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A story of achievement in areas where others fail: a case study of secondary school reform in mathematics at Pacific North High School
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Content
A STORY OF ACHIEVEMENT IN AREAS WHERE OTHERS FAIL:
A CASE STUDY OF SECONDARY SCHOOL REFORM IN
MATHEMATICS AT PACIFIC NORTH HIGH SCHOOL
by
Jahnell Jones Nichols
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 of
DOCTOR OF EDUCATION
August 2007
Copyright 2007 Janelle Jones Nichols
ii
DEDICATION
First, my sincerest gratitude and appreciation goes to my parents who have
always supported and encouraged me in all endeavors. Your unwavering belief and
constant faith in me that I would succeed in all that I wanted to accomplish gave me
the strength and ability to fulfill my dreams. Because of the love and affection you
bestowed, I have succeeded in accomplishing all my educational goals and attaining
the highest educational achievement in my field. From childhood to now, you two
have always believed in me, supported me, and celebrated triumphs with me. You
will always be my most significant mentors, compassionate guidance counselors, and
caring best friends. I am thankful to God and feel truly lucky that I was blessed with
the most excellent parents in the world. I am truly honored to be your daughter, and
will continue to do all that I can to make you proud. Words are not enough to honor
and articulate all that you have done for me. I am overcome with emotion as I try to
express to both of you what you mean to me. I sincerely I love you both, and so I
dedicate my dissertation in tribute of you.
iii
ACKNOWLEDGEMENTS
I would like to thank sincerely all who have encouraged and supported me
through my entire educational career. My gratitude is immeasurable. To Steven
Shideler, thank you for being an awe-inspiring and phenomenal educator that
truly epitomizes all the excellent qualities and refined artisanship associated with
the profession. Your mentorship and guidance, helped me grow into an educator
that strives to motivate, encourage, and inspire all students that I teach to always
reach for their highest goals. You are the reason I became an educator.
To Linda Powell, thank you for providing me with the foundations for
success. You constantly challenged me, and pushed me to never stop learning.
Your jubilant and vibrant nature and ability to always see the humorous side of
life helped me through difficult times. I want you to know that I listened to all
your life lessons, especially those about having high expectations for all students,
and remind myself daily that everything I do as an educator is to better students’
educational experiences.
I want to communicate my gratitude to Dr. David Marsh. Because of your
meticulously detailed organization and constant encouragement, getting through
this process was expedient, understandable, and efficient. Thank you for always
keeping me on track in the process and ensuring that I always celebrated my small
successes. In addition, I would also like to thank Dr. Russo and Dr. Olsen for
always giving such great advice and support. It has been an honor to learn from
all of you. To Tina, you were a great asset to the team, and without you
communicating regularly with each of us, this task would have been significantly
iv
much harder.
To the dissertation cohort, thanks. I have been with most of you since the
beginning, especially the weekenders. I am glad that we made it through the
process together, always encouraging and helping each other. I truly could not
have completed this process without each of you, and so I thank you dearly.
To my family and friends, I greatly appreciated that you still love me and
stayed with me through this process. I appreciated that you understood my reasons
for wanting this educational achievement and accepted the pressures it put on our
relationships. You were always there for me, as I will always be there for you. I
truly thank all of you.
Finally, to my husband, thank you for all your expertise with technology.
You combined your knowledge and talent to provide me with efficient tools that
helped me successfully accomplish difficult elements of my dissertation. You were
with me through the entire process as my confidant and supporter. If not for you,
there would be no chapter two, three, graphics or chart representations of
questionnaires. I feel especially lucky that I was able to have my husband as a
dissertation cohort member, and I treasure the fact that we got the chance to share
this monumental accomplishment in our lives together. Thank you and I love you.
v
TABLE OF CONTENTS
DEDICATION……………………………………………………………………...ii
ACKNOWLEDGEMENTS…..…………………………………………………… iii
LIST OF TABLES …………………………………………………………………xi
LIST OF FIGURES ……………………………………………………………….xii
ABSTRACT………………………………………………………………………xiii
CHAPTER 1: INTRODUCTION TO THE STUDY ................................................ 1
Statement of the Problem .................................................................................... 11
Purpose of the Study .......................................................................................... 11
Research Questions ............................................................................................. 11
The Importance of the Study ............................................................................... 12
Assumptions ........................................................................................................ 14
Limitations .......................................................................................................... 14
Delimitations ....................................................................................................... 15
Definition of Terms ............................................................................................ 16
Organization of the Study ................................................................................... 20
CHAPTER 2: REVIEW OF THE LITERATURE .................................................. 21
History of Student Performance .......................................................................... 21
A Nation at Risk ............................................................................................ 22
Trends in International Mathematics and Science ....................................... 24
National Assessment of Educational Progress .............................................. 26
Trial Urban District Assessment .............................................................. 26
Program for International Student Assessment ............................................. 29
Achievement Gap ................................................................................................ 30
Reasons for the Achievement Gap ................................................................ 31
SES ......................................................................................................... 31
Teachers .................................................................................................. 34
Opportunities .......................................................................................... 38
Conclusion ................................................................................................... 40
Mathematics Effects on Students ........................................................................ 40
National and State Efforts to Improve Mathematics ........................................... 43
National Efforts ............................................................................................. 43
NCLB ...................................................................................................... 45
State Efforts .................................................................................................. 46
Improved Curriculum and Instruction ................................................................. 49
School Reformation ...................................................................................... 50
SLC ....................................................................................................... 50
vi
Math Programs ...................................................................................... 52
Professional Development ........................................................................... 56
Professional Learning Communities ...................................................... 58
Reform Efforts ........................................................................................ 60
Instructional Methods ................................................................................. 62
Instructional Leadership .................................................................................... 65
CHAPTER 3: RESEARCH METHODOLOGY ..................................................... 81
Sampling Criteria and Process ............................................................................ 82
The School District ....................................................................................... 86
Selected School ............................................................................................. 88
Participants in Study ..................................................................................... 89
School Site Administrators ..................................................................... 89
Teacher Leaders ...................................................................................... 90
Classroom Teachers ................................................................................ 90
Instrumentation ................................................................................................... 90
Frameworks for Instrument Design .............................................................. 91
Conceptual Framework A ...................................................................... 92
Conceptual Framework B ...................................................................... 95
Conceptual Framework C ...................................................................... 98
Conceptual Framework D .................................................................... 101
Framework for the First Research Question ......................................... 103
Framework for the Second Research Question ..................................... 104
Framework for the Third Research Question ........................................ 105
Framework for the Fourth Research Question ...................................... 105
Framework for the Fifth Research Question ......................................... 106
Data Collection Instruments ........................................................................ 106
Instrument 1: Teacher Questionnaire ..................................................... 106
Instrument 2: Key Instructional Leader Interview Guide ..................... 107
Instrument 3: The Teacher Interview Guide ......................................... 108
Instrument 4: The School Profile .......................................................... 108
Data Collection ................................................................................................. 109
Data Analysis ..................................................................................................... 112
Validity and Reliability ..................................................................................... 113
Conclusion ........................................................................................................ 113
CHAPTER 4: FINDINGS, ANALSYIS AND DISCUSSION ............................... 115
Data Findings ....................................................................................................... 117
Research Question 1: Patterns of Mathematics Achievement ..................... 117
PNH’s Overall Math Demographics...................................................... 117
CST ................................................................................................. 117
CAHSEE .......................................................................................... 118
State, County, and PNH CST Data .................................................. 119
CAHSEE State, County, and PNH Data ......................................... 121
vii
PNH, SBC, and California Math Class Data ............................... 125
Conclusion ....................................................................................... 132
Research Question 2: Policy, Curriculum, and Instruction .......................... 134
Policies ................................................................................................ 134
NCLB .............................................................................................. 135
PNH’s Response to NCLB ............................................................. 136
PSAA .............................................................................................. 139
School Response to PSAA ............................................................. 140
CSR ................................................................................................. 143
PNH Response to CSR ........................................................................ 143
CAHSEE ......................................................................................... 144
School Response to CAHSEE ........................................................ 145
DU’s API Policy ........................................................................... 146
DU’s Honors and AP Math Policy ................................................. 147
DU’s CPM Policy ........................................................................... 147
PNH’s Response to DU’s Policies ................................................. 148
School Design ..................................................................................... 149
Student Performance Assessments ................................................. 149
Curriculum ..................................................................................... 150
Learning Activities ........................................................................ 152
School Culture ................................................................................ 152
Math Program Design ......................................................................... 159
Curriculum Design ........................................................................ 159
Classroom Practices ....................................................................... 168
Standards-Based Instruction .......................................................... 172
Conclusion ..................................................................................... 173
Research Question 3: Change Process ................................................................. 174
Historical Background .............................................................................. 175
Change Process through CBAM ............................................................. 177
CBAM ............................................................................................... . 177
CBAM Level 0 ................................................................................. 178
CBAM Level 1 ................................................................................. 179
CBAM Level 2 ................................................................................. 179
CBAM Level 3 ................................................................................. 180
CBAM Level 4 ................................................................................. 182
CBAM Level 5 ................................................................................. 183
CBAM Level 6 ................................................................................. 184
Change Process through Four Frames .................................................... 186
Story of PNH’s Secondary School Reform through Four
Frames ................................................................................. .. 187
PNH’s Current Administrators through Four Frames ..... 196
Conclusion .......................................................................... 198
Research Question 4: Instructional Leadership ...................................................... 199
Vision for Learning .................................................................................. 201
viii
Developing the Vision ....................................................................... 201
Communicating the Vision .............................................................. 203
Implementing the Vision .................................................................. 204
Monitor and Evaluate the Vision .................................................... 205
Address Obstacles to Vision Implementation and
Realization ....................................................................................... . 206
Supervision and Monitoring of Instruction and Personnel .............. 206
Allocation of Resources ............................................................... 206
Hiring of Personnel ..................................................................... 207
Community and Political ....................................................................... 208
Culture of Teaching and Learning ........................................................ 208
Data Driven Decision-Making Analysis .............................................. 210
Conclusion ...................................................................................... 211
Research Question 5: Resolving Instructional Leadership
Dilemmas ............................................................................................... 212
Principal’s Expertise Framework ......................................................... 213
Lack of Subject Matter Competency Strategies ................................... 213
Delegation of Leadership ........................................................... 214
Teacher Leader ............................................................................. 215
Specific Instructional Dilemmas ................................................. 218
Conclusion ..................................................................................... 219
Discussion ............................................................................................. 220
Research Question 1: Patterns of Mathematics Achievement .......... 220
PNH Patterns of Math Achievement .......................................... 221
CST ..................................................................................... .... 221
CAHSEE ............................................................................... 222
PNH Math Classes ............................................................... 225
PNH Gender Data by Course Name .................................... 228
Research Question 2: Policy, Curriculum, and Instruction ............ 229
Policies ........................................................................................... 229
NCLB ................................................................................... . 229
PSAA ..................................................................................... 230
BTSA ..................................................................................... 234
CSR ........................................................................................ 238
CAHSEE ............................................................................... 238
DU’s Policies ........................................................................ 239
School Design ............................................................................... 243
Student Performance Assessments ..................................... 243
Curriculum ........................................................................... 244
Learning Activities ............................................................. 245
School Culture ..................................................................... 246
Math Program Design .................................................................. 252
Curriculum Design .............................................................. 252
Classroom Practices .......................................................... 258
ix
Standards-Based Instruction ............................................. 259
Research Question 3: Change Process ............................................. 260
Change Process Using Four Frames and CBAM ..................... 260
Symbolism ......................................................................... 260
Political ........................................................................... ... 262
Human Resources ............................................................. 263
Structural .......................................................................... .. 265
Current Administrator and CBAM Levels and Four
Frames………………………………………………..266
Research Question 4: Instructional Leadership .............................. 267
Vision for Learning .................................................................. 267
Developing the Vision ..................................................... 271
Communicating the Vision ............................................. 271
Implement the Vision ...................................................... 273
Monitor and Evaluate the Vision .................................... 273
Address Obstacles to Vision Implementation and
Realization ........................................................................ 274
Supervision and Monitoring of Instruction and Personnel ... 275
Hiring of Personnel .......................................................... 275
Community and Political ......................................................... 276
Culture of Teaching and Learning .......................................... 277
Research Question 5: Resolving Instructional Leadership
Dilemmas .......................................................................................... 277
Principal’s Expertise Framework ........................................... 277
Lack of Subject Matter Competency Strategies .................... 278
Delegation of Leadership ............................................... 278
Teacher Leader ................................................................. 279
Specific Instructional Dilemmas .................................... 280
CHAPTER 5: SUMMARY, CONCLUSIONS, AND IMPLICATIONS ............... 282
Purpose of the Study ........................................................................ 285
Research Questions .......................................................................... 285
Methodology ..................................................................................... 286
Sample .................................................................................... .. 286
Data Collection and Analysis .................................................. 286
Summary of Findings ...................................................................... 288
Research Question 1: Patterns of Mathematics Achievement…….288
Research Question 2: Policy, Curriculum, and Instruction………. 290
Research Question 3: Change Process…………………………….292
Research Question 4: Instructional Leadership………………….. 293
Research Question 5: Resolving Instructional Leadership
Dilemmas………………………………………………………….293
Recommendations for Future Research……………………………………….294
Implications for Practice………………………………………………………297
x
School Boards and Key District Leaders……………………………….…297
School Site Administrators…………………………………………….….300
REFERENCES ....................................................................................................... 303
APPENDICES ...................................................................................................... 315
Appendix A: Teacher Questionnaire—All Teachers ....................................... 315
Appendix B: Teacher Questionnaire—Math Teachers .................................... 319
Appendix C: Teacher Interview Guide ........................................................... 326
Appendix D: Key Leader Interview ................................................................ 327
Appendix E: Evaluation Design Chart ............................................................. 331
Appendix F: School Design Framework ......................................................... 332
Appendix G: Effective Math Programs ............................................................ 333
Appendix H: Bolman and Deal’s Four Frames ................................................ 334
Appendix I: Instructional Leadership Guide ................................................... 335
Appendix J: School Profile Spreadsheet ......................................................... 336
Appendix K: Assessment of Principal’s Expertise in Math ............................. 341
Appendix L: Strategies to Overcome a Lack of Subject Matter
Competency ................................................................................................... 342
Appendix M: Math Teacher Questionnaire Spreadsheet Database ................. 343
Appendix N: Non-Math Teacher Questionnaire Spreadsheet ........................ 344
Appendix O: CPM Sample Algebra 1 Question ............................................. 345
Appendix P: CPM Sample Question 2 ............................................................ 346
xi
LIST OF TABLES
1. Data Collection Instruments and Research Questions Relationships .............. 90
2. State, SBC, and PNH Ninth Grade Algebra 1 CSTs 2003-2005 ...................... 120
3. State, County, and School Data with CAHSEE Math Results 2003 ................. 122
4. Gender and Ethnic Designation 2003 with State, County, and School ............. 122
5. State, County, and School Data with CAHSEE Math Results 2004 ................. 123
6. Gender and Ethnic Designation 2004 with State, County, and School ............. 123
7. State, County, and School Data with CAHSEE Math Results 2005 ................. 124
8. State, County, School with Gender and Ethnic Designation 2005 ................... 124
9. PNH, SBC, and State Math Class Data ............................................................. 125
10. PNH, SBC, and State Course Name Data with Gender 2003-2005 .................. 129
xii
LIST OF FIGURES
1. Framework for Effective School Design .......................................................... 94
2. Effective Math Programs ................................................................................. 98
3. Bolman and Deal’s Four Frames …………………………………………….101
4. Instructional Leadership Framework……………………………………….104
5. CPM Sample Algebra 1 Question……………………………………………163
6. 2
nd
CPM Sample Algebra 1 Question ……………………………………….164
xiii
ABSTRACT
The purpose of this study was to understand how a comprehensive urban high
school raises its students’ mathematical achievement. In addition, the study explored
how instructional leaders without mathematical expertise, implemented policies,
curriculum, and school reforms that helped increase the students’ math achievement.
