
of it was actually learned.
Using students’ prior knowledge and providing them with timely
interventions is also built into the math department’s system of effective instruction,
assessment and intervention when needed. Again, the common assessments provide
this information for teachers. They know each student’s knowledge level based on
regular assessments and also have a system for tracking each student’s performance
in their course the prior year. Each teacher turns in their grades to the department
chair that then downloads them into a shared file and then burns a copy for each
teacher to review at their discretion. For those students who show early signs of low
performance, interventions are provided in the classroom and in a more structured
fashion by placing them in smaller class sizes or intervention courses such as the
CAHSEE support class.
The strategies that teachers use, as mentioned before, are becoming
increasingly uniform throughout the department. Even those teachers that the
department chair could not initially convince that the use of individual whiteboards
were of value are now using them. Individual whiteboards in math instruction are
typically a small whiteboard about 15 inches square that students use to solve math
problems that the teacher gives them. The student writes and solves the problem
using an erasable marker and then displays the answer to the teacher for prompt
individual feedback. During collaboration, teachers reported how rapidly they could
assess if students understood a concept, formula or solution when they solved and
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equation and held up their whiteboard for the teacher to see. They no longer had to
walk up and down the aisles of the classroom looking down at small and sometimes
illegible print. Teachers that had not tried the whiteboard strategy or who were
critical of it listened continually to various teachers’ feedback and finally tried it
themselves. Often these teachers would return with their own success story
explaining how it got students to collaborate with each other and share how they
solved the problem.
You get a lot of teachers using the same strategies now. Sharing
during collaboration has changed our department. We do in and outer
circle, gallery walks. A lot of these are things we come up with on
our own. We do pair share, we set appointments with students. Our
big thing is self tutoring. Our appointment system consists of students
taking time to make appointments for help from other students. They
are forced to think about what they need help with and to organize
themselves so that they can go ask for help with out feeling
uncomfortable by letting others know that they don’t know the
material. I use this strategy of pairing students up a lot. I pair up
students who are solid with others that don’t understand the concepts
and give them problems that are similar. The proficient students
tutors the other students on how to do the first problem and then the
other student has to show the tutor how to do the second problem that
is similar to the first. All along we are teaching students but also
teaching students how to be appropriate tutors. We actually have
tutors in class and many of them are very effective because we have
trained them. My most effective strategy is getting students who
know the material to share how they learned it with other students.
Making this school-wide is something we are still working on. But
because we have data that is made public with other teachers, we ask
each other during collaboration how we get students to do well and I
tell them that peer tutoring works for me. You have more and more
teachers applying what works for other teachers in their own
classrooms. Some teachers are still working on how to develop good
tutors in their classrooms, but because of the competitive nature we
have created, people are trying (interview, 11.17.06).

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The use of tutors has produced good results for BHS math teachers and
students. Rather than hire college tutors or other personnel that receives training to
support student learning, they use their own tutors who have shown that they
perform well in math. Teachers report that using well trained tutors is like having
more than one teacher in the classroom. Like other teachers in the department
Teacher D depends a lot on tutor help and reports that whole classes have been
developed where the sole purpose is to have tutors help other students. Students who
have met the district’s math graduation requirement and who are not interested in
taking higher level math courses get elective credit for helping their peers in math.
The creative thinking of BHS math teachers therefore shifted from giving more
assistance to lower achieving students to training higher achievers on how to assist
their own peers.
The structural changes are thus at the master schedule level and how courses
are organized to meet the needs of students and at the classroom level in terms of
how students get the intervention that they need. The goal continues to be that entire
classrooms achieve well on common assessments and that each individual student
score at proficiency. Once interventions such as tutoring, teacher appointments and
other in-classroom supports have been executed, students get the opportunity to
retest.
The idea of the retest made a big impact. We got out of the idea that
if students don’t get it by a certain date then too bad. We have
changed our philosophy on learning. It doesn’t matter when they
master it as long as they master it. It is pretty much policy now that
whenever a test is given, in a week or so, we have a retest. Now with
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tutorials, students remediate and fix what was wrong. The second test
is very similar and students almost always test at higher levels. Prior
to this year, tutorials were done after school. Now they are more
effective because we do them during school hours. We accept any
improved score, it doesn’t matter by how much, as long as it has
improved (interview, 11.17.06).

Bailey High School math teachers feel that the policies, rules, and procedures
that were established as well as the clear set of goals that were set is what brought
about change in the department and in the performance of students. Later, when
teachers were expected to collaborate and share their successes or negative
experiences, the rate of change increased. The change process framework classifies
these elements as structural. These changes, whether deliberate or inadvertent,
created a system of accountability. The principal does not feel that he needs to hold
math teachers accountable since they are apparently holding each other accountable.
The department chair asks every teacher to turn in an electronic copy of their grades
at the end of each year and reports, “I place everyone’s grade book on a CD and burn
a copy for each teacher. Now that teachers are aware that others will be looking at
their grade book, they know they cannot fudge on the grades like they used to back
in the good old days. This adds a critically important systematic component to the
math program that has built in accountability measures. These accountability
measures are internal, unlike NCLB and PSAA and appear to have made a bigger
impact.
Bailey High School’s sustained achievement results transpired in the
course of four years. The change process started prior to a new administrative
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team and new the department chair being assigned to the school. It began with
political pressure at the federal, state, district and finally the school level. The
human resource frame was the next lens applied to the change process when new
leadership was assigned to the school. Structural and symbolic changes followed
and were the foundation for instructional changes that would develop through
strong instructional leadership by the administrative team, and for the math
department, provided by the math the department chair.
Research Question Four:
To what extent was strong instructional leadership important in improving
A) the math programs/strategies and B) math achievement among students?

Effective schools are usually led by effective leaders who understand all
levels of schools and the learning process as illustrated by Conceptual Framework D,
Instructional Leadership. Kannapel & Stephen (2005) found that devoted individuals
who cared deeply about the community and about establishing a culture of high
expectations, high performance, collaboration, and mutual respect are what make
effective school leaders. Particularly in urban high schools where students have
challenging needs, leaders need to have this set of knowledge in order to overcome
the challenges associated with large urban high schools. In the case of BHS, once
changes in the structural and symbolic frames were exhausted, it was critical for the
school’s administration to take on the role of instructional leadership.
The changes in the BHS math department are validated due to changes in
student performance. Who initiated, approved and implemented the changes needs
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closer investigation. Although survey results indicate that most BHS teachers, both
math and non-math, believed that the principal has impacted changes that have led to
increased student achievement, interview data centers on the department chair taking
on most of the leadership that led to changes and improvements both in the math
department and the changes directly related to students.
∞ 76% strongly agree that the principal has been an agent of change
∞ 24% agree somewhat that the principal has been an agent of change
∞ 78% of non-math teachers agree that the principal works hard to monitor and
supervise instruction in the classroom
Much of principal’ focus was on developing a culture within the school and
setting a positive climate school-wide. Additionally, the assistant principal worked
closely with principal from the first day they were assigned to BHS.
The first year and a half involved a lot of change and restructuring.
A lot of what the principal and I did was common sense ideas that
had worked for us before at other schools. Larry has a great
personality and establishes a good relationship with everybody. My
role was to facilitate and support those who were doing good work.
We were trying to learn the idiosyncrasies of this district and made
our ideas work (interview, 10.15.06).

Conceptual Framework A, School Design has four central themes and culture
building is one of them. The other themes relate to curriculum, learning activities
and students assessment. These themes were being addressed by the department
chair in the math department and there is indication, based on interview and survey
data that they were not well developed in other departments within the school.
Therefore, the characteristics of an effective school when evaluated by Conceptual
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Framework A, show that although the math department designed its program with
the culture, curriculum, learning activities and assessment centered on students, it
may not be the case for other departments at BHS. Hence, the instructional
leadership was provided largely by the department chair and the principal took on a
supportive role that facilitated what the department chair was attempting to
accomplish with his math team.
Teacher C, again being assigned to both the social science and math
departments, has a clearer perspective of how other departments operate as compared
to the collegiality and professional learning community (Dufour, 2004) that has been
developed in the math department.
I think that taking responsibility for student learning varies here by
department. Working both in the social science department and the math
department I can clearly see what the issues are that keep the one
department from making the kind of gains we are making in math
(interview, 11.17.06).

