University of Southern California Dissertations and Theses

High school reform to improve mathematics achievement

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High school reform to improve mathematics achievement

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Content HIGH SCHOOL REFORM TO IMPROVE MATH ACHIEVEMENT
by
Kimberly Tresvant
A Dissertation Presented to the
FACULTY OF THE ROSSIER SCHOOL OF EDUCATION
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF EDUCATION
August 2007
Copyright 2007 Kimberly A. Tresvant
DEDICATION
To my mother and all my mentors who have
provided great support and encouragement
ACKNOWLEDGEMENT
My heartfelt thanks to Shirley James of SJ Designs, etc.
for the gift of friendship and encouragement; but more importantly,
for the long hours spent proofing and re-formatting my typing. Her
knowledge, skills, and insightful assistance at the very last hour contributed
greatly to shaping this important writing into a cohesive whole.
TABLE OF CONTENTS
Page
DEDICATION
ACKNOWLEDGEMENT
LIST OF TABLES
ABSTRACT
CHAPTER 1 : OVERVIEW
Statement of the Problem
Purpose of the Study
Importance of the Study
Limitations
Delimitations
Organization of the Study
CHAPTER 2: LITERATURE REVIEW
The Status of Student Performance
The Achievement Gap
Importance of Mathematics
Policies to Improve Mathematics Achievement
Leadership
. .
11
. . .
111
vii
CHAPTER 3 : METHODOLOGY 83
Sample and Population 84
Figure 1 : The Relationship of Data Collection Instruments
To Research Questions 89
Data Analysis 97
Summary 9 8
CHAPTER 4: THE FINDINGS 99
Pattern of Mathematics Achievement for Various Students at Kando
Medical Magnet High School 100
Policy Initiatives, Curriculum, Instruction and Related
Conditions that are Seemingly Related to Improved Math
Achievement at Kando Medical Magnet High School 103
Change Process 110,136
The Effect of Leadership in Improving Math Programs1
Strategies and Math Achievement Among Students 114,137
Dilemmas About Instructional Leadership 126,140
Analysis and Discussion 132
TABLE OF CONTENTS
(continued)
Page
CHAPTER 5: SUMMARY AND IMPLICATIONS
Summary of Background
Purpose of the Study
Methodology
Sample
Instrumentation, Data Collection and Data Analysis
Summary of Findings
CONCLUSION
GLOSSARY
BIBLIOGRAPHY
APPENDIX A
Conceptual Framework For Model Math Programs
APPENDIX B
Conceptual Framework for School Design
APPENDIX C
Framework For The Change Process
APPENDIX D
Conceptual Framework for Research Question 4
APPENDIX E
Conceptual Framework For Research Question 5:
Does The Principal Have A Minor Or Taught Math?
APPENDIX F
Conceptual Framework For Research Question 5: Does The Principal
Use The Following Strategies: Delegate Leadership To Assistant
With Great Expertise, Bring In Outside Experts, Emphasize Inquiry
And Problem-Solving, Emphasize Quality Instruction, Emphasize
Strategies To Engage Students In The Learning Process, Articulate
With Feeder Schools, Emphasize Raised Expectations, Emphasize
Strategic Teacher Assignments, Emphasize Revised Course Scope
And Sequence And/or Curriculum, Emphasize Interventions For
Lower Performing Students, Or Emphasize Professional
Development?
TABLE OF CONTENTS
(continued)
Page
APPENDIX G
Key Leadership Interview Questions
APPENDIX H
Math Teacher Interview Questions
APPENDIX I
A Teacher Survey: Non-Math Teacher Questions
APPENDIX J
Standards-Based Instructional Process Criteria Checltlist
APPENDIX K 188
School Continuum for Implementing Standards-Based Education
APPENDIX L
Unofficial Classroom Observation Form
LIST OF TABLES
Table 1 AYP Bands for Kando Medical Magnet High School 10 1
Table 2 CAHSEE Math Results 2003-2005 103
ABSTRACT
This study examines math achievement as a result of policy initiatives in
combination with school design, best practices and school leadership. The study
focuses on five research questions: What was the pattern of math achievement for
various students at the school? What policy initiatives, as well as curriculum,
instructiodand related conditions seem to be related to improved math achievement
at the school? What change process did the school use to enhance its math program
and strategies to assist students in math? To what extent was strong instructional
leadership important in improving the math programslstrategies, and math
achievement among students? Details of implementation and adoption of specific
policy initiatives and school based programs for mathematics was examined in the
context of improving mathematics performance. Instructional leadership and its
impact on mathematics achievement where leadership lacks strong pedagogical
content knowledge in mathematics education were examined, incorporating an
understanding of how leaders work effectively in this context. The study utilized
both qualitative and quantitative data in conjunction with a school profile,
instructional leadership interviews, teacher interviews and surveys. The study
investigated the pattern of math achievement for various students using data
collected from Annual Yearly Progress (AYP) data and results from the California
Department of Education High School Exit Exam office. Policy initiatives, as well
as curriculum, instructiodand related conditions that seem to be related to improved
math achievement at the school was standards-based instruction and the California
...
Vlll
High School Exit Examination. A change process could not be substantiated. Strong
instructional leadership in improving the math programslstrategies was important in
establishing a vision for learning, supervision and monitoring of instruction,
community and political knowledge, the leader's knowledge regarding the culture of
learning and in the use and analysis of data. How instructional leaders responded in
academic areas for which they were not experts was delegation of authority,
empowering the department chairperson, brining in outside experts and changes in
outside experts and changes in personnel assignments.
CHAPTER 1
OVERVIEW
Calvin Coolidge once said, "No enterprise can exist for itself alone; it
ministers to some great need; it performs some great service; not for itself, but for
others, or failing therein, it ceases to be profitable and ceases to exist." Coolidge's
words are now applicable, although not initially applied to or intended for America's
public education.system. Public education exists for the nation's good. It ministers
the three Rs-reading, writing and arithmetic to students that provide a foundation
that enables participation in life.
America continues to believe that education is a life's foundation. Its belief,
such that the federal government, on behalf of its taxpaying citizens, has introduced
accountability measures to state education systems by using annual assessments,
setting goals, and implementing sanctions to ensure Americans are getting a return
on their investment. Public schools are saturated with constant reminders that
schools are failing. This is documented through federal mandates, state
accountability reports, newspaper editorials, real estate reports, and political attacks.
Public schools are criticized by local politicians, higher education institutions, and
education research organizations for persistent low performance and achievement in
all areas; more specifically, in mathematics.
Inadequacies of public school education in grades kindergarten through
grades 12 ("K- 12") education in relation to Mathematics ("math") achievement did
not just arise with the publication of A Nation at Risk, in 1983, but is noted as early
1
as the Second World War. In The Math Wars (2004), Alan H. Schoenfeld writes:
"In the 1940s it became such a scandal that army recruits knew so little math that the
army itself had to provide training in the arithmetic needed for basic bookkeeping
and gunnery" (Schoenfeld, 2004; p. 257).
Nationally or internationally, since World War I1 curriculum changes began
to take effect, but America's students did not fare well. America again focused on
the importance of mathematics with the onset of the Cold War and the successful
launch of Sputnik; criticism was once again focused on mathematics achievement in
the 1980s. America felt vulnerable that its national debt swelled, while the economy
in Asian countries began to soar. It was these conditions that gave rise to the
publication of A Nation at Risk, which exposed our nation to the deficiencies in its
educational system (Scholenfeld, 2004).
In 1990, An Agenda for Action was published by the National Council of
Teachers of Mathematics ('NCTM"); they "proposed that the primary goal of
mathematics curricula should be to have students develop problem-solving skills."
Problem-solving involves understanding the conceptual nature of the problem and
knowing when to employ sltills and facts as a tool to solving problems (Kuth, 1991).
Back-to-basics was replaced by "problem-solving" (Schoenfeld, 2004, p. 258).
Regardless of the approach to math instruction and its focus on student
learning, achievement gaps persist between American high school students and their
international peers. While America continues to raise standards to prepare students
for international competition, students are unable to meet national standards. Since
the publication of A Nation at Risk, math achievement has not increased
significantly, and in some periods it decreased.
Internationally, according to the Third International Mathematics and Science
Study (TIMSS), "the scores of both our overall student population tested on general
math and science knowledge, and of the more advanced students tested in math and
physics, were well below the international average" (Forgione, 1998; p. 12).
America's best students are not prepared to lead this country in competition in areas
where math and science are essential. Even with the elimination of Japan and other
Asian countries, which tend to score highest in international comparisons, students in
grade 12 in the United States were outperformed by 14 countries, and outperformed
two countries (Forgione, 1998).
Nationally, improvements in math are positive. Improvements in "basic'y1
and "proficient" levels on National Assessment of Educational Progress ("NAEP")
are consistent overall, as well as, for African-American, Hispanic, and low income
students. "But, particularly when it comes to poor and minority students,
improvements have been greater at the basic level than at the proficient level"
(Olsen, 2006, p. 10).
In California, a recent study conducted by the RAND Corporation found that
California students ranked 43rd on NAEP math test scores. California's university
' The NAEP Assessment Report not only average scores for each racial or ethnic group; it also places each
individual test-taker in one of four different "achievement levels." The bottom level is labeled "Below Basic,"
which is reserved for students unable to display even "partial mastery of prerequisite knowledge and skills that
are fundamental for proficient work at at their grade. Those who have only a partial mastery are at the "Basic"
level. To rate as "Proficient," the next step up, a student must have a "solid academic performance,"
demonstrating "competency over challenging subject matter." "Advanced," the highest level is reserved for a
performance that is "superior."
system found that only 55% of high school juniors are prepared to enroll in college
level math courses. In 2002, California's Standardized Test ("CTS") results
indicated that 82% of all students (tested in grades 8-1 1) scored below proficiency in
Algebra I. In 2003-2004, more than a quarter of students failed the math portion of
the California High School Exit Examination ("CAHSEE") (Center. for Teaching
and Learning, 2005). Additionally, standards set forth by national peers, colleges,
and state standards are not being met.
As a result of the dismal statistics reported for U.S. high school students in
math achievement, federal and state efforts to increase competency in math has led
to the creation of standards for high school students and university teaching
preparation programs. High schools nationwide are combining standards-based
instruction, new curriculum, intervention programs, and instruction to meet the
standards set forth. In the fall of 1989, standard-based goals ("standards") were
published by the National Council of Teachers of Mathematics ("NCTM)
(Schoenfeld, 2004). Its goal was to set standards and benchmarks for students in all
grades. Standards would become the foundation of instruction and a measure of
accountability.
Preliminary studies indicate a positive relationship between state
implementation of standards, assessments and accountability systems, and gains on
NAEP. One can draw a moderate positive relationship between each state's overall
embrace of standards-based education and gains in student math achievement. With
the implementation of standards, states have adopted stronger accountability
4
systems. In turn, strong accountability systems have had a clear, positive impact on
student achievement (Olson, 2006).
Over the past ten years, high schools have recognized the need to change
their methods and operations to enhance instruction. In the early 1990s, the
Comprehensive School Reform ("CSR) movement began and adopted both top-
down and bottom-up methods to remedy targeted areas such as instructional content
and methods, scheduling requirements, school culture, and staffing needs (Kilgore,
2005).
CSR has modified the traditional high school structure to better meet the
needs of students. One major modification is the introduction of Small Learning
Communities (" SLC"):
SLCs are small learning communities such as career academies or
"school within a school" that break students up into subgroups to
provide them an environment where students are able to develop
closer relationships with teachers and peers. SLCs such as career
academies emphasize the relationship between academies and the
workplace; they have been shown to decrease dropout rates and
improve work attendance and job performance (Pluker, Zapf &
Spradlin, 2004, p. 5).
As a project adapted and promoted by the Bill and Melinda Gates Foundation, the
concept of smaller high schools is to provide "high quality, dynamic schools that
provide students with a new version of the Three R's: rigorous academic
coursework, meaningful relationships with instructors who can help students meet
high standards, and relevant learning opportunities through internships and
community partnerships" (Bill & Melinda Foundation, N.D., p. 4). Such schools
have been established in San Diego, California, Cincinnati, Ohio, and New York,
New York. Its main goal is to improve academics, increase graduation rates, and
college preparedness.
Another modification to the traditional high school is Curricula Alignment,
where secondary and post-secondary institutions align curricula. "Curricula
Alignment prepares students for college or the workplace and ensures that they have
attained the necessary skills for a successful transition" (Pluker, Zapf & Spradin,
2004, p. 5). The high school works in conjunction with the state's university to
implement similar or transitional curriculum so that transition from high school to
college level academics is smooth, easily adapted, and assists students in a successful
transition to full college life.
New rigorous graduation standards are said to be very positive. In the San
Jose Unified School District ("SJUSD"), reading and math scores at the high school
level have improved significantly, and at a much greater rate than at schools across
the rest of California that have not implemented rigorous graduation standards.
Rigorous graduation standards include provisions for the number of years a student
must take history, English, math, science, foreign language, and visual or performing
artslelectives (Pluker, Zapf & Spradin, 2004).
The aforementioned modifications to the traditional high school are so highly
regarded, and achievement is seemingly improving at these types of schools that
schools across the nation are in the process of changing their traditional high schools
into one of the above models. Not only is the high school configuration changing
6
and impacting students, it calls for a new "shared leadership." The one principal
model is obsolete, but also co-principals, assistant principals, and lead teachers
collaboratively operate the modified high schools.
With new policy initiatives from national and state educational entities and
the creation of new school designs create local capacity that must be empowered and
allowed in order to achieve national goals set forth in mathematics. However, the
policy initiatives are "over invested in testing" the focus on measuring growth in
school performance against fixed standards, while it "under invests in capacity
building" (Elmore, 2003; p. 1). Various instructional specialist promising math
programs and intervention math programs also promise increased test scores but
none have been touted as major. What is available are "ungrounded theories of
school improvement, weak knowledge about how to turn around failing schools,
perverse incentives for quality and performance, and policy-making by remote
control" (p. 2). School leaders and teachers at best use the state standards and state-
approved textbooks in combination with "hit and miss" instructional theories,
pedagogy, and practices to improve mathematics achievement.
Key in educational leadership in the context of new policy, initiatives, and
designs. The Interstate School Leadership Licensure Consortium ("ISLLC"), a
professional organization of the State Education Agency ("SEA") staff directors who
are responsible for administrator standards and licensure criteria, testing, preparation
programs, evaluation, professional development programs, program criteria (e.g.,
leadership academies and on-line training), and school improvement strategies,
7
researched and combined the standards-based oriented age and developed six key
elements that facilitate the contemporary visions of school leadership. These
elements are: (1) facilitating shared vision; (2) sustaining a school culture conducive
to student and staff learning; (3) managing the organization for a safe, efficient and
effective learning environment; (4) collaborating with families and community
members; (5) acting with integrity, fairness, and in an ethical manner; and
(6) influencing the larger political, social, economic, legal and cultural context.
These standards are now the guide in principal preparation programs and its origins
found in practicing effective principals (Lashway, 2003).
In the context of school reform where student achievement is central,
principals and/or instructional leaders must connect their supervisory roles and
student outcomes. Teachers are the key in connecting the two. Research conducted
by Jo Blase and Joseph Blase in their Handbook of Instructional Leadership outlines
researched based practices that have proven effective and directly impact instruction.
The areas that instructional leaders must focus on are: supervision, teacher
empowerment and school reform.
In the area of supervision, Blase and Blase cite five tasks that instructional
leaders or principals must implement that will have a direct impact on instructional
improvement. These tasks are: direct assistance to teachers, group development,
staff development, curriculum development and action research (p. 10). In the area
of teacher empowerment, Blase and Blase recommend that principals and/or
instructional leaders: (1) create a supportive environment for critique of instruction
8
by educators; (2) create stimulating critique by instructional educators; and (3) make
it possible for educators to voice by publishing and acting on the results of the
critique (p. 13). In the area of staff development Blase and Blase suggest that
principals andlor the instructional leader involve teachers in the act of teaching,
assessing, observing and reflecting that lead to understanding and development.
Next, instructional leaders should respond to the.need to the participants as revealed
through inquiry, reflection and experimentation. Third, staff development must
focus on collaborative communities of practitioners. Fourth, it should be related to
real work with real students. It must also sustain and support participants through
collaborative problem-solving. Finally, it must connect to school improvement
(p. 28).
Instructional leaders of standards-based high accountability schools are no
longer able to shoulder all the schools' instructional responsibility. Effective leaders
are able to: provide "coherent instructional vision and rigorous standards; use data to
make decisions with an emphasis on professional development; to create learning
communities; and to clearly demonstrate through behavior, as well as words, that the
principal is fully engaged with classroom instruction" (Lashway, 2003, p. 5).
Additionally, school leaders are change agents, as follows:
A change agent is a person who leads a change project or business-
wide initiative by defining, researching, planning, building business
support, and carefully selecting volunteers to be part of that change.
A change agent must have the vision to state the facts based on data,
even if the consequences are associated with unpleasantness
(Bhardwaj, 2003).
Effective school leaders create collaborative learning communities and are
the moral center of the education community. Leaders are able to sharpen their own
skills, develop teacher leadership, find resources to support professional community
growth, give teachers the confidence to grow, and manage the leadership agenda
systemically. They are able to listen to the voices of teachers, parents, and students;
they balance accountability against responsibility; and they protect the educational
community's "lifeworld." "The "lifeworld" consists of the values, beliefs, and
purposes that knit the school community together and give significance to everyday
activities" (Lashway, 2003; p. 8).
Effective leaders respond to challenges. They constantly scan the
environment for new ideas, tools and solutions, and reflect on the implications. They
attend to the learning of all members of the education community. They explore
current practices, beliefs, and assumptions that serve as a basis for posing inquiry
questions; "these questions are signposts in the hunt for evidence and the struggle
with dissonance. Dissonance is tackled in dialogue, thereby lowering defenses and
increasing shared understanding" (Lashway, 2003; p. 9).
Statement of the Problem
In the state of California and in the overall United States high school
students' math achievement are considerably less than students in other countries
such as Japan and Germany, as highlighted on TIMSS. This "achievement gap" is
made worse in many urban high schools. Focused attention is placed on increasing
math achievement by national and state agencies through No Child Left Behind's
10
Annual Yearly Progress and Highly Qualified Teacher requirements, California's
Public School Accountability Act's ("PSAA"), Annual Performance Index ("API"),
and the High School Exit Examination. District imposed A-G requirements and
Algebra as a graduation requirement are also means used to increase student
achievement in mathematics. The ability to identify and implement best conditions
and practices to increase math achievement is somewhat unknown despite efforts on
federal, state, district and school levels.
Federal and state pressure has forced schools to undergo a process of change
that has pressured school districts to implement standards-based education where the
ultimate goal is to elevate students' mathematics competency. School districts are
compelled to implement standards and best practices to meet the standards set forth.
Urban schools, although similar because they share common characteristics, are
considered to have unique characteristics and populations which differ based on
diversity, socio-economics, perspectives, and culture. Schools must discover and
implement best practices that will positively impact their student body. Marrying
policy initiatives and best practices is challenging and is further impacted because,
nationwide, the gap is widening between policy goals and students' achievement in
mathematics.
Curriculum committees, universities, field experts, and textbook publishing
companies have provided curriculum aligned with state standards and the CAHSEE.
Districts have allotted special funds and positions for "math experts," and states have
funded after-school programs to assist students who are not faring well in math.
11
Despite efforts and choices presented to districts, one program is not packaged to "fit
all." This is evident in the continual, dismal math scores posted annually.
Discernment in adapting a mathematics program or moving a culture and people to
achieve a higher standard in mathematics is an essential element that has been
challenging the school districts. It is yet to be known if this goal's embryonic stages
lie in the curriculum framework, the instructional leadership of a school, or a
combination of the two.
Effective instructional leadership is viewed as critical in a school's success.
Having the ability to communicate a vision, build internal capacity, create an
atmosphere that includes academic rigor, and carry out the duties effectively are
seemingly lacking when it comes to math achievement. School-based administrators
and district leadership alike, continue to struggle in defining the characteristics that,
in the context of improving math performance for students, create good instructional
math leadership. Several issues seem to be especially relevant to instructional
leadership in this setting. Leaders often do not have strong pedagogical content
knowledge in mathematics education; yet, need to carry out functions related to
fiscal, personnel, and organizational leadership and data analysis. Little is known
about how leaders work effectively in this context.
Purpose of the Study
The overall goal of this study is to identify the best conditions for student
mathematics achievement that, through research and experience, have proven to
reliably lead to success. This study will investigate math achievement as a result of
policy initiatives in combination with school-based curriculum and instruction.
Details of the implementation and adoption of specific policy initiatives and school-
based programs for mathematics will be examined in the context of improving
mathematics performance. Instructional leadership and its impact on mathematics
achievement where leadership lacks strong pedagogical content knowledge in
mathematics education will be examined, incorporating an understanding of how
leaders work effectively in this context.
The study will attempt to answer the following 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 its math program
and strategies to assist students in math?
4. To what extent was strong instructional leadership important in
improving a) the math programslstrategies; and b) math achievement
among students.
5. How did instructional leaders respond in academic areas for which
they were not experts?
Importance of the Study
The results of this study should be of value to school district officials, school
site leadership, classroom teachers, and educational researchers.
School district officials will acquire a broader understanding of how to
increase mathematics achievement. District officials will establish how teaching
pedagogies, mathematics curricula, school organization, and intervention programs
are most effective at improving and enhancing math instruction and achievement.
Obstacles to significant improvement will be delineated and will provide districts
with considerations for instructional practices, reorganization of mathematics
courses, and related programs.
School leadership will see how best to organize their personnel, curriculum,
and courses that will foster optimum mathematics instruction and achievement. This
will include knowing how best to gather personal knowledge as to how to effectively
and efficiently lead mathematics instruction without having the mathematics
specialization required to instruct mathematics. Site leaders will gain a better
understanding of math programs, curriculum and teaching practices that will allow
them to promote mathematic achievement on their school sites. They will gain
knowledge of successful practices that can be implemented on their sites.
Classroom teachers will recognize effective instructional practices for
implementation in their classrooms. Ever-changing curriculum, practices, and
textbook adoptions will be limited. The implementation of federal, state, and district
policies will searnlessly integrate. Effective pedagogy will no longer shift with
14
leadership at school sites, district and government appointments, but will be
integrated with teaching practices exercised in the classroom.
School district officials, school site leadership, classroom teachers, and
educational researchers will benefit from this study as it will make an affirmative
contribution to the existing body of knowledge on the subject of math achievement,
curricula development and teaching methodology. School districts and schools will
benefit from the opportunity to examine their own organization, curriculum and
teaching practices and to evaluate them in light of the most effective practices.
Limitations
This study was limited to one school because of the broad scope of the study,
resulting from the use of both qualitative and quantitative methodologies. Because
all data was collected from the faculty and administration at a single school site, the
ability to generalize the results to other school sites is limited. The selection of
teachers and site leaders to be interviewed for this study was based on the site
administrator's recommendations, and thus, may contain biases that could have
bearing on the findings of the study. In addition, the researcher's own bias as a
district level administrator may also have an impact on the interpretation of the
findings of the study.
Delimitations
This study contained a number of delimitations relative to the district, school,
and individual participants in the study. The school was selected as one that was
representative of districts in California based on the range of students' socio-
economics status and ethnic diversity.
Organization of the Study
Chapter 1 of the study has been presented an introduction .to the study
including the rationale and value of studying one's school's practices in improving
high school student achievement in mathematics. Chapter 2 will review and discuss
the current literature in the area of mathematics reform and instructional leadership.
Chapter 3 presents the research methodology of the study, a description of and the
rationale for the sample selection, data collection and instruments used, and methods
of analyzing the data. Chapter 4 is an analysis of the findings of the study as they
relate to research questions. Chapter 5 summarizes the research findings and draws
conclusions based on those findings and identifies implications for future research.
References and appendices conclude the study.
CHAPTER 2
LITERATURE REVIEW
This chapter will review the current literature on what is already known about
mathematics achievement in secondary schools from the perspective of international
comparative studies, national objective standards and the state. The current status of
academic achievement will be appraised, including consideration of the historical
trends and patterns of sub groups and the achievement gap. The importance of
mathematics achievement in schooling and its impact on college success, and the
economic status of our country will be discussed. Efforts to improve mathematics
achievement will be analyzed; including a focus on national and state efforts,
improve curriculum and instruction, better-prepared teachers, and related school
reforms. Factors at the school level that are seemingly related to students'
mathematic achievement will be studied. The role of school leadership in improving
mathematics achievement will be studied and the essential ingredients of an
instructional leader that influence mathematics achievement. Case studies of
exceptional schools will be provided with an analysis of students' math success and
instructional leadership within the contexts that they were achieved.
The Status of Student Performance
A Nation at Risk not only exposed America's sub-standard education system,
but also uncovered that America's education system is inadequately preparing
students to compete internationally, which debunks the core beliefs of the purposes
of education which are, but not limited to economic development, social
17
participation and international competition. Besides poor performance, deeply
rooted in the report were low expectations, lack of preparedness, and a lack of
interest in ascertaining higher levels of math skills and knowledge.
We offer intermediate algebra, but only 31 percent of our recent high
school graduates complete it. . . .
Calculus is available in schools, enrolling about 60 percent of all
students, but only 6 percent of all students complete it. . . .
Thirty-five states require only one year of math, and 36 require only
one year for a diploma (The National Commission On Excellence in
Education, 1983; p 63).
Substandard achievement is not surprising if students are not required to
participate in higher levels of mathematics. Despite the recommendations in A
Nation at Risk for higher standards and consistency, subsequent years did not
produce progress. Achievement in the United States: Progress Since A Nation at
Risk (1 998), Pascal Forgione reports:
Long-term trends in science and mathematics show declines in the
1970s and early 1980s, followed by modest increases. For example,
the average math score of 17-year olds declined from 1973 to 1982,
and then increased to a level in 1996 similar to the 1973 level (p. 3).
Achievement declined to levels lower than those noted in 1983. Scores
among our highest achievers continued to remain behind our international peers.
In 12th grade the achievement scores of both our overall student
population tested on general mathematics and science knowledge, and
of our more advanced students tested in mathematics and physics,
were well below the inteniational average (p. 3).
Not only are we scoring below our international peers as a nation, we are not
meeting goals set forth by our nation. Apparently, A Nation at Risk did not positively
impact mathematics since scores did not increase.
Goals 2000, A Progress Report. This report is an "outgrowth of State-led
education reform" based on the recommendations cited in A Nation at Risk, and it
contradicts Forgione's assessment that no significant progress has been attained.
The report asserts "these education reforms yielded important results in academic
performance (which increased), and increased the performance gap between African-
American and White and minority students (which decreased)." It cites gains in
math; however, these gains are extracted from 9 and 13-year old students. There was
no mention of high school mathematics increases, but the report noted the increased
enrollment in challenging academic courses from 14% in 1983 to 52% in 1998.
Increases were in Advanced Placement (AP) courses and AP scores.
Third International Mathematical and Science Study. In the context of
TIMSS there appears to be no direct correlation between student course taking
patterns and achievement. If the opposite were true, the 14% who enrolled in higher-
level courses would reflect a 14% increase in mathematic achievement on tests
administered by TIMSS, and decrease the performance gap between American
students and their international peers. Since 1983 scores amongst American students
in comparison to international peers have shown no significant increase in student
achievement.
In 1999 the National Center of Education Statistics published Pursuing
Excellence: A Study of US. Twelfth-Grade Mathematics and Science Achievement in
International Context. In summary, it stated that grade 12 students in the United
States were unable to compete amongst their international peers. The 12th graders
scored below the international average and were among the lowest of the 21 TIMSS
nations in both math and science general knowledge in the final year of secondary
school. Other key points of the study affirm U.S. students' international standing
was stronger at the 8th grade level than at the 12th grade level in both math and
science. In both international and national test students' math achievement declined
and gaps widen as students matriculate to higher-grade levels.
In response to the 12th grade findings, William ~chmidt? Director of the
U.S. participation in TIMSS, in accordance with the findings and recommendations
cited in A Nation at Risk, cite curricula, lack of student participation in higher level
mathematics, and tracking as causes of students' lack of achievement in
mathematics. In regards to curriculum, Schmidt states:
Those curricula and our textbooks are highly repetitive and
unchallenging in grade after grade of the middle school years. How
could they provide a sound foundation on which to build during the
high school years? The middle school curricula in most TIMSS
counties cover topics from algebra, geometry, physics and chemistry.
For most U.S. students these are the first studied, if at all, in high
school. Many students (about 15 %) never study algebra, geometry
(about 30 %), advanced algebra (40 %) or other mathematics (around
80 %), . . . (P 1).
William H. Schmidt is Professor of Applied Statistics, Department of Educational Psychology at Michigan State
University. William Schmidt is also the National Research Coordinator and Executive Director of the center that
oversee the participation of the United States in the Third International Mathematics andscience Stzrdy (TIMSS).
2 0
Schmidt further states that U.S. students frequently opt out of advance study
of math and if they do continue to take math course, they are in less demanding
courses. "So high school mathematics and science is unlikely to overcome the poor
foundation provided during U.S. middle school education and reverse the downward
trend in comparative performance for average students" (p 2).
To further validate Schmidt's viewpoint, data in the Multiple Comparisons of
Advanced Mathematics Achievement of the Top Ten Percent of all Students in the
School-Leaving Age Cohort (IEA TIMSS, 1995-1996) indicated that the U.S. mean
achievement is significantly lower than Slovenia, France, Australia, Denmark,
Switzerland, Canada, Sweden, Germany, Austria, Italy and Greece. This pattern of
course taking and achievement is repeated in subsequent years up to the present
(TIMSS 2003,2004,2005).
In 2004 TIMSS revealed significant increases in student achievement in
grades 4 to 8 from 1995 to 1999. However America's 15-year-olds continue to
perform below the international average in math literacy and problem- solving. If,
according to Schmidt, it is poor mathematical foundational issues in earlier grades
that are producing poor performance results, it appears that the U.S. will eventually
see growth when these students matriculate in the high school level. Based on the
information provided above the U.S. should come into alignment in achievement
with their international peers within the next three to five years.
National Center for Education Statistics. On a national level the National
Center for Education Statistics ("NCES") who publishes assessment data annually
2 1
that is commonly referred to as "Americas Report Card" runs comparison data
between states. In its most recent report in 2004, National Trends in Mathematics by
Performance Level, and the National Trends in Mathematics Performance-Long
Term, data was extracted from the period of 1978 to 2004. Overall, according to the
data, achievement levels for 9 year olds were highest in 2004 than in any other
assessment year. But as noted earlier, as student matriculate into middle and high
schools, achievement levels declined.
This pattern of major high achievement is recorded for 13 year olds in
the annual assessment and the long-term comparison. One the other
hand, the data for 17-year-olds shows only moderate increases for the
annual assessment and a seven percent gain from 1978 (p. 6).
NAEP most recent statistics for the 2005 assessment year rank California
students in 4th and 8th grades at 4% as advanced, 24% proficient, 43% at basic, and
29% below basic.
The national average mathematics score at grade 8 showed a 1-point
increase between 2003 and 2005 and was 16 points higher in 2005
than in 1990. The national average mathematics score at grade
8 showed a I-point increase between 2003 and 2005 and was 16
points higher in 2005 than in 1990 (NAEP, 2005, p. 2).
Data from students in grade 12 who participated in the April 2005 assessment is
currently not available.
California Standardized Test. In 2005 the California Department of
Education's, Policy and Evaluation Division report, Accountability Progress Report,
revealed that California's students had not met adequately yearly progress in the area
of "percent of students proficient in mathematics." Statewide only 45% of students
are proficient. For other sub-group proficiency levels are extremely grim. Students
22
with disabilities are the least proficient with 19.8%, following closely by African-
Americans with 27.4% proficient, Hispanics with 32.6% proficiency and socio
economically disadvantaged with 32.8% being proficient. Overall, less than half of
the total student population is proficient in mathematics, with the exception of
Whites at 59.6% proficiency.
Nationally, American students are not meeting goals set forth in A Nation at
Risk (1983), Goals 2000 (published in 1998), and Standards Based Goals (published
in 1989) by the National Council of Teachers of Mathematics; nor Annual Yearly
Progress ("AYP") as set forth in No Child Left Behind (NCLB, 2000).
The Achievement Gap
The implementation of the NCLB, Federal Education Act, is at present the
single most powerful tool that brings attention to the achievement gap. State and
local education agencies not only must increase overall student achievement, but also
must disaggregate standardized scores and monitor progress of the subgroups.
Serious consequences are issued if lower performing subgroups such as African-
~merican,~ Hispanic, English Language Learners (ELL), socioeconomic