The five research questions in this case study focused on were patterns of the schools
math achievement, policies, math curriculum, math instruction, the school’s change
process, instructional leadership, and how the school’s instructional leaders resolved
dilemmas. Results indicated that the school raised their students’ math achievement
through a variety of methods, and that there was instructional leadership that clearly
developed and outlined the vision for comprehensive secondary reform. Instructional
leaders used the delegation and teacher leader method as a means to resolve problems
that occurred during and after implementation.
1
CHAPTER 1
INTRODUCTION TO THE STUDY
Since the space race with Russia and the Cold War, there has been a steady
push towards higher mathematics achievement for American high school students.
Consequently, as there has been a call to action for better mathematics achievement,
scores in mathematics have continued to decrease or remain stagnant. The United
States continues to fall behind their peers in most industrialized countries in
mathematic achievement, which is causing a widening achievement gap between
U.S. students and those of their peers in other countries. The mathematics
achievement gap has also increased in the United States between European American
students and students of color. As an answer to the public’s pressure to raise
American students’ mathematic performance levels, the United States federal
government and states have put forth special effort in attempting to correct the
educational deficiencies of American students with laws, policies, and programs
such as No Child Left Behind (NCLB) and the Public School’s Accountability Act
(PSAA) of 1999. The new laws, policies, and programs have caused several school
districts to push for reform of their high schools, specifically pertaining to increasing
mathematics knowledge, skills, and test scores.
The dark implications of the 1983 report A Nation at Risk only further
illustrates that American students are in the throws of a mathematics’ crisis: “Our
once unchallenged preeminence in commerce, industry, science, and technological
innovation is being overtaken by competitors throughout the world….the educational
foundations of our society are presently being eroded by a rising tide of mediocrity
that threatens our …Nation…” (National Commission on Educational Excellence,
1983, p. 1). In the 1950s, educators knew with the space race that our students were
2
already behind other industrialized nations, and in 1983, it was again stipulated that
not only were we behind other countries in math achievement, but we were at the
bottom of the spectrum in high school math performance on standardized tests.
Today, educators and researchers reiterate the same information about United States
students’ achievement gaps in mathematics achievement that they said many years
ago—vast numbers are American students are drastically underperforming in math.
The National Assessment of Educational Progress (NAEP) provides
assessment information that presents the achievement of different subgroups of
American students. The NAEP data suggests that students’ scores today have
remained relatively the same since the early 70s. On the other hand, even though
student scores have remained relatively the same since the 70s, the achievement data
indicates that there is an increasing achievement gap between European American
students and those of their African American and Hispanic counterparts (NCES,
2003).
Another comparative study that further stresses the decline of American
students in the area of math is the 1999 Trends in International Mathematics and
Science Study (TIMSS). The TIMSS study is a compilation of students’
mathematics scores on standardized tests in fourth, eighth, and twelfth grades from
38 different countries. The study does note that in the eighth grade, American
students outperformed 38 different countries math averages. However, American
students’ scores for mathematics in twelfth grade were abysmal: “…U.S. twelfth-
graders scored below the international average and among the lowest of the TIMSS
nations in mathematics and science general knowledge, as well in physics and
advanced mathematics” (NCES, 2002, p. 1). The TIMSS findings only further
reinforce the point that there is a growing achievement gap in math between
3
American students and their international counterparts. The dilemma for educators
is in understanding why American fourth and eighth graders outperform many
countries in math, but by the time, American students became seniors, their math
scores are considerably lower than their international counterparts are.
Statistics indicate that performance in high school mathematics, particularly
Algebra 1, determines whether a student will have future academic success in high
school and beyond (Rose & Betts, 2001). Murnane, Willet, and Levy (1995)
reaffirm Rose et al. belief that math scores affect students’ future:
Scores on the math test is a strong predictor of subsequent
educational attainment. For both males and females in the two
data sets, the average math scores for those who went on to
graduate from college is almost twice that of those whose
highest educational attainment was graduation from high
school. (p. 253)
Math Matters (2001) also stipulates that taking advanced mathematics courses in
high school help determine success in adulthood. Suppose a student does not pass
Algebra 1, he or she then does not progress towards taking advanced mathematics
courses in high school. Without advance math courses, research indicates that he or
she will be less likely to graduate from high school or continue onto postsecondary
education: “Students of all income levels who take rigorous mathematics and
science courses in high school are more likely to go to college, and among low-
income students (students in the bottom third of the distribution), the difference is
particularly dramatic” (Riley, 1997, p. 6). With American high school students
lagging behind other industrialized nations in math, compounded with the evidence
from Math Matters and Riley that emphasize the important role advanced math plays
4
in the lives of students having future postsecondary or economic success, illustrates
to educators that American high school students are in desperate need of
mathematical reform.
Riley’s report goes on to state that many industries need students with higher
math skills, and that a few industries are giving their applicants high school level
mathematics tests to determine whether they qualify to work for the organization.
Loveless and Coughlan’s (2004) article agree with Riley in that American students
are lacking basic mathematic computation skills and “computation skills are an
increasingly important predictor of adult earnings” (pp. 56-57). Without math
knowledge and skill, students’ future socio-economic status is affected:
“Considerable evidence suggests that differences in years of schooling explain a
large portion of the income gap in the nation and in California….the growing gap
can be narrowed by better educating [lower income] people…especially minority
students” (Rose et al., 2001, p. v). Lee (2004) reinforces Rose et al. research by
presenting the fact that “The Black-White achievement gap in mathematics increased
during the 1990s…regressing back to the level of achievement disparity of the early
1980s…. As of 1999, the overall Black-White and Hispanic-White mathematics
achievement gaps remained substantially large…” (pp. 53-54). With TIMSS
implying that American students do not currently possess the math knowledge to be
competitive in a workforce that requires math skills and Loveless et al. and Lee,
indicating that America has math equity issues contributing to the nation’s socio-
5
economic achievement gap suggests that math achievement and success is tied
America’s economic and educational future.
The federal government has tried to alleviate the achievement gap issues in
America by requiring states to create state subject standards, focusing effort towards
improving curriculum and instruction, and demanding educational requirements for
the profession. Standards are now the guidebook for states and districts to improve
their educational structure: “Statewide academic standards not only provide the goal
posts for teaching and learning across all of a state’s public schools; they also drive a
myriad of other educational policies” (Klein, 2005, p. 9). The National Council of
Teachers of Mathematics (NCTM) created mathematics standards in 1989. The
government, because of NCLB, has made standards the basis of the math
assessments that states give students. States and school districts expect educators to
be using standards-based instruction in all their classes. Standards drive instruction,
but only three states received a report card score of A on their mathematics standards
such as “clarity, content, and sound mathematical reasoning, and the absence of
negative features” (Klein, 2005, p. 9). This fact is disturbing when one knows that
America’s high school students are scoring very low on mathematics assessments
and that the school reform used (state standards) to help increase their scores lacks
clarity, is unreliable and confusing. Even though Klein states that California is one
of the few states that received an A for their math standards. California continues to
have lower math scores than many other states in America (NAEP, 2006b).
6
Not only was California attempting to reform curriculum and instruction, but
reformers also wanted to alter their teachers. The California Commission on
Teaching Credentialing and the California Department of Education in 1997 created
the California Standards for the Teaching Profession. Standards not only drive
classroom instruction, but they are a significant portion of Standards for the
Teaching Profession.
Even with California attempting to reform its curriculum instruction,
assessments, and teaching standards, researchers found that increases student
achievement is professional development. Success in increasing teachers’
capabilities, which leads to increasing students’ scores and performances, is due to
effective professional development. One such example of specialized professional
development that is helping to increase students’ scores in Mathematics is from the
Relationship between Professional Development, Teacher’s Instructional Practices,
and the Achievement of Students in Science and Mathematics (2003) by Huffman,
Thomas, and Lawrenz. The authors of this article state that research evidence
indicates that “for both science and mathematics teachers participation in two types
of professional development, namely, examining practice and curriculum
development, are related to the use of standards-based instructional practice”
(Huffman et al., webpage). “In addition, previous research suggests that the use of
professional development focused on student thinking can be helpful for instruction
designed to improve student understanding of mathematics concepts” (Fennema et
al., 1996, webpage) is an example of how specific professional development
7
increases student performance in mathematics. Reorganizing and finding different
ways to perform professional development is one way of helping to reform
mathematics in schools and increase students’ math scores.
Another way schools are attempting to increase math achievement is through
school reformation. Schools and districts are reforming schools in several ways.
The reason behind their decision to redesign and reform current mathematical
teaching practices, techniques, and programs is because “Numerous scientific studies
have shown that traditional methods of teaching mathematics not only are ineffective
but also seriously stunt the growth of students’ mathematical reasoning and problem-
solving skills (Battista & Larson, 1994, p.178)” (Blume, Garcia, Mullinax, & Vogel,
2001, p. 15).
One more way in which school reformation is taking place is through
Comprehensive School Reform (CSR). Schools refer to CSR by many names, but a
common name is Small Learning Communities (SLCs). SLCs have various
constructions and appearances. SLCs can be small independent schools-within a
school or they can be academies within a school. SLCs “such as career academies or
school-within a school, break students up into subgroups to provide them an
environment where students are able to develop closer relationships with teachers
and peers” (Pluker, Zapf & Spradin, 2004, p. 5). A SLC trademark is that students
are receiving specialized attention from a core group of educators that share the same
students, and many SLCs provide students with classes specifically designed for
their SLC across the curriculum (Gates Foundation, 2005). Many teachers that
8
participate in SLCs have a strong commitment to cross-curriculum assignments,
assessments, benchmarks, and instructional guides and plans. In most SLCS, the
students form something close to a cohort as they travel throughout their high school
years. Sometimes SLCs are career related or they are college preparatory. It is the
choice of the school. Some SLCs even alter their instructional time to give teachers
more instructional flexibility.
Schools are also trying the Professional Learning Communities (PLCs) as a
school reform measure. PLCs can occur at the district or school site level. A typical
PLC is one in which a community of educators meet to dialogue about school issues,
professional literature, and school data. The key to PLCs is that educators build a
culture or community about learning for the purposes of increasing student
achievement and creating a community where professionals collaborate to achieve
common goals (Dufour, 2004). Schools are concurrently creating PLCs with SLCs
such as in some Los Angeles Unified schools. However, note that some schools
have PLCs without SLCs. PLCs provide another venue for principals to share power
and responsibility with other school stakeholders in trying to solve the dilemma of
increasing student achievement.