The gains that were made in math are mostly credited by most teachers to the
department chair’s leadership. Although they do credit administration for providing
support and not creating obstacles, they feel that the department chair’s direct
involvement in the classroom is what made the most significant changes that led to
improvements for both the department and student achievement. The principal and
assistant principal worked out the logistics and made it possible to attain those goals
the department identified as important.
There are several factors that distinguish a principal and manager from an
instructional leader as outlined in Framework D: Instructional Leader. Both would
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be expected to visit classrooms and supervise the instructional program. An
instructional leader, however, visits classrooms frequently, not just on occasion.
Visits consist of close observation and a peer-like relationship with the teacher where
feedback is provided and dilemmas in the teaching and learning process are
addressed. Teachers at BHS were very impressed with the department chair’s
“hands-on” attitude.
He embeds himself in the courses he wants to help. What was high
stakes, it was Algebra so he put himself in that course, helped develop
the curriculum and the course and then handed it off to the course
lead. The next year he went into geometry. Now the course lead is
doing great and knows what he needed to do. Then he went to
Algebra II. He impacted the structure of the course, developed a
leader for that course, assessments, alignment and then moved on to
the next course. He is in the trenches with us, which is why we want
to work for him (interview, 11.17.06).
The department chair has done more than just shape the math program and
impact student achievement. He motivated his teachers to become excellent teachers
and strong leaders within the department. He built credibility by remaining a peer
and colleague, yet established himself as the leader and mentor. While the
department chair was executing the plan to improve the math program, his skills as
an effective teacher himself were not forgone. He continued to make a direct impact
on student achievement.
The department chair has taken on one course in each of the levels.
He started with Algebra and improved the program. He then came to
the Geometry the next year and we too had an incredible boost in our
scores. He then went to Algebra II, a course that was suffering and
taught a course and again tremendous boost in scores. It is no
coincidence that this is occurring; it’s the department chair. He comes
in, he is infectious, he is innovative, he is creative and makes us think
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outside the box and really pushes collaboration. The collaboration
brings the best out in everybody. He was an actual teacher in each of
these courses. He participated in everything just like the rest of us.
He came to meetings, he was a part of the testing, the strategies and
implemented the data analysis that we continue to do after he left.
Once the department chair left we didn’t have any more growth. But
we had such an improvement and growth that just sustaining was good
(interview, 11.17.06).

The leadership that the department chair provides for the math department is
due to a resolute and determined attitude. He is nurturing and sustaining (Framework
D) the math program in order to build on the successful practices they have already
demonstrated. He has taken the time to bring even the most reluctant teachers along
by coaching and giving them the opportunity to participate and remain involved in
the learning community.
I value the teachers. I don’t micromanage. Teachers are given the
opportunity to identify where they need help and then ask for it. They
look at the data on the sheet and then say, look I am on the low end here,
what can I do, what are other teachers doing? I had a very traditional
teacher who had been teaching for more than 25 years who had never
used a white board. In one case we had a teacher who had 92% of his
students master a standard while everyone else was at about 42%. We
asked him, what did you do, how did you get your students to achieve
this? He said, “Well, I put 15 problems on the board and would point to
one. All the students had to do the problem on their white board and then
hold it up. I gave each student individual accountability and guess what?
I did not have to walk around the classroom to see who had the problem
right or wrong.” The students love the white board. The reluctant teacher
decided to use the white board and now uses it as a regular teaching
strategy (interview, 11.17.06).

While the department chair provides much of the leadership tasks outlined in
Framework D, the principal and the school district support the department by
providing leadership in data driven decision-making. The principal begins each
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school year by sharing and reviewing what the API and AYP results were for BHS.
He then compares those values to state and federal targets and why these indicators
are important to the school. Through the course of the year he also makes time to
gather his teaching staff to analyze D and F rates, on track for graduation rates and
how the school compares to other districts and other schools in the district. The
principal emphasizes the importance of tracking performance through data by
providing time for the whole staff to analyze data at various times during the school
year. One of his activities consisted of analyzing general scores and trends. He then
gave them a short quiz that was meant to be fun, but gave teachers something to
focus on and so that they could become active participants. Later that afternoon he
gave each department packets that contained data by each teacher in their department
so that they could compare their grade breakdowns, how each teacher’s students
performed on common assessments and STAR assessments so that again teachers
could compare and discuss some possible solutions. The packets also had
breakdowns of department specific data so that they could compare longitudinally
where they were before the present. They also compared how their departments
performed in comparison to other schools.
Gathering this data is effortless for the principal. The act of gathering the
data and in many cases organizing and synthesizing it is performed by the district. It
is the principal’s choice on how and whether or not he will use it. He sees this data
as valuable because it not only informs him and his staff of their progress, but it
forecasts trends and guides the planning process. One of his preferred reports looks
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at his tenth grade class (class of 2009) and gives a comparison by schools in the
district. It provides a percentage of students that are on target for graduation. BHS
class of 2009 students are 74% percent on track for graduation. “This is not great,
but compared to other schools in the district, we are behind High School A, ahead of
High School B and High School C, so we are doing okay but we know we can do
better,” stated the principal. In the same report, BHS’s current 12
th
grade class is the
lowest in the district. The principal then takes this report to teachers. Teachers are
asked to disaggregate the data and determine why seniors are performing so poorly
school-wide and why they feel tenth graders are experiencing more success.
These data review activities led by the principal are school wide. In some
cases he gives department specific data to the department chairs and also provides
them with guiding questions as an assignment. Some departments also get data such
as college prep math and Advanced Placement results. Much of the data that the
principal provides to his teachers, with the exception of D and F grade distribution
reports, is summative in nature. How students performed on AP tests, STAR
examinations, and whether or not the school made AYP targets is all summative and
informs the staff as to how the school performed after an academic year of
instruction. The difference between the data that the principal provides for teachers
and what the department chair provides for math teachers is that math teachers, in a
systematic way, review ongoing formative assessment data that math teachers
analyze frequently throughout the school year. This data informs on current learning
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and how effective teachers were in getting students to learn the material that was
recently taught.
The principal provides other types of leadership actions that are related to
instructional leadership and that do support the goals that the math department at
BHS is trying to meet. Although he has involved the department chair in math
teacher interviews during the past four years, he takes an active role in this process
himself. He also supported the math department by working with a teacher that was
not performing at the expected level and who did not make the adjustments he was
asked to make to his instructional practices. In this case, the principal began the
process of documentation and dismissed the teacher altogether. “This makes a big
impact. Replacing a poor teacher with a high D and F rate with an effective teacher
that helps students become successful in math makes a big difference.”
The principal’s support for the math department is clearly evident. It is also
clear that he is well informed of what is taking place within the math department.
The common assessment program and system of collaboration is not foreign to him.
He acknowledges and believes that regularly assessing students and having
meaningful department-wide discussions about the results is what has made the math
department successful. He is currently trying to get other the department chairs to
replicate what has transpired with the math department. After many attempts with
other the department chairs, the principal is convinced that what the department chair
has done is due to the department chair’s instructional leadership in his department,
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but also questions how much of the department chair’s initiative comes from a
natural ability and desire to lead that is hard to replicate with others.
Whether it is natural ability or a true understanding of the elements of
instructional leadership, the department chair has been instrumental in creating a
culture of teaching and learning that centers on learning as an outcome and not on
causes that impede learning. Instructional leadership includes the creation of a
culture of teaching and learning that celebrates teachers, students and staff,
particularly when measurable gains have been made (Framework D). Bailey High
School does not have a formal teacher recognition system other than local
community organizations such as the Lions and Rotary Club recognitions. BHS does
not recognize teacher of the year or teacher of the month. Thus, absent these overt
forms of recognition, the assistant principal believes that it is a very intrinsic sort of
motivation that teachers are feeling. It comes from being successful and knowing
that teachers have a voice and also feeling like the work that is being done is not
always being monitored for evaluation purposes. Assistant principal reported, “you
want people to feel comfortable sharing and that an administrator is not going to sit
in a meeting and get too involved. If I am sitting at a meeting, a teacher is not going
to tell his colleague that he is absolutely stomped on how to teach this next lesson
and ask for help.” The administration understands that if they are observing and
monitoring for evaluative purposes then teachers will not share this kind of
information. The motivation and reward comes from seeing students progress and
seeing the improvement in D and F rate, test scores and teachers’ own self efficacy.
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The culture of teaching at BHS goes beyond the teacher-student relationship and
extends to how teachers interact as professionals. The department chair has created a
culture of teaching and learning through the professional learning community he has
established. Teachers learn from each other and they learn from the department
chair.
The department chair has definitely taken on the leadership of the
math department. I could not envision how we could all work all day
during this math day without the department chair’s leadership. Any
idea that the department chair has, the principal and AP both support
him and the math department. The department chair is definitely the
innovator and the cause for all change (interview, 11.17.07).