disadvantaged, and students with special needs. Ginger M. Reynolds, Ph.D., defines
the achievement gaps as:
The term achievement gap is used to denote differences in the
academic achievement of particular groups of students. Actually, it is
' African-American is currently the official identifying category for people of African descent. However the
racial or ethnic category, or title has evolved over the years. Prior to becoming known as African-American this
group's official category or title has been: "Black," Afro-American, "Colored" and Negro. The term African-
American and Black are used interchangeably throughout this paper due to the time period in which the research
on the group was produced.
more accurate to say that there are achievement gaps rather than
merely one achievement gap. The issue is not as simple as difference
between blacks and whites or rich and poor. There are many gaps,
and the gaps themselves have changes over time (NCREL, 2002, p 6).
Within the nation, assessments done by NAEP compare achievement data
between states and sub-group and analyze historical trends in achievement. Data
collected from NAEP is the best evidence to analyze what is known about student
achievement. NAEP data shows the achievement gap between African-American,
Hispanic and White students is much wider and has persisted over a longer period of
time than the gap between American students and their international peers.
African-American/White Achievement Gap. The gap between African-
Americans and Whites has been part of America's history since compulsory
education was enacted by all states in 191 7.4 The infamous 1866 court ruling, Plessy
v. Fergerson, established the separate but equal clause and the subsequent
establishment of the Jim Crow laws5 that lasted from 1870s to 1950s. During this
period African-Americans experienced very little education despite the enactment of
compulsory education laws. African-Americans have made tremendous progress
since the days of Jim Crow . . . "when roughly 80% of African-Americans grew up
The first Compulsory Attendance Law was adopted in Massachusetts in 1852. During the next 15 years, no
other state followed Massachusetts. However, beginning in 1867, a steady stream of states began adopting
compulsory attendance laws and by 1918 all states had enacted them.
5.
Jlm Crow laws were state and local laws enacted in the Southern and border states of the United States, and in
force between 1876 and 1964; they restricted access by African-Americans to public facilities. Jim Crow, the
Jim Crow period, or the Jim Crow era refers to the time during which this practice occurred. The most important
laws required that public schools be segregated by race, and that most public places (including trains and buses)
have separate facilities for Whites and Blacks. In 1954 the U.S. Supreme Court declared school segregation
unconstitutional in Brown v. Board ofEdz~cation. All the other Jim Crow laws were repealed by the Civil Rights
Act of 1964.
in the south and were legally required to attend segregated school" (Thernstrom,
2003; p 18).
Abigail Thernstrom and Stephan Thernstrom chronicle the achievement gap
between African-Americans and their White counterparts in No Excuses: Closing the
Racial Gap in Learning (2004). Their research found that in the 1950s, "only 24
percent of Blacks ages 25-29 had completed high school" (p 18). The number of
African-Americans completing high school increased over the next decade, however,
given what is known over the quality of Jim Crow schools, "the racial gap in actual
knowledge was undoubtedly much larger than the number of years in school
suggest" (p. 18).
Although graduation rates of African-Americans have increased, "Blacks
nearing the end of their high school education perform a little worse than White 8th
graders in both reading and U.S. history, and a lot worse in math and geography"
(p 13). "By 12th-grade on average, Black students are four years behind those who
are White or Asian" (p 12). "By the end of high school African-American students
have math and reading skills that are virtually the same as those of 8th grade White
students" (p I)."
However, some progress for African-America has been made since the
publication of A Nation at Risk (1983) but the gap between African-Americans and
their White peers continues to exist. According to Forgione:
The mathematics and science achievement gaps between Black,
White and Hispanic students have narrowed somewhat since A Nation
at Risk. Blacks and Hispanics in each of the age groups test (9, 13
and 17 year olds) tended to make larger gains than Whites during this
period (p 3).
The greatest gain for African-American students in mathematics was in the
1999 assessment. This gain was greater than gains from 1973- 1982. "However,
Black student performance had no significant change since the 1980s." (Status and
Trends in the Education of Blacks, 2003-2004; p 50).
Despite the persistent gap African-American mathematics achievement
scores have increased, but not at the rate of Whites. Gains in achievement are also
more prevalent in younger grades and steadily decrease by grade 12. According to
the National Achievement Results by Race/Ethnicity Report (2000):
. . . For each of these groups the percentage at or above proficient in
2000 was at least double that in 1990. The percentage of White 4th
graders at or above proficient level increased in each assessment year
from 1990 to 2000, while percentages of Black and Hispanic students
at or above this level decreased in 1992. Percentages at the advanced
level remained small for all groups in 2000, though there was a slight
increase since 1990 for White 4th graders (p 8).
Of all the sub-groups African-Americans are second to the bottom, slightly
above students with disabilities (but by no more than 5 percentage points), and are 15
percentage points below the Hispanic population.
Hispanic/White Achievement Gap. Hispanics perform slightly better than
African-Americans although their history and experience greatly differs. When
reviewing achievement data for Hispanics, it is assumed that all Hispanics fit into
one group similar to African-Americans. However, according to Thernstrom and
Thernstrom (2003):
"Hispanics" are not a single ethnic group, but an ethnic category, an
umbrella label that was first employed in the U.S. Census of 1970 and
now carried over in data categories that report student achievement
rates. The term embraces roughly two dozen national origin groups
that have little in common beyond the fact that they originated in
countries in the Western Hemisphere that once were part of the
Spanish empire, and that have remained predominately Spanish-
Speaking since then (p 102).
National school systems data reporting agencies and test makers focus much
attention on immigrants from Mexico because it is the majority Hispanic group,
especially in Texas, California, New Mexico and Arizona.
The lack of academic achievement for Hispanics is rooted in their
immigration background and in their movement back and forth across the border,
and in the specific cultural characteristics of the families who choose to migrate
(Thernstrom, 2003). The first wave of immigrants arrived shortly after the Mexican
Revolution that broke out in 1910 (Jaffe, Cullen, & Boswell, 1980). Many accepted
jobs as migratory farm laborers and they went wherever there were crops to plant or
to harvest, and their children went from school to school, if they were enrolled
(Gamino, 1930). Consequently, the Mexican-American community lagged far
behind the national norm in its educational development. As late as 1960 the
average Mexican-American who was at least 25 years old and lived in the Southwest
had just over seven years of schooling, as compared with 12 years for non-Hispanic
Whites. Even African-Americans in that region had more education than
Mexicans-almost two years more" (Gerber, Moore & Guzman, 1970).
These figures are thus misleading though the mixing of different generations
of Mexican-Americans. In 1960 second-generation Mexican-Americans had nearly
27
four more years of schooling than their immigrant parents. This second generation
continued to make gains educationally and economically acquiring higher levels of
education and better jobs. But the 1970s and subsequent decades the influx of
uneducated and unskilled legal and illegal immigrants from Mexico accelerated at
unprecedented levels and the gains made by the earlier generations obscured those
earlier intergenerational gains (Thernstrom, 2003).
According to the National Center for Educational Statistics, Condition of
Education in 2002, Hispanic children account for nearly 30% of the total enrollment
in K-12 education. This has profoundly affected the education of Hispanic children
because educational attainment levels differ for different generations. Those
immigrants who are first, second, and third generation Hispanics, have made
tremendous strides in education, and are saturated with new immigrants that reflect
poor statistics when it comes to education levels. Therefore, when scores and
achievement level of Hispanic students are analyzed one must consider the differing
populations and differing experiences.
In considering the backgrounds and history of both the African-American and
Hispanic students, one could expect that achievement gaps continue to persist
between these groups and their White counterparts. Forgione reports that average
math scores for White, African-American and Hispanic students increased since
1982, but decreased in the 1990s. He reports:
For 17-year olds, for example, White students improved 9 points;
black students improved 14 points; and Hispanics students increased
15 points. The gaps between white and black students narrowed
between 1982 and 1990, but has also widen again through the 1990s
to 27 points in 1996. The gaps between white and Hispanic students
narrowed somewhat since 1982, though the change was not
statistically significant, and the gap remained at 21 points in 1996
(P- 3)-
Despite early gains and subsequent drops, the gap between White, African-American
and Hispanic students has narrowed somewhat since A Nation at Risk.
According to the NCES, African-American student performance was higher
at all three ages in 1999 than their performance in 1973 - 1982. The same is true for
Hispanic students during the same time period. African-American mathematics
performance has not statistically changed in the 1980s (p. 50). However, Hispanics
scores were higher in 1999 than in the 1970s and early 80s; the gaps between
Hispanic and White students' NAEP scores have decreased at two age levels, but
there were no statistical differences since 1994 (iVCES, 1999).
In 1999, African America 13-17 year olds had average math scaled scores
lower than scores of both White and Hispanic students for the same age groups.
While gaps in mathematics scores between White and African-American and White
and Hispanic 13-17-year olds narrowed considerably since 1973, the gaps still
remained in 1999, and no clear trend was apparent (NCES, 2004).
At grade 12, there have been few changes in student performance for both
African-American and Hispanic students (NAEP, 2000). "Despite increases in
mathematical scores from 1990 to 1992, the average scores for both groups of
students in 2000 were similar to that in 1990" (p. 6). The percentages of White
29
students at or above proficiency and at or above basic were higher in 2000 than in
1990. These increases for White students were accompanied by a concomitant
decrease in 2000 since 1990 at the Below Basic range.
Similar to overall achievement trends of all students, African-American and
Hispanics perform progressively lower as they matriculate into higher grades. Also
remaining are gaps in achievement between all groups. White students continue to
outperform African-Americans and Hispanics at a minimum average of 7 points.
Despite educational movements in both communities and overall aimed at improving
achievement and narrowing the achievement gap, the wider and more persistent the
gaps seem to become.
There are volumes of information as to why the achievement gap persists.
Often these theories focus on the disparate backgrounds with which students enter
school and the continued family and cultural obstacles that poor and minority
students encounter through their school tenure. However, other research shows there
are significant factors in schools that perpetuate inequity of opportunity.
Researchers with Education Trust revealed that minority students often attend under-
funded urban schools, and receive poorer-quality instruction than their White or
suburban peers (Johnson & Viadero, 2000). Minority students "take fewer
Advanced Placement (AP) and honors courses, have less qualified teachers, get
fewer resources, and in fact harsher discipline when they violate school rules"
(NCREL, 2002).
In July of 1999 three students from Inglewood High School represented by
the American Civil Liberties Union (ACLU) filed a statewide class action lawsuit
against their school district and the State of California, alleging inequitable access to
AP courses. The complaint states: "differential access to AP classes denies the
Plaintiff, Rasheda Daniels, and a class of primarily low-income students of color,
equal educational opportunity" (Oakes, Muir & Joseph, 2000, p. 1). The
significance of this case is that "the case and its proposed remedy reveal both what
we know and what we don't about the enduring, yet changing, relationship among
diversity, mathematics and science course taking, achievement, and equity" (p. 1).
Children who attend schools that serve a population of low-income, minority
students are denied the opportunity to learn because higher-level courses, more
specifically in mathematics, are not offered. Achievement trends for African-
American, Hispanic and the socioeconomic ally disadvantaged testify to the lack of
access and course tracking trends.
In 2002, 97 students (as plaintiffs) also represented by the ACLU filed a class
action lawsuit against the State of California alleging that it deprived, low income
and non-White students of basic opportunities, and are being denied the bare
minimum necessities of an education (CDE, N.D.). The plaintiffs represented 46
different schools in 18 school districts throughout the state in the case that became
Williams, et al. v. State of California, et al., (Supr. Ct., San Francisco). The
plaintiffs argued:
. . . State is failing to provide thousands of public school students,
particularly those in low-income communities and communities of
color, with the bare minimum necessities required for an education,
such as textbooks, trained teachers, and safe and clean facilities. The
State's failure to provide these bare minimum necessities to all public
school students in California violates the state constitution, as well as,
state and federal requirements that all students be given equal access
to public education without regard to race, color, or national origin.
Specifically, the lawsuit seeks to remedy the following school
conditions: . . . (State of Cal., N.D.; p. 1).
The case was settled with the State of California agreeing to "ensure that students
have fundamentally equal learning opportunities" (State of California, N.D., p. 1).
Overwhelming evidence of poor instruction, non-credentialed teachers, dilapidated
facilities and shortage of textbooks was more persistent in schools where majority
populations were socioeconomic ally disadvantaged African-American and Hispanic.
The two aforementioned cases address issues that are seemingly related to the
achievement gap. It also foreshadowed the disproportionate numbers of minority
and socioeconomic disadvantaged students' ability to successfully pass the
CAHSEE. "Aslting minority kids to pass the same test as other students when their
schools are inferior is like saying, 'even if you're 5 feet 8 inches tall,' that you're
going to jam the ball" (Thermstrom, 2004; p. 152). Passing of the high school exit
exam is a requirement to receive a high school diploma. A high school diploma is
necessary for college admission. It is also the minimum that employers are willing
to accept even in marginally paying jobs. Therefore, those students who are African-
American, Hispanic and/or socioeconomic disadvantaged are more likely not to
attend college and will be relegated to jobs that do not produce livable wages.
Importance of Mathematics
High school mathematics achievement levels are indicators of high school
completion and future success in college and the worlcforce. Proficiency in math is
also important for America's military and economics. Since the passing of NCLB in
2000 nationwide, schools have implemented mandated testing and school
accountability mechanisms where students are to meet AYP in an effort to improve
student achievement and decrease the achievement gap. In order to meet AYP
growth levels, schools began to require students to successfully complete two years
of mathematics as a graduation requirement, with a minimum of one year of
successful completion of Algebra 1 (Schiller & Muller, 2003). A passing score
required on the CAHSEE, another tool used in California states' accountability
report, as a necessary component in receiving a high school diploma. University of
California ("UC") and California State University ("CSU") systems require three
years of college-preparatory mathematics, but recommends four years that include
topics covered in elementary and advanced algebra and two-and-three dimensional
geometry (Univ. of Cal., 2006, and Cal. State Univ., 2006). Community colleges
offer remedial mathematics courses and require a one year algebra course for an
Associate of Arts Degree.
The importance of mathematics in post high school life is clearly spelled out
in the Principles and Standards for School Mathematics, (NCTM, 2000). In this
report there is shift in focus from pure curricula to the development of a core
curriculum that prepares all students with the mathematical background for
33
quantitative literacy, for the workplace, and for study at the college level
(Schoenfeld, 2002).
Mathematics in the workplace is quickly becoming an essential
quality in our technological society. According to the Department of
Labor, [60%] of all new jobs will require skills possessed by only
22% of young people entering the job market now. These jobs
require the use of a computer and pay about 15% more than jobs that
do not, and those jobs that do not are dwindling (Moses, 2001; p. 9).
Mathematical knowledge is not only essential for college and workplace
success, but more than ever before today's students need to learn to reason and
communicate using mathematical ideas for economic enfranchisement, making
decisions in one's personal life, and in the matter of public interest for quantitatively
sophisticated reasoning (Schoenfeld, 2002).
America's workforce and "social status" as a whole is negatively impacted
when students underachieve in mathematics. Poor performance diminishes
America's ability to compete economically and militarily. The inability to compete
translates into decreased opportunities in the fields of engineering, mathematics,
science, aeronautics, statisticians and technology. The lack of mathematics
knowledge further add to a stratified society where those who can perform well in
high school, generally succeed in college and are sub sequentially gainfully
employed, while those students with negligible skills wind up having access to the
lowest paying jobs (Sells, 1975, 1978, as quoted in Schoenfeld, 2002). Success in
high school mathematics has long been seen as a critical filter in post-high school
success.
For historically lower achieving groups such as African-Americans,
Hispanics, and the socioeconomic disadvantaged, access to college and higher
paying jobs are more limited; thus, leaving these groups in an underclass status.
Disproportionate numbers of poor, African-American, Latino, and Native American
students drop out of mathematics, perform below standard on tests of mathematical
competency, and are thus denied both important skills and a particularly important
pathway to economic and other enfranchisements. (Madison & Hart, 1990; Miller,
1995; National Action Committee for Minorities in Engineering, 1997; National
Commission on Mathematic and Science Teaching for the 21'' Century, 2000;
National Science Foundation ("NSF") (2000); (Schoenfeld, 2002; p. 1).
Mathematics achievement levels further impacts college enrollment and
opportunities for higher education. As many as half of all college students do not
have adequate preparation and are required to take remedial courses. Civil rights
organizations frequently and rightly bemoan the scarcity of African-American
engineers, physicians, Silicon Valley computer whizzes, and the like. But when we
see how little math African-Americans typically knows at the end of high school, we
see the source of the problem. Too few are ready for rigorous math and science
education that such professions demand (Thernstrom, 2004). This statement not only
pertains to African-Americas, but all students who are not participating, or achieving
in core mathematics curriculum that will prepare one for more opportunities post-
high school and college life.
Policies to Improve Mathematics Achievement
National Efforts. The 2002 NCLB federal education bill is the most
influential education reform bill that directly impacts education. It has built-in
accountability mechanisms that focus on student achievement levels through the use
of benchmarks, assessments, standards and goals. It loosely, but highly,
recommends research-based practices and placed emphasis on "highly qualified
teachers." Severe sanctions are issued to schools that are not meeting achievement
growth levels with the threat of state takeover, and gives parents the option of
transferring students out of poor performing schools to other schools at the failing
schools cost.6 What separates NCLB from its predecessors is the single
accountability system that effectively ensures that all districts and schools make
adequately yearly progress,7 and is based on academic standards and assessments
including achievement of all students and includes sanctions and rewards to hold all
public schools accountable for student achievement (ED. Gov., 2002). However, an
If states do not make AYP for two consecutive years the Secretary of Education will provide technical
assistance. States determine if each school district makes AYP by reviewing annual progress, and then
publishing and disseminating results to parents, teachers, schools and the community; they also review the
effectiveness of current school programs. The school improvement times are as follows: Year one, Miss AYP;
Year two, placed in school improvement status and must offer parents a choice of a different school; Year three,
supplemental educational services must be offered; Year four, school or LEA must submit a corrective action
plan; Year five, plan for restructuring; and Year six, implement new plan.
7~nnual Yearly Progress starting point was based on data from 2001-2002 assessments. The following were also
taken into consideration to determine and gather baseline data and growth rates: rank of all schools by
percentage of proficiency, and then count up to reach 20% of total enrollment. The percent of student proficiency
in that school is the starting point. For sub-group data, the percentage of students proficient in the lowest
achieving group, economically disadvantages, major raciallethnic groups, students with disabilities, and students
with limited English proficiency. States may, but was not required to establish starting points by grade span.
APY requires: the same high standards of academic achievement for all children must be statistically valid and
reliable, continuous and substantial academic improvement for all students, separate measurable annual
objectives for achievement, and includes the graduation rates for high schools and one other indictor for other
schools (ED. Gov., 2002).
effort to improve student achievement has been ongoing since the beginning of the
2oth Century.
As part of the Cardinal Principles of Secondary Education (1923), William
Heard asserted that "nothing in mathematics should be taught unless it is probably
valuable could be shown, and recommended the tradition high school mathematics
curriculum for only a select few" (Klein, 2003; p. 4). The National Council of
Teachers of Mathematics ("NCTM") published a counter-report that same year that
refuted Kline's claims. The report included a survey secondary school curriculum,
documented the training of mathematics teachers in other countries, "discussed
issues related to the psychology of learning mathematics, and justified the study of
mathematics in terms of its application as well as its intrinsic values" (p. 4). It even
proposed curricula for the schools and even underscored the importance of algebra to
"every educated person." The NCTM's report was the first to influence public
education, and no significant changes in curriculum were implemented.
The 1930s produced the Activity Movement whose adapted slogan was "We
teach children, not subject matter." The Activity Movement promoted the integration
off all subjects in the elementary schools and was against the high school stance of
separate subjects. "Some proponents of the Activity Movement would not
acknowledge that reading and learning multiplication tables were legitimate
activities" (p. 4). Due to the onset of World War I1 and the out-cry of military
generals and the need of recruits to master basic skills to operate military equipment
and gunnery, thus, the emphasis on mathematics instructions was deemed important
once again.
By the mid 1940s there was a demand for unskilled workers and educational
leaders began Life Adjustment Movement whose basic premise was that secondary
schools were "too devoted to an academic curriculum" (p. 5). They further
promoted a curriculum that helped students in everyday life and asserted "they
would need appropriate high school courses, including math programs that focused
purely on practical problems, such as consumer buying, insurance, taxation, and
home budgeting, but not on algebra, geometry, or trigonometry" (p. 5).
The 1950s bought about tremendous advances in Mathematics and Science,
especially in light of the U.S.S.R's launch of Sputnik-the first space satellite. In
response, the American press focused attention on the lack of math and science
achievement by American students. In rebuttal, in 1958 Congress passed the
National Defense Education Act to increase the number of science, math and foreign
language majors, and contribute to school construction. More importantly, "New
Math" was introduced whose curricula emphasized "logical explanations for the
mathematical procedures taught in schools" (p. 7).
The "New Math" movement was the first educational movement to bring
about changes in public school curricula. One of the most important was the
introduction of calculus courses at the high school level. However because it was
overly formal, abstract and leaned heavily on theory, and it provided little attention
to basic skills, the movement lost momentum;, public criticism grew, and it
eventually dissipated. By the 1970s it was back to the basics.
In the 1980s two reports that investigated the K-12 education system were
published, A Nation at Risk (1983), and An Agenda for Action (1990). A
commission appointed by then Secretary of Education, Terrell Bell, wrote A Nation
at Risk. It warned "our nation is at risk . . . the educational foundations of our
society are presently being eroded by a rising tide of mediocrity that threatens our
very future as a Nation and a people" (p. 6). It addressed shortcomings in
mathematics education and the increased need of remediation in math at the college
level. It described high school course offerings as a "curricular smorgasbord" (p. 8)
that offered mathematics courses that students were not completing, or less than half
of the student population enrolled.
The National Council of Teachers of Mathematics ("NCTM") published An
Agenda for Action, which recommended that problem-solving be the focus of school
mathematics along with new ways of teaching. It asserted complete mastery of skills
before participation in higher-level problem solving courses, as counterproductive.
To remove barriers caused by pencil-paper calculations and assist students in gaining
access to higher level of mathematics curriculum, the NCTM advocated the use of
technology.
In 1989 the NTCM furthered their ideas and agenda and published The
Curriculum and Evaluation for Standards for School Mathematics, more commonly
known as the NTCM Standards (or as the "Standards"). This document focuses
39
attention to general standards for bands of grades K-4, 5-8 and 9-12; it included lists
of topics that should receive "increased and decreased attention;" and another section
is devoted to "Evaluation Standards." This document was the foundation for what
we now called "Standards Based Education."
It should be noted that other events in America's society led to the production
and great acceptance of this document. First, American's economic markets had
been eroding over the past decade. Secondly, the publication of TIMSS comparisons
of mathematics scores highlighted America's students' poor performance. Third, the
federal government reimbursed districts for purchasing adoption textbooks that were
approved and on the state's adoption textbook lists. As a result, "Teaching tended to
be textbook driven (which constrained textbook choices to the point where the
United States had a de facto national curriculum in mathematics), and one that
changed slowly at that" (Schoenfeld, 2002; p. 9). Because the textbook industry was
the driving force for academic instruction and curriculum, and content was aligned
with curricula goals, and California was a model state participating in the program,
California's textbook adoption and its goals aligned curriculum to set the stage for
standards-based instruction.
State Efforts. In 1992, the California Department of Education published the
Mathematics Framework for California Public Schools, Kindergarten through
Grade 12, otherwise known as the Frameworks. By 1993 and 1994 all textbooks
were aligned to the standards. California Superintendent of Education, Bill Honig,
pushed educational reform strongly and the California Mathematics Council (the
40
state affiliate of NCTM) actively supported standards-based practices. In 1994, the
California State Board of Education approved instructional materials consistent with
the Frameworks, then Assembly Bill 170 was passed that required the State Board of
Education to ensure that basic instructional material it adapts for reading and
mathematics are based on the fundamental mental skills required by these subjects.
Concurrently, the federal government was in the process of developing
programs to support state efforts and push states to improve student achievement,
and implement standards in the areas of mathematics and readingllanguage arts. In
1989 at the Educational Summit, the National Governor's Association and the
President, adopted the National Education Goals which later become known as
Goals 2000; they also signed into law the Educate America Act which "supports the
development and implementation of state standards for student learning, and
achievement that drive systemic improvement at various levels" (Goals 2000, 1998,
p. 1). By 1998,47 states outlined standards and used them as a basis for instruction.
Results of large-scale standards-based reform movements indicate that there
are "no significant performance differences between students who learn from
traditional or reformed curricula" (Schoenfeld, 2002; p. 16). However, on test of
conceptual understanding and problem-solving, "students who learn from reformed
curricula" [standards-based] consistently outperform students who learn from
rational curriculum by a wide margin" (p. 16). In relation to the achievement gap,
"there is some evidence that reform curricula can narrow the performance gap
between Whites and underrepresented minorities (p. 16).
4 1
As a result of increases in student performance overall since the
implementation of the standards-based reform movement, it has become the driving
force behind most federal, state and local educational policies in the U.S. today. The
focus on raising academic standards for all students has led to an ambitious agenda
for improving schools. At the heart of standards-based education lie academic
content standards. Content standards specify what students should know at each
grade level and by, extension, what should be taught. In turn, teachers must have a
firm grasp of this more demanding content in order to teach it to their students and
know how to effectively use the curriculum materials and strategies (Ed Source,
N.D.), Today, the development and implementation of standards have been largely
taken over by the states; however, states are accountable to the federal government
for the implementation and assessment of student academic progress using state
standards. States, districts and schools are now judged by how well they are
educating their students and whether they are raising academic achievement for all
children. The goal now is 100% proficiency (Klein, 2005).
NCLB boosted standards and assessments, and was signed into law in
January of 2000. It is the reauthorization of the Elementary and Secondary
Education Act of 1965. "The reauthorization strengthen federal pressure on all states
to pursue a standards-based reform agenda" (Ed Source, N.D., p. l), to promote high
academic standards for all students, extra support to help students and schools meet
those standards, increased flexibility for local schools in organizing them to do so,
and "greater accountability for the results, particularly as measured by student
performance on standardized test" (p. 1).
NCLB indirectly forces states to work on closing the achievement gap and
"make sure all students, including those who are disadvantaged, achieve academic
proficiency" (Ed Source, N.D., p. 1). "Annual report cards are issued to parents and
communities regarding state and local progress" (p. 1). Supplemental services, such
as tutoring or after-school assistance must be provided if progress has not been
made. If adequate yearly progress has not been made after five years, states and
schools must take dramatic action to change the way the school is run.
Under NCLB, states and schools have flexibility in how they use federal
funds. Theses funds are separated into 10 sections, called titles that establish the
requirement of a program of set or programs. Title I provides extra support for
students who live in poverty; Title I1 funding is used for "preparing, training, and
recruiting highly qualified teachers and principals. Title I11 is used for language
instruction for Limited English proficiency in immigrant students. Title IV provides
grants for out-of school programs aimed at keeping students safe and supporting
academic achievement. Title V promotes informed parental choice and innovative
programs such as Public Charter Schools and Title VI provides funds for states to
improve the "quality, validity, and reliability of their testing systems (Ed Source,
p. I). Since the enactment of NCLB, flexibility in funding allows states, local
education agencies and schools to "use funds for their particular needs" (Ed Source,
NCLB places emphasis on educational methods that have been proven
effective through rigorous scientific research. "Federal funding is targeted in support
of these programs and for teaching methods that work to improve student learning
and achievement" (p. 1). For example, "NCLB requires that federal funding go only
to those programs that are backed by evidence" (ED. Gov., p.1). Although NCLB
does not list any math programs specifically aimed at increasing student
achievement, it has allocated "an estimated $1 billion over five years for results-
oriented partnerships between local districts and universities to bring urgent, tested
methods, and high level expertise to rebuilding math excellence" (p. 1). NCLB also
invites partnerships with businesses, science centers, museums and community
organization to unite with schools to improve achievement, and rewards states for
increasing participation in advance math courses and for passing AP examinations.
Mathematics has become a primary focus beginning in 2005 when the NCLB began
requiring annual states to report annual math progress in grades 3-8 (Ed Source; The
Facts About. . . Math Achievement, N.D.).
In a report released in May of 2006, NCLB credits itself with benefiting
children and through the analysis of multiple reports, has increased student
achievement nationwide. The report indicated an all time high increase in math
scores for African-American and Hispanic 9 and 13 year olds. The achievement gap
between White and African-American and White and Hispanic 9 year olds decreased
to an all-time low. It sites the state-by-state Nation's Report Card results, released in
October 2005 that indicated across the board improvements in math; African-
44
American and Hispanic all time high achievement in all categories; and said that 43
states either improved academically or held steady in all categories (ED. Gov.,
N.D.).
On the other hand, Richard Elmore, in A Pleas for Strong Practice (2003),
states that the design of NCLB is flawed, and based this largely on the problem of
the law itself being separate from the problems of failing schools, and the
prescription of the policy. He states that NCLB "over invests in testing, yet under
invests in capacity building, which creates only short-term solutions like test
preparation rather and curriculum focused professional development. He also states
that NCLB cites ungrounded theories on improvement that are not based on
empirical evidence on how schools are to improve. He states:
If one can draw any conclusion from that research it is that a small
number of schools may emerge from classification as failing schools;
that some of these will quickly return to failing status; and that only a
few will continue to improve after they have emerged from failing
status (Elmore, 2003; p. 7).
He also' states the clause regarding parents' right to transfer only creates
instability. It is difficult to implement new curriculum and instructional designs, and
measure their effectiveness if students are continually transferring to other schools.
Finally, Elmore recommends that solutions for long and short term improvement
"focus state, local and school resources and effort on development of strong theories
and practices of school improvement, and not rely on policies produced by
policymakers who "know little about the problem for which they purport to make
policy" (p. 6).
4 5
Nevertheless, NCLB and California's Department of Education ("CDE")
policies are in alignment. California, as noted earlier, was a model state in the
development, use and implementation of state standards. However, NCLB's new
emphasis on using "scientifically proven" means those districts in California will
have to select from a list of state approved materials that meet the requirement in
order to continue receiving federal Title I funding. However, California does use
standards based mathematics curriculum based on the states adopted textbooks list
published annually. California is consistent with NCLB's assessment, accountability
and teacher quality requirements (ED Source, N.D.). California exercises its own
systems derived from the Public Schools Accountability Act ("PSAA") of 1999,
where the state holds schools accountable for demonstrating academic progress of
student in their charge.
Public Schools Accountability Act ("PSSA'). PSAA is based on the dual
premise that accountability in education should be aligned with the central goal of
the system-this is, student achievement-and that school should be the principle
unit of accountability, since the entire school environment influences student
success. It rewards schools for academic improvement, provides external
intervention for lower performing schools and potentially sanctions schools that
continue to fail after receiving external assistance. PSAA has three components:
the Academic Performance Index ("API"), Immediate InterventionKJnder
performing Schools ("IIIUSP"), and the Governor's Performance Award ("GPA")
program (CDE, 2001).
46
API is a composite score used to measure the academic performance and .
growth of schools. It ranges from a low of 200 to a high of 1000 and is calculated
from individual student test scores on the Stanford-9 (prior to 2003), and on the
California Standards Test ("CST"). The annual API school-wide growth target for a
given school is 5 of the distance between that school's current baseline API and the
statewide interim API goal of 800 (Amer. Inst. for Rsch. 2003).
IIIUSP provides funds to support low performing schools' effort to improve,
including one year for planning and two years for implementation. In exchange,
schools make themselves subject to future sanctions if they do not improve.
Eligibility fluctuated somewhat from year-to-year but primarily involves a school's
ranking in the bottom half of API scores statewide, whether it is failing to achieve its
annual growth targets.
The Governor's Performance Award program provides financial incentives to
reward schools that meet their school-wide API growth target, shows comparable
growth among all significant subgroups of students, and satisfies participation rates
(Amer. Inst. for Rsch. 2003). It features monetary awards, listing on the
Superintendents Distinguished Schools list, public commendations or school honor
roll and waiver of education code requirements (CDE, 2001).
According to the American Institute for Research (2003) evaluation report on
the implementation and the effects of the two PSAA school programs, the IIIUSP
and the GPA found that overall the general model of accountability common to
results based policies has worked to improve instruction and student achievement.
47
Researchers found "the PSAA has successfully focused the attention of K-12
educators on student achievement and low performing schools" (p. 4). Secondly,
although California schools have experienced large increases in student test scores,
the achievement from either IIIUSP or GPA programs were negligible. Of the