Local schools and districts are trying to find ways in which to improve their
mathematic scores through the implementation of new school reforms.
Consequently, with creating new school reforms, schools and their districts have to
create local capacity to deal with the new policies and initiatives to sustain these new
reforms. Not only are school’s faced with local capacity issues, but with the
9
dilemma of not knowing which school reform will inherently help their students
increase in their achievement.
Another issue that surfaces with school reform happens to the role of
instructional leader or principal. With school reform and change, schools require a
different type of school leader. Today’s school reform has altered the role of the
principal from operational to instructional. Amanda Datnow (2003) stresses the
importance of the role of principal in school reformation. Her piece illustrates how
the role of principle in today’s schools is transformative. Datnow suggests that
today’s principals must be transformative change agents that have the ability to be
leaders and managers, to guide the instructional energies of the school while being
an effective processor of the school’s daily operations, all the while being a
spokesperson for the teachers, staff, students, and community. The problem for most
schools is that the role of instructional leader is new to many principals, especially
those used to only dealing with the management side of school.
Some research such as Marzano (2003) and Blasé and Blasé (2004) try to give
clear information to educational leaders on how to help effectively their schools and
students. Cudeiro (2005) gives information about how to effectively support
principals in this time of change: “First, they supported the principals by
reorganizing central services….Second, these superintendents increased direct
support to the principals, giving them more time to be effective instructional leaders
and specific tools to help them maintain that focus” (webpage). Giving the principal
10
enough resources, tools, and the correct policies can aid him or her in
accomplishing the task of transforming an underperforming school into a high
achieving school.
Some principals find it difficult to create school change because the mandates
of the federal and state governments, or even district offices, do not offer them the
flexibility to create dynamic change: “The challenge is that often, good leaders are
inhibited by the many rules, regulations, and restrictions imposed at the district,
state, and federal level” (North Central Regional Educational Lab, 2000, p. 14).
Effective principals must also sustain the school transformation that they helped to
create, which is an even harder task. The North Central Regional Educational Lab
suggests that active leadership is the ways in which principals can successful sustain
his or her school’s reformation.
A specific way in which to help educational leaders increase student
achievement is through the development of principal’s standards, which are similar
in many ways to teaching standards. However, Waters and Grubb (2004) explain
that there are too many indicators and standards for principals to abide by, which
does not make standards for principals an effective tool to help these educational
leaders: “However, the scope of the standards includes everything the developers
deemed to be important. The developers of these standards did not distinguish
between what is important and what is essential to improving student achievement”
(p. 1). Waters and Grubb argue that clarity is essential and needed if school leaders
are to understand how to effectively help their schools increase student achievement.
11
Some research out there does try to give clear information to educational leaders
on how to help effectively their schools and students such as Blasé and Blaze’s
(2004) book, which is a compilation of reflections from teachers and principals that
gives administrators a guide on how to be an effective instructional leader at a
transformative school.
Statement of the Problem
What is still unknown is how urban high schools that had low mathematics
achievement scores a few years ago have increased their students’ mathematics
achievement. What needs to be discovered is what instructional practices, policies,
curriculum, and school designs were used to increase their students’ mathematics
performance, and how the instructional leaders without a mathematics background
effectively helped to increase the school’s mathematics achievement scores.
Purpose of the Study
The purpose of this study was to examine how some urban California high
schools effectively increased their students’ mathematic achievement. In addition,
the study explored how instructional leaders without mathematical expertise,
implemented policies, curriculum, and school reforms that helped increase the
students’ math achievement.
Research Questions
The study will be guided by these following questions:
1. What was the pattern of math achievement for various students at the school?
12
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 programs/strategies and b) math achievement among students?
5. How did instructional leaders respond in academic areas in which they were
not experts?
The Importance of the Study
This study can provide educators with insights into how an effective secondary
reformation program can increase mathematics achievement and scores throughout a
school and a district. The study can shed light upon how a school transformed itself
and what roles leaders played to bring about the reformation. Discovering key
elements and methods to improving instructional practice in mathematics is also an
important role this study will play—especially for the underserved populations of
students of color, Special Education students, and students from low social and
economic backgrounds. This study will have relevance for all educators, educational
practitioners, federal and state policy makers, and educational researchers.
This study will help districts ascertain what an effective math reform or
intervention can accomplish at a school site. It is so often districts are asked by the
state and federal government to produce higher standardized test scores, and they are
looking for ways to institute successful programs that increase achievement
13
throughout their district. Districts are looking for ways to implement best practices
from successful schools to schools that are in need. This dissertation will provide
school districts with opportunities to fulfill their need for reflection, method study,
techniques, program evaluation, and demonstrate effective generalizable results to
implement and transfer to any program improvement schools within their district in
need of finding ways to help those students who are continually underserved.
The dissertation can also serve in aiding school site administrators in the form
of helping them understand how their role as educational leader for the school can
positively increase mathematics achievement. Learning about what other
educational administrators have done to turn around their failing schools can give
them ideas about how they can best transform their school. In addition, site
administrators can use the information in this study to determine which is their best
method, technique, and program intervention that would be the most effective for
their students—particularly their underserved populations. One of the most
important factors that they will glean from the study is how to effectively be the
catalyst for change and reform throughout their school, and how to sustain that
transformation through progressive educational ideas.
Teachers will benefit from the study because they are at the epicenter of the
challenge to raise students’ scores and achievement in math. The study will guide
the teachers in determining how to effectively implement math interventions and
reform within their classroom. It will also give them knowledge on how they can
provide their underserved students with a more effective mathematics curriculum
14
while continuing to differentiate instruction for all students. The study will give
them insight into how to increase and sustain their students’ mathematics
achievement, while helping them better communicate with their leaders as to what
they need to provide effective instruction to ensure that all students succeed.
Educational policymakers and researchers could use the information as a tool
to inform instruction for professional developments and district policies. They can
also use the information from the dissertation to help them develop more effective
and efficient mathematics curriculum and interventions.
Assumptions
The first assumption is that students at the school received quality mathematics
instruction with because of effective instructional pedagogy. The second assumption
is that instructional leadership was a factor in the school’s academic success. The
third assumption is the school studied met the criteria indicated in the delimitation
section. All study instruments were developed using current education research,
methodology, and conceptual frameworks that made the data collection instruments
reliable and valid. The last assumption is that all participants in the study were
truthful and the information they provided was triangulated with other information
gathered from the school site to ensure accuracy.
Limitations
The study was limited by the area and region—Southern California. The
school was picked because of proximity and accessibility due to travel restrictions,
so school districts outside of Southern California were not chosen because they
15
would not have been accessible to all members of the dissertation group. Because
of time constraints and USC dissertation regulations, data collection took place in the
Fall of 2006. Some parts of the data are subject to researcher and interviewee bias
because that is the nature of qualitative study. Information from this study has a
limited generalization capacity because it is a qualitative case study.
Delimitations
The dissertation group determined that it would be more beneficial to study
one school within an urban school district. The group chose not to include schools
that were not improving because we felt that learning from schools that exhibited
best practices were more beneficial. Because the sample size of the dissertation is
only one school, the study is limited in its ability to generalize. The school studied
in this dissertation was purposefully selected using the following criteria:
1. Improvement in math achievement.
2. School’s student population is at least 1200 students with 50% of the students
from traditional ethnic minority groups.
3. The school is a public comprehensive high school with grades 9-12.
4. The principal has been at the school for at least three years.
5. The school has an API of 600 or better and overall state rank of 5 or higher.
16
Definition of Terms
For the purpose of this study, the following terms were operationally defined
below.
The Academic Performance Index (API): The API is the cornerstone of the
Public Schools Accountability Act (PSAA). The API ranks school performance, sets
growth targets, and provides similar-school comparisons. The API is a single
number on a scale of 200 to 1,000, indicating how well a school has performed
academically the previous school year (California Department of Education, 2001).
1
Adequate Yearly Progress (AYP): AYP is an individual state's measure of
yearly progress toward achieving state academic standards. "Adequate Yearly
Progress" is the minimum level of improvement that states, school districts and
schools must achieve each year.
Achievement Gap: denotes differences in the academic achievement in of a
particular group of students. (NCREL, Bridging the Great Divide, 2002).
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).
2
1
Taking Center Stage. California Department of Education, 2001.
2
Los Angeles Unified School District: English/Language Arts Middle School Instructional Guide
Grade 7. 2
nd
Edition, 2005.
17
Benchmark: Formative uniform measure of student progress relative to
standards. Standards-aligned assessments and assignments provide information
about progress toward the end target (California Department of Education, 2001).
Best Practices: A best practice is a technique or methodology that, through
experience and research, has proven to reliably lead to a desired result (Target Teach,
SearchVB.com Needham, MA).
California High School Exit Examination (CAHSEE): A graduation
requirement, authorized by state law in 1999, 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 (California Department of Education,
2001).
California Standards Test (CST): Pupil achievement by grade level, as
measured by the Standards Testing and Reporting (STAR) (California Department of
Education).
Content Standards: Stated expectations of what students should know and be
able to do in particular subjects and grade levels. They define not only what is
expected of students, but also what schools should teach (LAUSD, 2005).
Cultural Capital: The term cultural capital represents the collection of non-
economic forces such as family background, social class, varying investments in and
18
commitments to education, different resources, etc. which influence academic
success (Hayes, Elaine).
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).
3
Deficit Theory: Assumes that some student cannot achieve at thigh levels
because of deficits inherent in their race, ethnicity, language, or culture (Villegas,
A.M., 1991).
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). (Department of Education, NCLB).
Instructional Leadership: An influence that guided the activities designed to
impart knowledge or skills to students (Olsen, 2005).
4
3
Massell, D. (2000, September). The district role in building capacity: Four strategies
[Electronic Version]. Consortium for Policy Research in Education: Policy Briefs, RB-
32. Retrieved July 3, 2003, from www.cpre.org/Publications/rb32.pdf
4
Olsen, C. (2005, May). Connecting Districts and Schools to Improve Teaching and Learning: A
Case Study of District Efforts in Los Coyotes High School District. A Dissertation Presented to the
Faculty of the Rossier School of Education University of Education.
19
Master Schedule: This is a construct that reflects the format of the school
day. The following elements are included in and are specified by the master
schedule; the length of each instructional period, when and how frequently courses
are offered, which teachers are assigned to teach specific courses and grouping of
students.
National Assessment of Educational Progress (NAEP): The NAEP is an
ongoing, national assessment of what America’s students in grades four, eight, and
twelve know and can do in various academic subject areas. NAEP is administered
by the National Center for Education Statistics of the U.S. Department of Education.
One NAEP component provides states with a measure of their students’ academic
performance over time and a comparison to the results of other states and students
nationwide (California Department of Education, 2001).
Performance Bands: Bands that identify levels of student achievement based
on a demonstrated degree of mastery of specified content standards. California has
identified five performance levels for its statewide standards based assessments:
Advanced, Proficient, Basic, Below Basic, and Far Below Basic (California
Department of Education, 2001).
Sanctions: The consequences imposed for not meeting expected performance
outcomes in accountability systems (Olsen, 2005).
Social Capital: The central premise of social capital is that social networks
have value. Social capital refers to the collective value of all “social networks” [who
20
people know] and the inclinations that arise from these networks to do things for
each other [“norms of reciprocity”].
Organization of the Study
Chapter 1 begins the dissertation with an introduction to the study that argues
for why the study needed to be conducted. The chapter then goes on to describe the
statement of the problem, purpose and scope of the study, the reason and significance
for conducting the study, moves onto the research questions that guide the study, and
the last part of the chapter defines the terms that are pertinent to the study. Chapter 2
is an overview of the relevant literature that indicates what is known of this topic in
the field of education. The review of the literature in this chapter longitudinally
illustrates American students’ performances in mathematics, which moves into a
discussion about the achievement gap and its relationship to students’ math scores;
the understanding of how mathematical knowledge affects American students future,
and how the American government has tried to increase mathematic ability in
students; the end of the chapter discussed the new math programs, polices, reforms,
and how professional development and key instructional leadership is key to
improving students’ mathematical achievement in schools. Chapter 3 of the study
explains the methodology used in the study. The chapter also clarifies the sampling
and selection process of the study. Then, the study illustrates the research design,
instrumentation, methodology, and conceptual frameworks. The last part of the
chapter discusses the study’s findings. Chapter 4 of the study is where analysis and
discussion of the findings took place, and the final chapter of the study summarizes
the entire study and indicates some possible ideas and implications for future
practice.
21
CHAPTER 2
REVIEW OF LITERATURE
Even though there have been many attempts to improve American students’
mathematical performance throughout the years, reports such as A Nation at Risk, the
TIMSS, and NCLB only further reinforced the fact that there was an increasing
achievement gap between America and other industrialized countries, and the gap
was growing within America itself between European American and students of
color. The American public demanded solutions to resolve these problems. In order
to appease the social outcry, the government (state and national), instituted several
reforms. The reforms sparked educational movements and transformations
throughout schools that led to new school curriculum, designs, and programs. The
undiscovered arena of the educational puzzle of how to increase students’ math
performances is in the area of instructional leadership. How does a leader, with no
mathematical background, institute policies, reforms, and effective mathematics
curriculum to turn a low mathematically performing school into a high achievement
school?