As the principal has indicated, teachers also feel that the department chair’s
easy going and humorous personality helps him attain what he wants which is
teacher empowerment and describes the department chair as having “a very
disarming personality. He will tell a teacher hey that was really bad. You don’t
want to do poorly, you want to do well and this is what you want to do get better.”
The assistant principal knows that nor can he or any other administrator be
successful with this approach and effectively coach a teacher. Teacher B has been
teaching at BHS for eight years and has grown professionally due to the department
chair’s leadership and mentorship. She is often considered the department’s leader
in the department chair’s absence.
I don’t think I could ever fill the department chair’s shoes, but I have
enough of his ideologies and methods that I could inspire those around
me and we could continue to collaborate. Another thing is that it is
systemic the way we all plan together, test together and analyze data
together, this is very powerful. I think a lot of schools do the
assessment, but they don’t do the analysis, reteach and retesting
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correctly. Because we are all on the same page and know that we
need to improve in how we reteach, I think the department can move
forward with or without the department chair. Teaching here is
amazing, it really is. I wouldn’t consider teaching anywhere as long
as things keep moving this way (interview, 11.17.06).

Like any organization that has benefited from strong leadership and desired
results, losing the leaders is always possible and steps need to be taken to make
successful strategies systemic so that they can sustain a transition if the leader leaves.
As Gross (2002) found in his investigation of mentorship in reforming high schools,
the agenda for the curriculum, instruction and assessment reform was often lost when
an effective leader left a high school. Those that incorporated systemic mentorship
programs were more successful in sustaining the achievement they had gained with
the previous leadership. Even when asked directly, the department chair has no
immediate plans to leave BHS. Nevertheless, he has created an atmosphere where
information is freely exchanged and where all teachers take on some level of
leadership. Just as teachers rotate and take on the leadership of coordinating the
common assessments throughout the school year, they also become occasional
experts with a particular standard or teaching strategy. Because the leadership within
the math department has been distributed first to the department chair and then
throughout the entire department, sustaining math achievement at BHS is very likely.
When the administration was assigned to BHS four yeas ago their immediate
task was to raise student achievement in all content areas, especially in English and
math. It was opportune to have the department chair also transfer to BHS to assist
with this challenge. Bailey High School’s administration recognized the department
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chair’s strengths and background and opted to support him and allow him to assume
the role of instructional leader of the department.
Research Question Five
How did instructional leaders respond in academic areas in which they were
not experts?

When compared to Framework D, Instructional Leadership, the data related
to the preceding research question points to the department chair as the leader who
took on most of the tasks and role associated with instructional leadership for the
math department. Although the principal and assistant principals exhibit qualities of
instructional leaders, they are not experts in math. Framework E, Principal’s
Expertise in math is very linear and makes a precise evaluation based on the
principal’s credentials and math background. Based on the Federal NCLB’s
definition of highly qualified (HQ), Framework E deems a principal as high expertise
if he or she has a math credential and is considered highly qualified under NCLB.
The principal or assistant principals have medium expertise if they have a credential
in math or have a major in math. Those school leaders who have a minor in math or
who have taught math before would also be considered medium expertise. As is the
case for administration at BHS, those administrators with no math background,
experience or credentials would be considered low expertise. For those not familiar
with BHS but aware of their progress, the question would be how administrators
achieved growth in math student achievement for the past four years? The
department chair believes that the principal is very modest in his leadership style and
that he and his team are good delegators. He states that they know we are the experts
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and they allow us to do things.” The principal is very familiar with his math team
and does not control what happens for his sake, but instead allows math teachers and
the department chair to meet the needs of students. The department chair feels the
principal has the best interest of students in mind and that he will surrender his
leadership authority to others if it serves students best.
Remaining unobtrusive and giving consent to the department does not mean
the principal is not involved with the math team or somehow related to student
achievement in math. As discussed in research questions, two, three and four, the
principal provides some direction by leading in the development of goals for the
school and department, providing student performance data, and giving the math
department various resources to carry out their policies. In the case of math day, the
principal worked with the school district and provided the justification for why this
professional development day would be effective and should be approved.
Members of the math department appreciate that BHS administration does
not demand results, particularly since the department has generated significant
results in the past four years without pressure from the administration. They
principal is aware that his math department is made up of professionals that are not
resistant to change. The fact that the team works well together and is attempting to
find solutions to complex teaching and learning problems gives the principal reason
to allow the department some independence. The department chair sees the
principal’s level of involvement as strategic.
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It was not apparent that the principal was focused on results at first, I
am sure there were many things going on, but now it is. They did
hold us accountable but they do not push very hard at all. The
principal’s philosophy is that you cannot force things upon people.
He allows things to work themselves out in some other way. For
example, some of the other departments have not had as much
success. The problem was that they were not able to find key people
earlier. Now those departments are moving. Once things start
moving in the right direction, then they come in and do what needs to
be done to keep the ball rolling. I think this is a noteworthy strength
in a leader. Administration puts itself in a place of support. All the
movement is not going to come from them. They find key people to
put in the role of department heads and place them there (interview,
10.30.06).

When comparing Framework E to each of the administrators at BHS it is
apparent that both the principal and assistant principals lack content expertise in
math. Each of their credentials is in areas other than math and their master’s degrees
are related to instructional and educational leadership and not a specific content area.
When asked how he overcomes his lack of expertise in math in order to support and
lead the math department, the principal replied by saying that he hires great
department leaders, “I honestly believe that the best personnel move that has had the
greatest impact on an entire school is bringing the department chair in as the
department chair.”
The math department chair has confidence in his leadership ability and
teachers respond to his strengths in this area. After four years, the department chair
has impacted not only the teachers’ instructional practices and student achievement
scores, but he has developed leadership within his department. Developing
leadership capacity within the department has led to more effective course leads that
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have further distributed the leadership. As a result, there are more people in the
math department sharing the responsibility of guiding the department toward
meeting its goals. The department chair reported that other departments have seen
what has transpired in math and are now beginning to implement those successful
practices for themselves. With the support of the administration, the department
chairs have taken on a more essential role of instructional leadership and not left the
department’s success to the principal or assistant principal. The empowerment of the
department chairs puts them in greater control of their departments and they can now
avoid departmental erosion in the absence of the principal. Fullan (2002) found that
charismatic leaders that were too absorbed in their school’s departments without
distributing leadership to others were actually a liability for sustained improvements.
With a distribution of leadership and a greater leadership role given to the
department chair, the principal has devoted more time to address other needs in the
school. He continues to seek out good practices in the department and other areas of
the school and promotes them by praising staff and acknowledging those responsible
for implementing them. He takes the problems and dilemmas and allows for the
department chair to focus on moving the department forward instead of getting
caught up in the problems himself. The department chair sees this level of support as
invaluable because he does not get bogged down with political issues. “We use the
principal to take care of the behind the scenes things that need to be taken care of”.