schools in the study, only relatively small differences were noted between IIIUSP
and similar comparison schools. The study found no direct correlation between
IIIUPS participation and a school's likelihood of meeting its API growth targets.
Moreover, there was no significant impact of the GPA program on achievement.
Mixed motivation affected PSAA incentives; however, neither strong sanctions nor
promises of rewards motivated school personnel or students to increase achievement.
However, the most important motivation cited via surveys and interviews was public
scrutiny for low performance, and the possibility of direct monitoring of the district.
Local school districts were central in influencing the improvement in low performing
schools and in the implementation of the IIIUSP. Instructional coherence and
capacity at the school site were key factors in determining the success of IIIUSP
schools with respect to learning. Collaboration and professional communities among
teachers and leadership substantially impacted the capacity to develop a coherent
instructional program (Amer. Inst. Rsch. 2003). In all, PSAA "Theory of Action" of
Results-Based Accountability Policy does impact student achievement when student
achievement is policy's focus.
In addition to PSAA, California implemented a High School Exit
Examination as a mandatory exam that must be passed in order to receive a diploma.
48
The CAHSEE was selected as the best measure of what all high school students
should know and be able to do. Also, unlike some end-of-the year course tests, all
high school students take the CAHSEE; thus, making it appropriate for the 95%
participation criterion included in NCLB (Hum. Resources Rsch. Org., 2006). The
examination covers both Mathematics and EnglishILanguage, however, for the
purpose of this paper, the mathematics component only will be explored.
The Mathematics section includes multiple-choice questions on material that
is covered through Algebra I, and it is a high school graduation requirement.
Algebra was selected because it is the only math course that is a requirement for
graduation (Ed Source, 2003). Similar to API scores, states hold schools accountable
for their students' test scores and expect them to improve over time. Students may
take the exam in grade 10 and up, and students have a total of five times to pass. A
score of 350 or above is needed in order to receive a passing status. Students can
receive a passing score if they answer at least 55% of the questions correctly. The
class of 2004 was the first class to take the CAHSEE. The class of 2006 was the first
class that was required to pass the examination in order to receive a diploma. The
exam was postponed from 2004 to 2006 because an independent study indicated that
improvement had not been effective for all students, especially those who did not
benefit from standards based instruction before entering high school (Human
Resources Rsch. Org., 2006).
Better Quality Teachers. Besides goal setting and standards based
curriculum, teacher effectiveness has been viewed as an essential factor in improving
49
student achievement. According to Robert J. Marzano's What Works in Schools
(2003), "all researchers agree that the impact of decisions made by an individual
teacher is far greater than the impact of decisions made at the school level" (p. 71).
In a study titled, Teacher Quality and Student Achievement: A Review of State
Policy Evidence by Linda Darling-Hammon, she writes:
In all cases, the proportion of well-qualified teachers is by far the
most important determinant of student achievement; it is highly
significant in all equations for both subject areas in all years and at all
grades (p. 30).
Moreover,
A large number of variables associated with teacher quality appear to
bear a significant relationship to student achievement. Variables such
as teachers' knowledge, skill, and preparation matter for the student
achievement (p. 32).
She goes on to state:
When aggregated at the state level, teacher quality variable appear to
be more strongly related to student achievement than class sizes,
overall spending levels, teaching salaries, or such factors as statewide
proportion of staff who are teachers (p. 38).
A study conducted by Celeste Alexander entitled Does Teacher Certijkation
Matter? Teacher Certification and Middle School Mathematics Achievement in
Texas (2004), she concluded:
Students who had certified teachers compared to non-certified
teachers were statistically significant. This indicates that one average
student who had a certified teacher had greater gains on the TAAS
mathematics exam than students having non-certified teachers, after
controlling certain variables (p. 12).
As such, NCLB in its effort to enhance student achievement recognizes the need for
well-qualified teachers and includes a portion of its legislation to address "Highly
Qualified Teachers ("HQT")."
NCLB defines HQT as one who has a bachelor's degree, full state
certification or licensure, and proves that they know each subject they teach. For a
teacher to demonstrate full competency, teachers in middle and high schools must
prove they know the subject they teach. Requirements for HQTs in middle and high
school include a major in the subject they teach, credits equivalent to a major in the
subject, passage of a state-developed test or HOUSS (state developed alternate
method of demonstrating subject matter competency), or advanced certification from
the state or a graduate school degree.
NCLB requires states to measure the extent to which all students have HQTs,
particularly minority and disadvantaged students. States must adopt goals and plans
to ensure all teachers are highly qualified and publicly report plans and progress in
meeting teacher quality goals (ED. Gov, 2004). California has adopted the
requirements in NCLB; however, it has its own certification requirements that
recently underwent tremendous changes once the standards-based movement came
online in the mid 1990s.
The CDE in collaboration with other education groups drafted and
implemented the California Standards for the Teaching Profession ("CSTP") and
uses them as the bases for developing new standards for teacher preparation
programs and assessments for new teachers. These standards are designed to:
Prompt reflection about student learning and teaching practice;
formulate professional goals to improve teaching practice; and guide,
monitor and assess the progress of a teacher practice toward
professional goals and professionally-accepted benchmarks (Cal.
Comm. on Teacher Credentialing, 1997; p. 1).
These standards embrace the diversity of the student and teacher population and are
centered about six interrelated categories of the teaching practice. The six standards
are :
1. Engaging and Supporting all Student in Learning.
2. Creating and Maintaining Effective Environments for Student Learning.
3. Understanding and Organizing Subject Matter for Student Learning.
4. Planning Instruction and Designing Learning Experiences for all Students.
5. Assessing Student Learning.
6. Developing as a Professional Educator.
The standards-based movement for teachers is a direct reflection of the standards-
based models for student learning in the K-12 system that has been key in improving
student achievement, and is believed to assist in developing and preparing teacher for
the classroom effectively.
Darling-Hammond's research on teacher qualification vacillates between
supporting standards for teacher preparation programs and rejecting standards. In
one instance while discussing high standards for teachers, she states:
As part of policy, intervention is itself a support for student learning,
leaving educators free of regulations that might force greater attention
to procedures than learning (p. 33).
Then later she writes:
. . . The presence of a professional board prior to 1990 proves to be
significantly related to district hiring standards; a relationship that
holds up after controlling for student characteristics. . . . The presence
of a standards board is significantly associated with the proportions of
certified and uncertified teachers (p. 36).
In the first instance she suggests that policies that include standards may hinder the
teacher's ability to effectively teach; while on the other hand, she reports the strong
correlation between teaching standards to district practices that subsequently drive
district-hiring practices of fully qualified teachers. However, California opted to
implement standards as a guiding principal for teacher credentialing programs.
In 1998 Senate Bill 2042 was passed, and it directed the California
Commission on Teacher Credentialing ("CTC") to revamp the standards guiding
subject matter preparation for elementary teachers, professional teacher preparation
programs, teacher induction programs, and to add a Teaching Performance
Assessment that is aligned to the CSTP and requires new teachers to demonstrate
competency in teaching to the states academic content standards for students (Ed.
.Source, N.D.).
Programs for on-the-job new teacher support was created when Senate Bill
1422 was signed to implement the Beginning Teacher Support and Assessment
Program ("BTSA"), which serves as a bridge between teacher preparation programs
and classroom practices (Ed. Source, N.D.). BTSA offers ongoing support to new
teachers and utilizes seasoned teachers to act as mentors, roll models and coaches.
These support services are to assist in decreasing the number of teachers who enter
5 3
the field but are immediately disenchanted once they are in the classroom, and thus,
leave the profession.
Teacher preparation programs and the CTCYs CSTPs teachers in theory are
fully prepared to education students to meet the state standards. What they must now
master and deliver effectively is the curriculum. With thorough subject matter
knowledge and instructional techniques that are proven effective, California's
achievement trend should continue to rise when highly qualified teachers and sound
curriculum combine.
Curriculum and Instruction. The standards, as noted earlier are the
foundation for curriculum and instruction for mathematics. Mathematics curriculum
or disciplines as defined by the California Standard Workbook for high schools is a
series of courses that include: Algebra I, Geometry, Algebra 11, Probability and
Statistics, Trigonometry, Linear Algebra, Mathematical Analysis, Advanced
Placement Probability and Statistics and Calculus. The standards are not necessarily
linear and local districts and schools have the autonomy to select how they want to
present the course. Courses are not necessarily separated into disciplines, but can be
taught in a traditional linear or integrated manner (CDE, 1997). Therefore, scope
and sequence only exist prior to Algebra I; thereafter it is irrelevant in mastering
mathematical concepts. These courses are also not limited to one-year, but can be
divided over multiple years or given in semesters.
In addition to the Standards, Robert Marzano describes curriculum or
classroom curriculum design, as the "sequencing and pacing of content along with
5 4
the experiences students have with that content" (Marzano, 2003, p. 106). He
recommends the following action steps to implement effective curriculum designed
classroom instruction:
1. Have the teachers to identify the important declarative and procedural
knowledge in the topics that are to be the focus of instruction.
2. Have the teachers to present new content multiple times using a variety of
input models.
3. Have the teachers to make a distinction between those skills and processes
students are to master versus those they are not.
4. Have the teachers to present content in groups or categories that demonstrate
the critical features of the content.
5. Have the teachers to engage students in complex tasks that require addressing
content in unique ways (p. 1 1 9).
The content, as defined by Schoenfeld in What Do We Know About
Mathematics, is "what a person can do mathematically?" California wants students
to minimally master Algebra, Geometry, Algebra I1 and Probability and Statistics.
Overall, the goal of mathematics according to the CDE, is "conceptual understanding
of math principals and to "teach students logical reasoning" (CDE, 1997; p. 36). As
students progress through the study of mathematics:
They learn to distinguish between inductive and deductive reasoning,
understanding the meaning of logical implication; to test general
assertions, realizing that one counter-example is enough to show that
a general assertion is true in a few cases, but is not turn in all cases; to
distinguish between something being proven and a mere plausibility
argument; and to identify logical errors in chains of reasoning (p. 37).
Merely lcnowing these skills are not enough, but the ability to use what they know is
the key (Schoenfeld, 1994; p. 5).
The National Center Improving Student Learning and Achievement in
Mathematics and Science support Schoenfeld's theory. Its research recommends that
the best learning, or instructional practices, is the "conception of learning with
understanding." This concept states:
Real learning has only taken place, if and when the students acquire
knowledge with understanding . . . and apply that knowledge to
learning new topics and solve unfamiliar problems. Knowledge must
be acquired in ways that clarify how that knowledge can be used
(Carpenter, Blanton, Coll, Feranke, Kaput & McClain, 2004, p. 3).
Understanding is defined in the context of mental activity "that contributes to
the development of understanding rather than as a static attribute of an individual's
knowledge" (p. 2). They further believe that mathematics understanding emerges
through the instructional process of constructing relationships, extending and
applying mathematical knowledge, justifying and explaining generalization and
procedures, and developing a sense of identify related to taking responsibility for
malting sense of mathematical knowledge (p. 3).
Best instructional practices are when teachers teach for understanding. To
help students learn mathematics with understanding, teachers need to know how to
help students:
56
e connect knowledge they are learning to what they already know;
construct a coherent structure for the knowledge they are acquiring rather
than learning a collection of isolated bits of information and disconnected
skills;
engage student in inquiry and problem-solving; and
take responsibility for validating their ideas and procedures (p. 5).
Robert J. Marzano suggests several instructional strategies for classroom
teachers that are researched based and practical and can be used in any and
classroom situations. Most importantly, he recommends using these strategies
because they furthered Schoenfeld, and the National Center for Improving Student
Learning and Achievement in Mathematics and Science Institute's theory that
students must be able to apply their knowledge. He suggests teachers be provided
with an instructional framework for units that employ researched-based strategies.
These strategies includes: identifying similarities and differences, summarizing and
notetaking, reinforcing efforts, providing recognition, homework and practice,
nonlinguistic representations, cooperative learning, setting objectives and providing
feedback, and generating and testing hypothesis and using questions, cues and
advanced organizers (Marzano, 2002).
Math Program. In an effort to promote math achievement, the U.S.
Department of Education recommended several math programs and categorized them
as Exemplary or Promising. The programs recommended include: Cognitive Tutor
Algebra, College Preparatory Mathematics ("CPM), Connected Mathematics
Program ("CMP"), Core Plus Mathematics Project and Interactive Mathematics
Program ("IMP") (Klein, 2003). All programs were categorized as Exemplary. In
the following paragraphs the Cognitive Tutor Algebra, CMP and IPM will be
discussed.
The Cognitive Tutor Algebra I was developed and funded by Carnegie
Learning. According to Carnegie, it is researched based and field-tested. The
program is based on the ACT-R theory of learning, memory and performance. It
supports student achievement and states that students who have used the program
preformed 30% better on questions from the TIMSS assessment, and students
demonstrated an 85% increase in assessments of complex math problems and
thinking. It further states that there is a 70% likelihood that students will complete
subsequent geometry and Algebra I1 courses. Students exposed to the program
experience a 15-25% increase in scores on the SAT and the Iowa Algebra Aptitude
("IAAT") Test (Carnegie Learning, N.D.).
The Baltimore public school system implemented Cognitive Tutor to enhance
its student success on the Maryland High School Assessment For AlgebralData
Analysis. Assessment of the program's effect was conducted in partnership with
neighboring counties by collecting data and analyzing the decrease in the
achievement gap. They found that the program positively correlates to with the
Maryland High School Core Learning Goals for mathematics; however, no
correlation was indicated to increased student achievement on the Maryland High
School Assessment for Algebra test (Balt. Cty. Pub. Schl., 2006). Other than
5 8
research conducted by Carnegie Mellon University that claims that student perform
better using the Cognitive Tutor than students in traditional math courses, other
results are preliminary and have not concluded a positive correlation with student
achievement.
The National Science Foundation funds the Connected Mathematics Program
("CPM") and its goal is to develop a mathematics curriculum for grades 6, 7, and 8.
The Connected Math Program aims to "help students develop understanding of
important concepts, sltills, procedures, and ways of thinking and reasoning in
number, geometry, measurement, algebra, probability and statistics" (CMP, N.D.).
Key features of the program are that it is problem centered, provides skills practice,
is complete, benefits teachers and students, and is research-based and effective.
Research conducted by CMP is commonly divided by the special populations
involved in each study. These populations include, minorities, gifted, LowIHigh
Socioeconomic, geographic diversity and English as a Second Language Learners.
Tests were done using a control group and experimental group. Overall, CMP
claims to achieve gains in all areas, including basic sltills and problem-solving
overall (CMP, N.D.). However, gains noted were no more than 5 points overall on
basic assessment test given to all groups in the study
The Core Plus Mathematics Project ("CPMP") is a curriculum designed to
make important and broadly useful mathematics meaningful and assessable to a wide
range of students. An international advisory board, mathematics, instructional
specialist, and classroom teachers developed CMPM. It is a three year core
59
curriculum for grades 9-12 that interweaves strands of algebra and functions,
geometry and trigonometry, statistics and probability and discrete mathematics.
The CPMP is based on four key principles. The first is the belief that
"mathematics is a vibrant and broadly useful subject that should be explored and
understood as an active science and patters" (Senk & Thomas, N.D.; p. 14-4). The
second principle is that "problems provide a context for developing student
understanding of mathematics" (p. 14-4). Third, "mathematics as a science of
patterns, explorations and experimentation necessarily precede and complement
theory" (p. 14-4); and last, the "incorporation of graphics calculators, and project-
development calculator software as tools for developing mathematics understanding
and for solving authentic problems" (p. 14-4).
In research conducted by Harold L. Schoen, the University of Iowa, Christian
R. Hirsh, and Western Michigan University, findings state that CPMP curriculum
does have a positive effect on quantitative things as measured by the Iowa Test of
Educational Development ("ITED"), with greater effects occurring in the first year
of use. The strongest effect, as indicted by the Interpreting Information and Solving
Problems subtest, the impact of curriculum is greatest in the areas of making
inferences, applying quantitative procedures, reasoning and evaluating
reasonableness of solutions (Senk & Thomas, N.D.).
Mathematics programs alone do not and cannot improve student achievement
in isolation. Other factors such as instructional practices by the teacher impact the
effects of any given program. However, the aforementioned programs were
60
recommended programs from the U.S. Department of Education and were
categorized as exemplary. All programs are research based and encourage continual
and outside research to determine effectiveness.
Effective Mathematics programs are a combination of effective and efficient
curriculum and instruction. The framework of this paper is based on effective
mathematics programs that bring together standards based instruction where the
assessments are aligned with standards, student achievement data drive instruction,
and a common performance rubrics is developed and exists through collaboration of
all instructional personnel in the subject area. Effective programs also used
curriculum designs that are student centered, driven by learner outcomes, focuses on
problem-solving, builds on prior knowledge and a logical and coherent scope and
sequence exists. Finally, classroom practices where lessons are designed effectively
and coherently, promote high levels of student engagement, build on prior
knowledge, and consider cultural relevancy contribute effective math programs.
"Given this, the policy issues that need to be addressed are: what kind of systemic
support structures will support the successful implementation of such curricula, and
their progressive refinement over time" (Schoenfeld, 2002, p. 19). The answer may
lay in the reorganization of the public school system and how it educates students.
School Reform. National and State policy standards-based instruction,
revised and/or improve cuniculum and instructional practices, have led to a
movement of total school reform efforts aimed at improving student achievement.
The Comprehensive School Reform ("CSR) movement is gaining momentum in
6 1
both the public schools arena though NCLB and California's School Improvement
Plan, as well as, private organizations whose interest is to increase student
achievement using student assessment to drive instruction, implement new
curriculum modes, change tradition school culture, and offer a variety of learning
activities that are engaging, collaborative and is problem-solving based.
The necessity to increase student achievement has resulted in the consensus
that the traditional structure and functions of the public school system must change.
The process of change that is currently taking place in the school reform movement
will be discussed using the Change Process Theory of Lee G. Bolman and
Terrence E. Deal's, Reframing Organizations (2003). Change is viewed through
lenses and it is: Structural, Human Resources, Political, and Symbolic. The
structural lens involves the current or traditional top-down hierarchies, rules, policies
and procedures, specialized tasks, and the goals and objectives of the entity that is
being changed; in this case, it is the tradition public school system. The human
resources lens involves employees, partners, family, people of the organization,
productivity through group effort and self-actualization. The Political lens involves
power, bargaining, competition for limited resources and negotiation. The symbolic
lens involves the school's vision or vision of education, beliefs and faith, stories and
culture (Bolman & Deal, 2003).
When discussing school reform it will be discussed in the context of the four
lenses. The current shape of American's high school where students merge onto one
campus, rotate from one classroom to another and participate in a standard course of
62
schooling evolved during the industrial ages and was modeled after the effectiveness
of the assembly line. The Bill and Melinda Gates Foundation recognized that
currentltraditional school models are not meeting the need of students nor are they
preparing students for the technological age.
Today's high schools were conceived at the beginning of the 20"'
century to prepare students to work in an industrial economy that look
very different from the economy that we have today. In the early
1900s large comprehensive high schools were designed to educate all
communities' students efficiently, providing different programs, or
tracks, for students based on their perceived academic prowess. Top-
performing students were guided through a relatively challenging
academic track to prepare them for college. Other students-almost
always poor and minority students, regardless of their knowledge and
skills, were guided into softer academic course (e.g., business general
science) or vocational classes (e.g., shop or automotive repair) with
the assumption that they were not college material (Bill and Melinda
Gates Foundation, N.D.; p. 3).
Other researchers on school reform agree the industrial age schools are not
meeting the economic needs of today. The proposal for new schools that will
prepare students to compete in this modem society must build schools that produce:
(1) "Mathematically literate workers, (2) lifelong learners, (3) opportunity for all,
and (4) an informed electorate" (Schoenfeld, 2002; p. 15).
CSR is a strategy that relies on a combination of methods to improve school
quality and performance. Their primary goal is to implement scientifically proven
reform strategies to help all children meet the state standards (Unknown, N.D.).
CSR focuses on redesigning and integrating all aspects of a school-
curriculum, instruction, assessment, teacher training, professional development,
school governance, management, and parent and community involvement in a
63
coordinated fashion (Education Commission of the States, 2006, p. 1)). Congress
gave the movement a major boost in 1997 when it provided nearly $300 million in
federal grants to help low performing schools across the nation to develop and
implement "research-based, school wide" reform strategies (Datnow, 2005).
Under the federal school wide CSR program, key requirements must be met
in order to qualify for the grant. The requirements are being grounded in scientific
based research must be supported by effective technical assistance providers, and
funding must be targeted to students and schools with the greatest educational need
who meet the following 1 1 components:
1. Employs proven methods and strategies that are grounded in scientific based
research.
2. Integrates a comprehensive design with aligned components.
3. Provides ongoing, high-quality professional development for teachers and
staff.
4. Includes measurable goals and benchmarks for student achievement.
5. Is supported within the school by teachers, administrators and staff.
6. Provides support for teachers, administrators and staff.
7. Provides for meaningful parent and community involvement in planning,
implementing and evaluating school improvement activities.
8. Uses high quality external technical support and assistance from an external
partner with experience and expertise in school-wide reform and
improvement.
9. Annually evaluates strategies for the implementation of school reform and for
student results achievement.
10. Identifies resources to support and sustain the school's comprehensive reform
efforts.
1 1. Has been found to result in, or has demonstrated strong evidence that it
significantly improves the academic achievement of students (Unknown,
N.D.).
Beyond Islands of Excellence. What can Districts do to Improve Instruction
and Achievement in all Schools, by Wendy Togneri and Stephen Anderson (2003),
identified seven factors that are essential to school improvement as follows:
(1) acknowledging poor performance and seeking solution; (2) using a system wide
approach to improving instruction; (3) instilling visions that focus on student
learning and guided instructional improvement; (4) making decision based on data,
not instinct; (5) adopting new approaches to professional development that involve a
coherent, district organized set of strategies to improve instruction; (6) redefining
leadership roles; and (7) committing to sustaining reform over the long hall.
Once a school or district realizes that reform is necessary then it has several
models to adapt. Amanda Datnow researched several models used for the CSR
movement in order to determine sustainability of school reform models.
Although the reforms differ in their approaches to change, common
among many of them are an interest in whole-school change, strong
commitments to improving student achievement, new conceptions
about what students should be expected to learn, and an emphasis on
prevention rather than remediation (Oaks, 1993 as quoted in Datnow,
2005, p. 122).
There are many CSR reform models to implement in any given school. In the
next couple of paragraphs several key programs and their key components will be
discussed. CSRs range from various curricula programs to full school-wide reform
that involves total reconstruction of the school's design. In most cases, the primary
aim of the reform is to improve curriculum, enhance the school's culture, implement
various learning activities and most importantly, improve student performance.
Accelerate Schools is a K-12 reform model established in 1986 by Henry
Levin from Stanford University. Its primary goal is to provide students with
enriched instruction based entirely on the school community's vision of learning.
The main features are: gifted-and-talented instruction for all students through
"powerful learning," a participatory process for whole-school transformation, and the
use of three guiding principles-unity of purpose, empowerment plus responsibility,
and building on strengths. Teachers adapt instructional practices usually reserved for
gifted-and-talented children for all students. The governance structure empowers all
whole school community to make'key decisions based on the Inquiry Process.
Parent and community involvement is built into participatory governance structure.
The impact on grade levels under secondary have been proven effective, however, no
research has been done on its impact on the middle and high school level.
The Coalition of Essential Schools is a K-12 reform model founded by
Theodore R. Sizer, but is currently served by the Coalition of Essential Schools'
national office in Oakland, California. Currently this model serves over 1000
students and its primary goal is the improvement of teacher quality and student
achievement. The main features are: personalized instruction to address individual
needs and interests, classrooms and other learning environments where teachers and
students know each other well and work in an atmosphere of trust and high
expectations; multiple assessments based on performance of authentic tasks; the
achievement of equitable outcomes for students; democratic governance practices;
and close partnerships with the school's community. Its impact on instruction is that
teaching and learning at the school is organized around the concepts of
personalization, depth over coverage, demonstration of mastery, and the teacher as
coach. The school's leadership structures are designed to support a democratic
school and equitable outcomes for students. Teachers share in decision-making and
have common planning time, but the degree to which school engage in other
activities depends on school needs and resources. The community and school work
together and hold each other accountable for achievement of all students. The
school's common principles are: learning to use one's mind well, less-is-more,
depth over coverage, goals apply to all students, personalization, student-as-worker,
teacher-as-coach, demonstration of mastery, a tome of decency and trust,
commitment to the entire school, resources dedicated to teaching and learning, and
lastly, democracy and equity. Independent evaluations conducted by the state of
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New York and Boston's public schools indicate that the program is overall
successful.
High Schools That Wbrk is program established in 1987 for students in
grades 9-12, founded by the Southern Regional Educational Board in Atlanta,
Georgia; and it continues to serve as it provider. The entire school model serves
approximately 1,320 students. Its primary goal is to increase the achievement of all
students with special emphasis on career-bound students by bending the content of
traditional college prep studies with quality vocational and technical studies. Its
main features are upgraded academic core, common planning time for teachers to
integrate instruction, and higher standards/expectations. Sites are expected to end
low-level courses for all students, increase the use of engaging instructional
strategies, and provide extra help to all students. Sites develop a guidance and
advisement system and aligned with middle school and postsecondary instructions,
more teachers work together and faculties from focus teams. The school uses large
blocks of instructional time, or block schedules. Parents are expected to help their
children select a four-year program of study that reflects HSTV principles. No
outside research was conducted on this model; the only research conducted was by
the school's developer and it is included in the most recent application.
The Modern Red Schoolhouse is program for grades K -12, and the entire
school program was established in 1992 by the Hudson Institute. It currently
services 250 schools and its primary goal is high achievement for all students
through development of a coherent instructional program aligned with state
6 8
standards, and implementation of school governance practices that support school
improvement. The main features are; differentiated instruction, database school-
wide planning process, alignment with state standards and assessments, participatory
governance (leadership team and task forces), integration of instructional technology,
and parent and community partnerships. Use of best practices is performance
assessments, cohers across grade and subject's impact and/or guides instruction.
Family/cornmunity task force receives tools and training to increase parent
engagement. Studies conducted by New American Schools concluded that student
achievement rose as a result of the program's implementation.
Urban Learning Center is a program for grades pre-K -12 and its entire
school model was established in 1992 by the Los Angeles Unified School District
("LAUSD", United Teachers of Los Angeles, and the Los Angeles Educational
Partnership. Its current service provider is the National Center based at the Los
Angeles Educational Partnership. It currently serves 3 1 schools and its primary goal
is to build learning environments where a well-organized school that is strongly
connected to its community supports high quality instruction. Its main features
include: thematic, interdisciplinary curriculum, transitions from school-to-work and
postsecondary education, integrated health and human services on the school site,
and a collaborative governance model. Instructional program works with staff in
developing curriculum and instructional approaches. The school structure consists of
heterogeneous grouping, team teaching; and shared decision-making with the school
community. School hours are longer than traditional school hours; schools are
69
opened for longer hours throughout the summer; and block scheduling is optional,
depending on the school. Parental involvement is governance; school/home
partnerships and adult programs are on campus. No research has been conducted to
determine the effectiveness of the program outside of the LAUSD, which concluded
in their research that student achievement increased slightly in both reading and
mathematics (NW Reg. '1 Edu. Lab., N.D.).
Small Learning Communities ("SLC") is the practice of organizing high
schools into smaller units called houses, academics, schools-within a school. The
term small learning communities are used here in its generic sense. It refers to all
school redesigned efforts intended to create smaller, more learning-centered unites of
organization, including small school and career academies. SLCs were first
established in the late 1960s; "magnet programs, career academies and mini schools
in the 1970s; charter schools in the late 1980s and 1990s; and finally, small learning
communities today" (Oxley, 2005, p. I).
Best Practices of SLC have been divided into five domains, as follows:
1. Self-Determination: autonomy making, physical separateness, self-selection
of teachers and students, and flexible scheduling, requiring all too just be
present to allow small learning community members to create and realize
their own vision.
2. IdentzJj/: small learning communities profit from developing a distinctive
program of study that originates in the vision, interest, and unique
characteristics of their members.
3. Personalization: small learning communities' members know each other
well. Teachers are able to identify and respond to student's particular
strengths and needs.
4. Support for Teachers. SLC teachers assume authority, as well as,
responsibility in educating their students. School leadership does not reside
only in the administrative staff, administrators teach, and teachers lead.
5. Functionality Accountability: SLC teams use performance assessment
systems that require students to demonstrate their learning, and the SLC to
demonstrate its success (p. 2).
SLC is a combination of interdisciplinary teaching and teach teams that are
made from rigorous, relevant curriculum, instruction, inclusive program practices,
continuous program improvements, and is supported by the district level (Oxley,
2005).
Site Specific Approaches are a design where intervention is used as a reform
approach that increase student achievement at the school level, and is an essential
aspect in increasing student achievement. A site-specific approach allows schools to
identify factors on the school level that can be altered in a school to enhance student
achievement. Robert Marzano, Timothy Waters and Brian A. McNulty state in
School Leadership that Works (2005) that school leadership cannot just implement
models that seem promising, but must select models that are right for the school
context. Whichever model is selected for implementation, they list 11 factors that
schools can address and alter in order to increase student achievement. These school
7 1
level factors include: guaranteed and viable curriculum, challenging goals and
effective feedback, parent and community involvement, safe and orderly
environment, and collegiality and professionalism. Teacher level factors include:
instructional strategies, classroom management, and classroom curriculum design.
Finally, student-level factors include: home environment, learned intelligence, and
background knowledge, and motivation. These factors can help schools identify the
focus of their work and design an intervention that is specific to the needs and
context of a given school.
Data Driven High School Reform is focused on success for all students, more
powerful and systemic change strategies and new capacities using data to support
student success and continuous school improvement. By using the best available
data, its goal is to create learning environments that support the individual success of
each student in both the willingness and capacity to continually examine the results
of the school's efforts. It is geared toward helping low-performing urban high
schools become more student-centered, personalized, and intellectually rigorous
through the implementation data driven school improvement. The heart of this
reform is a "fundamental commitment to student centered accountabilityy'-a
commitment that requires a sustained focus on student results. The school's mission
emphasizes high levels of learning for all students, learning is organized around what
students should know and be able to do, the curriculum is derived from standards
that define what student should know and be able to do. Assessment is integrated
with instruction and focuses on what student understand and can do. The school is
72
accountable for demonstrating that all students are developing proficiencies that
represent high-level standards for what student should know and be able to do.
Finally, the emphasis is on systematic reform of school structures, the curriculum,
and instructional practices (Lachat, 2001).
Although all of the above models have proven to support student
achievement, in order to be considered successful it must be sustainable. Sustainable
reforms are defined as "becoming institutionalized;" and "when it becomes a taken
for granted feature of life in a school" . . . "the point in which an innovative practice,
having become implanted, loses its 'special project status,' . . . "becomes a legitimate
and ongoing practice" (Datnow; p. 123).
Leadership
The Role of Leadership. The role of the principal has evolved into one that
primarily focuses on instruction. All of the aforementioned reform efforts are built
on the notion that instruction and student achievement is primary. Therefore, in this
era of high stakes testing, academic achievement and accountability, and high school
reform movements, school leaders must have the ability to distribute leadership.
Leaders must also be able to build teams, integrate data, implement effective
instructional strategies, and produce results that not only display improvement in
student's achievement, but also meet goals set forth by state and national standards,
and is satisfactory to parents, community and other stakeholders.
According to Larry Lashay's Developing Instructional Leaders (2002),
leaders are essential in creating coherence in improvement efforts. In other words,
7 3
the leader is responsible for setting a vision or common goal for reform, and in
ensuring that all players understand the common goals or vision. Secondly, leaders
must balance mandates and empowerment. In other words, they must make it clear
that change is not an option, and that common goals may require teachers to give up
or defer some individual preferences. Leaders must not only lead, they must model
learning. Principals should be able to recognize whether lessons are aligned with