History of Student Performance
For several decades, American high school students have struggled with
mathematics. The public felt that the American educational system and schooling
was deteriorating (Cuban & Tyack, 1995). However, the report that sparked the
current educational debates on mathematical achievement and made it readily
apparent to the public that there was an international achievement gap stems from the
report A Nation at Risk in 1983.
22
A Nation at Risk
The report, A Nation at Risk, is an 18-month study created by the National
Commission on Excellence in Education. Then Secretary of Education T.H. Bell
commissioned the report. The report’s mission consisted of six facets: Assessing
the quality of teaching and learning in our Nation's public and private schools,
colleges, and universities; comparing American schools and colleges with those of
other advanced nations; studying the relationship between college admissions
requirements and student achievement in high school; identifying educational
programs which result in notable student success in college; assessing the degree to
which major social and educational changes in the last quarter century have affected
student achievement; and defining problems which must be faced and overcome if
we are successfully to pursue the course of excellence in education.
What startled the American public is the frankness in which the report
describes the inevitable downfall of American society due to the deplorable
condition of its public education system. One of the reasons that the piece is so
poignant is because not only does it describe how historically American society is
being dismantled by foreign business prowess, but it is being eroded within because
no one’s eye is on the prize of keeping our educational system from toppling:
Our concern, however, goes well beyond matters such as
industry and commerce. It also includes the intellectual,
moral, and spiritual strengths of our people which knit
together the very fabric of our society. The people of the
United States need to know that individuals in our society who
do not possess the levels of skill, literacy, and training
essential to this new era will be effectively disenfranchised,
not simply from the material rewards that accompany
competent performance, but also from the chance to
23
participate fully in our national life. A high level of shared
education is essential to a free, democratic society and to the
foster of a common culture, especially in a country that prides
itself on pluralism and individual freedom. (National
Commission on Excellence, webpage)
The report stresses to the nation that systematic destruction. of our
establishment follows without a healthy and strong educational system. All belief
systems, democracy, and freedom American’s share rely on the backbone of its
educational system. The report states that keeping a sound educational system
should be the nation’s first priority because the educational system is America’s
backbone. The disenfranchisement of several generations of American students has
continued to take place for over half a century and will continue unless measures are
taken to stop the regression of the American education system.
All of the indicators in the piece projected a bleak future for the American
educational system. The first indicator was from international comparative studies
performed 10 years before the report stated that American students never scored first
or second and scored last on academic tests seven times. The second and third
indicator reports that over 23 million American adults and 13% of 17-year-olds are
functionally illiterate. The fourth indicator states that students scores on standardizes
tests have dropped from during the Sputnik era when America first put a major
emphasis on improving mathematics and science education in our schools. The fifth
indicator suggests that half the gifted children do not perform at their level in school.
The sixth and seventh indicators report that on the Scholastic Aptitude Test (SATs),
American students’ scores have decreased in math and English skills by 40 to 50
24
points from 1963 to 1980. The ninth indicator states that 40% of America’s 17-
year-olds cannot perform the higher order thinking skills necessary to succeed, and
only one-third can solve multi-step mathematics problems. One of the last
indicators illustrates how colleges are trying to compensate with the achievement
gaps of American students in comparison to other countries: “Between 1975 and
1980, remedial mathematics courses in public 4-year colleges increased by 72% and
now constitute one-quarter of all mathematics courses taught in those institutions”
(webpage). These disheartening indicators only further reinforce the concept that
American schools are in significant trouble by failing to educate mass amounts of
students, which only increases the achievement gap. After this report, the
educational community in the United States mobilized to resolve the deplorable
condition of the American education system. However, even though many educators
and researchers strove to increase students’ achievement, American students’
performances on several standardized and comparative international studies only
continued to plummet.
Trends in International Mathematics and Science
The First International Mathematics and Science Study (TIMSS) took place in
the 1960s, and the second in the 80s. The Third and some of the most insightful
information come from the study performed in the 90s. The TIMSS was another
comparative study that made several educators and researchers take notice, similar to
the A Nation at Risk. The TIMSS results were published in 1995, 1999, and 2003. A
new TIMSS will be published in 2007. Each study examined the performances of
25
students at various grade levels on math and science assessments. Then TIMSS
compared these assessments with assessments taken by students in other countries.
The report reflects the data gathered from all the students’ assessments.
In 1995, TIMSS compiled information from half a million third, fourth,
seventh, eighth, and twelfth grade students. The International Study Center at
Boston conducted the TIMSS and 38 countries participated. What is unique about
the TIMSS is that it not only provides the data from the students’ assessments, it also
provides researchers and educators with information regarding how other countries
teach math and science to their students such as their math and science curriculum.
The study found that American fourth graders outperformed other countries, but
eighth and twelfth graders in the United States severely underperformed on math and
science assessments.
The 1999 TIMSS study continued to indicate that America’s fourth grade
students were performing well in comparison to other countries and the eighth
graders had increased their scores, and people commonly refer to it as the TIMSS-R.
TIMSS published this information in 2003. However, it also continued to reflect that
American high school student achievement scores in math and science continued to
decline. Similarly, to 1995, 38 countries participated in the report. This version of
the TIMSS report has some interesting aspects such as a videotape of eighth grade
math and science teachers teaching lessons in seven different countries. It also
incorporates a U.S. study that links to the National Assessment of Educational
Progress (NAEP). Eighth grade American students did make some gains in this
26
report; however, the American twelfth graders are still failing math at astounding
rates.
National Assessment of Educational Progress
The NAEP, or The Nation’s Report Card, has conducted nationwide
assessments of American students since 1969. The NAEP is similar to the TIMSS as
it reports information drawn from American students’ assessment scores from their
fourth, eighth, and twelfth grade years. Before NCLB, states had the right not to
participate in the state NAEP. However, after NCLB, the federal government began
requiring states to participate in the NAEP state assessment. Unlike the TIMSS, the
NAEP has assessments for a wide variety of subjects, not just math and science.
However, this paper will only focus on the aspects of the NAEP assessments that
relate to math. The NAEP math assessment consists of constructed-response
questions and multiple-choice questions. There were five areas of math content on
which the questions were based: “…number properties and operations,
measurement, geometry, data analysis and probability, and algebra” (NAEP, 2005,
website).
Trial Urban District Assessment. The Trial Urban District Assessment
(TUDA) first took place in 2002 and only focused on reading and writing. Atlanta,
Chicago, Los Angeles, New York, and Houston were the school districts upon which
the assessment focused. However, in 2003, the assessment included mathematics in
as one of their assessments and more school districts. In 2005, 17,600 schools and
27
over 170,000 fourth graders, 160,000 eighth graders, and 9,000 seniors participated
in the mathematics assessment.
Part of the TUDA is the main assessment that is given yearly to various
schools and school districts and another complimenting part is the Long-Term
Mathematics Assessment (LTMA). The LTMA “1) measure student progress over
time, and 2) as educational priorities change, develop new assessment instruments
that reflect current educational content and assessment methodology” (website). The
LTMA give researchers and educators a way to observe American students’
performances on math assessments and other data trends over multiple years. The
NAEP has performed this type of assessment over 10 consecutive times: “in the
school years ending in 1973, 1978, 1982, 1986, 1990, 1992, 1994, 19999, and 2004”
(website). Similar to the yearly assessment, it tested students in the fourth, eighth,
and twelfth grades.
The LTMA math assessments functions as a measure to study what
mathematical knowledge American students’ posses:
measures students’ knowledge of basic facts, ability to carry
out numerical algorithms using paper and pencil, knowledge
of basic measurement formulas as they are applied in
geometric settings, and the ability to apply mathematics to
daily-living skills (such as those related to time and money).
(NCES, Trends in Academic Progress, 1999, p. 2)
What is interesting about this particular math assessment is that it studies what
practical and basic arithmetic knowledge American students should posses in
combination with algebraic and geometric elements. However, the LTMA does
28
admit that it is concerned with analysis of how American students “are measuring
up to traditional procedural skills,” (website) while other countries are measuring
their students not on procedural mathematics knowledge but on conceptual
mathematics knowledge.
Similarly, to the TIMSS and other NAEP reports, the fourth and eighth grade
math students’ math prowess have increased. However, the LTMA from the 1970s
to 1999 is different than the other two reports because it notes that twelfth graders
math scores declined in 1973-1982, but then increased by 10 points between 1982-
1992. This report stipulates that “Because average scores have remained at or about
their 1992 level, the average mathematics score of 17-year-olds in 1999 was higher
than it was in 1973” (website). The report also shows quartile scores for students in
mathematics. For 17-year-olds, math scores declined between 1978 to 1982 for the
middle two and upper quartiles, but then those scores increased in the 1980s and
early 1990s. However, it is important to note that average mathematics scores
remained “unchanged in the lower quartile” (website) from 1978 to 1982. The report
also disaggregates the mathematics data by subgroups. The subgroup data indicates
that for Caucasian students, their math scores have increased since the 1990s.
However, African American students of all ages and Hispanics from 9 to 13 have
remained constant. This is a disappointing development because it only further
indicates that there is a disparity between students of color math scores and those of
their Caucasian counterparts, which means that the achievement gap is continuing to
grow between the majority and the minority groups.
29
The LTMA produced a report in 2004 that showed different results from its
1999 LTMA report. In 2004, high school students’ average mathematics scores did
not increase. However, as is seen in both the NAEP report and the TIMSS, the 2004
LTMA report indicates that fourth and eighth grade students are continuing to raise
their mathematics achievement. These developments only continue the
befuddlement of educators and researchers as to why American high school students’
scores continue to remain constant or decline while eighth and fourth grade students’
math achievement continues to rise.
Program for International Student Assessment
The Program for International Student Assessment (PISA) is another
comparative studies assessment that examines American student performance with
that of other countries. There are less countries that participate in this study than in
other international comparative studies, however, the countries that do participate are
what the PISA assessment calls Organization for Economic Cooperation and
Development (OECD). The PISA is given through NCES every three years.
Another significant difference between the NAEP tests, the TIMSS, and PISA is that
PISA’s focus group for testing is ninth and tenth graders.
The 2003 PISA results indicate that the mathematics literacy and problems
solving “was lower than the average performance for most OECD countries” (NCES,
2004, p. iii). These findings are similar to other assessments presented earlier in this
piece. However, the PISA does describe the elements in which American students
were poor: “The United States also performed below the OECD average on
30
mathematics literacy…(space and shape, change and relationships, quantity, and
uncertainty)” (p. iii). Note that the PISA does test students on more broad and
general mathematical ideas not mathematics concepts like the TIMSS or NAEP. The
report also indicates that the United States had more students performing at the lower
levels of understanding problem solving than the OECD countries.
Achievement Gap
The achievement gap is an important singular factor that is influencing the
disparity between the mathematics scores of American students and those of other
countries, and the math scores of Caucasian American students and their students of
color counterparts:
Despite countless school reform efforts during the last two
decades of the 20
th
century, we begin the 21
st
century with
continuing gaps in academic achievement among different
groups of students. The gaps in achievement appear by
income and by race and ethnicity. Large percentages of low-
income, African American, Latino, and Native American
students are at the low end of the achievement ladder, and
large percentages of middle-and high-income white and Asian
students are at the top of the achievement ladder. (Johnson,
2002, p. 4)
The TIMSS, NAEP, and PISA reports indicate that in relation to their counterparts in
other countries American students’ mathematic scores are decreasing. High school
students’ scores in the other countries are surpassing the American students to the
degree that the United States students’ scores have sunk to the bottom on most
reports.
In America, the LTMA reports do show that recently, Caucasian students’
mathematics scores have increased slightly from the 1970s. However, students of
31
color math scores have remained constantly low. Similarly, to the achievement
gap that exists between American students and their counterparts on math
assessments, there exists that same gap between Caucasian American students and
their student of color counterparts. The College Board (2001) reports indicates that
on national tests such as the SATs, European American students had many more
advance academic classes such as Advanced Placement and honors classes than
students of color. These opportunities for taking advanced academic classes surely
increased their scores over their counterparts of color, further increasing the
achievement gaps between those groups.
However, the NAEP does indicate that over time, the achievement gap does
fluctuate: “[the NAEP] indicate a narrowing of the achievement gap among diverse
groups in the 1970s and 1980s. This pattern began to reverse in the 1990s, at which
time the gap began to widen again…” (p. 4). The report indicates that 80% of
European American students at our above their eighth grade basic math level, while
only 40% of the students of color were at or above their math grade level. This gap
only grows with each passing school year (NAEP). The same gap for math
assessments exists for American students with high SES and those with low SES.
The multitude of achievement gaps that exist in the United States only contribute and
compound the growing gulf of high and low achievement on math assessments
between the United States and those of other countries.
Reasons for the Achievement Gap
SES. One of the most common reasons researchers give to explain America’s
achievement gap is students’ family background, history, and SES affect students’
performance in schools and on assessments. There are several reports that indicate
that there is a strong correlation between SES and student performance: “The
32
assumption about the correlation between low income and low achievement is
reinforced by a steady stream of data” (p. 6). Johnson is not the only researcher that
discusses SES as a motive that increases the America’s achievement gap.