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Discussion
The findings in this chapter were deduced from a careful analysis of the data
followed by a synthesis and organization of the findings by research question.
Although there were several findings that led to increased math achievement at the
research site, there were three salient themes that emerged in the study of BHS’s
math department.
Theme One: Political demands triggered a need for change
Prior to BHS’s identification as a program improvement school, a culture of
mediocrity existed in the math department. As teachers and the administration
reported, there was a segment of the student population that was achieving at high
levels. The majority of students, however, were not achieving proficiency in math
and other subjects. Other than grade reports or archaic data-producing systems that
measure student progress, BHS and the BUHSD were not accurately assessing
student progress. The poor systems of measuring student achievement were further
exacerbated when attempting to measure student achievement by subgroup such as
English learners, Hispanic/Latino and those economically disadvantaged. It was not
until the implementation of federal and state accountability systems that school
district leaders at BUHSD acted by beginning to produce some changes affected by
the employment of the human resource, structural, and symbolic frames (Framework
B).
Bailey High School, as was the case for many California high schools, could
not overlook the demands of No Child Left Behind and the Public Schools
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Accountability Act. The essence of these two accountability systems is that the
performance of every student was considered, not just the aggregate score of all
students. Those students who were performing at proficient and advanced levels in
math were too few to bear the expected school performance targets by state and
federal accountability measures. In addition, prior to the implementation of these
measures, the advocacy and support for lower performing students was minor or
practically nonexistent. The fact that NCLB and PSAA separated the level of
student proficiency by subgroup ultimately highlighted the lack of student
performance at BHS resulting in the necessary political pressure to initiate the
process of change and equity in instructional support for all students.
Thus the political frame was initially prompted by policy set by state and
federal legislators and later served as leverage for district and site leaders who used
the political impetus to marshal the onset of change. While BUHSD leaders
continued to use the political frame to bring about change, the next frame employed
was that of human resource. By appointing a new administrative team and the new
department chair, the BUHSD was successful in producing structural changes to the
math department that eventually led to improved teacher capacity and increased
student achievement.
Theme Two: Change through teacher collaboration
Although BHS, due to low academic achievement, was headed in the
direction of program improvement, it is likely that some teachers were effectively
meeting the needs of some struggling students. Because the success of these
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students was not necessarily being measured and monitored, teachers and the
administration did not know which teachers were successful in moving students into
proficiency levels. Moreover, teachers who were effective in meeting the
instructional and learning needs of low achieving students were not being identified
or given a forum for sharing their expertise with others.
The early stages of program improvement had low levels of accountability
for teachers and therefore did not encourage teacher collaboration for the purpose of
increasing student achievement. As evidenced by teacher survey responses, many
teachers did not feel that NCLB and PSAA were the means that compelled change at
BHS. The accountability in these two systems was not enough to promote the
development of a professional learning community at BHS. The need for
collaboration was instead developed and promoted by the internal accountability
system created by the math department’s chairman and supported by the school’s
administration. It is important to note that other departments at BHS have not
developed a successful professional learning community and hence assume a lower
level of responsibility and accountability for student learning.
Collaboration in the BHS math department first led to teachers brainstorming
on how to solve complex math problems. Teachers were forced to think of new
strategies for delivering instruction. At times, when frustration grew among
teachers, the use of what at one time were considered unconventional strategies were
utilized resulting in improved learning levels. Brainstorming through collaboration
not only led to enhanced teaching and improved learning, but teachers released their
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dependence on ineffective teaching practices and the pernicious philosophy that
some students do not learn because they were unmotivated or incapable of achieving
high levels of learning.
As teachers changed and improved their instructional skills they also began to
make structural changes within the department. Collaboration led to ideas related to
the master schedule, course offerings, curricula design, grading policies and
interventions for those students who struggled with algebra, geometry and algebra II.
These structural changes compelled even those teachers that the department chair
and principal considered resistant to change, to deliver instruction to students in such
a way that students had improved chances of mastering rigorous math content.
Students also found that they were placed in situations that were conducive to
learning content they had struggled with in the past.
By making collaboration a regular practice, the BHS math department created
its own internal professional development program. Marsh & Codding (1999)
suggest that high schools should be organizing themselves to support the concept of
professional development as a strategy for getting all students to achieve at high
levels. Math teachers, through the leadership of the department chair, have achieved
this. They not only support each other, but they increase the capacity of the entire
department and math program that has resulted in higher math achievement for all
subgroups at BHS.

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Theme Three: Instructional leadership
Improved results in math have been sustained for at least four years at BHS.
As formerly stated, the renewed professional capacity of the math department’s
teachers has given virtually every student at BHS access to effective instruction in
math. This capacity was absent five yeas ago and took time to develop. Before the
department learned to successfully meet the needs of the students they needed a
leader to not only to increase the capacity of the teachers, but someone to manage
and lead the instructional program. The results were initiated and sustained due to
the instructional leadership provided mostly by the math department chair.
Teachers in the interview process of the study emphasized repeatedly how the
department chair began teaching algebra along with his own colleagues. As he
taught and worked directly with students, he also began to analyze the curriculum,
the assessment program, his own instructional practices and those of the teachers in
his department. As a result of this analysis, the reasons for the lack of student
achievement became evident. As he looked for solutions to the gaps in the teaching
and learning process, he included other department teachers teaching algebra. The
teachers brainstormed ideas on how best to intervene that resulted in structural
changes as well as instructional changes. Modifications were made to the curriculum
and other elements of the algebra program. Eventually, the effective instructional
practices, interventions and other elements such as grading policies and a common
assessment became uniform throughout the entire algebra program. These changes
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became systemic and the algebra teachers were devoted to the program because they
helped develop it.
The department chair successfully replicated this process with the other
departments. Geometry, Algebra II and CAHSEE support classes also benefited
from a calibration of instructional practices, curriculum, assessment and
interventions in their own sub-departments through the leadership of the department
chair. As each course and the teachers that taught it improved, the department chair
provided the instructional leadership to help merge the courses together in order for
students to transition from one course in the department to subsequent courses
successfully. Grades and common assessment results from prior years were made
available to all teachers creating not only valuable information for teachers, but a
transparent system of internal accountability throughout the department. The
changes created by the department chair became part of the culture of the math
department and initiated a system for getting all students at BHS to proficiency in
math.
Instructional leadership includes adequate knowledge of the content and
elements that make up the instructional program. Fink and Resnick (2001) suggest
that the principal, in order to be an effective instructional leader, must understand the
instructional programs that the school has adopted well enough to actively guide
teachers in its implementation (Fink & Resnick, 2001). In the case of the math
program at BHS, prior to reorganization due to low student performance, the
program had neglected the needs of most students. The math program needed to be
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redesigned and the principal, who had low expertise in math, depended on the
content expertise of the department chair. The department chair, however, had more
than just content knowledge; he also possessed leadership skills and thus took on the
role of instructional leader. Four years later, the math the department chair at BHS
continues to enhance the math department and increase its capacity to reach higher
levels of student proficiency in math.
Along with the successful changes that are now part of the system in BHS’s
math department, the math the department chair has also instituted a culture of
continuous improvement. The cycle that teachers go through on a regular basis is
elastic and designed to adapt to the changing needs of students. These changes can
be to the curriculum, how the curriculum is delivered (instruction) and the
interventions offered to students. These changes are all due to effective instructional
leadership that is clearly present in the math department at BHS.
The three themes highlighted in this study represent a process that led to
improved math achievement at a high school that previously was failing to meet the
needs of a significant population of its overall student body. The first theme relates
to defining and articulating what is important to the department and how achieving
that goal will be measured. In this case, federal and state legislation created the
priorities for the department and mandated that progress be measured on a yearly
basis. The second theme centers on the method for problem solving and eliminating
barriers that were keeping the department from meeting its goals. Through
collaboration, teachers found solutions to complex learning problems and began to
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systematically remove common teaching and learning problems from their
department. Finally, theme three provides a leadership practice that yields the best
return when translated to student achievement. These three themes blend together to
create a system that supports student learning. The absence of any one of these
themes affects the effectiveness of the others. Once present at BHS’s math
department, the three themes began to synergistically move the department forward
in meeting the needs of all students.
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CHAPTER FIVE
SUMMARY, CONCLUSIONS AND IMPLICATIONS
Soon after America’s post-war economic growth, the public perception of
how America compared to other industrialized nations and even developing
countries underwent a change. The American public had believed that the nation
ranked amongst the highest in technology and other fields related to science and
math. However, events such as the launching of Sputnik by the Soviet Union in
1957 and reports like A Nation at Risk in 1983, created a cause for concern. Those
concerns were validated just a decade later when The Third International
Mathematics and Science Study (TIMSS) revealed that elementary, middle and high
school students in the United States were performing below the international average
even when compared to students in developing countries. Since then, American
educators have made a concerted effort to improve student achievement in math and
science, and more recently, these efforts have been mandated by state and federal K-
12 education targets.
Recent policies, such as NCLB and California’s PSAA, are designed to
incrementally increase the percentage of students proficient in math and other
content areas. Ironically, the policies have compelled schools to focus on meeting
the yearly minimum proficiency rates by means that Elmore (2003) has referred to as
short-term solutions such as test preparation and cursory tutoring designed to assist
students in passing a test by accessing short-term leaning rather than seeking long
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term solutions that would help both teachers and students to solve considerable
learning gaps. The drive for educators to increase the percentage of students
reaching proficiency has inadvertently caused less attention being paid to increasing
the number of students enrolling and succeeding in higher level math courses.
The High School Survey of Student Engagement (2004) reveals that students
are not taking advanced levels of math. Many seniors, discouraged by their
frustrations with math in earlier years, choose not to take any more math coursework
than what is required for high school graduation. This frustration leads to more
global problems that affect college acceptance and college completion rates. The
College Board (2005) maintains excellent data on AP enrollment patterns and
statistics throughout the nation consistently reveal that students in advanced math
courses have an increased likelihood of getting into college and succeeding once
there.
Above having an impact on college acceptance, higher level math also poses
an equity concern for educators. While students enrolled in AP programs succeed at
higher levels, the majority of students in AP programs are white and many states
throughout the country are doing little or nothing to address this inequity. California,
a state with highly diverse public high schools, is one of many states that is not
recognized for having a program with a significant percentage of African American
or Latino students passing the AP calculus exam with a 3 or higher (College Board,
2005).
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Collecting and accessing data related to math achievement and college going
rates further highlights the problem that educators have failed to repair for more than
fifty years. A different leadership structure along with a new system for supporting
students who struggle in math is necessary. The traditional role of the principal as
the site manager will no longer meet the demands of the country and economy to
produce high achieving, problem solving students with a high aptitude in science and
math. School principals must increase their capacity as instructional leaders and
increase the capacity of their own teachers and staff as they build the efficacy of their
school and work towards a common goal and for a collective purpose (Fullan,
Bertini & Quinn, 2004).
School leaders and policy makers have developed a curriculum and system
for assessing student learning that serves as a vehicle for principals to design and
guide the instructional program. Leading and managing the instructional curriculum
is guided by performance and content standards that were adopted by the State of
California more than ten years ago. Standards are a guide for teachers,
administrators, parents and students themselves to understand what knowledge and
skills students must master (Haycock, 2002). What students are expected learn, how
they are assessed and what it takes to produce a high school graduate ready for
college admission is virtually defined by the state department of education and
colleges and universities themselves. What instructional leaders and teachers must
do is find solutions and implement the elements of school design that lead to higher
levels of student achievement.
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Marsh & Codding (1999) suggest that the four critical elements of school
design are curriculum, learning activities, student performance assessments, and
school culture. Each of these elements has sub-elements that can assist school
leaders in designing an effective school or to help ascertain why problems with
learning may persist. Marsh & Codding (1999) and other K-12 school researchers
agree that one important aspect of school design is to support the concept of
professional development as an integral part of their strategy for getting all students
to standards. Consequently, the goal is not only for students to achieve, but for
teachers and the support personnel to develop professionally to meet the needs of the
differing needs of each learner.
Overview of the Problem
American students in urban high schools are encountering great difficulties in
getting through higher level math, a subject that is vital not only in completing high
school, but in gaining acceptance into college. Mathematics has become a
“gatekeeper” controlling entrance into college, particularly into programs such as
engineering (McGee, 2005) and has produced a higher number of remedial math
programs both at the high school and college level. These remediation programs are
disproportionately filled with students of color and those coming from under-
privileged communities.
Recent accountability programs initiated at the state and federal (PSAA &
NCLB) levels have sparked a reaction from high schools and school districts that
have resulted in programs to help all students reach minimum proficiency levels in
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math and other subject areas. While high schools have designed programs to reach
this objective and extended services to many students not yet reaching proficiency in
algebra, high schools, specifically those in urban communities, have not designed
programs to help students achieve in courses that better prepare them for college
acceptance and college success.
The Purpose of the Study
The purpose of this study was to understand how school design, policy
initiatives and instructional leadership shaped patterns of math achievement at a
single urban Southern California High School that led to sustained improvement in
math achievement. To guide the study, the following research questions were used:
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 instructional leaders respond in academic areas in which
they were not experts?
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This study was designed to examine leadership constructs at an urban high
school whose students are performing high in mathematics compared to other
schools with similar demographics. More specifically, the goal was to determine the
relationships, patterns and practices that lead to high achievement in math. In
addition to the leadership roles, the study examined the policies, curriculum and
instructional practices that have led to math proficiency in students who generally
perform poorly. The study focused on mathematics primarily because numerous
data that show that students who take rigorous and high-quality coursework in math
are more likely to complete a bachelor's degree and accomplish it within four years
or less.