standards, develop classroom assessments consistent with standards, and evaluate
student work for evidence that standard(s) have been achieved No longer are school
principals only accountable to the community in ensuring after school activities,
outreach programs and extra-curricula activities are accessible, but now they must
ensure that students are improving in academics subjects, meeting specific outcomes
and performing at proficient or advanced levels.
Not only is the expectation of leaders changing in their primary responsibility
and/or focus, but also in how they manage and lead their staff. Blase & Blast2
describes the essentials of instructional leadership as:
Being shared with teachers, and in its best form it is being cast as
coaching, reflection, collegial investigation, study teams, explorations
into uncertain matters, and problem-solving. Alternatives, not
criticisms, are the focus, and administrators and teachers work
together as a community of learners engaged in professional and
moral (even noble) service to students (p. 4).
Leadership is shared among other administrators and allows faculty and staff
members to participate in leadership. All members of the school's family take
responsibility for ensuring that all students achieve. The principal's role is to
support each teacher's passion, purpose and capacity; and in turn, allow teachers to
support and promote student engagement and learning (Fullan, 2003).
In a study conducted by Michael Fullan, principals that have experienced
success in creating and establishing cultures that nurture student achievement
encompassed the following nine improvement strategies:
1. setting high expectations for all students;
2. sharing leadership and staying engaged;
3. encouraging collaboration among faculty and staff;
4. using assessment data to support student success;
5. keeping the focus on learning;
6. addressing barriers to learning;
7. reinforcing classroom learning at home by engaging families;
8. employing systems for identifying interventions; and
9. defining special education as a path to success in the general education
program.
The effectiveness of this is displayed in the testimony of a newly appointed principal
of an elementary school. In A Leadership Journey by Michelle Hancock and
Barbara Lamendola (2005), the newly appointed principal of John Williams
Elementary Wchool recalls his actions that transformed a low performing school into
a high performing school. Williams states that upon his appointment a staff that was
highly dissatisfied with the conditions and practices of the school met with him. His
first step was to capitalize on exiting resources, and to invest them in the physical
7 5
structure, materials, and supplies necessary to improve practices. Next, he
established a process for collaboration by identifying goals, values and beliefs that
were shared among faculty and staff. Committees were established aligned with
each goal. Guidelines were then established and processes for effective
communication. A common sense of purpose was developed by posting test,
messages, math problems of the week, best instructional practices, and schools'
improvement plan. Opportunities for staff to display expertise and to collaborate
with traditionally isolated teachers were then established. As a result, a workable
organization was established where all staff was concerned with the success of all
students, not just their own. Moreover, high academic expectations were set for all
students with the use of student data, the alignment of curriculum, instruction and
assessment with an in depth focus of how all students learn. This process was
further enhanced through the monitoring of student progress using periodic
assessments.
In another study conducted by Robert J. Marzano, Timothy Waters and Brian
A. Mc Nulty (2005), researchers were able to develop a set of coordinated actions
that a school leader can take to enhance student achievement. This plan for effective
leadership involves:
1. Developing a strong leadership team by crafting a purposeful community,
i.e., one with collective efficacy and the capability to develop and use assets
to accomplish goals that matter to community members, through agreed-upon
processes.
76
2. Distribute responsibilities throughout the leadership team.
3. Select the right work-this involves implementing the "right" instructional
practices, curriculum, reform efforts, etc. that will work in the context of the
school setting.
4. Identify the order of magnitude implied by the selected work. Work is
identified as the next powerful step the school can take to enhance the
academic achievement of students.
5. Match the management style to the order of magnitude to the change. The
principal must personally take on nine of the following 21 responsibility
roles: (a) Optimizer - one who inspires and leads new and challenging
innovations; (b) Affirmer - one who recognizes and celebrates
accomplishments and acknowledges failures; (c) operate and communicate
from strong ideas and beliefs about schooling; (d) is aware of the details and
undercurrent in the running of the school and uses the information to address
current and potential problems; (e) have quality contact and interactions with
teachers and students; (f) demonstrate an awareness of the personal aspects of
teachers and staff, (g) establish strong lines of communication with and
among teachers and staff, (h) foster shared beliefs and a sense of community
In School LeadershipTthat Works, Marzano et al., listed the following 21 responsibilities of the School
Leadership. They are: Affirmation, Change Agent, Contingent Rewards, Communication, Culture, Discipline,
Flexibility, Focus, Ideas/Beliefs, Input, Intellectual Stimulation, Involvement in Curriculum, Instruction and
Assessment, Knowledge of Curriculum, Instruction and Assessment, Monitoring and Evaluation, Optimizer,
Order, Outreach, Relationship, Resources, Situational Awareness and Visibility.
and cooperation; and (i) involve teachers in the design and implementation of
important decisions and policies (Marzano, Waters, & NcNulty, 2005).
With accountability and data being the basis for measuring student
achievement, it is also a tool in increasing student achievement. Leaders must be
able to build teams of like-minded staff, parents and community members where
there is a consensus that positive changes in student achievement must be based upon
meaningful data. Once this consensus is built, leaders are able to establish data
teams that are properly trained and allowed adequate professional time to collect and
analyze data for the schools. Data analysis is the beginning steps in improving
student achievement by discovering, through the use of data, how to increase student
achievement (Johnson, 2002). Not only is data used to display where students are
now, but also it can detect patterns of under-achievement, gaps in learning individual
students, as well as, between students. When used well, data can guide instructional
practices, forecast trends and root out unsuccessful practices that hinder student
progress.
In each study, the overriding themes for instructional leadership are
collaboration, distributed leadership, setting high expectations, and the monitoring of
student progress. These ingredients are essential in increasing student achievement.
In order for any reform to the be implemented, a vision proposed and/or a
team built to enhance a positive school culture that promotes high expectations for
student performance by any school leader, leaders must, as stated by Richard Du
Flour and B. Brunette in Pull out Negativity by its Roots (Summer, 2002). In the
7 8
school environment "weeds" are the unwillingness on the part of the faculty and staff
to accept responsibility for student achievement. It is also the insistence of teacher to
work in isolation and not collaborate professionally with peers and other
stakeholders on best practices. The focus is on the continual "turf war," rather than
on what unites constituencies, resulting in an "us" versus "them" mentality. Finally,
focusing on activities such as interventions and reform efforts that are seemingly
fads, rather than on quality and depth of improvement efforts, and the impact of
those efforts that improve student achievement. These "weeds" negatively impact
school cultures and take out any and all efforts a leader may have in changing a
school's culture, and setting a vision that includes high expectations for student
achievement. Leaders must take action to rid the school's culture of
"weeds" by
improving self-efficacy, creating a culture of collaboration, uniting stakeholders
under a common ground, and just "saying no" to focusing on activities rather than
results.
In most cases, school leaders do not have strong pedagogy in mathematics
education, nor are they required to be "highly qualified" in the areas that they
supervise-the academic core areas that are measured through federal and state
accountability systems, subject areas where the achievement gaps continues to exist
or areas of instructional and teacher pedagogy, all of which are important in
increasing student achievement. Therefore, leaders must look to other sources that
will assist in enabling them to become more effective leaders, especially in areas
where they experience a significant lack of knowledge in both content and pedagogy.
79
Several indicators directly link to student achievement, effective and
professional development, the building of professional communities, and the
establishment and promotion of environments that promote collegiality and
professionalism (Marzano, 2003; SEDL 2000; Wong & Nicotera, 2003). Student
achievement is more directly linked to teacher practices in the classroom; therefore,
leaders must ensure that educators are in an environment where professional learning
and collaboration are exercised consistently and effectively.
Creating and nurturing an environment of collegiality and professionalism is
a school level factor where studies have found a significant relationship between
school climate and student achievement. "This factor deals with the manner in
which staff members in the school interact, and the extent to which they approach
their work as professionals" (Marzano, 2003; p. 60). Collegiality is the tacit norms
of professional behavior, while professionalism is a sense of efficacy on the part of
teachers. Combined, an environment is created where teachers perceive that they
can affect change in schools that are reflected by student achievement. An
atmosphere where collegiality and professionalism is practiced and values allow
leadership to model learning, share learning, and gain knowledge of professional
practices in content areas and pedagogy from teachers who are knowledgeable in
areas where the leaders may lack.
Research on effective professional development demonstrates that peer
coaching programs encourage professional growth, recognition, experience-
enhancing roles, and collegiality for teachers is significantly linked to the teaching
8 0
and learning process which in turn, impacts student achievement (Wong & Nicotera,
2003, p. 3). Moreover, it establishes a culture of standards and expectations,
improve instructional capacity, support a process of on-going evaluation, and
connect classroom practices to policy context. Professional development is a source
of knowledge that not only benefits teachers, but also school leaders in areas of new
curriculum and instructional techniques. It is also used as a tool to reflect on current
practices, increase professional dialogue, and identifying treating specific problems
(Wong & Nicotera, 2003).
The Southwest Education Development Laboratory's ("SEDL") research on
professional learning communities concludes that there is a direct link of staff and
student results. When staff work together to change classroom pedagogy, greater
gains are evident in mathematics. Professional Learning Communities are schools
where the professionals (administrators and teachers) continuously see and share
learning to increase their effectiveness for students, and act on what they learn
(SEDL, 2000).
As noted earlier by R. Marzano, a teacher whose practices directly and
significantly impact student achievement. Teacher knowledge in the content area
and, more importantly, in pedagogical practices must continue to grow, evolve and
be implemented in the classroom setting. Best practices and effective results on
student achievement being shared amongst staff and administrators allows for a
library of knowledge within the school, as well as, allows the school leader to learn,
focus the staff on learning, and creates a vision that focuses on high expectations
where all members of the community teach one another.
CHAPTER 3
METHODOLOGY
This study will investigate math achievement as a result of policy initiatives
in combination with school design, best practices and school leadership. Details of
the implementation and adoption of specific policy initiatives and school based
programs for mathematics will be examined in the context of improving mathematics
performance. Instructional leadership and its impact on mathematics achievement
where leadership lacks strong pedagogical content knowledge in mathematics
education will be examined, incorporating an understanding of how leaders work
effectively in this context, as follows:
1. What was the pattern of math achievement for various students at the school?
2. What policy initiatives, as well as curriculum, instructiodand related conditions
seem to be related to improved math achievement at the school?
3. What change process did the school use to enhance its math program and
strategies to assist students in math?
4. To what extent was strong instructional leadership important in improving the
math programslstrategies, and math achievement among students?
5. How did instructional leaders respond in academic areas for which they were not
experts?
Qualitative methods will be used through the use of systematic case study that is
designed to provide sound, well-developed images, understanding of the activity,
atmosphere of the community and depth, and detail and individual meaning (Patton,
8 3
2002; p. 16). The use of a qualitative case study creates a conceptual framework that
supports the researcher in building a comprehensive picture; which allows the views
and beliefs of the interviewees to be shared in a natural environment which fosters
more authentic responses (Creswell, 1998). As such, the pattern's perspectives and
themes evolve from case studies and the rich material for analysis is the essence of
qualitative inquiry (Patton, 2002). The study will use the summative evaluation to
"determine the effectiveness of human interventions and actions (e.g., programs,
policies, personnel, products, etc.)" that are explored through research-based data
collection and analysis methods, which are founded upon and directed by conceptual
frameworks (Patton, 2002, p. 224).
Information revealed by the examination of documents combined with data
from multiple interviews and surveys will be employed. The instrumentation will
clearly and concisely draw out answers to the research question. The instruments
that will be employed are reproductions of those found in the current research in the
field of education. While data and informational profile of the school, instructional
leader and/or instructional leadership team, and interviewees will be discussed in the
study, alternate names will be used in all cases to ensure anonymity.
Sample and Population
Purposeful sampling will be used in selecting the district of study. This
method will allow an "in-depth understanding," where "one can learn a great deal
about issues of central importance to the purpose of the research" (Patton, 2002;
p. 46). A single high school will be selected for study as a means to develop a
84
deeper understanding of instructional improvement efforts and effective leadership.
The following criteria will be used in selecting the school site.
1. Schools that have shown improvement on the California Standards Test ("CST")
in Algebra I.
2. Schools with at least 1200 students and with at least 50% diversity.
3. Public comprehensive high school (which is magnet equivalent because of size).
4. Principal in place for at least three years.
5. API is greater than or equal to 600 and a state comparison ranking greater than or
equal to 5.
Originally, the criteria for diversity of student population was 60%, however, this
eliminated a significant number of schools from the sampling pool. Therefore, the
percent was decreased to 50%, which allowed 114 schools to meet the selection
criteria identified. A second elimination process was completed where the original
114 schools were evaluated to analyze if scores in Algebra I remained the same or
increased over a three-year period. Of the one hundred and fourteen schools, 44 met
final criteria.
Kando Medical Magnet High School, although it is not a comprehensive high
school, met all aspects of the sample criteria and, therefore, is the subject of this
study. The participants in the study included the Principal, Key Instructional
Leader(s), All Teachers, and Math Teacher(s). One or two interviews that were
directed by the case study were conducted with all of these participants in an effort to
collect detailed information. Each of the approximately two-hour interviews was
85
conducted at the site where the participants were employed. Interviews and surveys
were both based upon the Case Study Guide, which was rooted in current
educational research, Model Math Programs, Change Process, Instructional
Leadership, and Leadership Expertise in Mathematics.
Selected District. Los Angeles School District covers 710 square miles; in
addition, LASD serves four cities within LASD, and 12 cities partially within the
LASD. According to the November 2005 enrollment information, the district's total
enrollment totaled 877,010 in over 858 K-12 grade schools, 194 other schools and
centers, and 79 charter schools. The district's ethnic breakdown was 72.8%
Hispanic, 11.6 % Black, not Hispanic, 9% white, 3.8% Asian, 2.2% Filipino, .0.3 %
Pacific Islander, and 0.3 % American IndianIAlaska Native. The Lost Angeles
School District comprises a socio-economically diverse student population where 2.4
% of the students receive free or reduced-pay lunches, and 60% are English
Language Learners.
Selected School. Within Los Angeles School District there are 138 magnet
schools, 15 self-contained magnet schools, and 53 comprehensive high schools,
excluding charter schools. Of those, eight met the criteria for the study. Of the
eight, the doctoral student doing this case study selected Kando Medical Magnet
randomly.
Kando Medical Magnet is a magnet high school serving grades 9 through 12
with approximately 1,668 students. The most heavily represented ethnic group on
campus were African-American who accounted for 39.7% of the population,
8 6
followed by Whites at 35.3%, Hispanics 13.2%, Asians 10.3%, and no other ethnic
groups are represented. Sixty-two percent are English Language Learners ("ELL")
and 62.9% benefit from free or reduced priced lunches.
The school's mission statement, as stated on the school's website, claims that
Kando Medical Magnet High School's Medicine and Science college preparatory
program emphasizes scientific inquiry, critical thinking, and effective
communication. According to its mission statement:
We extend our classroom into a larger world by offering experience-
based learning in hospital, research laboratories, and community
clinic settings, while at the same time introducing our students to the
rigors of math, social studies, and science project competitions.
These experiences nurture our students to become life-long learners
and responsible citizens.
Working towards this mission, the school employs one principal, 6 other
administrators, 12 pupil services personnel, 68 teachers, 7 paraprofessionals,
8 office/clerical staff, and 18 other employees. Of the 68 teachers, 57 are fully
credentialed, 9 are university interns, 2 are district interns, and 6 are emergency
credentialed. The school was initially opened in 1982 as a result of a grant from the
Robert Wood Johnson Foundation for curriculum development.
School Principal: The principal of the school is an African-American female
who has held the position for seven years. Prior to being appointed principal, Mrs.
Hood was an assistant principal for seven years. Ms. Hood's professional
background includes cluster mathematics instructional advisor, coordinator of the
Mathematics and Science Magnet at Curtis Middle School and Klenier Middle
School, and a teacher of middle school math at El Amy Middle School. She received
8 7
a Bachelor of Science in Applied Mathematics from the University of San Diego,
and a Master of Arts in Education from Pepperdine University
Lead Teacher(s): Mr. McClellan is a white male who has been employed at Kando
High School for 21 years; he serves as the Mathematics Department chairperson and
organizes the Mathematics Mentor Program which is comprised of 1 1 and 12 graders
who mentor and tutor freshman and sophomore students in math. He also teaches
several all-male math courses aimed at improving achievement of African-American
male students in mathematics.
Instrumentation. The instrumentation for this study was developed during
the summer of 2006 at the University of Southern California in a seminar led by
David Marsh, Ph.D., Dean of Rossier School of Education. The 1 I-team members
involved in the study were Ed.D. Candidates. The team members were divided into
three teams. Team one collaborated, developed, and analyzed the School Profile and
Key Leader Questionnaire; team two developed and analyzed the teacher interview
guide; and team three developed and analyzed the Teacher Questionnaire. This was
t
followed by collaboration on an extensive review of the current literature,
construction of the conceptual frameworks and formation of data collection
instruments. A matrix that defined the relationship between the data collection
instruments and the research questions were formed to ensure that the research
questions were properly addressed and that the various instruments validated one
another. This matrix can be seen in Figure 1.
FIGURE 1
The Relationship of Data Collection Instruments to Research Questions
Key Leader
Interview Guide
Math Teacher
Interview Guide
Teacher
Questionnaire
Conceptual Framework For Research Question I: Three of the five research
questions of the study corresponded to a conceptual framework which provided a
firm direction for the study of that particular research question. The frameworks in
the study are located in the appendixes and are labeled. These frameworks provide a
broad understanding of the research questions.
Conceptual Framework For Research Question 2. Conceptual Framework for
Model Math Programs (Appendix A) provides the basis for collection of evidence for
research question two, which asked: "What policy initiatives as well as curriculum,
instruction and related conditions seem to be related to improved math achievement
at the school?" This framework was divided into six questions:
1. What teacher training andlor professional development were provided to teachers
aligned with curriculum, coachinglreflection and teacher practices?
2. What promoted student engagement, i.e., note taking, use of blackboard, use of
other resources?
3. What are the instructional practices in policy and instructional alignment and
classroom communication?
4. What technology was used to supplement instruction?
5. How did stakeholders support the improvement of student achievement?
6. What is the lesson quality, high quality instruction, coherent instruction, concept
and skills, problem-solving tasks, effective use of blackboards, adequate and
collaborative lesson preparation?
Conceptual Framework for School Design (Appendix B) provides a basis for
collection of evidence for research question two, which asked, "What policy
initiatives as well as curriculum, instruction and related conditions seem to be related
to improved math achievement at the school?" This framework was divided into
five questions:
1. What assessments are used to measure student achievement to capture
conceptual understanding, problem-solving and communication?
2. What is the curriculum foundation used for school to career applications,
constructive knowledge, and student outcomes?
3. What is the school's culture in relation to enhanced learning, meaningful staff-
student interactions and ongoing professional development?
4. How does size impact personalization, rigorous course work, positive adult-
student relationship, and better prepared students?
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5. What learning activities challenge student to think, solve problems and
collaborate?
Conceptual Framework for Research Question 3. "What change process did the
school use to enhance its math program and strategies to assist students in Math
(Appendix C)?" The basis for collecting data with respect to the extent of change
was completed. The change process is divided into five areas where the change
process may occur: (1) Structural; (2) Human Resources; (3) Political; and
(4) Symbolic.
Conceptual Framework for Research Question 4. Data collection for research
question 4 asked: "To what extent was strong instructional leadership important in
improving (a) the math prograrns/strategies, and (b) math achievement among
students?" Was the focus for conceptual framework for instructional leadership?
1. What was the leadership's vision for learning? .
2. What supervision and monitoring of instruction was done?
3. What community and political knowledge does the instructional leader have?
4. What does the leader know about the culture of learning?
5. What knowledge does the leadership have to data and the analysis of data
(Appendix D)?
Conceptual Framework for Research Question 5. Research Question 5 asked:
"How did leaders in the school resolve dilemmas about instructional leadership?"
The basis for collecting data with respect to dilemmas was established using an
assessment of the principal's expertise in math:
9 1
1. Is the Principal a highly qualified compliant?
2. Does the Principal have a credential or major in math?
3. Does the Principal have a minor or taught math (Appendix E)?
4. Does the Principal use the following strategies: delegate leadership to Assistant
with great expertise, bring in outside experts, emphasize inquiry and problem-
solving, emphasize quality instruction, emphasize strategies to engage students in
the learning process, articulate with feeder schools, emphasize raised
expectations, emphasize Strategic Teacher Assignments, emphasize Revised
Course Scope and Sequence and/or Curriculum, emphasize interventions for
lower performing students, or emphasize professional development
(Appendix F)?
The conceptual frameworks provided the foundation for the data collection
instruments. These frameworks also guided the development of the instnunentation
that was designed to tackle the issues established in the five research questions. The
Case Study Guide was the underlying instrument that provided broad, yet detailed
instructions for the collection and processing of data. The instruments that were
developed from the directions of the case study included the school profile, key
leadership interview questions (Appendix G), math teacher interview questions
(Appendix H), and a teacher survey (Appendix I). The variation in the selection of
interviewees allowed for the opportunity to more effectively triangulate the data that
were collected. Participation on the part of the interviewees was completely
voluntary. In addition, the use of interview guides and questionnaires provided
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another source of data; in this case, quantitative data, allowing for further
triangulation and the opportunity for analysis of statistics in seeking answers to
research questions.
Case Study Guide. As stated previously, the Case Study Guide provided both
broad as well as detailed instructions for the collection and processing of data in all
of the instrumentation. More specifically, the Case Study Guide organized for the
researcher, a list of questions that were appropriate for each of the three different
classifications of interviews that were to be conducted-Key Leader and Math
Teachers. The questions from these listed, which were only meant to act as a model
for the interviews, not as a formal script, served the purpose of helping the researcher
to avoid omitting critical areas of study during the interview while also maintaining
uniformity and alignment. The three interview guides were all formatted in sections
and directly mirror the research questions of the study.
The participants involved in the interviews were the Principal and the
Mathematics Department chairperson, who were identified by the Principal and the
Math Department as the key instructional leaders. All interviews followed the model
presented in the University of Southern California, Course EDUC 536, Inquiry 11.
Including, but not limited to the preservation of anonymity among the participants,
taking notes during the interviews and notifying all participants of how their answers
will be stored.
In addition to the interviews of selected personnel, all certificated teachers
were asked to complete a Teacher Questionnaire. The questionnaire, in addition to
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including an introduction that also served to assure the participant of the anonymity
of their responses, contained 41 survey questions. Participant responses were based
on a five point Likert scale, ranging from 1 to 5-1) Disagree Strongly, 2) Disagree
Somewhat, 3) Neutral, 4) Agree Somewhat, to 5) Strongly Agree. The Teacher
Questionnaire is divided into sections, aligned with the research questions to
measure the degree of awareness about policy initiatives, change process, strong
leadership, and how leaders resolved dilemmas. The survey questions focused on
the perception of participants, and about how the school practices, design and
strategies impacted student achievement.
Document Review Guide. The document review guide, much like the
Teacher Questionnaire, was used to align school documents to the research questions
developed in the study, addressing policy initiatives, the change process, strong
leadership, and how leaders resolved dilemmas. The Document Review Guide is
essentially an organizational tool, which enables the researcher to remain focused on
the research questions and maintain documents in an organized fashioned.
During the summer of 2006, the criteria for selection of potential
participating schools were established. Once these criteria were established, a list of
eligible schools was developed. The Principal of Kando Medical Magnet engaged in
a discussion with researcher regarding the study, and expressed interest in having the
researcher study the school's efforts and practices used to improve math
achievement. The researcher completed the Institutional Review Board (IRB)
Clearance Application Packet and received IRB clearance at USC. This phase
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involved document analysis that continued throughout all phases of the data
collection process. Relevant information, including school documents that described
efforts specific to the practices being studied, in addition to student demographic
data, were explored. The documents that were being examined were relevant to the
research questions of the study.
After initial document analysis, researcher contacted the Principal of Kando
Medical Magnet in an effort to arrange the logistics of administering interviews and
surveys with participants in the study. In addition, the Principal was given copies of
all instruments to be used for the data collection in the study. The Principal was also
asked to identify participants that were purposely selected to be interviewed for the
study, the key leader.
The second phase of the data collection involved two days of interviews.
The first round of interviews included the first formal interview of the
Principal/Instructional Leader. A second interview was conducted with the
Department Chairperson, who was identified as a key Instructional Leader by the
Principal and other department members. Extensive use of the key leader interview
guide was made during this interview in order to ensure that data collected were
aligned with the research questions.
During the third phase of data collection two surveys, Math Teacher and
Non-Math Teacher Questionnaires were administered. The Teacher Questionnaires
were distributed to certificated teachers through their staff mailboxes with a cover
letter explaining the survey and its purpose, as well as brief directions for completing
9 5
and returning the survey, for which a self-addressed, stamped, returned envelope was
provided. Much of this same information was also presented to the participants in
the survey during a staff meeting where the researcher was afforded the opportunity
to address the staff. During this address, the researcher provided some background
about both her and the survey, reinforced the anonymity of the participant's
responses to the survey, and highlighted directions for completion of the survey.
Collection of surveys was accomplished through the use of a locked file drop
box that was placed in the main office next to the teacher mailboxes. In order to
measure the return rate of the surveys and to distribute follow-up copies to
participants who failed to return surveys during the first round of distribution, the
envelopes were numbered on the front, as well as the survey itself, which allowed for
recording of returned surveys while maintaining anonymity of specific responses.
Of the 66 teachers on campus, surveys were distributed to 65 of them; one math
teacher was a rotating substitute who was not a permanent member of the staff. Of
the 55 non-math teacher surveys distributed, 13 were collected in three waves for a
24% return rate. Of the 10 math teacher surveys, 6 were collected in three waves for
a 60% return rate. The total return rate of the 65 surveys distributed was 30%. The
surveys were distributed and collected in three waves since an acceptable response
rate was not acceptable after the first two waves.
Finally, the fourth phase of data collection entailed interviews with three
randomly selected teachers-2 math teachers and 1 resource specialist. .All of these
interviews took place over the course of two additional days of visitation at the
campus being studied.
The Interview Guides (for teachers and for the principal) were used
extensively during these interviews in order to ensure that the focus of the discussion
remained centered on the four research questions. During the second interview with
the principal, the principal was afforded the opportunity to make any final comments
that they felt appropriate to the research being conducted.
Data Analysis
Using references to the Conceptual Frameworks and the Case Study Guide,
the researcher organized all quantitative and qualitative data by research question. In
an effort to develop a complete answer to each of the research questions, the
conceptual framework items included the case study guide which was analyzed
independently as a unique item for his study. As responses were formed to each item
by the researcher, the findings were validated with consideration of as many sources
of data as possible and appropriate. Relationships and patterns were identified in the
data that were collected from interviews, documents, surveys and questionnaires in
order to generate responses. The general approach to data analysis included this
systematic response to each of the research questions, coupled with the triangulation
of the data that were used to generate the responses.
Qualitative and quantitative data were both organized for analysis by research
questions. The table previously displayed in Figure 1 charted the relationship
between the four research questions, and the different instruments that were used
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assisted the researcher in this process of organizing the data (see Figure 1).
Microsoft Excel software was used to organize the data, for the tabulation of data,
and for averaging responses to the teacher surveys. Field notes were augmented and
then significant themes were identified, and questions and important points of
interest that were raised by the interview were noted. Questionnaire responses,
interview responses, documents, and artifacts were analyzed to formulate responses
to research questions.
Summary
This chapter presented the research methodology of the study including a
description of, and the rationale for sample selection, data collection and instruments
used, as well as the methods used for analyzing data. The purpose of this study was
to identify the best conditions for student mathematics achievement that, through
experience and research, has proven to reliably lead to success. In Chapter 4, a
discussion of the research findings of the study is presented.
CHAPTER 4
THE FINDINGS
This chapter presents the findings of the study as well as a discussion of those
findings. The overall goal of this study is to identify the best conditions for student
mathematics achievement that, through research and experience, have proven to
reliably lead to success. It investigates math achievement as a result of policy
initiatives in combination with school-based curriculum and instruction. Details of
the implementation and adoption of specific policy initiatives and school-based
programs for mathematic achievement, instructional leadership and its impact on
mathematics achievement where leadership lacks strong pedagogical content
knowledge in mathematics education will be examined, incorporating an
understanding of how leaders work effectively in this context. Within the parameters
of the research questions and the corresponding conceptual frameworks, the findings
are reviewed using an analysis of interview data, documents and survey results.
The first section of the chapter provides a pattern of mathematics
achievement within Kando Medical Magnet High School ("Kando") in an effort to
answer the first research question of this study: What was the pattern of math
achievement for various students at the school? The second section of the chapter
focuses on policy initiatives, curriculum, instruction and related conditions that
seemingly are related to improved math achievement at Kando Medical Magnet High
School. This section is designed to answer the second research question: What
policy initiatives as well as curriculum, instruction and related conditions seem to be
99
related to improved math achievement at the school? The third section of the
chapter will discuss the process of change that had taken place in order to.address the
third research question: What change process did the school use to enhance its math
programs and strategies to assist students in math? The fourth section of the chapter
will examine the effect of leadership in order to answer the question: To what extent
was strong leadership important in improving a) the programs/strategies, and b)
math achievement among students? The final section will appraise the effect of
leadership to answer the question: How did instructional leaders respond in the
academic area for which they were not experts?
Pattern of Mathematics Achievement for Various
Students at Kando Medical Magnet High School
Kando Medical Magnet High School has displayed significant growth within
a three-year period that is reflected in their CST scores in Algebra I. The criteria
established for this case study was the school's API scores that is greater than or
equal to 600, and a state comparison ranking greater than or equal to 5. Kando was
one of 44 schools in Southern California that met this criterion.
Algebra I, as noted in Chapter 2, is a "gateway" and indicator course for
future success in higher-level math courses, college entry and placement in the
worltforce. For the purposes of this study, Algebra I scores as measured and
reported by the federal Annual Yearly Progress ("AYP"), the state's measure of
yearly progress toward achieving state academic standards. AYP is part of the
federal NCLB legislation where the focus is on "how well schools and Local
Education Agencies ("'LEA") are meeting common standards or academic
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performance." NCLBYs AYP requires that all schools meet the same academic target
throughout the state, regardless of their baseline level of performance. AYP
calculations for high schools consider the API growth, graduation rates and passage
of the CAHSEE for grade 10 students with a 380 score or above (CDE, 2006).
Algebra I AYP scores from 2003 to 2005 are displayed in Table 1 to show
school's pattern of achievement.
TABLE 1
AYP Bands for Kando Medical Magnet High School
BELOW FARBELOW
ALGEBRA l ADVANCED PROFICIENT BASIC BASIC BASIC
Within a three-year period, Kando increased in the top two quintiles by 2%,
decreased in the bottom two quintiles by 6%, and its total gain equaled 8%.
The California Department of Education 2003 Academic Performance Index
("API") Base Report is the means by which the state's Public School's
Accountability Act rank school performance, sets growth targets, and provides
similar-school comparisons. API calculations include English-Language Arts,
Mathematics, History Social-Science, and Science scores for grades 2 through 11.
The state's API is a numeric index (scale) ranging from a low of 200 to a high of
1000. Each API cycle includes an API base and an API Growth. The base is
calculated from statewide test results of the continuing and new assessments from
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the prior year. The API base serves the baseline for comparison with the API
growth. The API growth is calculated with the same indicators as the prior year's
API base, but is based on test results from the following year. The API growth
established whether school met their API growth targets. 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 (CDE, 2006).
The 2004 API Base Report lists Kando with a 2003 API of 68 1, a rank of six
and a growth target of six. The 2004 API Base Report list Kando Medical Magnet