The Flanagan, Grissmar, Kawata, and Williamson (2000) study used NAEP
data from 1990 to 1996 to examine student increases in scores and patterns of
America’s achievement gap throughout the states:
Flanagan et al. recognize that resources are an essential factor
that determines why low-SES students have lower
achievement than higher SES students, and why some students
of color are not achieving at the same rates as their European
American counterparts: Our results show that resources can
make significant differences for minority and lower-SES
students in public school and that between-state, rather than
within-state, differences in resources are the main reason for
inequitable resource levels for lower-SES students. (Flanagan
et al., 2000, p. xxx)
Flanagan imports the crucial point that low SES students are not succeeding within
American schools, therefore increasing America’s achievement gap, because they
have a lower access to vital resources. It is a continually vicious cycle for students
of low SES and color because they have difficulty increasing their scores due to lack
of proper access to resources, and because they are poor students of color they will
not be able to access the resources they need to increase their achievement levels.
They are in a continuous stagnant circle of a perpetual achievement gap, and their
circumstances continually hold them in the circle. There are many other examples of
how low SES and lack of resources perpetuate the low achievement scores of
students of color. However, Kim (1992) has stipulated that the time a student has
suffered under low SES conditions is also a factor that continues the low
33
achievement cycle. The more time a student spends in poverty, the less they are
able to rise out of the guise of lower achievement than European American students.
However, low SES has consistently been the stock answer for why students
of color are not performing as well as European students. Johnson (2002) stipulates
that researchers and educators should not stop searching for other causes for the
achievement gap. She states that many educators and researchers use low SES as the
catch all excuse, but that there are other reasons that create the inequity we see in
American schools: “The gaps are found among these groups regardless of
socioeconomic level” (Johnson, 2002, p. 4).
Roscigno (1999) also indicates that a student’s achievement in school is
connected to “Research has identified multiple sources of racial educational
disparity, some of them having to do with differences in family background.
Socioeconomic status is important, for instance, given its consequences for family
educational resources…” (p. 159). Additionally, Roscigno also stipulates that it is
not just low SES, but the home environment where the student resides in low SES is
the significant factor in creating low achievement amongst students of color.
Roscigno’s study finds that the connections between home, SES, and ethnicity,
especially for African-American students is what is significantly increasing their
achievement gap with European American students:
Less often acknowledged, and certainly less theoretically
developed, is the linkage between educational disadvantage
and place. The findings were largely supportive of theoretical
contentions. Family SES and structure are depressed for all
students in areas of limited general opportunity, while Black
students are further disadvantaged relative to their White
counterparts in areas where racial opportunity is constructed.
(Roscigno, 1999, p. 181)
34
Roscigno claims that SES is a significant factor in why students of color in
America are underperforming, but he also stipulates that the problem is deeper than
just SES. SES involves family, home life, and ethnicity which also contribute to a
student’s economic status and affect their school performance. Furthermore, there
are counterarguments by other researchers that make a stronger claim than Roscigno
that SES is not the only reason or answer to why students of color are failing to
perform at the same rates as Caucasian students.
Similarly to Roscigno, Ainsworth (2002) also indicates that SES is an
important factor for students that low performing. Still, he believes that the
neighborhood, and its economic status, influence a student’s academic performance.
Ainsworth used the National Educational Longitudinal Study (NELS) from 1988 to
1990 about neighborhood characteristics and argues that “neighborhood
characteristics predict educational outcomes but also that the strength of the
predictions often rivals that associated with more commonly cited family- and
school-related factors” (p. 117). Yet, Ainsworth does give hope that the affects of
low SES and a negative neighborhood can be reconciled through “theoretical
mediators linked to collective socialization theory (educational expectations and the
amount of homework completed) are the ones that best mediate the relationship
between neighborhood effects and educational outcomes” (p. 144).
Teachers. Meier, Polinard, and Wrinkle (1995) make the counterargument
that there are other issues prevailing in student’s lives that contribute to low
achievement. In this study, Meier et al. states: “The link between education and
income has long been established, as has the link between education and upward
mobility (e.g., Cohen & Tyree, 1986; Duncan, 1984)” (p. 463). Meier et al. have
nine other factors that affect the achievement of students of color besides low SES.
35
Educational resources, sometimes an overlooked factor for the achievement gap
that Meier et al. mentions, is the need for same ethnic teachers:
For African-Americans in Texas, only one variable in the
group that composes educational resources was found to be
statistically significant. It is, however, an important variable:
the presence of African-American teachers. Our data show
that increasing the number of Black teachers helps close the
Black-White pass ratio. (Meier et al., 1995, p. 471)
The connection between an effective teacher and a student is well documented
(Marzano, 2003). So, it is important to understand that this bond between teacher
and student is exceptionally important towards the students’ academic success in
school. Meier et al. make reference to the idea in their study that students of color
perform better with a teacher that shares their same ethnicity. Remember, however,
that there are many factors that go into that equation to create that success. Keep in
mind that some reports stipulate that just because the teacher and the student are the
same ethnicity that the student will feel connected to the teacher and their
achievement will increase. There are factors such as SES and identification with
ethnicity that play a role in whether teacher and student make a connection.
In addition to Meier’s report, Stanton-Salazar (1997) also mentions in his
article that the teacher, creating access and networks for the student, increase a
student’s chance of academic success. Stanton-Salazar sees teachers as conduits or
channels for student academic success and or failure. A teacher has the ability to
give the student a gateway into the highway of academic achievement or be a
roadblock. Similar ethnicity or a connection to the teacher only increases a student’s
chance of networking the academic pathways to success.
Mier et al. and Marzano illustrate that there is a link between effective teachers
and student performance. Through this link, the problem of the growing American
36
achievement gap lessens or widens. Another researcher that stresses the idea that
teachers affect the achievement gap through their efforts or non-efforts is Bamburg
(2006). Bamburg (2006), in his monograph, states that teacher expectations
significantly affect student achievement and that there are various topics around how
teacher expectations affect student performance.
Bamburg’s first section “explores the relationship between teacher
expectations and student achievement” (p. 1). He uses Rosenthal and Jacobson’s
(1968) Pygmalion in the Classroom research. A disturbing commentary on the
relationship between teacher expectations and student achievement is that “…the
student often internalizes teachers’ expectations over time. When this internalization
occurs, the student’s self-concept and motivation to achieve may decline over time
until the student’s ability to achieve to his or her potential is damaged” (p. 2). One
could argue that a significant reason the achievement gap in America persists is
because students are fulfilling the low expectations of the teachers, or the teachers’
expectations of the students are damaging students’ potential because not all teachers
believe that all children can succeed.
Sustaining expectations is the second issue that Bamburg explores. He draws
upon research from Cooper and Good (1983), Edmonds and Frederiksen (1978), and
other studies to support his position that “low teacher expectations for students can
negatively affect student performance” (p. 3), and so students meet low teacher
expectations because the “teacher misses an opportunity to improve student
performance because he or she responds to a student based on how the teacher
expects the student to perform” (p. 3). However, there is hope that the achievement
gap will decrease because in the Edmonds et al. study, it showed, “that teachers in
instructionally effective inner-city schools had ‘high expectations’ for all of their
37
students” (p. 3). If teachers’ have high expectations for their students, research
indicates that the students will perform better in school.
Bamburg suggests that there are interventions to address low teacher
expectations affecting students’ achievement in school. He insists that each of these
prescriptions is not to be performed in sequence but simultaneously throughout the
various levels of the school system. The first of the interventions is “They must
focus on interactions inside the classroom between the teacher and students” (p. 13).
This requires that teachers are knowledgeable in how students learn, the newest brain
research, understand the culture of poverty, and have a strong sense of culturally
relevant and responsive teaching. The second intervention involves the classroom
and the school/district. This involves a changing the leadership style or roles at the
school, and creating a positive school culture and climate. The third intervention is
Haycock (1998) agrees with the idea that teachers are a significant factor that
contributes to students’ academic performances:
Parents have always known that it matters a lot which teachers
their children get. That is why those with the time and skills to
do so work very hard to ensure that, by hook or by crook, their
children are assigned to the best teachers. (That is also at least
part of the reason why the children of less-skilled parents are
often left with the worst teachers…). (Haycock, 1998, p. 3)
Haycock’s piece studies the research from Tennessee, Texas, Alabama, and
Massachusetts. The findings indicate that to decrease students of color achievement
gap with Caucasians, leaders should focus on “quality in teacher preparation,
recruitment, hiring, assignment, and ongoing professional development” (p. 19).
Haycock also agrees with Meier in that “…poor and minority children depend on
their teachers like no others. In the hands of our best teachers, the effects of poverty
and institutional racism melt away, allowing these students to soar…as young
38
Americans from more-advantaged homes” (p. 20). Good teaching affects change
in students is what Haycock believes.
Marzano (2003) is also another believer that teachers and the quality of their
instruction are the key to creating academic success or failure in students: “The
results of this study will document that the most important factor affecting student
learning is the teacher” (p. 72). Marzano’s research indicates that an effective
teacher can create an immense amount of sustained increase in student performance
over the course of prolonged amount of time: “…the most effective teachers
produced gains of about 53 percentage points in student achievement over one yea,
whereas the least effective teachers produced achievement gains of about 14
percentage points…” (p. 72). Another interesting side note that Marzano states is
that “Effective teachers appear to be effective with students of all achievement levels
regardless of the levels of heterogeneity in their classes…” (p. 72).
Opportunities. The opportunity or chance to receive a good education is also
another factor for the mathematics achievement gap for American students. The
TIMSS mentions that the American mathematics curriculum is not as demanding as
other countries such as Japan, Singapore, Korea, and Germany. The American
students spend most of their math class time on doing homework within the
classroom setting, or focusing their math time on mathematical procedures. The
other countries spend less time on doing homework within the classroom setting, and
focus more on letting their students discuss and explore the mathematical concepts
and topics. There are more demonstrations of math by the students, and they have
more pair share time. The classrooms also have less interruptions than American
classrooms.
39
Another significant problem that Silver (1998) stipulates is that American
students learn more concepts and mathematical language within a year than these
other countries. However, the other countries take the opposite approach of America
concerning math education by requiring their students to learn only a small number
of mathematical verbiage each year. Rather, the other countries want the students to
fully grasp the mathematical concepts and have a strong basis for arithmetic before
progressing onto more advanced mathematics. American mathematic education is
procedural, while other countries math education is more conceptual. Silver also
indicates that the American mathematics curriculum has too many topics and
concepts per year, than other countries leading in mathematics. Whereas, other
countries give their students a few mathematical concepts because they believe in
mastering these mathematical aims. American curriculum duplicates and repeats
concepts each year, and bases the curriculum on performance—not mastery of math.
Yet another difficult problem for the American education is the idea of access
and networking. Stanton-Salazar emphasizes throughout most of his work that
achievement gaps are created and continued because students of color lack access
and networking ability within American schools. As mentioned earlier, many
students of color do not possess the ability to access higher or advanced mathematic
classes, which means they do not receive the same quality education as their
European American counterparts. This is the reason why a larger percentage of
students of color do not do as well on national tests (College Board, 2001). Without
access to higher math classes, students of color are relegated to lower math classes,
which mean they do not score as high on standardized math tests, and do not have as
great a chance as their European American counterparts to succeed in high school
and going onto college. Students of color have less of a opportunity to access the
40
mathematics curriculum, which only further reinforces the data that schools in
which there is a majority of students of color less than 50% of the students graduate.
Less chances to graduate and access the curriculum they need to succeeded is the
groundwork for why the achievement gap in America continues to grow.
Conclusion
Studying America’s achievement gaps can provide educators and researchers
with new insights into how America will perform on future math assessments.
Analysis of the achievement gap will also provide more information on how
American students will perform in relation to their international counterparts in the
future. If one is to look at the data today, it indicates that America’s students will
continue to be at the bottom of international comparative math studies if measures
are not taken to restructure how America teaches mathematics to its students and
other areas of explanation for the achievement gap are not explored (Balfanz &
Legters, 2004).
Mathematics Effects on Students
Achievement gaps in math are particularly detrimental to students, especially
those of color, because it propagates the inequality that already exists within the
American educational system. Several studies allude to the fact that American
students are not passing math in significant numbers (College Board, 2000, 2005).
Students, who do not perform well in mathematics in their formative high school
years, do not take advance math, which leads them to not graduating from high
school and not going to college: “Success or failure during the freshman year sets
the tone for a student’s entire high school career (Hertzog & Morgan, 1999;
McIntosh & White, 2006). Research also indicates that “Black high school students
participate in advanced math classes at low rates. In 1999, 24% of White high
41
school juniors and seniors enrolled in Pre-calculus or Calculus, but only half as
many black junior and seniors…”(Klopfenstein, 2002, p.1).
If students do not perform well in math, during early stages in high school, it
only leads students into a life of subjugation through only being able to live a life of
low SES. Klopfenstein indicates that “The low rates of advanced math-taking
among black students should concern policymakers given that a rigorous high school
math curriculum has been shown to have long-run implications for future labor
market earnings and college success” (p. 1). In 1998, the graduation rate for
African-Americans and Hispanics were around 50%, while the Caucasian graduation
rate was almost 80% (Greene 2002). This achievement gap is continuing to increase
throughout American schools because of the difficulty that low SES and students of
color have with passing Algebra I. These figures only further illustrate the growing
gulf between Caucasian students and those of color in all realms of society,
especially entrance into college and graduating from high school. Taking low math
classes in high school even translate into having effects that follow students
throughout college: “The highest level of math completed is potentially a stronger
predictor of bachelor’s degree completion than socioeconomic status and has a
greater impact on the graduation rates of black students than on white students”
(Adelman, 1999; Klopfenstein, 2002, p. 1). Klopfenstein also cites Rose and Betts
(2001) that the math classes student take in high school affects their wages for “ten
years after high school; the more demanding the math courses taken, the greater the
earnings gain” (p. 1).