Instrumentation
Each of the instruments was designed to elicit information and data that that would
later be examined and studied. Four data collection instruments were developed by
the research team that consisted of 10 doctoral students in the Rossier School of
Education’s Doctoral Program under the direction of Dr. David Marsh in order to
collect data and to interpret it by way of the conceptual frameworks. The school
profile, teacher interview guide, key leader interview guide and teacher questionnaire
were the research tools employed to gather the data.

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School profile
The school profile was the first data instrument to be developed since it was
used to identify the cohort of schools studied by the research team. The data
collected by way of this instrument was limited to demographic data such as total
school population, ethnic breakdown and economic standing. The school profile also
provided student achievement data in math and other content areas which illustrated
the trend in mathematics achievement that this study was seeking to examine.
Teacher interview
In order to record and examine the accounts of teachers who were active
participants in the math department, the teacher interview was created and acted as a
guide to elicit a conversation. Math teachers at BHS had various prior experiences
and were all at different levels in their careers. Having an open-ended interview
guide allowed for differences in perspective and response and later allowed the
researcher to draw important conclusions
Key leader interview
Like the teacher interview, the key leader interview guide provided a tool to
initiate a discussion in which the subject, in this case the principal, assistant principal
of instruction and the department chair, that made it possible to convey the strategies
and processes that led to the current level of math achievement at BHS. Each key
leader had a different role and different set of prior experiences all which were
manifested in their responses to the key leader interview guide questions.

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Teacher questionnaire
Two versions of the teacher questionnaire were developed. The purpose for
two teacher questionnaires was to differentiate and decipher the data from math
teachers as opposed to non-math teachers at BHS. Having questionnaires
specifically from math teachers would allow for perspectives, philosophies, practices
and other distinctive features associated with the math department to emerge.
After careful review and several revisions, five conceptual frameworks were
developed in order to examine and analyze the data gathered by the data gathering
instruments. Each of the frameworks is grounded in research and serves as a lens in
order for the researcher to evaluate the policies, practices and other findings
associated with this study.
Conceptual Framework A – School Design
In order to discern the elements of a successful school design, Marsh and
Codding’s (1999) framework for school design was used. This framework not only
centers on the essentials of school design that have a direct effect on student
learning, but it also concentrates on the concept of professional development as a
built in feature for getting all students to standard. Other elements of this framework
are related to the conditions in which students learn. While the framework discusses
curriculum, learning activities and performance assessment, it also emphasizes
school culture that is based on enhancing student learning.

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Conceptual Framework B – Change Process
Of particular importance to this study was the change process that the school
went through and how leaders at the school either produced change or responded to
it. When leaders confront a challenge, Boleman and Deal (2003) offer a tool that
serves as a set of metaphoric windows that classify the problem and provide possible
solutions. The four frame model organizes issues that necessitate or cause change
into four areas including structural, human resources, political or symbolic.
Conceptual Framework C – Effective Math Programs
It is important to distinguish between successful elements of school design
and those elements related specifically to math education. Ball and Cohen (1996)
offer a framework that centers on three core themes present in an effective math
program. If students are expected to meet rigorous standards and perform well on
standards based exams, then it is apparent that instruction needs to be standards-
based. Within standards-based instruction, Ball and Cohen (1996) underscore the
need for student achievement data to drive instruction and for teachers to collaborate
regarding achievement results. The second theme relates to curriculum design.
Curriculum should be designed so that students meet a year long scope and sequence
based on current learning theory. In order for students to develop a true
understanding of the material they are presented with, curriculum should focus on
problem-solving and conceptual learning. The final theme centers on classroom
practices that promote high levels of student engagement make use of prior
knowledge and provide opportunities for accelerated interventions when necessary.
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Conceptual Framework D – Instructional Leadership
The practices related to instructional leadership differ from those involved in
school management. Although most of the duties and actions from school
administration are primarily tied to student achievement, there are those standards
and research based-models that relate directly to instructional leadership. The
Laboratory for Student Success (LSS) at Temple University has developed standards
for school leadership practice. The standards center on the need for principals and
other school leaders to be instructional leaders who strengthen teaching and learning,
professional development, data-driven decision making and accountability.