High School with a 2004 API base rank of 708, a rank of seven and growth target of
five. In 2005 the API Base Report list Kando Medical Magnet High School with an
API base rank of 71 1; a rank of 6 and a growth target of 4. In two of the three years
Kando met or exceeded its target growth rate. Although the school did not meet its
target in 2005, the API base rate did grow three points from the previous year. It
should also be noted that Kando met their API in the following subgroups as well:
African-American, Hispanic, and Socio-economic disadvantaged.
According to the California Department of Education, High School Exit
Exam office, as of November 2006, 527 students were tested. Of those 363 (or 69%)
received passing scores on the mathematics portion of the CAHSEE. Of those, 410
were female with a passing rate of 68%, 116 male with a passing rate of 72%, 389
African-American with a passing rate of 6896, 8 classified as "special education"
with a no-pass rate indicated, and 30 classified as English Language Learners
("ELL") with a pass rate of 57%. The following data in Table 2 is the 2003 to 2005
combined tests results:
TABLE 2
CAHSEE Math Results 2003 - 2005 (All Students Tested)
Kando Medical Magnet High School's growth pattern, as shown in both
federal and state official measurement instruments and reports, is significant for
Algebra I. The federal APY measurement shows an 8% growth over the three-year
period. API bands met or exceed growth targets two out of three years. CAHSEE
passage rates for mathematics equals 69% of the student population who have been
tested.
Policy Initiatives, Curriculum, Instruction and Related
Conditions that are Seemingly Related to Improved Math Achievement
at Kando Medical Magnet High School.
Standards-Based Instruction. Policies such as No Child Left Behind
("NCLB"), Public School Accountability Act ("PSAA"), and CAHSEE are policies
in place at Kando. However, the policy that has seemingly contributed to
mathematics achievement is the implementation and practice of Standards Based
Instruction ("SBI'Y. In 1992, the California Department of Education published the
Mathematics Framework for California Public Schools, Kindergarten through
Grade 12, otherwise known as the Frameworks. By 1993 and. 1994, all textbooks
were aligned to the standards.
Standards Based Instruction was emphasized with the opening of school for
the 2000-2001 school year when Los Angeles School District's ("LASD")
Superintendent outlined its annual goals that included SBI, accountability talk, high
expectations for all students, and learning walks by district and school administrators
to ensure that standards were being taught in all classrooms. From this meeting the
principal of Kando, Ms. Hood, introduced the mandated use of SBI to her staff in an
effort to bring Kando in alignment with district and state goals.
During this first year of implementation LASD stripped its classroom walls
of district standards and replaced them with state standards. Posters were displayed
in all classrooms, common areas and hallways. Teachers were highly encouraged to
begin each class session informing students of the standard(s) focus and what they
were expected to know by the &d of class. Standards were to be written into lesson
plans. Although outward signs were used to give the perception of compliance with
the district's mandate, teachers (specifically veteran teachers) were hesitant in
integrating standards into their daily lessons. According to Ms. Hood teachers
expressed concern that their "creativity" was being taken away. However, the issue
was resolved through discussions, training, classroom observations, the teacher
evaluation process, and the modeling of implementation by teachers new to the
profession.
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Ms. Hood stated that teachers were resistant in implementing the practice. In
an effort to resolve the resistance, Ms. Hood explained the use and importance from
a student's point of view and how important it was to expose students to the
standards set for by the state. Once a common understanding was evident, she issued
teachers a template titled, Standards-Based Instructional Model and the "Standards-
Based Instructional Process Criteria Checklist (Appendix J)" to use for planning
lessons around the standards. She used teachers new to the profession as role models
in the use of SBI because these teachers were trained in SBI in their University
Teacher Preparation Programs. Ms. Hood and her administrative staff utilized an
observation checklist entitled "School Continuum for Implementing Standards-Based
Education" (Appendix K), adapted from California Department of Education,
"Achieving Schools Recognition Program."
In 2003, a core group of teachers and administrators from Kando Medical
Magnet High School developed an unofficial classroom observation form for use in
classroom observations (Appendix L), conferences and the teacher evaluation
process. The form has six major areas with one area focusing on how SBI is
exercised in the classroom. From the 2000-2001 school years to the 2002-2003
school years, SBI became common practice.
Ms. Hood concludes that standards have impacted student scores and with the
use of standards, "they [the students] know what they are working towards" and,
"standards allow schools and teachers to become more focused." The Chairperson of
Math, Mr. McClellan, stated "Standards set a standard for both student and teacher,"
105
"It forces teachers to cover more material and assists teachers in planning
instruction." Teachers interviewed cite SBI as key in student math achievement.
One teacher stated "Standards have to be met;" while another, "Standards-Based
Instruction with No Child Left Behind" exposes students to curriculum and makes
students and teachers accountable.
In observing seven periods of Algebra I classes over a two-day period, all
classes had standards posted and included them in the "daily agenda." The
implementation of standards was evident in classroom handouts and tests where the
standards were posted as a subtitle under the question: "What students should know
after this lesson?" Teacher survey results indicate SBI is wholly used in the school.
Responds to the survey question: "Teachers at our school teach standards-based
lessons," the mean for non-math teachers was "Strongly Agree" with most selecting
"Agree Strongly." The same question was posed to all math teachers and their
response mean was "Agree Somewhat" with most selecting, "Strongly Agree." The
question posed to math teacher only, "The implementation of standards-based
instruction has served as an important foundation in improving student
achievement," the mean response was "Agree Somewhat" with most selecting
"Strongly Agree." Responses gathered from key leaders and teacher interviews and
surveys affirm that SBI has positively impacted student math achievement at Kando.
The implementation of SBI at Kando Medical Magnet High School was
accompanied with all the necessary supports, expert witnesses, and tools to fully
implement SBI. Kando Medical Magnet High School is located in California. In
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1992 California's Department of Education published Mathematics Framework for
California Public School, Kindergarten through Grade 12. Although Kando was not
implementing standards in their lessons, it had been using standard aligned textbooks
since 1994 when the California State Board of Education approved instructional
materials consistent with the Frameworks in Assembly Bill 170.
As noted in the literature and evident in the findings, SBI educated students
out-performed students who learned from a rational curriculum. The elimination of
remedial courses as a prerequisite for Algebra by Kando testify to the NCTM's
original assertion that complete mastery of skills before participation in higher-level
problem-solving courses as counterproductive (NCTM, 1990).
In relation to the achievement gap, subgroups grew within the three-year
period that standards-based practices were implemented. AYP data is not available
for the 2003 school year for the various subgroups. However, the 2004 report lists
African-American - 36.1 as proficient or above, and Hispanics - 3 1.8 as proficient or
above. In 2005 African-Americans proficient or above ranking was 36.8 and
Hispanics 42.6. Within one year African-American achievement grew .7 points and
Hispanics 10.8. On the other hand, API data for African-American shows a growth
while Hispanic achievement levels declined. In 2004 African-Americans baseline
was 702 with a target growth of 4. The subgroup surpassed the target growth rate by
7. In 2005 the baseline was 7 13 with a target growth rate of 3. African-Americans
met their targeted growth rate. Hispanics did not have a listed growth target from the
2003 school years, but has had a base of 710 in 2004 with a growth target of 4;
however, achievement rates declined by 14 points during this period.
The impact of SBI on teachers at Kando Medical Magnet High School is
demonstrated in their classroom practices, lesson planning, and evaluation of student
work that they [the teachers] have a firm grasp of this demanding content, and know
how to effectively use the curriculum materials and strategies to improve math
achievement.
California High School Exit Examination. The passage of the CAHSEE is a
policy introduced by the state that has significantly impacted student achievement in
mathematics at Kando. Although within itself, the CAHSEE is not method or
content of instruction, but the necessity to pass the examination as a requirement to
receive a high school diploma, and has been a key motivator for the school, its
teachers, students and families to master the test content. The California High
School Exit Examination was first introduced and mandated for the graduating class
of 2004; however, the test was suspended to 2006 by the state of California based on
a study that concluded that improvement had not been effective for all students,
especially those who did not benefit from SBI before entering high school (Hum.
Rsch. Org., 2006). The math portion contains multiple-choice questions on material
that is covered through Algebra I. A passing score of 350 is required in order to
receive a high school diploma. In order to achieve a passing score, students must
correctly answer at least 55% of the questions.
In 2001 when the CAHSEE was first administered, Kando Medical Magnet
High School achieved a 33% math portion passage rate. With an upcoming visit
from the Western Association of School and Colleges ("WASAC"), a committee was
formed to address the dismal passage rates. In 2002 WASAC reported Kando set a
growth target of 4% annually. Within a three-year period Kando increased passage
rates by 29% from 2003 to 2004, but decreased 9% from 2004 to 2005. Overall,
passage rates increased 38% over the three-year period.
The CAHSEE requirement impacted student math achievement. The
realization that less than half of its student body would graduate with a high school
diploma lead to the conclusion that additional attention must be paid to the
mathematics program. This reality hit all stakeholders, especially students who
began to realize they may not graduate. Parents got involved by pressuring teachers
to deliver instruction that would prepare them to pass the required exam, according
to Ms. Hood. The math department chairperson stated, "The CAHSEE is the
biggest influence in student achievement." Another math teacher stated that the
CAHSEE impacted math achievement because it ended social promotion as we know
it, and "students know they must pass in order to graduate." As a result, Kando
Medical Magnet High School organized a tutorial for all grade 10 students where
Advance Placement ("AP") students prepare materials and tutor during homeroom
periods.
Teacher responses to the survey statement: "The requirement that students
pass the CAHSEE to earn a high school diploma has contributed to the school's
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effort to improve student achievement" was affirmative. However, when asked:
"Our school S effort to improve student achievement in math instruction had nothing
to do with external accountability such as NCLB regulations and the CAHSEE
requirement, the mean response was "Neutral" with most selecting "Disagree
Strongly." Overall, teachers affirmed that the CAHSEE impacted student math
achievement.
Both the Math and English Departments whose teachers pledged a 100%
passage rate, and began a sort of departmental competition provided additional
school efforts. Departments continue to compete and this was evident in teacher
interviews. Several math teachers wanted to "make it known" to the English
Department that their department was being recognized for the increase in math
scores. Both instructional leaders acknowledge that the intra-departmental
competition was present.
Based on survey results, key leader interviews, and teacher interviews, the
CAHSEE has positively impacted student achievement in math. The pressure on
students, parents and teachers has forced Kando Medical Magnet High School to set
achievement goals and inspire an internal competition between departments to
increase passage rates. All these items combined are a result of the implementation
of the CAHSEE that is seemingly related to the increase of student achievement.
Change Process
The Change Process is an evolutionary process viewed through frames
according to Bolman and Deal's Reframing Organizations (1991). They explain that
frames are both windows to the world and lenses that bring the world or organization
into focus. These frames become tools that can help leaders identify the various
options inherent in any situation. Bolman and Deal go on to explain that there are
four frames that exist in every organization: structure, human resources, political
and symbolic. The structural frame views the alignment and negotiating of formal
patterns and polices or the realignment and renegotiating of formal patterns and
policies. The human resources frame focuses on employees as partners and family;
the people of the organization, productivity through group efforts, and creates for the
employee the development of new skills, creating opportunities for involvement, and
psychological support. The political frame involves managing change effectively
using power, bargaining and creating an arena where issues can be negotiated.
Lastly, the symbolic frame looks into the creation of a vision, establishing a belief
and faith in the organization, organizational stories and the establishment of a culture
unique to the organization. The symbolic frame creates meaning and purpose.
This research concludes insufficient evidence and/or data to substantiate
through the triangulation process that a change process occurred structurally in
human resources, politically, or symbolically. The finding that a change process did
not exist within the framework given can be attributed to the findings themselves.
SBI was first introduced approximately 15 years ago that neither teachers nor
instructional leaders were able articulate any change because the practice is so
ingrained in the culture. Moreover, the change process at Kando Medical Magnet
High School did not significantly involve any of the focused area, but was a result of
11 1
SBI, CAHSEE and leadership practices. Reform strategies primary goal is to
implement scientifically proven reform strategies to help all children meet state
standards (Unk., N.D.), while SBI, CAHSEE and leadership practices are not viewed
as scientific. Changes that did occur, such as those involving human resources were
so subtle, i.e., hiring of a middle school Algebra teacher, implementation of
classroom observation sheets and the reassignment of veteran higher-level math
teacher to freshman and sophomore classes, that they were not recognized outside by
anyone other than the principal. Neither surveys nor teacher interviews revealed
changes occurred in the human resources area.
However, a seamless change process occurred outside of the time frame of
this research, and over a longer period that impacted the findings of this study in all
the frames that placed significant emphasis on SBI. Formal and informal policies
and practices occurred in the structural frame; the practices of teachers occurred in
the human resource frame; data evolved as a powerful tool to enforce change in the
political frame; and a new culture of teaching and learning occurred as a result of the
changes in the other frames.
Structural changes began with the implementation of NCLB, CSTs and
benchmark assessments that emphasized data that is based on the mastery of the
standards. The results of these assessments communicated and presented to site
administrators, teachers and parents focused attention on SBI implementation in the
classroom. Moreover NCLB, CSTs and benchmark assessments promoted and
highlighted the necessity of SBI as a means to increase and measure student
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achievement. As a result, the school's policies and practices (both formal and
informal) changed to include SBI lesson planning, posting of the standards, teacher
observations that include assurance that SBI was being implemented, and
communicating standards mastery to students and parents as a measure of academic
achievement.
The human resources frame changed in a similar manner. The math
department consists of teachers, with the exception of the department chairperson
who entered the field within the last ten years and had been trained in teacher
preparation programs that emphasized SBI. These teachers who represent the
majority were not only SBI trained, but met NCLB's "highly qualified" ("HQT")
mandate, where teachers must meet subject matter competency by either possessing
a degree in the subject they are teaching, or meet alternative requirements that can be
used as evidence as subject matter competency (such as obtaining a minimum
amount of university credits in the subject area, pass a subject matter competency
exam, or provide evidence though an in-house process testifying that the teacher has
mastered the subject matter). Therefore, the school's change process in the area of
human resources occurred with the influx of newly hired teachers that were SBI
trained and met the HQT criteria.
In the political frame changes occurred as a result of data. Student and
school achievement data is a powerful variable that forced changed and enforced
compliance in the use of SBI as well as the increase efforts to improve CAHSEE
results. Since the implementation of NCLB and CSTs where data is used to measure
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student achievement and assess school performance, it is also public information that
is relatively simple to comprehend. The results of the abovementioned data has been
used to force teachers to implement SBI, drive instruction, and assess school and
teacher performance.
Symbolically changes have occurred as it did in the other frames. A culture
evolved that is SBI centered. The school accepted and adopted a vision that places
emphasis student achievement though the mastery of standards. The vision is
exercised in the daily instructional practices, the posting of standards and the
analysis of data that teachers use to drive instructional practices. SBI has given all
stakeholders a meaning and purpose, and both are ensuring that students master math
standards set forth by the state of California.
The Effect of Leadership in Improving Math Programs/
Strategies and Math Achievement Among Students.
The role of leadership in improving math programslstrategies and math
achievement among students was analyzed within the framework of Instructional
Leadership. The instructional leader framework looks at leadership's actions,
directly or indirectly that seemingly impacted student achievement. These areas
include leadership's vision for learning, supervision and monitoring of instruction,
community and political relationships, the leader's ability to create and maintain a
culture of learning, and if leadership uses and analyzes data to drive instruction.
Vision for Learning. The school's vision reads: "Kando Medical Magnet
High School cultivates life-long learners who communicate effectively, think
critically and see themselves as citizens in a world community." However, though
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several interviews teachers and administrators failed to refer to any words that the
vision contained. When teachers were asked: "What is your school S vision?" none
could articulate a particular vision, but all mentioned academic achievement and
subsequent college enrollment. When asked about the school's vision, Ms. Hood
stated the WASAC process was very instrumental in assisting the school in
developing the vision. It should be noted that the school's mission and vision
statement was in place prior to Ms. Hood being appointed principal and prior to the
increase in math achievement.
Survey results indicate that teachers of math feel that a vision for the school
is clear and in place despite not being able to articulate the vision. When asked:
"The district personnel, school leaders and teachers all have a shared vision for
increased math achievement, the mean response by teachers of math response was
"Agree Somewhat." When asked the statement: "There is a vision for increased
student achievement at our school, the non-math teachers response was overall
"Neutral." However, a vision was articulated and internalized during the WASAC
process and it was the goal of increasing CAHSEE passage rates. This is validated
through survey responses to the question: "The math achievement goals and
measures for my school were clearly articulated and easy to understand," and the
average response was "Agree Somewhat."
Supervision and Monitoring of Instruction. Ms. Hood began to set into place
personnel and other support programs to bring instruction in line with the vision.
The first thing that was done was directing the literacy coach at the school to work
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with literacy experts from the University of California, Los Angeles ("UCLA")' to
develop strategies for teachers and student to use to solve math word problems.
Teachers of math then received instruction and assistance in teaching strategies to
students. The results were successful and evident in students' grades and CST scores
where word problems were the focus.
The second focal point was the Summer Bridge Program where students
enrolled in a summer-based program aimed to assist in acclimating them into the
high school environment and the academic demands of Kando Medical Magnet High
School. In an effort to increase the appeal of the program, Ms. Hood, through the
effective work of an Assistant Principal who "knows the vision," discovered, that
credit could be awarded for attendance in the program. Using this information,
Ms. Hood increased enrollment and student's academic participation effort level.
The math section offers intense instruction in areas of weakness and enhancement to
students who are proficient. The math department chairperson states that it allows
the math department to analyze the needs of incoming students and plan the
academic year accordingly. Although it is unclear if this program is a form of
intervention, it seemingly assists students who are at risk of failing Algebra I and
seeks to increase skills needed for success in the school's math program.
In a follow-up interview Ms. Hood stated that the program is a form of
intervention. The math department chairperson, Mr. McClellan, states that program
is used to work with students in deficit areas as well as plan instruction and pacing
for the following year. Data taken from the Summer Bridge Program is used as a
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"talking point" for the math department. In all, if it is a means of intervention,
teachers indicate in survey results a strong affirmative that "quality interventions
have been implemented on our site to help students at risk of failing academically."
.
However, no intervention curriculum is used.
The administrative staff and teachers collaboratively developed a classroom
observation sheet aligned with the school's goals. Monitoring and supervision
begins in the beginning of the academic year with the issuing of data to teachers on
students who where in their classes the prior year. Data and observation sheets are
used to drive professional developments and instruction. Site administrators are
encouraged to use the observation sheets, and to collect data on and for teachers to
assist in improving individual teacher and instructional practices. Teachers use
student data to develop their annual professional goals and to discover areas of
mastery or areas that need improvement. When both teacher and administrator note
areas of improvement this information is used to pair the teacher with another
teacher, provide coaching or professional development. Survey responses from non-
teachers of math strongly affirm "the principal works hard to monitor and supervise
instruction in the classroom."
All teachers are all "highly qualified." According to Celeste Alexander,
author of Does Teacher CertzJication Matter? (2004), students who have had
certified teachers have greater gains in mathematics exams than students having non-
certified teachers. However, Ms. Hood stated that this alone was not enough. She
began to focus on professional growth for teachers relating to students, scaffolding
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and the Blooms of Taxonomy. Ms. Hood determined that subject matter mastery
was not the primary issues impacting student learning, but teachers relating and
connecting to the students. As a result, she hired a middle school teacher to teach
Algebra. Her justification was that elementary and middle school teachers teach to
the student, while high school teachers teach the subject matter only. She uses this
teacher as a transition teacher for students who experience difficulty in the Summer
Bridge Program. Survey results from teachers of math indicate a strong affirmative
to the statement: "The school's leaders emphasize the importance of quality
instruction as aprimary mission of the school."
Professional development for teachers is subject based and not school wide.
The practice grew out of reflections by teachers on past professional developments
highly supported in the 1990s. Through the implementation of professional feedback
sheets from district and school sponsored professional development, the
overwhelming theme was that the professional developments offered did not meet
their current professional needs. Kando Medical Magnet High School developed a
school-based professional development team comprise of representatives from all
departments. A committee of teachers plans professional development for the year.
Faculty professional development occurs on the third Tuesday of each month and
department professional development occurs bi-monthly. The focus has been data;
i.e., reading and analyzing, periodic assessments, data driven instruction, gaps in
achievement, and instructional practices relating the practices in Blooms Taxonomy,
scaffolding, SBI and culminating tasks.
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The math department participates in site based professional development and
attends professional developments outside the school setting, and then return to the
department and provides training. Upon the completion of professional development
the principal consistently and immediately follows up by having teachers write what
they have learned and how they are going to implement the new knowledge in their
classroom practices. This is followed up through administrative observations to
ensure implementation.
Survey results to the question: "Professional Development has played a key
role in increasing student achievement in math," teachers of math responded in the
affirmative where the average was "Agree Somewhat," and most teachers selected
"Agree Somewhat." On the other hand, when asked: 'My district supports teachers
with effective staff development in Mathematics Instruction," responses were
negative with the average response being "Neutral." It is clear that site-base
professional development has been more meaningful and impacting rather than those
sponsored by the district.
Culture of Teaching and Learning. Kando Medical Magnet High School
nourishes a culture of learning among students, teachers, parents and community
members. Kando is unique because its student population is 70% female and 30%
male. The under-representation of male students revealed in the data, grade reports,
classroom rosters and teacher reports that male students where achieving
significantly lower than the females7 population. In collaboration with the math
department chairperson, Ms. Hood allocated several sections of male-only math
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courses. The math department chairperson teaches all sections and the results have
been positive. During the time period this case study covers, the passage rates for
male students are approximately 97%, with increase enrollment in higher-level math
course that include honors and AP courses.
Within the school, grade and gender level meetings were established on a
quarterly basis to address various issues taking place in the school. For example, the
gender level meetings address matters such as, how to dress properly, etiquette and
gang involvement, African-American men "taking responsibility for their actions,
crime, etc. Popular "hip-hop" generation personalities have spoken at the school on
various issues related to the teen population. A Mentor-Mentee pairs freshmen and
senior students where the senior mentors the freshman. The mentor discusses the
A-G requirements, informs students on what to do as far as registering and selecting
classes, preparing for college, navigating the school and guiding the freshmen
students on whom to speak with regarding various issues. This process is used
throughout the year.
The teaching staff is a balance of African-American, White and Latino.
Ms. Hood noticed in staff meetings and in the faculty cafeteria that teachers only
mixed with those of their own race. She also noticed that when students were
disrespectful to one another using racial slurs, teachers rarely responded. As a result,
she moved to ensure that teachers were a collaborative group that modeled
appropriate behaviors and sought community assistance to educate teachers on the
need for positive diversity within the community. Survey results from non-teachers
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of math strongly affirm, "School leadership worlts to establish and maintain a respect
for cultural diversity."
Community and Political. Kando Medical Magnet High School is located in
an impoverished, majority-minority community of Taws. Taw is most noted for the
1965 riots. In recent years, Taws has gained attention for the closing of Kando
Hospital and for the loss of the university accreditation. Taws are also known for its
active community leader, Sweet Amy Harrison. Ms. Hood called upon this
community leader and grandparent of a Kando student. Sweet Amy Harrison has
been honored by Essence Magazine for her community food and clothing giveaways,
featured on Extreme Home Makeovers, and she resides in the home local political
leaders use as a backdrop for grassroots community involvement. The principal has
capitalized on Sweet Amy's popularity and influence. Sweet Amy sponsors an
annual community tour for teachers and staff annually so that teachers' awareness of
the community's poverty, diversity and history can be witnessed firsthand. Teachers
interviewed stated that the tour is the highlight of the year, and that the connection to
the community seemingly moves closer after each tour and community-sponsored
luncheon. Parents also join in on the community tour.
Ms. Hood has developed a relationship with Kando Hospital and University
that is located directly across the street from the high school. When the initial math
results where revealed, Ms. Hood contacted the president of the University for
assistance. Together, they established a program where students attend classes at the
university and work at the hospital for credits. The university supports the school by
sponsoring tutoring and mentoring programs.
The school established a connection with the Feeder Middle School. When
the school board mandated Algebra I as a graduation requirement and implemented
A-G requirements in all high schools, Kando Medical Magnet High School
established the Saturday Science Academy where students from the high school
provide tutoring in math and science to middle school students for service credit
hours. The program has led to the increase in applications for admission and a
decrease in failure rates in Algebra I.
Parents are involved in the academic process immediately upon enrollment.
Counselors are assigned to students and remain with the student throughout their
education at Kando Medical Magnet High School. The purpose is to establish a
long-term relationship with the family. Parent meetings consist of the presentation
and review of student achievement data. The first parent meeting of the year teaches
parents how to interpret CST scores and understand how CST scores impact NCLB,
and API. Both parents and students write goals for their own personal achievement.
Parents are also broken into grade levels to discuss grade level specific scores such
as PSAT, SAT and CAHSEE results. The goal according to Ms. Hood "is to make
test scores transparent" and for both parent and student to take responsibility for
academic achievement. Teachers perceive the principal as one who collaborates
with families and the community and responds to the communities needs. Survey
results indicate a strong positive response. When non-teachers of math were asked:
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"Our principal works to gain the support of the community for the school's
academic efforts," the average response was "Strongly Agree."
Within the school, teacher collaboration is practiced through the pairing of
teachers, teacher lead meetings, and professional development. When asked:
"Teacher collaboration has played a key role in increasing student achievement, the
average response was "Somewhat Agree," which affirms that collaborative practices
are perceived as positive in increasing student achievement. Interviews with
department members, resource teachers and the department chairperson all indicate
that they learn from other teachers; either by explanation, observation or through the
mentoring process. Mr. Grambling, a math teacher, stated that department meetings
involve teachers sharing and reviewing effective methods in delivering a lesson.
Ms. Hood uses new teachers to demonstrate the most current teaching trends and
strategies. Another math teacher stated that she takes her problems to the department
and they assist by making suggestions she can use to increase her effectiveness in
delivering a lesson.
Interviews of teachers indicate high expectations for academic achievement.
Lists called "Brag Sheets" are posted on the inner and outer walls and halls of the
school highlighting those students who have been accepted into universities across
the nation. Instructional leaders believe students and their families expect students to
attend universities upon graduation. Ms. Hood uses parents and data to pressure
teachers to ensure that students are mastering state standards and the requirements
for university acceptance.
Students are in charge of peer related functions and guide one another
academically and socially. The department chairperson is empowered to lead the
Math Department, and each assistant principal is given an opportunity to learn each
academic subject because of rotating assignments. Most importantly, parents,
teachers and students share in data review and analysis that is used to drive the
schools instructional process. Survey results indicate that teachers strongly affirm
teacher collaboration has played a significant role in increasing student achievement.
They also indicate an affirmative response that school leadership has worked to
implement a professional community.
According to a collection of best practices titled What Is School Leadership
That Work (2005), leadership at Kando Medical Magnet High School consistently
employs 5 of the 11 strategies that are researched-based practices that work for
school leaders. The first factor is setting a challenging goal. This was done during
the WASC process when the school set a goal to increase their growth annually
by 4%. The second was providing effective feedback where student data was
reviewed and teacher observation sheets were developed to assist in increasing
teacher-learning, reflection, and effectiveness. Third, Kando Medical Magnet High
School provides a safe and orderly environment. Finally, collegiality and
professionalism are exercised in department meetings with teachers sharing
knowledge, strategies and expertise. Teachers and administration collaborate on best
practices professional development and instruction in conjunction with an analysis of
data.
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Kando Medical Magnet High School's findings are aligned with Larry
Lashay's Developing Instructional Leaders (2002). Lashay states that effective
leadership is able to set a vision or common goal for reform and leadership, is able to
recognize that lessons are aligned to standards, that assessments are consistent with
standards; and that student work is being evaluated according to the standard. The
process of setting the 4% growth rate annual during WASC process for CAHSEE,
CST and other standardized test scores was a common goal. Classroom and teacher
observations sheets and the posting of standards ensure that lessons are aligned with
the standards. Benchmark assessments measure student progress and are in line with
standards and standardize test. Teachers, instructional leadership and parents
evaluate results. Kando Medical Magnet High School's leadership has practiced
Lashay's recommendations.
Data Driven Decision-Making Analysis. Kando Medical Magnet High
School has embraced data driven instruction. Data from CST, CAHSEE and
benchmark assessments are embedding into the school's culture. In an effort to
reach this point, Ms. Hood employed district office personnel and resources teachers
to give performance assessments to students enrolled in Algebra I. She then had the
district analyze and report the results of the assessments. Using this information
Ms. Hood was able to focus on students' achievement patterns and teachers'
practices. Ms. Hood cites this as an "informative and important process." The math
department chairperson cites performance assessments as being essential to the
department. He uses the information with department members to develop and share
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strategies to address student areas of need and to prepare for the CSTs. He also
stated the results and analysis guides department professional development, sharing
of strategies among department members, and financial resource allocation for the
up-coming year. Department members cited the use of this data as an instrument in
setting and attaining goals. Survey results regarding the use of periodic benchmark
assessments are strongly affirmed by all teachers.
Leadership's role in improving math programlstrategies and math
achievement among students was present in all areas of the framework, in
establishing a vision for learning, in supervision and monitoring of instruction,
community and political knowledge, in the leader's knowledge regarding the culture
of learning and in the use and analysis of data. The principal of Kando Medical
Magnet High School utilized each of these areas to seemingly positively improve
math achievement.
Dilemmas About Instructional Leadership
In general, school leaders do not have a strong pedagogy in mathematics, nor
are they required to be "highly qualified" in the areas they supervise. The basic
requirement for one to achieve the position of principal is a California State
Administrative Credential; however, a teaching credential is a preliminary
requirement for the administrative credential. In these cases, principals andlor
instructional leaders must look to other sources that will assist in enabling them to
become more effective leaders, especially in areas where they lack knowledge in
both content and pedagogy.
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This case study utilized the framework of assessing the principal's expertise
in math by asking: Is the principal highly qualzfied in math? Does the principal
have a minor of taught math? Does the principal use the following strategies:
delegate leadership to assistants with expertise, bring in outside experts, emphasize
inquiry and problem-solving, emphasize quality instruction, emphasize strategies to
engage students in the learning process, articulate with feeder schools, emphasize
raised expectations, emphasize strategic teacher assignments, emphasize revise
courses and sequence and/or Curriculum, emphasize interventions for lower
performing students, and emphasize professional development?
Instructional Leadership Qualzfications. Ms. Hood is a highly qualified
teacher of mathematics. She has a Single Subject Clear Credential in Mathematics
issued by the California State Commission of Teacher Credentialing. She received
her Bachelor's degree in Applied Mathematics from the University of San Diego and
a Master of Arts in Education from Pepperdine University. Her teaching career
began as a middle school math teacher at Dora Ann Middle School. She was then
promoted to the position of Math Leadership Magnet Coordinator at Kleiner Middle
School. Next, she accepted a position with the William Arts Cluster as an
Instructional Advisor for Mathematics. Ms. Hood has a thorough and
knowledgeable background in the subject of mathematics, policies related to
mathematics and the implementation of mathematics programs on the middle and
high school levels. However, when staff members were asked, "Our school leader is
aware of the mathematics instruction and academic progress of students in my class,"