The TIMSS highlights the need for educators and researchers to find
solutions to resolving American students’ mathematics achievement gap. Some
researchers feel that there is an achievement gap in mathematics between students of
42
color and Western European American students that stems from the instructional
practice in mathematics that each group receives. Thernstrom and Thernstrom
(2003) believe that teachers are continuing the achievement gap cycle for students of
color because they have low expectations and do not teach these students to master
mathematics skills. Teachers instruct students of color in only basic mathematic
elements, and never give these students the in-depth conceptual mathematical skills
and ideas they need to succeed in high school math and go onto college. Thernstrom
et al. feel that these teachers are handicapping students of color and need to provide
them with real learning.
A Nation at Risk also stipulates that mathematical knowledge is essential for
today’s American youth. The report states that American students cannot compete in
the future markets of the global economy without having the proper mathematic
education. Without mathematics, students are predetermined to live a life of low
SES because there is a correlation that students who do not pass Algebra 1 do not go
on to graduate from high school or go onto college. In today’s current societal
situation, for most of those that do not go on to college, they commonly stay in a
situation of low SES. America’s current business relations are taking all the
industrial jobs out of the country. The United States is quickly becoming a service
industry society where only those with skills requiring mathematics knowledge or
those college educated can earn enough money to produce a stable household living
wage. Those without college education will stay in the low SES category for their
lives, and will probably be dooming their students to a life of low SES. It is a
perpetual vicious cycle.
Because the country is facing an educational crisis in mathematics, the
government has tried to stem the tide of the ever growing achievement gap through
43
standards-based and mathematics reform efforts. Even though the federal and state
governments come up with their own solutions to resolving the math crisis, state
educators, researchers, and local school districts continue to strive for more practical
and effective solutions to their problems.
National and State Efforts to Improve Mathematics
National Efforts
For most of American history, the federal government has left schooling and
educating Americans to the states. However, since the Space Race era and the
discovery that American students are behind other countries in math and science, the
federal government has become increasingly involved in how the states deliver
education. In recent history, the federal government has increased its involvement in
uniforming American education with policy. The federal government lately has been
making educational policies that all states must follow because of the outcry from the
American public over the status of their educational system. Particularly in
mathematics, the federal government has tried to stem the wave of anger through
federal policies and measures to bring back equity into the system.
The achievement gap in America is growing between not only Caucasians
and students of color, but between American students and other industrialized
countries. Researchers and educators began to examine other countries methods of
teaching their students to understand how they can improve America’s educational
system (Resnick & Zurawsky, 2005). The difference between the American system
and other industrialized nations is that they had a national or country-wide
curriculum with educational outcomes and expected academic performances for
students and America did not. Resnick et al. stipulate:
44
The existence of the national curriculum allowed for the
creation of an entire education system geared to helping
teachers teach the curriculum well. Teacher preparation and
ongoing professional development were
powerful….examinations given toward the end of secondary
schooling were based directly on the national
curriculum….Publishing companies planned their textbooks
and supporting materials around the specific syllabi and
curricula. Finally, the curriculum and syllabi themselves were
typically easily available to the public….As a result, students,
parents, and teachers all knew what kids should be learning.
(Resnick & Zurawsky, 2005, p. 3)
A national curriculum was working for other industrialized nations, and the
government wanted to institute the same concept in the American educational
system.
The heart of American standards began with the discussion of national
educational goals by such organizations as the National Governors Association
(NGA) and the Council on Education Standards and Testing (Resnick et al., 2005).
The difficulty in creating American standards was to maintain the balance between
centralism and decentralization. The public wanted education to remain in local
control, but educators and researchers had seen the benefit that centralization could
have on the American educational system. American standards needed to retain that
delicate balance between national, state, and local control over the school system:
The idea was that a standards-based system could combine the
positive aspects of centralized curricula with the individuality
and energy of the American local control system. The
standards and assessments would be set by public entities such
as states, but the details of curriculum, teaching, and
professional development would be left to districts and
schools. The accountability systems, rather than detailed
regulations, would structure the priorities of schools and
districts and press them to make the changes necessary to
deliver effective teaching to all of their students. (Resnick et
al., 2005, p. 5)
45
President Clinton’s Elementary and Secondary Education Act (ESEA) was the
initial policy for the formation of standards. The ESEA is renamed the Improving
America’s Schools Act (IASA) and “required states to set statewide academic
standards for its Title I students that were the same as the standards that existed for
other students” (p. 6). The IASA is the basis of President George W. Bush’s No
Child Left Behind (NCLB).
NCLB. One way in which the federal government has tried to increase equity
throughout American schools is through NCLB. President Bush signed NCLB into
law on January 8, 2006. NCLB is a law that creates an educational framework that
states are required to comply with that includes principles, strategies, and mandates
about how states should conduct educational instruction. NCLB has several different
facets:
The NCLB Act, which reauthorizes the Elementary and
Secondary Education Act (ESEA), incorporates the principles
and strategies proposed by President Bush. These include
increased accountability for States, school districts, and
schools; greater choice for parents and students, particularly
those attending low-performing schools; more flexibility for
States and local educational agencies (LEAs) in the use of
Federal education dollars; and a stronger emphasis on reading,
especially for our youngest children. (U.S. Dept. Ed., website,
2002)
NCLB requires that states create systematic accountability assessments and state
standards. The accountability assessments must correlate to the state’s standards,
which then, using AYPs, determine school districts and schools that are progressing
or labeled as Program Improvement (PI). PI schools that have been in PI status for
five years or longer will be required to restructure or reconstitute. Teachers, under
46
NCLB, must be highly qualified, and have the mandate to ensure that every student
is engaged in lessons. One costly element of NCLB for school districts is “For
students attending persistently failing schools…[PIs] must permit low-income
students to use Title I funds to obtain supplemental educational services from the
public- or private-sector provider selected by the students and their parents”
(website). NCLB requires PI schools to use 20% of their Title I funds to ensure that
students have ways and means to go to non-failing schools. Because NCLB requires
each state to have state standards, the standards movement for teachers and schools
blossomed.
State Efforts
In response to the many educational issues plaguing California, the Public
School Accountability Act (PSAA) was enacted. PSAA has four components:
Academic Performance Index (API), Immediate Intervention/Underperforming
Schools Program (II/USP), Awards Program, and the Alternative Schools
Accountability Model (ASAM).
5
The API is a measure designed to gauge schools’
academic growth and performances:
It is a numeric index (or scale) that ranges from a low of 200
to a high of 1000. A school's score on the API is an indicator
of a school's performance level. The statewide API
performance target for all schools is 800. A school's growth is
measured by how well it is moving toward or past that goal.
(CDE API website)
The II/USP assists schools by providing them an intervention plan, funds, and other
resources to schools that did not meet their API growth goals. The Awards program
5
All information on the PSAA is from the California Department of Education’s PSAA website:
http://www.cde.ca.gov/ta/ac/pa/.
47
is for schools that meet their API growth targets. Each program is individualized
with its own particular set of criteria and rewards amounts. The ASAM is a scaffold
framework for alternative schools.
Creating state accountability systems through incentives, punishments, school
growth targets, and other resources is not the only way California attempted to create
educational equity. States such as California tried to resolve the inequities through
assessments and frameworks (Mazzeo, 2001). After NCLB, states were required to
create their own state standards and assess their students with statewide assessments.
Although, some states such as Kentucky and New York had long ago began revising
their educational curriculum by using standards based reform efforts and had already
created state standards and assessments.
Before standards based reform, every school district in every state had their
own expectations for student outcomes. Each school district even had their own
ideas of high school graduation requirements and high school graduation exams.
None of the school districts within a state had aligned their assessments, curricula,
expectations, or outcomes. This created significant problems because expectations
from school district to school district varied. Students and teachers were not aware
of what was acceptable student outcomes or expectations (Hirsch, Knapp, &
Koppich, 2001). Because of all this confusion, the state’s educational branch,
researchers, and educators from all sections of education helped to create each state’s
standards. By the beginning of the 21
st
century, most states had state standards for
48
their four core areas (Hirsch et al.). Not only did states develop standards for
instructional subjects, but professional standards for teachers and administrators.
Notwithstanding the fact that states have developed standards for many
subjects, the mathematics standards in America are not as progressive as those in
other countries. American mathematics standards believe in mathematical
procedural knowledge over conceptual. There are also many more standards that
students need to master per capita a year than other industrialized nations.
Particularly in California, the mathematics standards focus on having students
understand arithmetic very early and progress quickly to procedural understanding,
while countries such as Japan and Germany spend more time on conceptual matters
(TIMSS; Dr. Marsh Powerpoint). Even though California received an A on their
math standards (Klein, 2005), many students in California continue to fail
mathematics classes in high school, particularly Algebra I. Californian high school
teachers stipulate that their students do not fully understand mathematical concepts
and cannot adequately perform the arithmetical procedures required to succeed in
high school mathematics courses.
If California students do not possess the knowledge to pass high school
mathematics courses than they will not be able to graduate from college nor pass
math classes in college. This has already been proven by the entering freshman
class at University of California Los Angeles (UCLA) for 2006. The UCLA
freshman class is only 2% African-American out of 4852 freshmen that are attending
(Trounson, 2006). The rates of African American and Hispanics students enrolling
49
in the University of California (UC) system are decreasing as each year. Trounson
(2006) believes that the educational inequities students of color face make them less
likely to enter into the university because they lack the necessary skills that the
university demands: “…socioeconomic inequities that undermine elementary and
high school education in California and elsewhere, with minority students
disproportionately affected because they often attend schools with fewer resources,
including less-qualified teachers and fewer counselors” (p. 1). Because students of
color are not properly prepared for the university they do not get admitted, and there
is a strong correlation between college and university acceptance and Algebra I
passage rates. Therefore, students of color, because they did not perform well in
mathematics, would be relegated to a life of low SES and not make as much money
as a Caucasian who works in a field in which math skills are needed. (Watson,
2000).
Improved Curriculum and Instruction
With the federal and state educational policies such as standards-based reform,
schools and school districts have attempted to correct the inequities of the
achievement gap in their school systems. The ways in which schools and school
districts have tried to address the failure rates of their students is through improving
instruction and curriculum at school sites through school reformation and improving
teacher preparation.
50
School Reformation
School reformation is one way in which schools and school districts were
transforming their instructional environments to find ways in which to better help
their students succeed. Marzano (2003) collapsed all the school-level factors within
the last 35 years of secondary reform into five determiners that affect student
achievement:
1. Guaranteed and viable curriculum
2. Challenging goals and effective feedback
3. Parent and community involvement
4. Safe and orderly environment
5. Collegiality and professionalism
Marzano believes that a combination of all of these factors will create successful
student achievement and performance. However, other researchers believe that these
are not the only factors to influence student achievement. Recently in education,
some researchers believe that restructuring schools is an effective method to increase
student performance.
SLC. There are many variables to school restructuring such as changing the
school from a comprehensive site into a Small Learning Community (SLC). Often,
SLCs are described as Career Academies or schools-within-a-school. The purposes
of SLCs are to create an environment in which teachers are able to deliver to students
more personalized instruction: “Supporters assume that teachers will get to know
their students and respond to their needs better” (Supovitz, & Christman, 2005, p.
51
649). Another purpose of SLCs is to give teachers more collaboration time and
more flexibility in working to improve their instruction and their students’
performances: “There is also an expectation that small communities will make it
easier for teachers to share practices and will encourage them to create a culture for
sustained instructional improvement, which will in turn enhance student learning” (p.
649). Usually, SLC teachers work in teams or pairs, and they often share the same
students. They are a community of learners with the students and amongst
themselves as professionals.
SLCs have been receiving much more notoriety because schools and school
districts have been looking for ways to increase their students’ achievement and
performance levels, and SLCs have shown to increase students’ school
performances. SLCs have become an alternative choice for comprehensive high
schools, and those in New York and Maryland have succeeded in increasing their
student performance through the use of SLCs: “The focus on small learning
communities, long recognized as a key element of school success in terms of school
climate and student achievement (Cushman, 1999) is a cornerstone of the philosophy
that drives educational options” (Gates, & Stuht, 2006, p. 1).
The success of SLCs is why more urban school districts, such as Los Angeles
Unified, are feeling the need to change their comprehensive high schools into SLCs.
Many schools have a ninth grade academy or SLC that just serves freshman in order
to particularly give their freshman specialized attention. The ninth grade is crucial
for most high school students, and because many of them are failing Algebra I in
52
record numbers, they are not graduating from high school and going onto college.
Freshman SLCs are designed to correct this inadequacy in the freshman learning
experience in school, and to try to remediate the damage that often occurs when
freshman do not go on to become sophomores. Often times, the personalization in
SLCs occurs because the SLC changes instructional times or periods.