Conceptual Framework E – Leaders Expertise in Mathematics
It is not likely for any high school principal to be an expert in all the subjects
taught at a comprehensive high school. The expertise framework was developed to
measure the level of content knowledge the principal has in mathematics based on
NCLB’s highly qualified model. The higher the expertise the more directly the
principal would be able to lead the math program. If the principal had low expertise
in math, then the goal was to examine how the leader responded to challenges related
to his lack of expertise.
Data Collection and Analysis
Five rounds of data collection occurred at the research site over the course of
three months. Each of the five rounds of data collection included the disbursement
and gathering of completed teacher questionnaires, teacher interviews and key leader
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interviews. Every effort was made to conduct valuable and reliable data while
observing confidentiality and every subject’s right to decline participation in the
study.
The school profile was the initial instrument used to identify the research site.
The data collected using the school profile was purely demographic and related to
student achievement scores that are available to the public by way of the California
Department of Education’s website and published data and statistics. The rounds
made to the research site began in October 2006 and concluded in December 2006.
The rounds consisted of the disbursement and collection of teacher questionnaires,
math teacher interviews and key leader interviews.
Qualitative research and data analysis methods were used in order to
purposefully select both the participants and the site that would best help the
researcher obtain and understand the data related to the research questions (Creswell,
2003). Interviews consisted of six math teacher interviews and three key leader
interviews. Interviews were taped, scripted and reviewed in order to find saleable
points related to the topic under study.
Findings for Research Question 1
Although not remarkable, the pattern of math achievement at BHS is
impressive and uncharacteristic of other Southern California High Schools with
similar demographics. For the past four years, all students, including those
belonging to the school’s significant subgroups have sustained growth in math and
made minimum expected proficiency rates as defined by NCLB. A significant
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number of students, including those that belong to Hispanic/Latino, Economically
disadvantaged, and English Learner subgroups moved into proficiency levels in
algebra, geometry and algebra II from 2003 to 2006. It is important to note that not
only did more students become proficient in math over the course of four years, but
the percentage of students performing below basic levels was also reduced. There
were 7% less students at far below basic levels from 2003 to 2006 and 5% fewer at
the below basic level.
Student performance in higher level math courses, such as those courses that
are part of the Advanced Placement program, have not achieved the same rate of
success at BHS. Although the number of students in these courses is far fewer and
typically influenced by fewer teachers than standard math, students in courses such
as calculus have not achieved the same rate of success. While a greater percentage
of students passed the AP exam with a score of 3 or higher from 2003 to 2006, 5
fewer students took the exam. Although the school has made recent efforts to
increase the number of students in higher level math, the proportion of students in
advanced math when compared to those in algebra and math intervention courses is
extremely low.
The most important finding with respect to student achievement in math is
the upward trend that has continued for the past four years. When examining the
causes for this trend, there is evidence of systemic, student-centered changes to
school policies, the curriculum, math program, and approaches to the leadership
within the math department that have built a foundation for continued growth. With
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a higher number of students succeeding at lower levels of math, the school and math
department in particular, has positioned itself to extend needed support to those
students ready for higher level math.

Findings for Research Question 2
Both the survey data and interview data reveal that, by and large, teachers at
BHS agree that the federal NCLB legislation triggered improvements in math for
their school. This view is supported by the fact that most of the changes to policies
and the human resources at the school were made once the school was identified
program improvement. Fullen et al (2001) maintain that pressure that the state
accountability system puts on schools such as BHS is beneficial because it leads to
comprehensive strategies that result in patterns of improved achievement. Along
with the pressure, however, there needs to be support for meeting higher targets of
achievement. Although the pattern of incremental success has been set due to the
pressures of accountability, the school has not had much support from state and
federal levels. The funding schools receive in the form of assistance grants is
minimal and only provisional. The school district has provided some support by
giving the school financial resources and some latitude in making curricular
decisions. With this level of support, BHS has been able to remain ahead of minimal
NCLB targets in math. Yet school leaders and teachers at BHS feel that the math
program’s improvements in past years go far beyond the expectations of NCLB.
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According to the school’s administration, the math department has a different
attitude than other department teachers, and as a result, has a higher rate of success.
An example of the difference in attitude is related to math teachers’ sense of
responsibility for student learning. During their regular collaboration sessions,
teachers analyze student assessment results and ask “why” students did not score
well on specific questions or standards. Teachers who had better results share their
strategies with colleagues and brainstorming for how to solve the teaching and
learning problems. This has become the internal professional development system
for the department that Marsh and Codding (1999) argue creates the conditions for
all students to achieve.
The professional development four years into the new design of the program
has become a carefully planned training based on teacher needs and where they fall
in terms of what is considered to be a highly qualified professional instructor that
meets specific needs of students. The department chair stated that sending teachers
to trainings such as conferences and workshops will be more beneficial once teachers
have developed professionally within their own classrooms and with their own
colleagues. For now, the department is dependent on the expertise within their own
department. The least common denominator for the department has become the best
teaching strategies of each individual teacher.
The department chair and school administrators attribute the sustained growth
in math achievement to a cycle of collaboration that exists. The cycle incorporates
standards-based instruction, assessment, analysis of student achievement, re-teaching
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and modification of instructional practices. This cycle results in not only improved
student learning, but it enhances the skills and knowledge of teachers as
professionals. The data from prior years is preserved and recycled for following
years. When students experience “confusion” due to error in instruction on a
particular standard, teachers avoid these errors by noting and tracking errors in
practice so that they could be revisited the following year. As the system is
employed year after year, the team gains more knowledge and increases the
complexity of how they address teaching and learning problems.
As the math teachers and the math department chair analyzed patterns of
achievement, they not only made changes to their instruction and decided what
material to reteach, they also made long-term multi year changes to the master
schedule in order to address more profound learning problems. BHS teachers no
longer expected all students to improve and reach proficiency in time for state and
federal assessments. Instead, students were assessed and monitored over time with
most students eventually passing and meeting at least rigorous algebra standards.
Algebra students who did not meet standard by the end of their first semester were
placed in a second semester class with less students; approximately a 15:1 student
teacher ratio. Instruction in these classes consisted only of essential standards and
students were given a goal to meet in order to earn at least a “D” grade and receive
some academic credit. This strategy was successful as students were taught to
become self-regulated learners (Dembo, 2000) and watched their academic
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achievement increase in the next three semesters as they received intervention and
passed algebra the following year.
The teaching and learning process at BHS is well monitored and to some
degree controlled. Math department teachers have a good approximation of how
well students will perform on state exams well before results are returned from
contracted testing companies. They make decisions based on data and respond to
unfavorable results as a team and in a professional and systematic manner. The math
team, prior to identification of program improvement status and just thereafter, was
not operating at this level. It took several triggers that generated change in the
department.

Findings for Research Question 3
Initially, it was the global policy and accountability structure set by NCLB
and PSAA that provoked the beginning of the change process at BHS. Subsequent
to the identification of program improvement several changes occurred that clearly
can be categorized within the four frames of the change process (Boleman & Deal,
2003). The change process remained consistent and has become a built-in feature for
the math department at Bailey High School. Changes take place mostly due to data
and the variability in student needs.
The second and most evident change at BHS was implemented by the district
and related to the human resource frame. The district not only replaced the principal,
but brought in an entirely new administrative team with proven results of success. In
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addition to new administrators, the district persuaded a district teacher to take on the
role of department chair assuring him the support he needed to develop a successful
math department. Once the members of the math team were in place, school
administrators and the department chair began to take on leadership roles in order to
develop the human resource within the department and in order to begin the
structural changes necessary for increased student achievement.
Many of the changes that were made BHS that resulted in increased student
achievement were structural. At the outset, BHS leadership did not exert much
energy in changing the attitudes and philosophies of math teachers. Instead they
focused on setting goals and establish policies and procedures that would facilitate
meeting those goals. One of the first strategies was to initiate collaboration time
approximately ten times a school year. During collaboration time, teachers were
expected to share their successes and negative experiences based on common
assessment results, during these sessions teachers began to dialogue, lower their
guards and defenses. After several collaboration sessions, a change in attitude and
philosophy began to emerge naturally. Rather than find fault with issues outside of
their control, teachers began to brainstorm possible solutions to teaching and
learning problems. They not only reflected on their own teaching practices, they also
examined each others practices collectively by providing feedback to one another.
Teachers were not only accountable for their students’ performance data, they were
also accountable for sharing their experiences in the classroom in a collective way to
ensure that all students were subject to the best instructional practices. All the work,
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including teacher and student performance, is now transparent at Bailey High
School. Grades and test scores are shared and published despite the results. The aim
for publishing the data is for reasons related to improvement of instructional delivery
and not at all used for evaluation purposes.
Although many of the elements that have caused change in the department
fall into various frames of the change process framework, most are due to the
collaboration that Dufour (2004) labels a professional learning community. Through
collaboration, the math team has created a systemic method for solving various
obstacles the department is faced with. The math department at BHS has established
a sequence of systems that encompasses how students are scheduled into classes,
how and when data is analyzed, when students are assessed, what material is
retaught, and even how students structure what they ask their peers when they need
assistance; a notion that is usually uncomfortable for most students.
Bailey High School’s math department has instituted a socialized learning
and intelligence concept (Resnick, 1999) by not only demonstrating this through the
department’s professional learning community, but by depending on their own
students to help each other. Accountable talk is used in classrooms with students on
a regular basis as students help their own peers reach standards they are experiencing
difficulty with. This concept was brought up by teachers who reported to their
colleagues that what they struggled to teach was more successfully taught by
students who were mastering concepts that peers were unsuccessful with. This
extended collaboration and a community of learning to the student level.
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Although BHS math teachers refer to the time they spend discussing student
achievement as “collaboration” the transformation in the effectiveness as a
department happened when the “shift—from a focus on teaching to a focus on
learning (Dufour, 2004, pg 6)” occurred which built the foundation for their
professional learning community. During this collaboration time, teachers asked the
three questions Dufour (2004) suggests are crucial in driving the work of a
professional learning community:
1. What do we want each student to learn?
2. How will we know when each student has learned it?
3. How will we respond when a student experiences difficulty in learning?