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the average response was "neutral." When asked: "My district and school leaders
seem knowledgeable about instructionally effective math practices and assessment
strategies; the response was overall "Neutral."
Dilemmas. The first dilemma was the development and use of benchmark
assessments that are aligned to SBI and assesses student knowledge periodically
throughout the year to ascertain areas of growth and weakness in comparison to the
standards. Although she could not explain the core of the resistance, the use of the
assessments prevailed. Ms. Hood invited district personnel into the school to assist
in implementing the assessments and interpreting and using the results to drive
instruction. The support from the local district was year-long. Ms. Hood requested
that the department chairperson use assessment data during department meetings to
develop and adjust pacing plans focus on areas of student need, and to align
professional development activities.
The department chairperson aligned the information from the assessment data
with the CST scores. Teachers bought into the idea that data from the benchmarks
assist the department in preparing for the CST. Mr. McClellan also explained to the
staff that the CST not only measured students' laowledge, but also teacher's ability
to effectively prepare students for college and market the department to the public
(since scores are published annually). Benchmark assessments are constantly
reviewed and used by the department and the department chairs. The department is
now requesting that the district to expand the benchmark assessments to levels of
math higher than Algebra I.
Once assessment data from the benchmark assessments was implemented,
Ms. Hood then found it necessary to have teachers use CST - AYP bands to focus on
students scoring basic, below basic, and far below basic. The band allocates students
based on scores obtained from the CST that is aligned with the standards. These
students were to be flagged for intensive instruction that included, but not limited to,
tutoring, CAHSEE tutoring, single-sex classes, peer counseling and/or mentoring
and summer school. Ms. Hood also wanted teachers to use the data to drive
instructional practices.
As noted earlier, the faculty does not recognize their principal, Ms. Hood, as
"the math expert;" as a result personnel set in place to assist in bringing about
improved achievement and delegated as the "expert" who has a strong content and
pedagogy in math was the department chairperson. According to Ms. Hood,
Mr. McClellan, department chairperson, is highly respected by his peers and
students; he is passionate, knowledgeable on teaching math, and is very informed
with the history of the school. He has been given wholesome authority in managing
and guiding the Math Department. As the Math Department chairperson,
Mr. McClellan leads department meetings, coordinates professional developments,
mentors teachers, uses the data given to him to share with the department, oversees
teacher assignments, serves on the school's curriculum leadership committee,
manages the department budget, and is the liaison between administration and the
math department. He has lead the school in changing the department's course and
sequence, moving Algebra I1 from a third tier course between Algebra I, and
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Geometry, to a second tier course that proved beneficial to student success in higher-
level courses. He organizes and works with the AP students, who in turn work with
students who have not passed the CAHSEE.
Survey results from teachers of math indicate that the instructional leader in
this case, the math department chairperson, has been an essential resource to the
math department and a leader in improving math achievement. When asked: "My
school S instructional leader provides professional development resources that I use
in my mathematics program," the average response was ''Somewhat Agree" which
indicates an affirmative response. When asked: "The school's instructional leader
encourages faculty members to discuss effective math instructional strategies," the
average response was "Somewhat Agree" which indicate an affirmative response.
When asked: "I receive coaching and mentoring from instructional leaders or peer
coaches," the response from teachers of math was affirmative with the average
response being. "Somewhat Agree."
Interviews with department members credit Mr. McClellan as a positive
guiding source within the department. One teacher stated that Mr. McClellan keeps
everyone informed on current practices and trends, explain data results and makes
suggestions for teachers to use to improve instructional practices. He uses other
teachers to share their best practices with other staff and has on several occasions
observed classroom teaching practices to assist teachers in effectively presenting
lessons and/or units of math instruction. Survey results affirm that they believe they
have regular support from proven leaders in math instruction. Mr. McClellan overall
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has proven himself as a leader. When asked: "The Math Department Chairperson
has been entrusted with and is empowered to make important curricular decisions,
the average response was "Somewhat Agree."
The principal developed a relationship with the middle schools to create a
better articulation process with the feeder school shortly after LASD Board adopted
the policy the mandatory Algebra requirement for graduation and implemented the
A-G requirements. As a result, to assist in the successful completion of Algebra I
and Algebra 11, Kando Medical Magnet High School established a Saturday Science
Academy where students from the high school provide tutoring in math and science
to middle school students for services credit hours.
Another strategy used by Ms. Hood to resolve dilemmas was in teacher
assignments. She hired a middle school teacher to teach Algebra on the high school
level. Again, her justification was that elementary and middle school teachers teach
the student while high school teachers teach the subject matter only. She used this
teacher as a transition teacher for students who experienced difficulty in the summer
bridge.
Ms. Hood reassigned veteran teachers from higher-grade level classes to
work with incoming freshman in Algebra I. Ms. Hood justified her actions by
stating that veteran teachers generally have mastered classroom management
whereas new teachers have not therefore, and veteran teachers can teach younger
students more effectively than newer teachers who had little classroom management
experience.
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Based on Ms. Hood's background she is very knowledgably in the academic
areas of mathematics; however, in other areas such as the implementation of
benchmark assessment and the use of data, Ms. Hood sought the expertise of district
personnel. She recognized that the department chairperson was influential and
respected by his peers and delegated to him the responsibility of having teachers use
the data to drive instruction. She developed a program to tutor middle school
students that has resulted in students being more prepared in math and science.
Finally, Ms. Hood recognized that personnel changes had to take place in order to
increase achievement. In all, each area where leadership recognized a deficit or an
opportunity to increase student achievement through the use of others, the results
have contributed to the overall increase ranking of student achievement in math.
Analysis and Discussion
Pattern of Mathematics Achievement for Various Students at Kando Medical
Magnet High School. Kando Medical Magnet High School's significant increase in
mathematics achievement over a three-year period is a result of the district's effort to
implement the practice of SBI that affects CST and CAHSEE scores. Through
professional development, lesson-planning templates, and teacher evaluations that
include the use of SBI; API, AYP and CAHSEE results ultimately increased.
Kando Medical Magnet High School showed strong compliance and vision
when NCLB was adopted, and its Superintendent's goals included the use of SBI and
maintaining high expectations in 2000. The school's administrative focus was now
on ensuring SBI was practiced and assessments highlighted. NCLB pressured states
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to adopt SBI that is researched-based and emphasized high academic standards and
accountability as measured by student performance on standardized results.
Although neither instructional leaders nor teachers credited NCLB or the Public
School's Accountability Act ("PSAA") as impacting student achievement, the school
consistently employs the data taken from these assessments to drive instruction and
monitor student performance. In addition to the schools use of data to drive
instruction, Lost Angles School District ("LASD:) developed intermediate
assessments such as benchmarks and pacing calendars to ensure students are exposed
to SBI.
The publication of AYP, API and CAHSEE results pressured the school to
increase performance for various reasons. One reason and the most obvious is
negative press. Secondly, administrators on both the district and school level are
indirectly evaluated or their perceived effectiveness is based on the school's
performance. School ranking and performance also impacts the real estate market
both positively and negatively. Finally community members, especially those in this
impoverished area expect high academic achievement and college enrollment
because the school markets itself as one, and has direct connections to the adjoining
hospital and medical university.
Standards-Based Instruction. The implementation of SBI as a means to
increase student mathematics achievement was a wise, cost effective choice and
reasonably simple to implement. SBI is an outline or blueprint for instruction that
sets learning goals for both the instructor and the student, and incorporates
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sequencing and pacing of content that is a proven research-based instructional
strategy (Marzano; 2003, p. 106). Moreover the district's adopted textbooks are
aligned to SBI and both state and federal policy include the use of SBI and therefore
eliminates competing strategies in obtaining achievement goals.
Most influential was the District's newly appointed Superintendent in July
2001. Ray Rogers's background included being a former Governor who served on
the President's Committee to adopt national standards and the Educate America Act.
As Governor of Colorado his focus was on "Improving K-12 education; reforming
higher education, and using technology to improve learning for all levels" (E.D.
Summit). He had also chaired the Education Commission of the States in 1994 to
1995; chaired National Education Goals 2000, and helped develop the first national
educational report card and was the co-vice chairman of ACHIEVE, an effort by the
nation's governors and major corporate leaders to reform education by the use of
standards and assessments. Kando Medical Magnet High School was under a leader
who exhibited a true passion for SBI.
While SBI in itself is an excellent means of obtaining academic achievement,
the district's focus on implementation is commendable. As noted by the principal of
Kando Medical Magnet High School, teachers initially resisted SBI claiming their
academic freedom would be eliminated. Although SBI was mandated several years
prior to its full fledge use, it became the district's major priority. In concert with the
implementation, professional development was provided to teachers and
administrators and SBI was included in the evaluation process. SBI was placed into
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practice with the use of templates and lesson planning guides to assist teachers in
planning instruction. This seamless yet all-inclusive practice allowed SBI to become
part of the school's culture. Additionally, the matriculation of recent university
graduates into the teaching field was trained using SBI; this allowed for the modeling
and practice of SBI to expand to those teachers resistant to the use of SBI.
California High School Exit Examination. The CAHSEE, although not an
instructional strategy, theory of learning, or a method for practice, also impacted
mathematics achievement because it directly affected students and their families.
According to the state's graduation policy a student must complete the prescribed
course of study and receive a passing score of 350 or above on the CAHSEE to
receive a diploma. Graduation from high school is not only proof that a student
completed the basic prescribed curriculum successfully, but it is a social matter.
For students and their families graduation is a "rite of passage" into
adulthood. Graduation from high school is the minimum and most reasonable
expectation that families place on children. This expectation brings planned
celebrations, decisions to attend college or enter into the workforce. Receiving a
high school diploma is the beginning and initiation into adulthood.
The pressure placed on the school to ensure students were able to pass the
examination grew when the initial results of the CAHSEE revealed that less than half
of its senior class would graduate. When passage of the test was mandated for the
class of 2006, all stakeholders at Kando Medical Magnet High School increased their
efforts'in ensuring greater passage rates and created a healthy internal competition
135
between the English and Mathematics Departments to see who can achieve higher
passage rates.
The CAHSEE passage rates increased over time because the school had
approximately three years to study the examination. During this time, passage rates
were examined and analyzed by the school. A tutoring program was established for
those who had not passed, changes in teacher assignments were made to provide the
environment for learning and released questions were studied and incorporated in
classroom instruction. The state superintendent supported and promoted the test and
mandated that passage of the test as a requirement for graduation after several
unsuccessful court battles.
Passage of the CAHSEE motivated all stakeholders. For the district, low
passage rates indicate poor instruction and the inability to educate students in basic
mathematical skills. For the school, poor passage and/or graduation rates are a sign
that the school is not serving the community. For the student and their families, a
non-passage signifies no rite of passage, a grim future and grave disappointment. On
the other hand, high passage rates indicate that the district and the school adequately
provide a basic education, and for the student it signifies that she is prepared to enter
adult life.
The Change Process
An investigation into the change process at Kando Medical Magnet High
School was inconclusive. The process as articulated by Bolman and Deal (2003) is
an evolutionary process where change occurs through four frames: structural, human
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resources, political and symbolic that will bring the organization into focus to reach
its goals. The methodology of this case study uses the process of triangulation where
three areas or sources intersect to reach a reliable and valid conclusion. In the case
of Kando Medical Magnet High School teachers, instructional leaders, documents,
nor observations, concluded a change process occurred in any of the four
frameworks.
Another reason why a change process was not revealed is due to the fact that
SBI is so common in education and has been part of education since the early 1990s.
Moreover, SBI was in place within the three-year period that this case study covers
and therefore was not viewed as a change made to increase student achievement.
Teachers were unable to recognize the change because many all members of the
Math Department, with the exception of the Department Chairperson were in teacher
preparation programs where SBI was used as the base in their training. The changes
that did occur were: (1) the way SBI impacts student achievement, and (2) the
alignment of visibility of SBI in all assessments.
The Effect of Leadership in Improving Math Programs1
Strategies and Math Achievement Among Students.
While SBI and CAHSEE seemingly increased student achievement in
mathematics, the school leadership's ability to set a common vision, to supervise and
to monitor SBI, to establish a culture of teaching and learning, to work in partnership
with the community and political aspects of the community, and to use data as a
medium for communication with all stakeholders fostered a school environment of
high expectations, professionalism, and community involvement where increases in
mathematics achievement can occur.
When leadership set the vision during the WASC process the principal,
Ms. Hood, was armed with current data fiom CST scores, AYP and API data as well
as the initial results of the CAHSEE. The process of setting the goal was a
collaborative effort with teachers and parents. Since the goal of increasing scores in
all areas was set at 4% annually; in all areas the goal was met provided extra
motivation. Another successful collaborative endeavor was the development of the
"unofficial" teacher observation sheets. These observation sheets were employed
and consistently used by administrators and teachers to determine effective
instructional practices and to evaluate teacher areas of strengths and weaknesses.
The collaborative methods of creating the document allowed for buy-in from
teachers and ensure that teachers are implementing SBI.
In supervising and monitoring instruction the templates issued by the district
for lesson planning brought the school into alignment using standards, and provided
structure to those unfamiliar with SBI lesson. Leadership's ability to merge SBI in
the curriculum, instructional practices of teachers, and in the teacher evaluation
process ensures that SBI is consistently the focus.
In the areas of community and politics, leadership was effective because each
relationship created a tangible outcome. For example, Ms. Hood's relationship with
the community leaders allows teachers to experience the community through tours
and community town hall meetings where Ms. Hood often addresses the audience, or
138
the community leaders address the faculty. In relation to Kando Hospital and the
university, students attend classes at the hospital; the hospital established programs
where students volunteer or earns credits. The university provides tutoring and
mentoring programs for Kando Medical Magnet High School students that are
heavily attended. All of these community connections have positively impacted the
students at Kando Medical Magnet High School.
The decision to share data with parents was a wise and effective means of
getting parents involved in the educational process. Parents who are aware of the
education process are able to partner with the school to increase student
achievement. In sharing the data with parents, parents also take ownership and are
moved to support the school's instmctional program. By connecting with parents
through the use of data the school is no longer viewed as a separate entity but as one
in partnership to assist the student in reaching educational goals.
Kando Medical Magnet High School is a professional community.
Professional development are planned and led by teachers, and teachers interact with
one another through partnerships and/or within departments supporting one another
and sharing best practices. The teachers at Kando High are viewed as professionals
in their field surrounded by professionals who are willing to assist one another in
developing their craft. When teachers feel empowered and their contributions are
recognized, they take ownership of the school, the instructional process, and work
collaboratively to reach common goals.
Dilemmas About Instructional Leadership.
While Ms. Hood met the qualifications as a "highly qualified" teacher of
math and possessed vast knowledge on mathematics programs, pedagogy, district
policies and the implementation thereof, staff was unable to recognize her as
possessing an awareness of mathematics instruction, assessment strategies and
academic progress of students in the school. Ms. Hood was able to recognize that
teachers, students and parents valued and recognize the department chairperson as a
leader in math and delegated that responsibility to the chairperson. The department
chairperson has been able to effectively lead the department and foster professional
growth within the department that impacts student achievement.
Ms. Hood's leadership style is one that empowers and motivates others. She
utilizes key personnel to implement policies and promote programs. Her ability to
focus in and select "the right person" is evident in how successful policies and
programs have been implemented. For example, she empowers the department
chairpersons and allows him to guide the math department and the math department
has faith and confidence in his ability to lead. She holds all teachers responsible for
the implementation of benchmark assessments by having them analyze the data and
select students for intervention programs, select courses of study to improve areas of
weakness, and plan professional development. She allows students to develop and
lead student activities with an almost "hands off' approach, yet is extremely
supportive and empowering.
When Ms. Hood established a relationship with the Feeder Middle Schools,
she also provided a service for the middle school students that benefits the high
school students. The Saturday Science Academy brings together high school and
middle school students. The high school students tutor middle school students in
math and science to increase their math skills. In turn, tutoring develops and
reinforces skills of the high school students that positively impact their academic
achievement in higher-level mathematics.
Ms. Hood's rearranged teacher assignments to optimize teaching and learning
opportunities. Ms. Hood reassigned veteran teachers to lower level math
courses/classes and new teachers to higher-level courses/classes. She based this
change in personnel on the belief that new teachers have the skills to deliver
appropriate instruction but do not possess adequate classroom management to create
the environment for optimum learning experiences. On the other hand, veteran
teachers possess classroom management skills gained through experience and can
manage freshman and sophomore classes so that learning can occur. This
reassignment of teachers sets the norm on classroom behavior and focuses on
academic instruction. Moreover, students who are in well-managed classrooms are
able to focus on instruction. This "focus on instruction" impact AYP scores because
grade 10 CAHSEE results are used as an indicator to measure student progress.
The findings that SBI and CAHSEE significantly impacted student
achievement is based on the knowledge and research that SBI is a proven
instructional strategy and policy that levels the playing field, addresses subgroups,
141
benefits students, and sets high expectations. Furthermore the implementation of
SBI was financially feasible, professional development was adequately provided,
textbooks were aligned to the state standards, and district and school administrators
supervised, monitored emphasized its use. Data released to the school can be
divided by standard. Teachers and administrators are able to analyze the data to
drive instruction and plan site-based or individual professional development
opportunities. CAHSEE's impact was that it motivated all stalteholders to achieve
passing scores. The district, school-based administrators, teachers, parents and
students all shared the same goal-passing the CAHSEE.
The leadership at Kando created a shared vision for student achievement;
actively supervised and monitored instruction; created a culture for teaching and
learning through the establishment of professional learning communities and student-
center communities; formed positive and productive relationships with the
community; and used data to drive instruction. The school's leadership was able to
resolve dilemmas regarding instructional leadership by delegating authority,
establishing a relationship with the Feeder Middle School and to change teacher
assignments to benefits students. In combination, SBI, CAHSEE, leadership and
leadership's ability to resolve dilemmas regarding instructional leadership created an
environment that seemingly resulted in increased student achievement in
mathematics.
CHAPTER 5
SUMMARY AND IMPLICATIONS
Summary of Background
Academic achievement in mathematics has been sub-par since the early part
of the 20th Century. Assessments such as the Third International Mathematics and
Science Study ("TIMMS") show that America's students are trailing behind their
international peers. Adding to the problem of not being able to compete
internationally, students are under-achieving on standards set forth by the nation.
Additionally, achievement gaps persist amongst African-American and Hispanic
students in comparison to their white counterparts. Moreover, as students progress
throughout their years of schooling, their achievement level decline and their ability
to compete is weaken more so. The problem is not just the achievement gap, but
American high school students are achieving significantly below state set standards.
While various legislative polices, curriculum innovations, and instructional
strategies seemingly increase student achievement in mathematics, factors shown to
have the most significant impact in much of the professional research literature on
the subject are standards-based instruction ("SBI"), teacher-effectiveness, and
effectual instructional leadership. Although the aforementioned have been
identified as critical factors to increase students academic achievement in math, no
certain mean of assuring their effectiveness has been found and no professional
development programs has been designed that work to bring all three together to
eliminate the poor academic achievement. Increased achievement in math has been
143
documented throughout the nation on the use of SBI, teacher effectiveness and
effectual instructional leadership. However, America's education system is
challenged with moving a highly diverse nation that ranges in socio-economic
statuses, ethnic multiplicity, and rural and urban landscapes into one where all
students achieve proficiently at the grade levels that coincide with their
chronological ages according to the national standard.
Implementing a policy, education program or selecting the right instructional
leader that will be effective in a given school or district is a continual experiment that
is trailed by the duty of ensuring that those policies, programs and instructional
leaders are implemented in an effective manner that will achieve the desired results.
Despite the excess of policies, programs, and instructional leadership styles, there is
no agreement as to what is the most effective in a given circumstance.
Comprehension of the impact on student math achievement of various policies,
programs and instructional leaders, and the context in which they are used is critical
to the successful replication of these practices in other appropriate educational
contexts.
Purpose of the Study
The overall goal of this study was to identity the best conditions for student
mathematics achievement that, through research and experience, that have proven to
reliably lead to success. . This study investigated math achievement as a result of
policy initiatives in combination with school-based curriculum and instruction.
Details of the implementation and adoption of specific policy initiatives and school-
144
based programs for mathematics was examined in the context of improving
mathematics performance. Instructional leadership and its impact on mathematics
achievement where leadership lacks strong pedagogical content knowledge in
mathematics education were examined, incorporating an understanding of how
leaders work effectively in this context. The research study questions were:
1. What was the pattern of math achievement for various students at the school?
2. What policy initiatives as well as curriculum, instruction and related
conditions seem to be related to improved math achievement at the school?
3. What change process did the school use to enhance its math program and
strategies to assist students in math?
4. To what extent was strong instructional leadership important in improving a)
the math programslstrategies; and b) math achievement among students.
5. How did instructional leaders respond in academic areas for which they were
not experts?
Methodology
The study used qualitative methods and quantitative case study that used
interviews, teacher surveys, and document reviews to develop conclusions about the
best conditions for student mathematics achievement that, through research and
experience, have proven to reliably lead to success. Qualitative insights were gained
through interviews of teachers and key leaders' interviewees shared personal
experience and beliefs about the conditions surrounding the increase in student
achievement in math. These experiences and beliefs were then focused and
145
organized by the researcher into a number of reoccurring themes. Quantitative data
were gathered from multiple surveys that were calculated and tabulated. Central
themes that arose from quantitative data were also identified and examined for the
study. Combining qualitative and quantitive data used triangulation of both data and
methodology. This triangulation increased the internal validity of the study and
worked to insure that findings were supported by multiple sources of information.
Sample
Purposeful sampling was for the process selection in the selection of the
school for this study. The parameters defining the selection of the school included:
it should have improvement on the California Standards Test (CST) in Algebra I; its
enrollment had at least 1200 students with at least 50% diversity; and that the school
is a public comprehensive high school. This school although not a comprehensive
high school, but a magnet, met all other criteria. The only component that differed
from a comprehensive high school was that students apply though a lottery process
where the common interest was an interest in medicine. The principal has to be in
place for at least three years; and the school's API was greater than or equal to 600;
and a state comparison ranking greater than or equal to 5.
Instrumentation, Data Collection and Data Analysis
Eleven Ed. D candidates developed instrumentation for this study during the
summer of 2006 at the University of Southern California in a seminar. Instruments
were filed tested and refined before being used for the actual study. The
development of the instruction used in the study, and was guided by four conceptual
146
frameworks that were developed for the study, one conceptual framework
corresponding to three of the five research questions. Instruments were then
collected into a case study guide that organized the collection and analysis of data for
the study. The instruments that were used in the study included the following:
1. Case Study Guide. This guide provided both board as well as, detailed
instructions for the collection and processing of data in all of the
instrumentation. It contained all the instruments with a description of each;
explained data collection phases, and included the four conceptual
frameworks.
2. School ProJile. This document set the parameters and criteria for school
selection for the study
3. Interview Guides. These guides were lists of questions that were appropriate
for the interviews that were to be conducted. These questions served the
purpose of helping the researcher to avoid omitting critical areas of study
during the interview while also maintaining the uniformity and alignment
among the different members of the team.
4. Non-Math Teacher Survey. This 20-item questionnaire was based the four
research questions and was intended to demonstrate teachers' knowledge
about the policies initiatives, curriculum, instruction, related conditions,
change process and leadership that was seemingly related to increased
student achievement in math.
5. Math Teacher Survey. This 50-item questionnaire was based the four
research questions and was intended to demonstrate teachers' knowledge
about the policies initiatives, curriculum, instruction, related conditions,
change process and leadership that was seemingly related to increased
student achievement in math.
Summary of Findings
Kando Medical Magnet High School 's best conditions for student
mathematics achievement that, through research and experience, have proven to
reliably lead to success have been the consistent practice of SBI and the
implementation of the CAHSEE. The school board and superintendent mandated
California State SBI in the fall of 2000-2001 school years. This mandate was a
response to the California Department of Education alignment of textbooks, the
publication of the Mathematics Framework for California Public Schools,
Kindergarten through grade 12 in 1992, and the alignment of California Standardized
Test (CST) to SBI. Standards Based Instruction is researched based and has a strong
link to state assessments. While SBI itself has become the norm in schools across
the nation; however, all schools are not increasing in math achievement at the rate of
Kando Medical Magnet High School.
In conjunction with the mandated use of SBI, Kando Medical Magnet High
School posted standards throughout classes, included them in daily agenda's, placed
standards on students work, also implemented template for teachers to use when
planning lessons. Classroom observations and the teacher evaluation process
148
included the use of the School Continuum for Implementing Standards Based-
Education adapted by the California Department of Education, Achieving School
Recognition Program.
Passage of the CAHSEE was mandated beginning with the class of 2006. A
passing score of 360 is required in order to receive a high school diploma. As a
result, all stakeholders got involved and their efforts increase to ensure that students
received the essential sltills needed to pass the CAHSEE. The school set up a
CAHSEE tutorial and intra-department competition was established to increase
passage rates.
Leadership's role in improving student math achievement was significant.
Leadership set a vision during the WASC process to increase CAHSEE passage rates
by 4% annually. The principal called in literacy experts from UCLA to assist in
developing strategies to assist teachers in teaching students have to solve word
problems. The Summer Bridge Program issued credits for math inventions and
enhancement to incoming freshmen. The principal also made personnel changes that
included the hiring of a middle school teacher and assigning veteran teachers to teach
lower level math course.
Teachers took on control of professional development that has played a
significant role in increased student achievement. On-site professional development
was teacher based that included the use of data, implementing periodic assessments
and improving instructional strategies such as Blooms Taxonomy, Scaffolding, SBI
and culminating tasks.
149
Kando Medical Magnet High School nourished a culture of teaching and
learning by establishing all male classes for the significant number of males under-
achieving in math. Gender and grade level meetings were established where students
could discuss issues and express themselves. A Mentor-Mentee program was
established that pair freshmen and senior students to assist the freshman in
maneuvering through there first year in high school. The principal also ensured that
teachers worked as a collaborative group in academic and non-academic areas.
In the community and political arena, the principal established relationships
with community leaders, community hospital and the medical university. A stronger
relationship with the Feeder Middle School was bridged and parents are involved in
the academic progress especially in the review of annual data on student
achievement. Most importantly, teacher collaboration is exercised throughout the
school but more so among the math department members.
Finally, data driven decision-making is embedded within the school's culture.
Data from CST, CAHSEE and benchmark assessments are embedded in the school's
culture. This data is used to inform staff,. parents and students on student
achievement patterns, teacher practices, and drove instruction.
Although Kando's principal is a credential math teacher having received a
B.A. in Applied Mathematics from Pepperdine University and held various
leadership positions involving policies, practices and implementation thereof of math
programs, other dilemmas about Instructional Leadership were resolved using
various strategies that contributed to increased student achievement. The principal
150
delegated leadership to an Assistant with greater expertise. She empowered the
department chairperson, brought in outside experts, emphasized inquiry and
problem-solving, emphasized strategies to engage student in the learning process,
emphasized articulation with feeder schools, raised expectations, strategically
assigned teachers, changed to math course scope and sequence and emphasized
professional development.
CONCLUSION
The information obtained through investigations conducted during this case
study has led this researcher to conclude that Kando Medical Magnet High School
has established best conditions for student mathematics achievement that, through
research and experience, have proven to reliably lead to success when the best
conditions. These conditions are the use and practice of SBI, the efforts to increase
passage rates on the CAHSEE, and leadership's involvement and ability to resolve
dilemmas. The conditions are aligned with the superintendent's annual goal set forth
in 2001, and the school board's policies. It is well aligned with the state and federal
government's emphasis on SBI Training, supervision and monitoring were all
thoroughly practiced and it was supported and share with the community. Teachers
at Kando Medical Magnet High School benefited from SBI training and students
fiom SBI aligned lessons. The implementation of the CAHSEE improves efforts to
increase student achievement and further practice SBI. Students at Kando have
shown steady progress in their scores on CSTs, CAHSEE, AYP and the API.
Implications. School district officials should be pleased to see federal and
state educational policies that are effectively being implemented on school sites and
that result in increased student achievement. The increase in student achievement
was in line with federal and state policies with respect to both SBI and CAHSEE.
Researchers in school and/or instructional leadership should be satisfied that their
research findings are practiced by site-based leaders and are continually being
proven through additional research. Both, with relative ease and no expense, the
152
school was able to increase student achievement through the use of SBI, the
implementation of the CAHSEE and practice of instructional leadership. However,
the implementation of CAHSEE in itself did not increase student achievement in
itself, but it increased the efforts of teachers and students to assure students would
receive a passing score.
Kando Medical Magnet High School administrators should also be pleased at
the extent and effectiveness of the implementation of SBI the increased efforts to
pass the CAHSEE. They should seek to maintain and strengthen the use of SBI
through a shared vision, leadership's ability to supervise and monitor, to nourish a
culture of teaching and learning, to maintain community and political support, and to
use data from CSTs and the CAHSEE to inforrn instruction.
Classroom teachers should be encouraged to see that the implementation of
SBI and collaboration can have a positive impact on their instructional practices, and
should seek to keep them current with respect to educational research in general.
They should also note that this researched-based strategy is easily adaptable with the
textbooks, CSTs and the CAHSEE. They should see the support and enrichment that
come from participation in a collaborative professional learning community and
should work to cultivate this kind of atmosphere at their school and in their
profession. Teachers should also attempt to be cooperative in working with federal,
state, district and site leadership in creating the best conditions to improve math
achievement at their school.
Future studies of schools with best conditions for student achievement in
math should give attention to the true impact of polices on improved student
achievement, as seen in standardized test. The impact of educational policies should
be weighed against other factors to gauge their true importance, and to increased
academic achievement in math in the midst of a myriad of other influences in a
student's life. Researchers must work with educators to implement effective reform
in the school that is guided by instructional leadership, is based on well developed
SBI and is implemented in the context of a learning community in order to ensure a
lasting impact.
GLOSSARY
For the purpose of this study, the following terms are operationally defined below.
The Academic Performance Index ("API"). The API is the cornerstone of the Public
Schools Accountability Act ("PSAA"). The API ranks school performance, sets
growth targets, and provides similar-school comparisons. The API is a single
number on a scale of 200 to 1,000, indicating how well a school has performed
academically the previous school year (California Department of Education, 200l).~
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 Achievement Gap denotes differences in the academic
achievement of a particular group of students.
Assessment. The processes used to collect information about student progress
toward educational goals. The form varies with what is being assessed and the
purposes for which the results will be used. Secondary Periodic Assessments