Trybus (2004) in her essay discusses how all CSRs (Comprehensive School
Reforms) must comply with the SBR legislation (Scientifically Based Research) that
is grounded in NCLB. There are 11 components to CSR that NCLB requires. The
American Institutes for Research (AIR) organization published a guide in 2000 that
gives educators a background of what they consider the most promising CSR models
in the nation, and the American Association of School Administrators (AASA) in
2003 provided educators with an online summary of the 24 programs.
Math Programs. Not all schools and school districts have taken measures such
as reforming the school through means such as SLCs. Some schools and school
districts have tried to increase their students’ mathematics performance through
restructuring a subject or program such as transforming their traditional math
program into one like Core Plus. Because Algebra I is the gateway mathematics
course that determines whether students’ succeed or fail high school or enter college,
many schools have chosen to restructure their traditional math program. Some of the
popular programs that schools are using are Core Plus, Integrated Math and Science,
Cognitive Tutor, and College Predatory Mathematics.
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Core Plus or Contemporary Mathematics in Context: A Unified Approach
(CPMP) is a mathematics curriculum was developed by Western Michigan
University and published by Glencoe/McGraw-Hill which is “a comprehensive
Standards-based three year high school curriculum for all students, plus a fourth-year
course continuing the preparation of students for college” (Western Michigan
University, website). The U.S. Department of Education has recognized CPMP as
one of five programs that they label as exemplary. Math modeling is a key function
of the program, as well as diversified instruction to accommodate the needs of all
students. Assessment in this program is both formative and summative, but allows
the teacher and students opportunities to revisit continually the material. One high-
performing school, that was once a low performing school, transformed themselves
by using CPMP: “PHS adopted …Core Plus….the program eliminates teaching
algebra and geometry as distinct courses….[it also] emphasizes helping students
learn how to communicate mathematics concepts in writing” (Southern Regional
Education Board, 2003, p. 6).
A second math curriculum that is increasing school achievement is Integrated
Math and Science. The concept of Integrated Math and Science incorporates
elements such as block schedules, using computers, or team teaching. In Blume,
Garcia, Mullinax, and Vogel’s (2001) research, they indicate that using Integrated
Math and Science curriculum increased students’ math efficacy and scores. The
students understood the mathematics concepts because they were in real-life form by
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using science as the basis of learning. Most integrated math programs include
some form of writing or the writing process in combination with the math
curriculum.
Other math programs such as Cognitive Tutor (CT) from Carnegie Learning
integrate computers into the math classroom. CT was developed by researchers at
Carnegie Mellon University. When students are using the CT program, 40% of their
time is spent on the computer with the CT software: “The software assesses the prior
mathematical knowledge of students on a step-by-step basis and presents curricula
tailored to their individual skill levels” (Carnegie Learning, website). The
curriculum is built so that the computer software and the classroom activities
complement each other. An essential component of the curriculum is that it provides
the students with real-world mathematical situations and heavily emphasizes
problem solving. Cognitive Tutor is a popular math curriculum that several districts
have purchased, which is why Koedinger’s (2002) article tries to discover the
success of the program while analyzing the psychological theory behind it. The U.S.
Department of Education’s What Works Clearinghouse has given Cognitive Tutor’s
Algebra I program the distinction of “having strong scientific evidence of
effectiveness” (website). CT also meets the requirements of Scientific Based
Research (SBR).
College Preparatory Math (CPM) is another popular mathematics curriculum
with school districts. It is used in 35 states, used in 900 schools, and is taught by
around 3,000 teachers. Math professors from UC Davis and California State
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University, Sacramento and 90 middle and high school math teachers, created
CPM. Before teaching a CPM class, teachers are required to attend CPM teacher
training, and during their first year of teaching CPM are required to attend additional
workshops. CPM is one of the few programs in which math teachers receive
mentoring “under the direction of mathematics professors from UC Davis and CSU,
Sacramento” (CPM, website). The purpose of CPM is to integrate “basic skills and
topics with conceptual understanding and problem-solving strategies” (CPM,
website). What makes CPM similar to other nations math programs such as Japan is
that student teams are an essential component to the curriculum. The curriculum
uses the math teacher as a facilitator that takes students on “guided investigations” of
math problems. Students typically only work through a few math problems a day in
teams, rather than the more traditional math method of working individually on
numerous math problems. CPM focuses on problem solving and mathematical
concepts instead of mathematical procedures. CPM, similar to CPMP, has garnered
the Exemplary Mathematics Programs award from the U.S. Department of
Education.
Because of the plethora of mathematics programs that districts could use, the
problem becomes picking the right program to revitalize their school’s scores. What
educators need are methods and strategies for determining which particular
mathematic program or reform will help increase our students scores, so that they do
not have to constantly keep altering their schools because they methods, strategies,
and programs might be successful for other schools but do not work with their
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particular school population and demographics. Performing more studies on math
programs would help educators determine which studies to use and which are
effective because data indicates that traditional math curriculum is not working for
American students.
Professional Development
The Center for Teaching and Learning (2002) suggests that most American
math teachers do not have the proper preparation to teach high school mathematics.
This statement suggests the need that American mathematics teachers are sorely
lacking in the proper professional development to be effective mathematics teachers
in American classrooms. Effective professional development for teachers, staff, and
administrators is another key component increasing students’ scores and
achievement. For the professional development to be effective, it must be seen as
relevant, meaningful, and engaging to teachers: “Although many schools have
regularly scheduled staff development sessions, much of what is done in these
sessions is not necessarily meaningful or useful in terms of impacting student
achievement” (Marzano, 2003). Once a school has determined that they will not use
professional development time for regular school business, but focus on student
achievement, curriculum, and teacher learning, the professional development will be
deemed as effective. Little (1993, 2002) feels that successful professional
development makes teachers critically think, have provocative dialogue, and ensure
that teachers constructing new learning.
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It is not enough to have an effective professional development just once
during the school year. Cohen and Hill (1998) speculated that the more exposures
teachers received with curriculum or their specific subject, such as mathematics, the
more it would transfer into their instructional practice in the classroom. Cohen et al.
found that if professional development was subject specific and relevant, teachers
would relate, and it would extend into their teaching practice. The approach to
professional development that the study examined had four approaches:
1. General orientation: teacher’s exposure to key ideas about reform
2. Specific content: teachers’ exposure to such education “instruments” as
improved mathematics curriculum for students, or assessment that inform
teachers about what students should know and how they perform
3. Consistency: the more overlap there was among the educational
instruments noted above, the more likely teachers’ learning would be to
move in the direction that state policy proposed
4. Time: teachers who had more of such exposure would be more likely to
move in the direction that the state policy proposed (Cohen et al., 1998, p.
300).
In the study, the research demonstrated that teachers’ effectiveness in mathematics
increased because of the specialized professional development they received. The
development was specialized because it dealt particularly with the mathematics
curriculum, which is what Huffman (2003) stipulates as a key reason for why the
professional developments he studied were so successful. The teacher’s
effectiveness increased with a focus on the specific mathematics curriculum and
teaching pedagogy, and so did the students’ performance and achievement in
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mathematics. Professional development is an exceptionally effective tool for
schools that want to increase their achievement. Understanding how teachers learn,
and how that translates into the classroom is what makes professional development
effective (McLaughlin, 1990; Cohen & Barnes, 1993; Joyce & Showers, 2002).
One of the reasons in which professional development was effective in the
Cohen et al. study was because teachers were exposed to the material multiple times
(American Federation of Teachers, 2002). There was a shift in education in regards
to professional development. The secondary school reform movement went from
developing professional networks to creating Professional Learning Communities
(PLCs).
Professional Learning Communities. PLCs give teachers time for teaming.
Teaming provides teachers with time for collaboration, dialogue, reflection, and
problem-solving which is essential in making teaching practices effective for
students (McIntosh et al., 2006). In addition, PLCs give teachers a supportive
network for professional communication with their peers. PLCs provide teachers an
opportunity to share best practices, and learn new instructional methods and
techniques that were successful in others classrooms. Research indicates that
teachers consistently learned in the forum of a professional learning community
(Darling-Hammond & McLaughlin, 1995). Senge (2002) believes that PLCs lead to
increased accountability for student outcomes and performance, which creates an
increase in student’s scores.
Blasé and Blasé (2004) in their book Handbook of Instructional Leadership
combine the work of several researchers to come up with five attributes of
Professional Learning Communities:
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1. Supportive and shared leadership (i.e., principals democratically shared
power, authority, and decision making with teachers)
2. Shared values and vision (i.e., principals and teachers developed an inspiring
yet realistic picture of a school based on common values and beliefs)
3. Collective learning and application of learning (i.e., principals and teachers
studied together, using data to develop programs, sharing practices, focusing
teaching strategies on student needs, fostering teacher leadership)
4. Supportive conditions (i.e., teachers had time to talk, plan, and solve
problems; teachers had opportunities to influence decisions; teachers
developed collaborative roles and responsibilities; principals and teachers
maintained an academic focus; principals and teachers developed norms that
supported ongoing learning; principals and teachers engaged others in
decision making; and principals were comfortable with relinquishing power)
5. Sharing of person practices (i.e., teachers held regular, structured peer
reviews of colleagues’ instructional practice; teachers accepted challenges
and risks
The work of Blasé et al. can be seen as a guideline for creating successful PLCs at
school sites. In the book, they also outline 10 principal maintenance behaviors
associated with a PLC. In addition, many of the behaviors for principals to create
successful PLCs align with the five attributes of PLCs:
1. Were action oriented
2. Had positive perceptions of teachers’ capabilities
3. Balanced the delicate interaction between support and pressure by letting go
of traditional role expectations and also by encouraging teachers to take on
new roles
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4. Developed shared values and vision
5. Supported shared decision-making
6. Promoted continuous learning
7. Encouraged collaboration
8. Provided support
9. Engaged all teachers and administrators in collaborative reflection, inquiry,
problem-solving, learning, and teaching
10. Provided regular opportunities to learn and grow
Reform Efforts. There have been three significant secondary school reform
efforts from the 1960s to the present. Marzano (2003) suggests that in the early
stages of reform “The emphasis in this phase was on the adoption of curriculum
materials. The materials were generally high quality, presumably because they were
well funded and produced by teams of psychologist and subject matter specialists”
(p. 157). This early phase defined successful academic achievement through the use
of the Carnegie unit (Marzano, 2003).
The second phase of secondary reform took place during the 1970s. Marzano
stipulates that “great efforts were made to determine the exact impact (or lack
thereof) school had on student achievement and the factors that contributed to it” (p.
157). The use of school-level factors from various researchers in this period
constitutes the bulk of secondary reform during this period (Edmonds, 1979, 1981;
Rutter, Maughan, Mortimore, Ouston & Smith, 1979; Brookover, Schweitzer,
Schneider, Beady, Flood & Wisenbaker, 1978).
The third phase of secondary reform was part of the late 70s in the 1980s.
Marzano describes this phase of secondary reform as confused and fraught with
problems: “Although this period saw some noteworthy successes, it was fraught
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with problems. In general, the projects did not produce the results promised or
implied by the research. This was not due to poor quality or validity, but to a lack of
understanding of the change process” (Marzano, 2003, pp. 157-158).
Marzano (2003) feels that American education is leading into another new
phase. He calls it the fourth reform phase; however, it does encompass some of the
elements of the past reforms. Marzano’s new reform stage has three principals:
1. The new era of school reform is based on the realization that reform is a
highly contextualized phenomenon.
2. The new era of school reform is characterized by a heavy emphasis on data
3. In the new era of school reform, change is approached on an incremental
basis
The first principal in the reform stipulates that every schools reform can and will
appear different than the other. Because schools are vastly different and serve many
different students, each school’s reform will be different: “Contextualized reform
should be interpreted cautiously from school to school. Just because the research
indicates that a particular school-level factor is important to student achievement
does mean that it is important in a given school” (Marzano, 2003, p. 158).
As evidenced in Johnson (2002), data is a significant element of the new era.
Many schools will be using quantitative data gathered from their school as the basis
for their school-making decisions and action plans. Because of federal and state
policies that rely on quantitative data, schools will define their actions through
statistical information. Not only will teachers, administrators, and staff will be
familiar with school data, but parents and students as well: “Indeed, one of the
defining characteristics of schools producing unprecedented gains in student
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achievement…is that they rely on data to identify probably successful
interventions (Hopkins & Ainskow, 1993; Marzano, 2003, p. 158).
The last principal by Marzano (2003) is about the change process.
Understanding and creating effective school change was a problem in the third
school reform stage. Schools are now beginning to understand how change
effectives a school, and that instituting change incrementally is what makes the
change process effective. Even though the success of incremental change were
known in the past, its implementation has not been widespread: “Although…an
incremental approach was certainly known in the early days of U.S. school reform,
this approach frequently was not taken. Thus, administrators and classroom teachers
are often overwhelmed by the sheer amount of change attempted and the work
involved” (p. 159).
Instructional Methods
Students need quality instruction. Without good instruction, students would
underperform. Some students drop out of school or become discipline problems.