Getting the math team to this level took leadership on the part of district
administration, school-level administration, and the department chair. The team took
years to develop and continuous to do so at present. The leadership that helped
develop the math team into a professional learning community takes a different form
when addressing specific teaching and learning problems. When attempting to
substantially improve student achievement by improving curriculum and instruction,
the need for instructional leadership transpires.
Findings for Research Question 4
“One of the misconceptions about leadership at the school level is that it
should reside with one individual (Marzano, 2003 pg. 174).” The instructional
leadership at BHS, although largely provided by the department chair, is distributed
throughout the math department and with administration. After evaluating the
practices of school leaders at BHS, it is clear that some of the behaviors and
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responsibilities of an instructional leader are performed by the principal and assistant
principal and others by the department chair. The department chair attributes some
of his success as an instructional leader to the principal’s willingness and enthusiasm
to collaborate with the district and other political entities to gather the resources and
support necessary to move meet the department’s goals. Nonetheless, elements of
instructional leadership that more directly impact the learning process are performed
by the department chair.
The department chair spends a great deal of his time observing and
monitoring the instructional program by visiting classrooms and teaching some
courses himself. He provides constructive feedback in a timely manner to all
teachers both during collaboration and through a coaching model directly with
individual teachers. He uses data as a tool for informing instruction, both
quantitative and observable data in terms of teacher and student behaviors. He uses
this data to make decisions related to supporting student learning. In order to
become more familiar with the content and issues related to student learning, the
department chair scheduled himself to teach algebra, geometry, algebra II and
intervention courses during the course of several years thus giving him the
background knowledge to better support teachers and to make more informed
curricular decisions. This commitment to instructional leadership has made the
department chair an invaluable resource for teachers.
Although several teachers responded that they had participated in district or
outside trainings earlier in their career, none of them stated that these trainings were
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very valuable or that such training sessions had a positive impact on their teaching
practices. All teachers that were interviewed stated that their most valuable
professional development came from collaboration directly with the department chair
or during formal collaboration time with their colleagues. This further exemplifies
the department chairs success in developing the capacity of his team.
Fullen et al (2001) links the importance of the principal’s development and
skills related to instructional leadership with those of the entire school as a
professional learning community. Along with his or her own professional
development, the instructional leader is responsible for getting the teaching
personnel to become more skilled and more autonomous in solving complex teaching
and learning problems. In the case at Bailey High School, the department chair took
on this role. Regardless of who took on the instructional leadership, the reality is
that the department’s teachers have developed and that students have benefited from
the instructional leadership. The final research question’s findings relate precisely to
how the principal responded to leading in an academic area in which he was not an
expert.
Findings for Research Question 5
Given that there are approximately seven to ten subject areas taught in
comprehensive high schools, it is unreasonable to expect a high school principal to
have subject matter knowledge in every area, particularly in advanced courses. Both
the principal and assistant principal over instruction at BHS have an educational
background in social science and can more closely lead the instructional program in
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that department due to the content knowledge they have. However, it may not be
necessary to have an advanced educational background in math when helping
students learn basic algebra standards such as California Algebra Standard 4.0 –
Students simplify expressions before solving linear equations and inequalities in one
variable, such as 3(2x-5) + 4(x-2) = 12. Most teachers and school administrators
possessing a teaching credential took one or more courses in college-level math thus
should be able to solve a simple linear equation. Higher level math, on the other
hand, may be more difficult. California Algebra II Standard 4.0 – Students factor
polynomials representing the difference of squares, perfect square trinomials, and
the sum and difference of two cubes is more challenging and may require some
subject matter competency, particularly when attempting to help teachers find
solutions to problems students have in mastering this standard.
The argument here is not a pedagogical one but one of whether or not a
school administrator can lead in the teaching and learning process in a specific
content area. Knowing the content standards and being able to teach them may
require two different sets of skills. Goldhaber & Brewer (2000) found that teachers
who have fully-licensed certification in math have a statistically significant positive
impact on student performance levels relative to teachers who either hold private
school certification or are not certified in their subject area. At the same time, and
contrary to conventional wisdom, mathematics students who have teachers with
emergency credentials do no worse than students whose teachers who have a
standard teaching credential when measuring achievement gains. In this case it is a
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difference between measuring student achievement gains instead of levels. Either
way, the question of whether or not a principal with low expertise in math can lead a
math department with a goal of significantly increasing math achievement is
feasible.
With a school of more than 2,300 students, more than 70 certificated teachers
and an aging physical building, the principal at BHS is likely to be constantly
interrupted and his attention needed on numerous issues. This makes it almost
impossible for the principal to be the key instructional leader. For this reason alone,
many highly capable teachers with content knowledge avoid the path of assistant
principal and principal because they see it as too far removed from curriculum and
instruction (SREB, 2005).
In the case of Bailey High School, the principal knows without a doubt that
he has a competent department chair and also possesses excellent leadership
qualities. When evaluating the behaviors of both the principal and the math
department chair based on the instructional leaders framework, one can argue that
both have the characteristics of an instructional leader. If the department chair had
not been transferred to BHS it is very possible that the principal would have found
somebody else to take on that role and produce the same results or the principal may
have stepped into that role himself.
Conclusion
Several factors led to the math achievement gains at BHS for the past four
years. Political pressure from the state and federal levels generated a series of
205
changes that are directly associated with the four frames (Boleman & Deal, 2003) of
the change process. In the course of the four years, various interventions were
offered, changes to the master schedule were made, course offerings changed,
tutorial support was offered and other structural efforts were made realigning how
curriculum was presented and instruction was delivered to students.
A feature of both the change process and of the math program itself is teacher
collaboration. The professional learning community that exists within the BHS math
department is the “idea generator” that has resulted in the policy and curricular
initiatives that helped raise student achievement as well as increase the capacity of
the teaching staff. Change within the department will likely be constant due to the
team’s willingness to collaborate and adjust itself to the changing needs of students.
While students benefited from teaching problems being solved through
collaboration, BHS math teachers also benefited as they developed as professionals
just as DuFour (2004) found that when teachers collaborate in professional learning
communities and share solutions to common teaching and learning problems, they
benefit as much as students do.
Most of the obstacles that affected the learning process were eventually
resolved through collaboration. It was not collaboration alone, however, that
initiated the need for change or that addressed other problems that surfaced as the
math department developed. There was evidence of many other factors associated
with each of the research questions that led to an effective math program at Bailey
High School. Before the teachers in the math department began to collaborate, there
206
was a sense of urgency and accountability triggered by state and federal policies that
demanded all subgroups demonstrate increased performance. Guiding the entire
change process and setting the stage for a method of collaboration was the
instructional leadership provided mostly by the department chair. As the department
chair developed the capacity of his team, he took his leadership a level higher by
identifying potential teacher leaders and distributing the leadership so that all math
levels had the guidance and support they needed to increase achievement. Much of
the department’s success is due to the support of the school district leadership and
the school principal. They did not refute the department’s ideas and initiatives and
often provided assistance in implementing them.
Recommendation
This study began by highlighting the need for a better prepared and qualified
work force that specializes in math. Historically the U.S. has had strong economic
and technological advancements that are associated with math and science. In order
to maintain its competitiveness in a global society, U.S. high schools and colleges
need to increase the nation’s capacity by increasing the number of graduates that
specialize in math and science related fields. Although BHS has had sustained
growth in subjects such as Algebra, Geometry and Algebra II, the pattern does not
exist in higher level math such as trigonometry and calculus. Many resources,
including funding, human resources and time to collaborate have been given to lower
levels of math such as algebra. Few students continue to graduate from BHS with