measure student proficiency toward California Content Standards for the explicit
purpose of improving teaching and learning (LAUSD, 2005).1°
Benchmark. Formative uniform measure of student progress relative to standards.
Standards-aligned assessments and assignments provide information about progress
toward the end target (California Department of Education, 2001).
Best Practices. A Best Practice is a technique or methodology that through
experience and research has proven to reliably lead to a desired result. (Target
Teach, tvvx-.Si.arch VB. ~0777, Nccdl-ta~n. MA
http:,'/sc~uchvk.tecl1ta1'~ct.com!sl8 gci498678,00.html).
California High School Exit Examination ("CAHSEE "). A graduation requirement
authorized by state law in 1999, that requires California public students, beginning
with the graduating class of 2004, to pass the CAHSEE in order to receive 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 (Cal. Dept. of Edu., 2001).
Taking Center Stage, California Department of Education, 2001.
'O Los Angeles Unified School District, EnglisWLangzlage Arts Middle School Insbtictiona~ Guide, Grade 7; 2nd
Ed. 2005.
California Standards Test ("CSTJ'). Pupil achievement by grade level as measured
by the Standards Testing and Reporting ("STAR). California Department of
Education; hftr,://www:cde.ca.,~ov/tai'aclsddcfi)5cstall .asp
Content Standards. Stated expectations of what students should know and be able to
do in particular subject and grade levels. They define not only what is expected of
students, but also what schools should teach (LAUSD, 2005).
Cultural Capital. Forms of knowledge; skill and education-any advantages a
person has which give them a higher status in society, including high expectations.
(Parents provide children with cultural capital, the attitudes and knowledge that
make the educational system a comfortable familiar place in which they can succeed
easily (Bourdieu, 1986).
Cultural Deficit Theory. Assumes that some students cannot achieve at high levels
because of deficits inherent in their race, ethnicity, language, or culture.
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).11
Highly Qualified Teacher. A Highly Qualified Teacher ("HQT") is one who has an
appropriate credential to teach in the area(s) assigned and who has demonstrated
subject matter competency through various acceptable [most often through passing
rigorous state exams or through a highly objective uniform state standard of
evaluation] HOUSSE, NCLB, Title IX, Section 9 10 1.
Leadership. Instructional Leadership is an individual who influences, motivates and
directs activities to improve student learning. Leadership is a process of influence
leading to the achievement of desired purposes. Successful leaders develop a vision
for their schools based on their personal and professional values [and goals]. They
articulate this vision at every opportunity and influence their staff and other
stakeholders to share the vision. The philosophy, structures and activities of the
school are geared towards the achievement of this shared vision (School Leadership
Concepts and Evidence, Spring 2003; P. 8);
~~tt~:!/~~v~v.ncsI.0r1;1,.uk/~~dia,~I~7A/88ibush-schoo1-Icadershipfull.pdf
" Massell, D. (2000, Sept.), The District 's Role in Building Capacity: Four Strategies [Electronic Version];
Consortit~m for Policy Research in Education: Policy Briefs; RB-32, retrieved July 3,2003,
www.c~re.org/Publications/rb32.pdf
Master Schedule. This is a construct that reflects the format of the school day. The
following elements are included in and are specified by the master schedule: the
length of each instructional period, when and how frequently courses are offered,
which teachers are assigned to teach specific courses, and grouping of students.
National Assessment of Educational Progress ("NAEP '7. An ongoing, national
assessment of what America's students in grades 4-8, and 12 know and can do in
various academic subject areas. NAEP is administered by the National Center for
Education Statistics of the U.S. Department of Education. One NAEP component
provides states with a measure of their students' academic performance over time,
and a comparison to the results of other states and students nationwide (Cal. Dept. of
Edu. 2001).
Pedagogical Content Knowledge. Identifies distinctive bodies of knowledge for
teaching. It represents the blending of content and pedagogy into an understanding
of how particular topics, problems, or issues are organized, represented, and adapted
to the diverse interests and abilities of learners, and is presented for instruction
(Shulman, 1987, p. 4); Knowledge and Teaching: Foundations of the New Reform,
Harvard Educational Review, 57(1), pp. 1-22
Performance Bands. Bands that identify levels .of student achievement based on a
demonstrated degree of mastery of specified content standards. California has
identified five performance levels for its statewide standards based assessments:
Advanced, Proficient, Basic, Below Basic, and Far Below Basic (Cal. Dept. of Edu.,
200 1).
Sanctions. The consequences' imposed for not meeting expected performance
outcomes in accountability systems (Olsen, 2005).
Social Capital. The central premise of social capital is that social networlts have
value. Social capital refers to the collective value of all "social networks" [who
people know] and the inclinations that arise from these networks to do things for
each other ["norms of reciprocity"].
BIBLIOGRAPHY
Alexander, C. (2004), Does Teacher CertlJication Matter? Teacher CertlJication and
Middle School Mathematics Achievement in Texas; University of Texas.
American Institute for Research (2003), California S Public Schools Accountability
Act (PSAA), Evaluation, Findings and Implications, Evaluation Brief, California
Department of Education; retrieved July 23,2006,
httl~:/~~xw?x .air.org:publicatims 'clcmscccducatio17.htm.
Bill and Melinda Gates Foundation (N.D.), High Schools for the New Millennium,
Imagine the Possibilities; retrieved May 2,2006,
I.~ttp://'~li/~'~/~v. gat~sfo~nd~tion.org/~~r!d~nloadslcd!cdwl-~itcpapcr. pdf.
Bill and Melinda Gates Foundation (N.D.), High Schools for the New Millennium,
Imagine the Possibilities; retrieved August 13,2006,
~p:l/i~1vw.r?;atesfoui1c1ation.org/nuidowr1loeac1!ed/edw11itewl~aper.pdS.
Blase, J. & Blase, J. (1998), Handbook of Instructional Leadership, How Really
Good Principals Promote Teaching and Learning, Corwin Press, Thousand Oaks,
CA.
Blase, J & Blase, J. (2004), Handbook of Instructional Leadership, How Successful
Principals Promote Teaching and Learning, Convin Press, Thousand Oaks, CA.
Bolman, L.G., Deal, T.E. (1991; 2003), Reframing Organizations: Artistry, Choice
and Leadership, (3rd Ed.), Jossey-Bass.
California Department of Education (2004), California High School Exit
Examination Report State Report; retrieved March 8,2006.
California Department of Education (1997), California Standards for the Teaching
Profession; California Commission on Teacher Credentialing; retrieved July 23,
2006,11ttr,:l/w~+~~.ctc.ca.~o1~/reports!cstp~por~.p~f.
California Department of Education (2003), Evaluation Study of the Immediate
Intervention/Underperforming Schools Programs and the High Achieving/Improving
Schools Program of the Public Schools Accountability Act of 1999; retrieved July 23,
2006, h&:/ u w\+ .ai~t_o~~publicationielen~sec educatiocm&tm.
California Department of Education (1997), Mathematics Content Standards for
California Public Schools: Kindergarten through Grade 12; retrieved July 24,2006,
http: /t$\;t M .cde.ca. ~0~!re/p1~/I'd;c1oci~1lie11~s~~nat11-stnd.pcI i'
California Department of Education (2006), Overview of the 2005-2006
Accountability Progress Reporting System, August.
California Department of Education (2001), Public Schools Accountability Act of
1999, Policy and Evaluation Division (Chapter 3, Statues of 1999; Attachment A).
California Department of Education (2004), State Accountability Report; retrieved
March 8,2006.
California Department of Education (N.D.), Willilams Case; retrieved July 3, 2006,
http:/lwww .cde.ca. gov/eo/celwc/index.asp
California State University (2006), High School Subject Requirements; retrieved
July 3, 2006, http:/lw~1~w.cs~1n~nt0r.~d~i~I~~nin~ihi.r!h~cl1o01/~~1bccts.asp
Carpenter, T. P., et al. (2004), Scaling Up Innovative Practices in Mathematics and
Science, National Center for Improving Student Learning and Achievement in
Mathematics and Science, Madison, WA.
Darling-Hamrnond, L. (1 999), Teacher Quality and Student Achievement: A Review
of State Policy Evidence, Center for the Study of Teaching and Policy, University of
Washington.
Datnow, A. (2005), The Sustainability of Comprehensive School Reform Models in
Changing District and State Contexts, Education Administration Quarterly, 14(1),
pp. 121-153.
Du Four, R. & Burnette, B. (2002, Summer), Pull Out Negativity by Its Roots: Those
who Grew Healthy School Cultures Must Root Out Weeds of Bad Culture, Journal Of
Staff Development, 23(3); retrieved August 13,2006,
htt~~://ut~tv.nsdcCorpI1i brarvlp~~ blitio sb-3 3 .cfm.
Ed Source Online (N.D.), No Child left Behind.
Ed Source Online (N.D.), Standards.
Ed Source (2003), The California High School Exit Examination; retrieved
August 13, 2006, htt~~:/l~x,rix,~~~.cd~o1u'c~.orf;l/pcl-E.~O~4, hsccfinal.r?df.
Education Commission Policy Issue ( 2006), Comprehensive School Reform:
Helping State Leaders Share Education Policy; retrieved July 27,2006,
http:~l~v~w.ecs.org.11txnI/issuc.as~3
Education Trust (2003), African-American Achievement, Washington, D.C.
Elmore, R. (2003, Nov.), A Plea for Strong Practice, Educational Leaderships, 62(3),
pp. 6-10; retrieved July 27,2006,
httpc
Forgione, Pascal (1 998), Achievement in the United States: Progress Since a Nation
at Risk? U.S. Department of Education, National Center for Educational Statistics;
Center for Education Reform and Empower America, Washington, DC.
Fullan, M. (2003), The Moral Imperative of School Leadership, Corwin Press,
Thousand Oalts, CA.
Garnino, M. (1930), Mexican Immigration to the United States: A Study of Human
Migration and Adjustment, Chicago Goals 2000 Progress Report, University of
Chicago Press (p. 71).
Gerber, L.; More, J.W. & Guzman, R.C (1970), The Mexican-American People: The
Nation's Second Largest Minority, Free Press, New York.
Hancock, M., & Lamendola, (2005, March), Learning From Urban Schools: A
Leadership Journey, 62(6), pp. 74-78.
Human Resources Research Organization (2006), Review of the Appropriateness of
the California High School Exit Exam in Content Standards for High School
Accountability; retrieved May 2,2006,
wl~ttp:l/ww.cdc.ca.govlta~lt,~ihsldocuments/appwpirateness.pdf.
Jaff, J.; Cullen, R.M. & Boswell, T. (1980), The Changing Demographics of Spanish
Americans, Academic Press, Chap. 6; App B., New York.
Johnson, R. C. & Viadero. D. (2005, Mar. 15), Unmet Promise: Raising Minority
Achievement, Education Week, 19(27), pp. 1, 18-1 9; retrieved May 13, 2006,
I~ttp:/iedtveel~.orgie~~ew~~sint~t~~~~~.~finslug27ir.li19.
Johnson, R. S. (2002), Using Data to Close the Achievement Gap: How to Measure
Equity in Our School, Corwin Press, Thousand Oaks, CA.
Kilgore, S. (2005, March), Comprehensive Solutions for Urban Reform, Educational
Leadership, pp. 55-47.
Klein, D. (2003), A Brief History of American K-12 Mathematics Education in the
20th Century, Information Age Publishing, Washington DC.
Klein, D. (2005), The State of Math Standards, The Ford Thomas Foundation,
Washington, DC.
Knuth, R.A. & Jones, B.F. (1991), Wat Does Research Say About Mathematics?
NCREL, Oak Brook.
Lashway, L. (2003), Distributed Leadership, Institute of Educational Management,
Report No. EA 032 546, ERIC Document Reproduction Service, No. ED 477 356,
Washington, DC.
Lashway, L. (2003), Role of the School Leader, Trends and Issues, Report No. EA-
032 700, Office of Educational Research and Improvement, ERIC Document
Reproduction Service No. ED 479 933, Washington, DC.
Marzano, R. J. (2003), What Works In Schools: Translating Research into Action,
ASCD, Alexandria, VA.
Marzano, R.J.; Waters, T. & Mc Nulty, B.A. ( 2005), School Leadership that Works,
MCREL, Aurora, CO.
Merseth, K. (1993), How Old is the Shepherd: An Essay About Mathematics
Education, Phi Delta Kappan, pp. 74,548-554; retrieved June 10,2006,
http://~rism.rnspnct.osa/indcx.cfn1/12723.
Moses, R. P. (2001), Radical Equations, Math Literacy and Civil Rights, Beacon
Press, Boston, MA.
National Center for Education Statistics (2005), The Nations Report Card:
Mathematics, National Assessment of Educational Progress.
National Center for Education Statistics (2005), TIMSS US.A. 2005, U.S. Dept. of
Education, Washington, DC.
National Commission on Excellence in Education (1984), A Nation at Risk: The Full
Account, USA Research, Cambridge, MA.
National Council of Teachers of Mathematics (1980), An Agenda for Action:
Recommendations for School Mathematics in the 1980s, Reston: VA.
National Council of Teachers of Mathematics (2000), Principles and Standards for
School Mathematics, Reston, VA.
NW Regional Educational Laboratory ( N.D.), The Catalog of School Reform
Models; retrieved July 27,2006,
I~ttp::'/l{CSl IducationPolicvIss~~cSit~C~om~sc~c~~sivcSc~ooI Kcform
Oakes, J., Muir, K. & Joseph, R. (2000), Coursetaking & Achievement in
Mathematics and Science: Inequalities that Endure and Change, National Institute
of Science Education.
Olson, L. (2006), A Decade of Effort, Education Week, 15(17), pp. 8-21.
Plucker, J.A., Zapf, J.S., & Spradlin, (2004), Redesigning High Schools to Prepare
Students for the Future, Center for Evaluation & Education Policy, 2(6).
Reynolds, G. M. (2002), Bridging the Great Divide: Broadening Perspectives on
Closing the Achievement Gaps, North Central Regional Education Laboratory, ED-
01-CO-0011p 9, Chicago, IL; retrieved July 20,2006,
http:/I?v~v~v. ncrel .orp/poli cy/~~ubs/pdfslbridgi~~&
Schiller, K.S. & Muller, C (Fall 2003), Raising the Bar and Equity? Effects of State
High School Graduation Requirements and Accountability Policies on Students'
Mathematics Course Taking, Education Evaluation and. Policy Analysis; 25(3),
pp. 99-3 18, H.W. Wilson Company.
Schoenfeld, A.H. (2002), Making Mathematics Work for All Children: Issues of
Standards, Testing, and Equity, Educational Researcher, 3 1 (I), pp. 13 -25.
Schoenfeld, A. H. (2005), Mathematics Teaching and Learning, Draft for the
Handbook of Educational Psychology (2d Ed.), Berkeley, CA.
Schoenfeld, A.H. (2004, Jan., Mar.), The Math Wars, Educational Policy, Corwin
Press, p. 18, Thousand Oaks, CA.
Schoenfeld, A.H. (1994), What Do We Know About Mathematics Curricula?
Journal of Mathematical Behavior, 13(1), pp. 55-80.
Senk & Thomas, D. (Eds.), (N.D.), Standards-Based School Mathematical
Curricula: What are They? What do Students Learn? N.J. Lawrence Earlbaum
Associates, Inc., pp. 3 1 1-343.
Southwest Educational Development Laboratory (2000), Issues About Chang, 8(1),
pp. 60-1 1 ; retrieved http:i/ August 13,2006.
Teaching to Change L.A. (N.D.), Educational Court Cases, Questions and Answers;
Williams et al. v. State of California et al; An Educational Bill of Rights, pp. 2, 1-10;
retrieved July 3,2006, http:!iitcla.gscis.ucla.cd~~'rights~liams.html.
Thernstrom, A. & Thernstrom, S. (2003), No Excuses: Closing the Achievement Gap
in Learning, Simon & Schuster, NY.
Togneri, W. & Anderson, S.E. (2003), Beyond Islands of Excellence: What Districts
Can Do To Improve Instruction and Achievement In All Schools, Learning First
Alliance and the Association for Supervision and Curriculum Development,
Washington, DC.
University of California (2006), Subject Requirement: A-G Coursework; retrieved
July 3,2006, bttp:.'/~v~v~-.~ni~-~rsitvofcalifomia.cduladmiss~nsi~~~~dt"r~~adadn~ipatI~
to adm~frhumaidsu~iectrcss.htinl
U.S. Department of Education, (N.D.), Four Pillars of NCLB; retrieved July 15,
2006, http:ilwwcv.ed.~o~~inclbiover~~iew/i11tro/4pjl1ars.ht~nl.
U.S. Department of Education (2004), New No Child Left Behind Flexibility: Highly
QualiJied Teachers; retrieved July 23,2006,
http:/ 'wu~w.ed.nov/s7ril1l/11clb/1ne tT~oc~s/teacI~ers/hc~ tflexibility .htrnl
U.S. Department of Education (2002), No Child Left Behind and AYP Student
Achievement and Accountability Conference; retrieved July2, 2006,
htt13://w~,'i.~.cd. rioTi.ladmins/lcadiaccount/aj!p/edI ite-index . htln I
U.S. Department of Education (2006), No Child Left Behind is Working; retrieved
July 13, 2006, hlfp:Ll~vw~:. ed,~o~~~~clb~ove~~i~'~1:~~~o1~1~nct!~~clh~~v~~~kin,~. pc!ff
U.S. Department of Education (N.D.), The Facts About Math; retrieved July 15,
2006, httn:liwww.ed. govlncl b/n~ethods/matI~~~nath.l~tn~l
U.S. Department of Education (2005), National Center for Educational Statistics,
Long Term Trend: The Nations Report Card, National Trends in Mathematics,
Level, kttp:/lnces.ed.gov/r1ationsrc~ortcard/1~~~=1 ts2004/natt~nat~~-~erff asp.
U.S. Department of Education (1998; revised Aug. 1998), National Center for
Educational Statistics, Pursuing Excellence: A Study of US. Twelfth-Grade
Mathematics and Science Achievement in International Context, U.S. Government
Printing Office, NCES 98- 049, Washington DC.
U.S. Department of Education (2003), National Center for Education Statistics,
Status and Trends in the Education of Hispanics; retrieved,
htt~://nces.ed.gov!ptibs2003/2003008.pdf
U.S. Department of Education (2002), National Center for Education Statistics, The
Condition of Education; retrieved, .htt~:l/~~~~.~d.p0~/~~b~2003/3003009.pdf,
895.9KB.
Villegas, A.M. (1 99 I), Culturlly Responsive Pedagogy for the 1990s and Beyond,
Trends and Issues, Paper No. 6; ERIC Clearinghouse on Teacher Education (Ed. 339
698), Washington, DC.
Waters, T., Marzano; R. J. & Mc Nulty, B. (2003), Balanced Leadership: What 30
Years of Research Tells us About the Effect of Leadership on Student Achievement,
Mid-continent Research for Education and Learning, Aurora, CO; retrieved,
http:, ltt71)x n~crcl.c)rg/l~l)F X ,eadcrshipor~anizationf lcvelopxncnf1503 1 Rfi ,HaIanccd
1eaderhip.pdi:
Wong, K. & Nicotera, A. (2003), Enhancing Teacher Quality: Peer Coaching as a
Professional Development Strategy, Laboratory for Student Success, Publication
NCES 98- 049, Series No. 5.
APPENDIX A
Conceptual Framework For Model Math Programs
, Classroom Practices \
o Effective and coherent o Assessments aligned
lesson design to standards
data drives instruction
Common performance
rubrics through
collaboration
v
Curriculum Design
* Student-centered curriculum
* Driven by learner outcomes
Emphasizes Conceptual
Focuses on problem-solving
* Incorporates current learning
( theory Year-Long Scope & Sequence -)
is supported by learning theory
/
APPENDIX B
Conceptual Framework For School Design
c
Capture
Understanding Problem skills
\
Solving J
\
f
Student Performance
Assessments
Challenge '
\
School-to-Career
Students to Applications
Think
J <
Constructivist
Curriculum ~~~~l~d~~
' Based on
Student
T
Outcomes
School
Culture
APPENDIX C
Framework For The Change Process
1 st Level of the Framework
Bolman and Deal's Four Frames
Structural
Top Down
Hierarchies
Rules, Policies,
Procedures
Specialized
Tasks
Goals &
Objectives
Human Resources
Employees as
Partners & Family
People of the
Organization
Productivity through
Group Effort
Self-actualization
Political
Power
Bargaining
Compete for
Limited
Resources
Negotiations
Symbolic
Vision
Belief and Faith
Stories
Culture
APPENDIX D
Conceptual Framework For Research Question 4:
What Knowledge Does the Leadership Have
To Data and the Analysis of Data?
development,
articulation,
implementation, and
stewardship of a vision
of learning that is shared
and supported by the
school community.
Vision for
Learning
Developing
vision
Communicating
the vision
Implement the
vision
* Monitor and
evaluate the
vision
- Addresses
obstacles to
vision
implementation
and realization
Supervision and
monitoring of
instruction
Observes and monitors
instructional program.
Provides constnlctive
feedback in a timely
manner to all teachers.
A- Classroom
observations on a
dailylweekly 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
Community and
Political
4.0--Collaborates with
families and community
members, responds
to diverse community
interests and needs, and
mobilizes community
resources.
Understands the value
of diversity
Understands
communities needs
Involves community in
the school
Provides opportunity
for community
involvement
Culture of Teaching
and Learning
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- Culhlre that is
inclusive of and
respectful of diversity
D- Implements practices
for culturally relevant
teaching and learning
E- Celebrates sh~dents,
teachers and staff
Data Driven
Decision Making
Analysis
Uses data as a tool for
informing instruction and
supporting student
learning
Utilizes assessment
data to place students
appropriately
Formative benchmark
school site
assessments
Sumrnative
standardized
assessment
Disaggregate data by
students, classes and
cohorts
Use data to guide and
improve teachers
instructional program
Use data to create
master schedule
Using data to inform
and improve pacing
I I I I
instructional plans
APPENDIX E
Conceptual Framework For Research Question 5:
Does The Principal Have A Minor Or Taught Math?
Assessment of Principal's Expertise in Math
Is the Principal
Step 1
n
HQT Compliant?
High Does the
Principal have a
Step 2
credential or
major in math?
Does the Principal
Expertise have a minor or
taught math?
Medium
I
I Expertise I
Yes
Source: NCLB Teacher Resource Guide [electronic version] located at www.
No
APPENDIX F
Conceptual Framework For Research Question 5:
Does The Principal Use The Following Strategies: Delegate Leadership To
Assistant With Great Expertise, Bring In Outside Experts, Emphasize Inquiry
And Problem-Solving, Emphasize Quality Instruction, Emphasize Strategies To
Engage Students In The Learning Process, Articulate With Feeder Schools,
Emphasize Raised Expectations, Emphasize Strategic Teacher Assignments,
Emphasize Revised Course Scope And Sequence And/or Curriculum,
Emphasize Interventions For Lower Performing Students, Or Emphasize
Professional Development?
I I I Instructional Strategies
Item
1
2
3
4
Strategy
Delegate Leadership to Assistant
with greater expertise
Empower Department Chair
Bring in Outside Expertise
Emphasize inquiry and problem
solving
5
I Emphasize Interventions for I Supplemental Services
ApproacWSource
Delegation Approach
(Northouse, 2001 p. 58)
Teacher Leadership (Gabriel, 2005)
Meaningful Staff
Development Activities
(Marzano, 2003 pp. 65-66)
Action Research
(Stringer 1999)
6
7
8
9
10
Emphasize quality instruction
Emphasize strategies to engage
(Marzano, 2003 pp. 78-87)
Student Engagement
students in the learning process
Emphasize articulation with
feeder schools
Emphasize raised expectations
Emphasize Strategic Teacher
Assignments
Emphasize Revised Course Cope
and Sequence and/ or
Curriculum
I 1
(Marzano, 2003 pp. 149-150)
Guaranteed, Viable Curriculum
(Marzano, 2003 pp. 22-34)
Challenging Goals and Effective
Feedback (Marzano, 2003 pp. 35-46)
HR Frame
(Bolman & Deal, 2003)
Guaranteed, Viable Curriculum
(Marzano, 2003 pp. 22-34)
12
lower performing students (NCLB, 2001)
Meaningful Staff
Do not use concept a, by c but just name each one.
Emphasize Professional
Development
Development Activities
(Marzano, 2003 pp. 65-66)
APPENDIX G
Key Leadership Interview Questions
Research Question Two. What Policy initiatives, curriculum instruction, and
related conditions seem to be related to improved math achievement in the
school?
Directions to Interviewer. Describe the purpose of the interview, the expected
timeline and introduce each topic as the RQ changes. For this section:
The first part of our interview, I will be asking you to describe your
perceptions about how policy issues have affected your efforts to
improve student achievement in math. Specifically, we will cover
policy issues related to:
Policies:
o NCLB-AYPIHOT
o District
o State PoliciesIAPI
o CAHSEE
Are you ready?
1. How do you perceive NCLB as having influenced your efforts to increase
student achievement?
o AYP?
o HQT
2. What board policies and/or practices (if any) are in place that support
increased student achievement in math?
o Benchmarks assessments
o Financial resources
o Additional StaffingICSR
3. How has Standardized testing and the requirements to meet your API
growth target influenced your efforts, to increase student achievement in math?
4. How do you feel the CAHSEE requirement has influenced your efforts to
increase student achievement in math?
(Appendix G, Continued)
Change Process:
Research Question 3: What change process did the school use to enhance its
math program and strategies to assist students in math?
"Let's turn our attention to how you handled the change process
related to your efforts to improve student achievement in math.
Specifically, I will be asking you about different aspects of the change
process as described in Bolman and Deal's Four frames. In case you
are not familiar with either of these models, Here is a copy of the
frameworks for your reference and clarification. (give the frameworks
to the interviewee). OK, so I will be asking you about":
Structural changes (school design, leadership, use of facilities, etc.)
HR-Key personal changes
o Teacher assignments and master schedule
Political issues related to the changes made at your schools
o How did you negotiate the political aspects associates with your
change process?
Symbolic methods used to add meaning and importance to your initiatives,
such as:
1. What structural changes have you made that you feel have contributed to
improved math achievement?
o School design
o Leadership
o Facilities
o CSR
(Appendix G, Continued)
2. What personnel changes have been implemented that has positively
influenced the math achievement?
o Teacher assignments
o Leadership roles
3. How did you negotiate the political aspects associated with the change
process?
o Site level
o District level
o Community level
4. What did you do symbolically to support and engage in the change process
that has been implemented to improve math achievement?
o Vision/mission
o Culture climate
o Ceremonial/awards
Leadership Instrument RQ 4:
Research Question 4: To what extent was strong instructional leadership
important in improving (a) the math programslstrategies and (b) math
achievement among students?
"I would now like to ask you about issues specifically related to the
role of instructional leadership in your efforts to improve student
achievement in math. Specifically, I will be asking about the roles
leaders played and issued related to the development of a professional
learning community on your campus."
1. Who were the leaders on your campus who helped bring about the
improved achievement in math?
o What were there roles?
2. How was the professional growth of the math teachers supported?
3. To what degree was teacher collaboration and/or reflection fostered and
encouraged?
(Appendix G, Continued)
4. How has the school leadership worked to implement a professional
community on you campus?
o Vision/mission
o Teacher leadership
o Peer collaboration
o Reflection
5. In what ways have site leaders attempted to make the focus on student
learning and results?
Leadership Questionnaire RQ5:
Research Question 5: How did leaders in the school resolve dilemmas about
instructional leadership?
"Now let's talk a little about how the site leadership went about
overcoming any obstacles you may have faced as you worked to
improve student achievement in math." You may find it useful to
refer to the frameworks on change that I provided to you earlier.
1. What particular obstacles did you school face in the implementation of
you changes related to improved achievement in math?
2. How did the site leadership work to overcome these obstacles?
o Structural Changes/Solutions
o Human Resource Changes/Solutions
o Political Changes/Solutions
o Symbolic Changes/Solutions
APPENDIX H
Math Teacher Interview Questions
Thank you for taking the time to complete this survey. It is hoped that the
results will serve as a rich source of data that may serve to better inform schools
seeking to improve in math achievement. Please return the survey in a sealed
envelope to the principal's secretary by Date TBA, 2006. Please be assured the
questionnaires will only be viewed by the researcher and not be viewed at all by site
leaders. Once again, your assistance is greatly appreciated.
Directions: Please rate each item on the following scale by circling the
response of your choice: 5 = Strongly Agree; 4 =Agree Somewhat;
3 =Neutral; 2 = Disagree Somewhat; 1 = Disagree Strongly
1. The No Child Left Behind 1 2 3 4 5
Legislation has promoted
increased student achievement
at our school.
2. The requirement that students
pass the CAHSEE to earn a
high school diploma has
contributed to the school's
effort to improve student
achievement.
3. Board Policies in our district
have contributed to improved
math achievement in our
school.
4. Our school has successfully
implemented common
assessments that support
increased student achievement.
5. Teachers at our school teach
standards-based lessons.
6. The master schedule at our
school is built based on
student need.
Directions: Please rate each item on the following scale by circling the
response of your choice: 5 = Strongly Agree; 4 = Agree Somewhat;
3 = Neutral; 2 = Disagree Somewhat; 1 = Disagree Strongly
7. Teachers at our school use 1 2 3 4 5
researched-based instructional
strategies to increase student
achievement.
8. Periodic benchmark
assessments provide useful
data that our teachers use to
drive instruction.
9. Student need is a major
consideration when making
teacher assignments in math at
our school.
10. The NCLB Act has been one
of the main external pressures
for improved math
achievement at this school.
1 1. The requirement that students
pass the CAHSEE in math in
order to earn a high school
diploma has contributed to the
school's effort to improve
math achievement.
12. Our school's effort to improve 1 2 3
student achievement in math
instruction had nothing to do
with external accountability
such as NCLB regulations and
the CAHSEE requirement.
13. Support classes have been
included in our master
schedule to improve student
achievement in math.
Directions: Please rate each item on the following scale by circling the
response of your choice: 5 = Strongly Agree; 4 = Agree Somewhat;
3 = Neutral; 2 = Disagree Somewhat; 1 = Disagree Strongly
14. The implementation of 1 2 3 4 5
standards-based instruction has
served as an important
foundation in improving
student achievement in math.
1 5. Our school has added the use
of math coaches or experts to
assist in the effort to improve
student achievement in math.
16. Teachers collaborate to
develop common assessments
and rubrics.
17. Professional development
'
offerings at our site are based
on student achievement data.
1 8. Teachers have helped develop
strategies used at our school to
improve instructional practice
in math.
19. The principal has served as a
"change agent" for improved
student achievement in math.
20. Student achievement in math
was made a priority as the
school allocated its financial
resources.
2 1. Our school had a clear
strategic plan to improve
student achievement in math.
22. Professional Development as
played a key role in increasing
student achievement in math.
Directions: Please rate each item on the following scale by circling the
response of your choice: 5 = Strongly Agree; 4 = Agree Somewhat;
3 = Neutral; 2 = Disagree Somewhat; 1 = Disagree Strongly
23. Teacher collaboration has 1 2 3 4 5
played a key role in increasing
student achievement in math.
24. Changes in the curriculum
have played a key role in
increasing student
achievement in math.
25. Professional Development has
played a key role in increasing
student achievement in math.
26. Our school has implemented
effective intervention
strategies for students having
difficulty in math.
27. My district supports teachers
with effective staff
development in Mathematics
Instruction.
28. My principal actively supports
opportunities for teachers learn
by watching each other teach
and discussing best practices
29. Our school has effective
strategies to support students
of various learning modalities.
30. Our school uses math coaches
to help teachers become more
reflective with their math
instruction.
Directions: Please rate each item on the following scale by circling the
response of your choice: 5 = Strongly Agree; 4 =Agree Somewhat;
3 = Neutral; 2 = Disagree Somewhat; 1 = Disagree Strongly
3 1. I have gained valuable 1 2 3 4 5
resources from math
coaches/instructiona1 leaders
that have improved the quality
of my math instruction.
32. My school's instructional
leader provides professional
development resources that I
use in my mathematics
instruction.
33. The school leader is aware of
the mathematics instruction
and academic progress of the
students in my class.
34. The school leader provides
opportunities for faculty
members to discuss
mathematics instruction.
3 5. The school instructional leader
encourages faculty members to
discuss effective math
instructional strategies.
36. My school's math instructional
practices are developed from
evidence-based strategies.
37. I have regular support from
proven instructional leaders in
math instruction.
38. The math achievement goals
and measures for my school
were clearly articulated and
easy to understand.
Directions: Please rate each item on the following scale by circling the
response of your choice: 5 = Strongly Agree; 4 = Agree Somewhat;
3 =Neutral; 2 = Disagree Somewhat; 1 = Disagree Strongly
39. I received coaching and 1 2 3 4 5
mentoring from instructional
leaders or peer coaches.
41. The district personnel, school
leaders and teachers all have a
shared vision for increased
math achievement.
42. My district and school leaders
seem knowledgeable about
instructionally effective math
practices and assessment
strategies.
43. The Math Department Chair
has been entrusted with and is
empowered to make important
curricular decisions.
44. Outside experts have been
used to promote greater
capacity in the area of math
instruction.
45. The school's leaders
emphasize the importance of
quality instruction as a primary
mission of the school.
46. Professional Development in
math has been a key tool used
by site leaders in our effort to
improve instruction on our
campus.
47. Site leaders emphasize having
high expectations for student
achievement in math.
Directions: Please rate each item on the following scale by circling the
response of your choice: 5 = Strongly Agree; 4 = Agree Somewhat;
3 = Neutral; 2 = Disagree Somewhat; 1 = Disagree Strongly
48. Quality interventions in math 1 2 3 4 5
have been implemented on our
site to help students at risk of
failing academically.
49. Our site leaders emphasize a 1 2 3 4 5
culture of collaboration as a
means of improving
instruction at our site.
50. Teacher assignments in the
math department are made
strategically and with student
need in mind.
APPENDIX I
A Teacher Survey: Non-Math Teacher Questions
Thank you for taking the time to complete this survey. It is hoped that the
results will serve as a rich source of data that may serve to better inform schools
seeking to improve in math achievement. Please return the survey in a sealed
envelope to the principal's secretary by Date TBA, 2006. Please be assured the
questionnaires will only be opened by the researcher and not by viewed at all by site
leaders. Once again, your assistance is greatly appreciated.
Directions: Please rate each item on the following scale by circling the
response of your choice: 5 = Strongly Agree; 4 = Agree Somewhat;
3 = Neutral; 2 = Disagree Somewhat; 1 = Disagree Strongly
1. The No Child Left Behind 1 2 3 4 5
Legislation has promoted
increased student achievement
at our school.
2. The requirement that students
pass the CAHSEE to earn a
high school diploma has
contributed to the school's
effort to improve student
achievement.
3. Board Policies in our district
have contributed to improved
math achievement in our
school.
4. Our school has successfully
implemented common
assessments that support
increased student achievement.
5. Teachers at our school teach
standards-based lessons.
6. The master schedule at our
school is built based on
student need.
Directions: Please rate each item on the following scale by circling the
response of your choice: 5 = Strongly Agree; 4 = Agree Somewhat;
3 = Neutral; 2 = Disagree Somewhat; 1 = Disagree Strongly
7. Teachers at our school use 1 2 3 4 5
researched-based instructional
strategies to increase student
achievement.
8. Periodic benchmark
assessments provide useful
data that our teachers use to
drive instruction.
9. In an effort to improve
instruction on our campus, our
school has focused on ensuring
that structures and policies that
support student achievement
are in place.
10. In an effort to improve
instruction on our campus, our
school has focused on
personnel issues including
hiring quality teachers and
fostering a positive working
environment amongst peers on
campus.
1 1. In an effort to improve
instruction on our campus, our
school has focused on
overcoming political obstacles
and gaining the necessary
support to move the school
forward.
12. In an effort to improve
instruction on our campus, our
school has focused on
motivating students and staff.
Directions: Please rate each item on the following scale by circling the
response of your choice: 5 = Strongly Agree; 4 =Agree Somewhat;
3 = Neutral; 2 = Disagree Somewhat; 1 = Disagree Strongly
13. There is a shared vision for 1 2 3 4 5
increased student achievement
at our school.
14. Our school had a clear
strategic plan to improve
student achievement.
15. Student achievement is a
priority when the school
allocates its financial
resources.
16. Professional development
offerings at our site are based
on student achievement data.
17. The principal works to gain
the support of the community
for the school's academic
efforts.
18. The school leadership works to
establish and maintain a
respect for cultural diversity.
19. Students and staff are valued
and their successes celebrated.
20. The school leaders used data
driven information to address
problems/issues related to
student achievement.
2 1. Our school had a clear
strategic plan to improve
student achievement in math.
Directions: Please rate each item on the following scale by circling the
response of your choice: 5 = Strongly Agree; 4 = Agree Somewhat;
3 = Neutral; 2 = Disagree Somewhat; 1 = Disagree Strongly
22. The principal makes effective 1 2 3 4 5
use of the department chairs
and relies on their expertise
when making important
curricular decisions.
23. The principal has delegated
some curricular authority to an
assistant principal with greater
expertise in curriculum and
instruction.
24. Outside experts have been
used to promote greater
capacity in the area of
instruction.
25. Site leadership fosters a
culture of inquiry and
collaborative problem solving.
26. The school's leaders
emphasize the importance of
quality instruction as a primary
mission of the school.
27. Site leaders emphasize having
high expectations for student
achievement.
28. Quality interventions have
been implemented on our site
to help students at risk of
failing academically.
29. Professional Development has
been a key tool used by site
leaders in our effort to
improve instruction on our
campus.
Directions: Please rate each item on the following scale by circling the
response of your choice: 5 = Strongly Agree; 4 =Agree Somewhat;
3 = Neutral; 2 = Disagree Somewhat; 1 = Disagree Strongly
30. Teacher assignments are made 1 2 3 4 5
strategically and with student
need in mind.
APPENDIX J
Standards-Based Instructional Process Criteria Checklist
APPENDIX K
School Continuum For Implementing Standards-Based Education
APPENDIX L
Unofficial Classroom Observation Form
.... -- .. _-
-
a I2 El I3 Numberof students: .............
9 10 I1 12
-... ---.- "-
I
......... IJ
AREAS OF EYALUnTIDFi
............ --
I
I. SIIPPOKT E'DR STUDENT LEhBiVfNC;
COMMEN'X'S "1
i
........... -. ................... ..". ............ ....... ........"...... .................... .......... .......... -
"+
,,
Uses the rcsults at' mihtip!e msessmenls LQ guide
j
~nsuuction
--- .... ......... ....... ..............
b
allides all srude!t& 10 he self directed 2nd assess rhcir own
......
. i
--..---.. -.
! ..., Er!gnges rmdents in problem solving, critical thinkkg md
1 . ': ............. ?$K. %9i!%j~.$$~e:*=t rn*cter fi%%i?8%:- "-" ...-. ---7"--M"" . ..
$, Uses a vaxiety of ki$$ructir~n~ st:a,s and resourns CG
........... .. .................. .......... ,._ :+~~5~5'
Integrate; srudent's prior kn:nnwIr;c!gc, lfc experiences, and
L-- ioterats into the~*~~~$~~;ral program. -.L-.L - .- .... -- - ".
I Ziddilronni Cnnlmenls:
I
i
........ .............
I~DNMEi.iTS
...... .................................... ......... ....
.. ..... ......
~m&,~>?g?go?l:. E?~Zts:'?.w~~~t~
". . ........... ...............-..... ...................... ---- ....
.. 18%rrrlaxes idea and informarion within end across suhjccc
lnafter eie~
.................. ................................. ...
d,
tlses iisstnictio1i81 r:iale@es. mterids, resaorcm, and
........... rccfin0!!?~i~~.~&~~e~~~k"~iO.~4~.~~i.".~~-. ......................... ..
-.---..... .................
"
Aridmosi;i Cnrnmn?nts:
--
I
,.,. ........... .... .- "-
i 3. CLASSROO&+ PERFORMANCE
I:i
i
.......".. .............-...... ..... ................. .... i .--.-r.-... ---.I !
; ,$, U:rnorirrr:tres knowicdge of state ?iid studenr de\elo;in~
................. ...... ......................................................... .. ? ,*.~ " *
i ?, !!%to gr:m.Ji;r$gcvt.loarion system that is aligned \vith
; c Sunrianis.
............................................ ...... ........................................
! F,$.Wi"
.,,,*.
i ,.
in .: ,!I-? an3 n~airiiexnr stznJards for student heha
L.., t~~~$,~~~$~S,,;?$!~!;~~~,!~?~~~,,~?~~;!~~~~~~$~~-+~~2?>>-~~~- .............................................. ,
11
Plan$ aai! nn;!emc:lti ciassmon; p?ocsil;~rt?s an2 rou:
.;E!22~~uii2?i?4~!.~.s.??'li!?.c:". ................... .............
U,es tns!:uctionaj rim* effefe-!ivr?y
I. .. ..': ... .
I
Pmvirlcr an ciiccrivc ci;tssroi)rn ~nvironment
i-.-'- ..................... - ..............................
j sddrrrond (7U:nmerlts.
\
(Appendix L, Continued)
@wm%vep
continuous growth. .*
b.
$'o&s '81th colleagues ro improve pmfmion
- -----
5. PU%CfUALXTY8 AWNDANCE AND
/ RECURDKhEFmC COIIMEVTS
.............. -. .
........... ...
......
... "-".
d. Scnfinldmg lesson's cuidenr
... ...-.......................

Abstract (if available)

Abstract This study examines math achievement as a result of policy initiatives in combination with school design, best practices and school leadership. The study focuses on five research questions: What was the pattern of math achievement for various students at the school? What policy initiatives, as well as curriculum, instruction/and related conditions seem to be related to improved math achievement at the school? What change process did the school use to enhance its math program and strategies to assist students in math? To what extent was strong instructional leadership important in improving the math programs/strategies, and math achievement among students? Details of implementation and adoption of specific policy initiatives and school based programs for mathematics was examined in the context of improving mathematics performance. Instructional leadership and its impact on mathematics achievement where leadership lacks strong pedagogical content knowledge in mathematics education were examined, incorporating an understanding of how leaders work effectively in this context. The study utilized both qualitative and quantitative data in conjunction with a school profile, instructional leadership interviews, teacher interviews and surveys. The study investigated the pattern of math achievement for various students using data collected from Annual Yearly Progress (AYP) data and results from the California Department of Education High School Exit Exam office. Policy initiatives, as well as curriculum, instruction/and related conditions that seem to be related to improved math achievement at the school was standards-based instruction and the CAHSEE. A change process could not be substantiated.

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Asset Metadata

Creator Tresvant, Kimberly A. (author)

Core Title High school reform to improve mathematics achievement

School Rossier School of Education

Degree Doctor of Education

Degree Program Education (Leadership)

Publication Date 07/09/2007

Defense Date 03/29/2007

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

Tag high school reform,leadership,Mathematics,OAI-PMH Harvest

Language English

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

Creator Email ktresvant@ca.rr.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m602

Unique identifier UC1315835

Identifier etd-Tresvant-20070709 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-519048 (legacy record id),usctheses-m602 (legacy record id)

Legacy Identifier etd-Tresvant-20070709.pdf

Dmrecord 519048

Document Type Dissertation

Rights Tresvant, Kimberly A.

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