higher level math courses on their transcripts and likely do not have the highly
207
demanding study habits recommended for college level success in math (High
School Survey of Student Engagement, 2005). One major finding in this study based
on the data collected from interviews is that collaboration was attributed as an
important factor contributing to student achievement. Thus, in-house, department
based professional development promises to be an important necessity for spurring
student achievement both at the basic algebra levels and can also be extended to
advanced levels of math.
Tucker (2003) suggests a series of steps that will lead to more equitable
success rates in mathematics that will also help American high schools like Bailey
High School incrementally raise the overall national level of mathematics
achievement. Along with creating a higher set of standards, an assessment system to
measure them, and finance reform, Tucker emphasizes the need “to create the
conditions that will make it possible for high schools to get their students to the new
college-ready standard” (p. 12). A great foundation for a culture of high
achievement in math has been established at BHS. It seems to come to an abrupt
stop when moving a significant number of students from all subgroups to math levels
beyond those required for high school graduation.
Bailey High School students would benefit from a plan to move students to
the next level of math. An important component of this plan would be to increase
the number of students accepted into four year universities. In order to do this,
students would have to be encouraged to take higher level math courses and provided
the support in order to succeed. As a predictor for college success, math
208
achievement exceeded all other single predictors, even including parents’
educational attainment and socioeconomic status (Center for the Study of Education
Policy, Illinois State University, 2005). As BHS math teachers have already
initiated, they would have to continue looking far beyond the goals that NCLB and
PSAA have set for them and see how they could improve the likelihood of their
students’ quality of life due to a college education. Achieving this goal would also
address some global goals related to a better prepared American workforce related to
the field of math.
Suggestions for Further Research
Although BHS has increased student achievement in math, the original intent
related to the problem that triggered this study was not significantly impacted. By
the time most students pass algebra or other required math courses, they are at or
near graduation and cannot advance into higher levels of math. Nonetheless, the
BHS teaching staff has sustained growth in the percentage of students reaching
proficiency levels in algebra, geometry and algebra II. With more time or with a
higher percentage of students entering high school with more advanced math skills, it
is very likely that BHS teachers could take students into higher levels of math.
A review of the literature, analysis of the data, findings and conclusions,
within the context of the research problem, suggests the following areas for further
research:
1. It will be a daunting challenge for any school, like BHS, which is already
exerting a wealth of time, energy and resources at increasing math
209
achievement to promote a significantly higher number of students into higher
levels of math without additional resources or without a higher number of
students coming into ninth grade with a solid set of algebra and pre algebra
skills. How can achievement prior to students reaching the high school level
be further accelerated? Students come to high school with large gaps in their
math skills. This is not to say that middle schools are causing these gaps or
even that elementary schools are the cause of the problem. The Northwest
Evaluation Association (2006) suggests that 70% of the math achievement
gap that is evident in high school is created before the beginning of second
grade and likely between birth and kindergarten. If the math achievement
gap is visible this early, then the K-12 system needs a longitudinal plan that
involves a pre-kindergarten through 12
th
grade strategy for increasing math
achievement.
Although the obvious challenge to this recommendation would be
time to carry it out, having high school math teachers and middle school
teachers collaborate using a vertical approach would forge a more seamless
transition with the content students engage in and help decrease the gap that
currently exists between the skills students come to high school with and
what is expected at the high school level. This would entail a change in
practice from having students complete a course in middle school, to having
students complete a set of essential standards that are prerequisites to more
rigorous material they will face in high school.
210
2. The data at BHS makes it evident that many students take multiple years of
their high school experience to pass algebra. Courses and curriculum have
been designed by the math department in order for these students to
experience some success with the most essential standards and in order to
keep them motivated to pass algebra and eventually graduate. Additionally,
students are faced with numerous graduation requirements that add to their
frustration in mastering rigorous content in multiple areas.
The amount of standards and curriculum that a teacher and student
must cover in one academic year is abundant. Particularly for those students
who are struggling, covering this much material at such a fast pace can be
overwhelming. As Klein (2005) indicates, there are many mathematics
standards where students come up short. This may be due to an
overemphasis on some standards over others. A better analysis of what
standards should be mastered not only for Algebra, but for other courses
leading to algebra would be beneficial. If possible, the goal should be to
reduce the number of standards a student should master in one school year so
that they can succeed with, at minimum, the most essential standards. In
addition to an analysis of essential standards, school leaders should analyze
comprehensive graduation requirements so that struggling students can have
more time with essential core material and not be diverted by other
requirements that are not as vital.
211
3. Not every high school has the advantage of a highly skilled department chair
with excellent leadership skills. In order for principals in large urban high
schools to take on the role of instructional leadership, the mundane
managerial tasks that they are absorbed with must be reduced or the
instructional leadership role must be assigned to somebody else. This
recommendation implies two research possibilities: (A) How can the school
system, both at the state and local level streamline and possibly eliminate
some of the tasks that principals spend an inordinate number of hours on in
order to become effective instructional leaders or, (B) How can school
leadership in urban areas be distributed to department chairs so that important
issues related to teacher and learning be addressed. The current reality is that
principals and assistant principals are bogged down with dilemmas that are
not necessarily academic in nature. These dilemmas are predominantly found
in urban high schools where much of the population is economically
disadvantaged. If mathematics is the gatekeeper (McGee, 2005) course
controlling a student’s acceptance into college, then either barriers need to be
removed in order for principals to become more effective leaders in courses
such as math, or leadership structures need to be redesigned in order for more
equitable opportunities for student success to exist.
The non-instructional demands that keep school leaders from exercising
instructional leadership are complex and not likely to diminish. Therefore, it is
important to increase the capacity and empower department leaders so that
212
curriculum and instruction is not forgone and instead becomes the central focus of
the school. As is the case at BHS, the department chair does not take on a peer to
peer evaluative role. The department chair leads and guides the team toward
reaching a common goal while the entire math team supports one another as a
professional learning community to overcome teaching and learning hindrances and
to increase student achievement.
While these and other confounding issues related to student achievement need to
be investigated and addressed at a policy level, some local schools and districts have
already begun to create the conditions and culture that promote student achievement.
At BHS, learning is an expectation both for students and teachers. Rather than
attribute the lack of student achievement to external entities such as parents and the
community, BHS math teachers instead choose to learn more about their students
and how they can overcome barriers to learning. What BHS teachers have learned to
predict is that their students can achieve at higher levels provided they fine-tune their
instructional practices to meet the needs of their students. By implementing a
professional learning community, teachers have coached each other through
challenging learning problems that have resulted in sustained growth and improved
results.
213
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Abstract (if available)

Abstract Various forces are compelling American high schools to increase student achievement in math, science and other content areas. Local schools and school districts are responding to state and federal accountability measures that are prompted by reports such as the Third International Mathematics and Science Study (TIMSS) that creates a sense of urgency in improving education particularly since the findings in this study convey that American students rank far below even developing countries in science and mathematics.

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Asset Metadata

Creator Flores, Sergio (author)

Core Title Improving and sustaining math achievement in urban high schools: a case study of a southern California high school

School Rossier School of Education

Degree Doctor of Education

Degree Program Education (Leadership)

Degree Conferral Date 2007-12

Publication Date 10/26/2007

Defense Date 05/01/2007

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

Tag instructional leadership,math achievement,OAI-PMH Harvest,secondary math

Place Name Bailey (city or populated place), California (states), Los Angeles (counties), USA (countries)

Language English

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

Creator Email florse@fusd.net

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m892

Unique identifier UC1421059

Identifier etd-Flores-20071026 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-580736 (legacy record id),usctheses-m892 (legacy record id)

Legacy Identifier etd-Flores-20071026.pdf

Dmrecord 580736

Document Type Dissertation

Rights Flores, Sergio

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