Quality instructional methods are essential tools that every educator should possess
because a student with a teacher that uses successful instructional strategies will
score 23% higher on standardized tests than students with an ineffective teacher
(Marzano, Pickering & Pollock, 2001). However, not every educator possesses
instructional methods that reach all students. In most cases, successful instructional
methods are developed over time, but this does not happen with every teacher. In
order to meet the diverse needs of today’s students, teachers need to have a
significant array of instructional tools and strategies that are easily accessible. This
is especially hard for new teachers with little to no teaching experience. This is why
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teacher education programs require new teachers to take instructional methods
classes.
Marzano strongly believes that teachers are the key to a student’s success or
failure in the educational system. This is why, in his book, Marzano (2003)
recreated the research study of Hattie (1992). Using that research, he designed
categories and subcategories that illustrate nine successful strategies to affect student
learning:
1. Identifying similarities and differences
2. Summarizing and note taking
3. Reinforcing effort and providing recognition
4. Homework and practice
5. Nonlinguistic representations
6. Cooperative learning
7. Setting objectives and providing feedback
8. Generating and testing hypotheses
9. Questions, cues, and advance organizers
These nine strategies will give teachers a foundation upon which to build their
instructional repertoire, and these concepts are research-based and known to be most
effective in the classroom.
Marzano uses his categories in conjunction with lesson planning and
frameworks to create effective teaching units: “A more useful practice is to organize
strategies to provide a framework of effective instructional design” (p. 81). Marzano
designed these techniques to effect successful change in students’ learning and
performance. He feels that teachers need to use these three strategies in conjunction
with the categories and framework units:
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1. those used at regular intervals in a unit
2. those focusing on input experiences, and
3. those dealing with reviewing practicing, and applying content
Marzano does end with the belief that “The expert teacher has more strategies at her
disposal than the ineffective teacher” (p. 87).
A category that is imbedded within Marzano’s nine effective instructional
strategies is the idea of problem-solving and critical thinking. Many state’s
standards require that students possess the ability to problem-solve and critically
think. It is even a significant portion or factor of the some state’s high school exit
exams or graduation qualifying expectations. Even today’s employers require that
student’s have the ability to troubleshoot for problems, assess situations, draw
conclusions, test theories, and find solutions. It is essential that today’s high school
students have the ability to critically think and solve problems. Other industrialized
countries have had this focus for years in their curriculums. Wenglinsky believes
that if teachers educate students in the ways of problem-solving, it will become
second nature, and it will help them further master the standards because they will be
thinking and learning on how to solve real-world problems (Wenglinsky, 2002).
Before the era of standards-based learning, teachers’ instructional methods and
curriculum were determined by their preferences. However, standards changed the
idea of teacher’s teaching whatever they chose to teach in their classrooms because
they possessed academic freedom of choice subject to their prerogative. With the
invent of standards-based education, teachers are using better tools to determine their
instruction such as data from assessments (authentic and traditional). In addition,
they are using only research-based instructional strategies. Teachers are also making
sure they are teaching to all students, and not just a selected or privileged few.
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Teachers know what they should be teaching and students know what they should
be learning, and everyone has clear and high expectations (Marzano et al., 2001,
2003). Good instruction leads to higher scores and student achievement, which leads
to students graduating and having success as an adult.
When considering the teaching of mathematics, the teacher’s curriculum
knowledge, pedagogy, and instructional techniques are key to students at the school
being successful in mathematics. Taylor, Anderson, Meyer, Wagner and West
(2005) believe that having a well-developed mathematics curriculum is key to
increasing students’ mathematic capabilities and achievement. They found that the
practice of mathematical lesson study performed by teachers gave them the ability to
go into depth with their mathematical practice. They could better grasp concepts;
therefore, helping the students to better understand math. Not only were teachers
able to further analyze math and decide upon the best course in teaching the subject;
they found that the focus of the lesson study increased their mathematical practice.
Teachers increasing in their mathematical prowess translates into students increasing
in their mathematical abilities.
Instructional Leadership
With the federal and state government focusing legislation on improving
instruction within schools, “This attention to accountability, in full view of the
public, places additional stresses on principals and challenges existing models of
school leadership” (Houle, 2006, p.144; Davis, Darling-Hammond, LaPointe, &
Meyerson, 2005). Houle also stipulates that the increased pressure of accountability
from legislation and the standards movement is amplified for principals of low
performing or program improvement schools. The role of the principal over the
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years has changed from a supervisory managerial role to one that entails
instructional leadership with a strong guiding vision.
Guiding the instructional agenda at the school through leadership, when most
principals are not trained in that area, requires that principals undergo professional
development. Principals need the development to combat the new pressures that
they face with today’s school system such as what Lashway (2003) describes: “20
years of school reform have stuffed the principal’s job to overflow with new chores
and have undermined comfortable old assumptions about the nature of school
leadership” (Houle, 2006, p.144).
In Houle’s article, she examines how Connecticut created professional
development for their principals. Leaders from schools, districts, and educational
researchers designed approaches to address professional development areas of need
for urban school principals. There were three areas in which the educational leaders
addressed were “(a) instructional leadership, (b) capacity building, and (c) personal
renewal” (p. 150). What Connecticut found was that the lessons they created with
the urban principals about capacity building were especially beneficial. In addition,
the principals needed “hands-on help,” but the researchers also needed to maintain
the principals’ sense of ego, and the principals’ egos were fragile (Houle 2006). The
group also gave principals needed time to reflect which is what The National Staff
Development Council (NSDC, 2000) and the Educational Research Service (EDS)
suggest: “principals should engage in professional development that…is long-term,
planned, and job-embedded; focuses on student achievement; supports reflective
practice; and provides opportunities to work, discuss and solve problems with peers”
(NSDC, 2000, p. 6; Houle, 2006, p. 146).
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Instructional leadership is important because “Leadership is second only to
classroom instruction among all school-related factors that contribute to what
students learn at school” (Leithwood, Louis, Anderson, & Wahistrom, 2004, p. 3).
Davis et al. (2005) study also reiterates the fact that principals have a significant
impact on the classroom:
Principals play a vital and multi-faceted role in setting the
direction for schools that are positive and productive
workplaces for teachers and vibrant learning environments for
children, but existing knowledge on the best ways to develop
these effective leaders is insufficient. (p. 2)
Even though knowledge is the best way to develop principals is lacking, researchers
do know what kind of effect the principal has on classroom instruction. Leithwood
et al. illustrate this point by saying that leadership has a 25% total effect on student
learning. With instructional leadership having such an impact student achievement
and classroom instruction, it is important that principals not only receive the proper
professional development to become an instructional leaders. Leithwood et al.
believe that instructional leadership is “a focus on improving the classroom practices
of teachers as the direction for the school” (p. 4). The researchers suggest the use of
Hallinger’s model of instructional leadership: “…it consists of three sets of
leadership dimensions (Defining the School’s Mission, Managing the Instructional
Program and Promoting a Positive Learning Climate), within which are 10 specific
leadership practices” (p. 4).
Another approach to examining the burgeoning role of principal as
instructional leader is that of Blasé et al. Blasé et al. (2004) stipulate that the main
elements of instructional leadership are: “Conducting instructional conferences;
Providing staff development; Developing teacher reflection” (p. 162). These
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elements stretch far beyond the typical supervisory, operational, and managerial,
principal of the past. Today’s principals are required to be instructional leaders for
their schools, and to provide their teachers, staff, faculty, and students with research-
based, insightful, relevant, and useful instructional information. What makes a
principal a good instructional leader is his or her ability to successfully and
effectively perform the duties required within the instructional role.
Principals need to know how to successfully conduct conferences—not only
with teachers and students, but also with parents on issues concerning instruction.
Principals need to be aware of what types of professional development they provide
their staff, faculty, and parents. Picking the wrong type of professional development,
not meeting the needs of the staff and teachers, not bringing relevant or current
research-based material, or misusing professional development time creates new
problems for today’s principals. Today’s principals must be aware of how to create,
plan, organize, and perform successful professional developments because
professional development is such a stressed educational topic.
Effective instructional leaders also find ways in which to get their staff and
faculty to be self-reflective. Creating time for metacognition and dialogue about
subjects is essential for teachers and staff. Remembering one’s practice and finding
ways to improve instruction is a major factor in raising student achievement. When
both teachers and students reflect on their work, scores and achievement for both
parties rises. Today’s principals need to know how to create a metacognitive or
reflective network at their sites because research indicates that America’s schools are
quickly becoming a non-competitor with their industrialized counterparts.
Blasé et al. gives principals advice on how to be an effective instructional
leader:
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School renewal and support for teacher performance and
growth should focus not only on solving problems through the
use of innovations. Beyond this, there must be a ‘fluid
inquiry’ into possibilities that may include redesign of job
assignments, democratic reorganization, study of data about
the learning environment, sharing a professional knowledge
base, new forms of staff development, and the creation of
caring professional communities. (Joyce & Calhoun, 1995, p.
169)
What is unique about Blasé’s et al. work is that they give the perspective of
what makes a principal an effective instructional leader from the teacher’s point of
view. What principals want to know is what are the key elements of being an
instructional leader, and Blasé describes what teachers feel are important elements
instructional leaders should possess:
1. Talk openly and frequently with teachers about instruction
2. Provide time and peer connections for teachers.
3. Empower teachers.
4. Understand and embrace the challenges of change.
5. Lead.
Principals need to be strong instructional leaders because Leithwood (2004) believes
that a principal’s instructional leadership is next in priority after a teacher’s
classroom instructional. In this way, Leithwood has a similar belief to Blasé et al.
about instructional leadership. Leithwood also recognizes that leaders must create a
way in which to cultivate their faculty and staff to become leaders themselves, or at
least to be a part of the instructional processes of the school. Here, Leithwood is
similar to Bolman and Deal (2003) and their human resource frame.
Blasé et al. are not the only ones with advice for principals on how to
successfully raise achievement and performance scores in their students through
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becoming an instructional leader. Resnick and Glennan (2002) emphasize in their
article that it is important to build solid core principals throughout the district for all
district educational leaders to be on the same page. In addition, they feel it is
important to remember that the capacity built for leadership by the central and
district offices is transmitted down into the schools: “Developing skills of
instructional leadership at all levels in a district…” (p. 17). Principals must
remember that they are not alone in being accountable for the instruction taking
place at their school. Everyone should be an instructional leaders. However, the
challenge for principals is to create an atmosphere where everyone feels as if they
are a part of a professional learning community working towards the same
educational goals and standards for their students, and that each school member
whether classified, certificated, parent, or student has a role in building the
educational capacity at the school. Everyone is accountable for educating the
students at the school because everyone feels it is their responsibility because the
principal has made everyone feel as though they are instructional leaders.
Joyce Kaser’s study (2006) is similar to Blasé et al. in the fact that the study
asks teachers what they feel makes a successful instructional leader. In her study,
Kaser examines specialized mathematics and science schools for the purpose of
gaining information to help comprehensive secondary high schools reinforce their
mathematics and science programs. The researched schools stipulated that what
made an instructional leader effective were flexibility, possessing the appropriate
background and orientation, and creating a diverse staff. Three of those interviewed
for the study emphasized flexibility because “principals need to switch gears very
quickly to adapt to changing circumstances….a principal has to be very
knowledgeable of school culture and respond to that culture to create a positive
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learning and teaching environment” (p. 11). When she asked the principals of the
different schools what they saw as important elements to creating a successful
mathematics and science program, the principals believed that addressing student’s
interests, creating positive school environments, and focusing on administrative
elements of the school made their programs effective.
Similarly to Blasé and Mednick’s (2003) article communicates the importance
that principals involve their entire faculty and community. One example of a
principal that involved the faculty in the decision-making is from the Forest Grove
Middle School: “He involved the whole faculty in the process by opening a broader
conversation about their vision for Forest Grove” (p. 1). In addition to the Forest
Grove principal, Mednick gives another example of a principal dedicated to shared
decision-making. When the Amherst Regional Middle School principal had to make
cuts in her faculty for the next school year, she involved the faculty and staff in
dialogue about the issue: “…Cavalier explains that she does not expect them to
decide which of their colleagues will lose their jobs. However, she wants the entire
faculty to spend time, guided by the school’s vision and Turning Points’ principles,
to think about the question…” (p. 1).
In the article, Mednick recognizes that the role of the principal has changed in
recent years:
In the new role, the principal recognizes that no one person in
the building is the most knowledgeable or experienced
practitioner. Rather the principal is aware of the strengths of
the staff and taps into each member’s expertise to improve
teaching and learning in the school. The principal works with
the staff to develop a strong professional culture in which
teachers continuously collaborate. (p. 3)
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It is also important for instructional leaders to recognize that they need to create a
team of leadership at his or her school site. Principals should be creating a
professional learning community of leaders to help the principal make educational
and instructional decisions. Mednick feels that principals should create a school
environment in which there are several instructional leaders working together in
unison to increase student’s performance on assessments. To create this type of
environment, principals can create leadership teams or groups. Research has shown
that leadership teams and communities are an effective force in creating positive
instructional change at school sites that increase student’s scores.
Mednick recognizes that the new role of the principal incorporates multiple
focuses, and she believes that there are five significant focuses: Sharing real
decision-making power with staff and faculty; Providing support for effective
functioning of teams; Being an instructional leader who prompts others to
continuously learn and improve their practice; Developing collaborative
accountability; and Managing and monitoring the change process to make sure it is
always moving forward (p. 3). Mednick sees the role of an instructional leader as
one who continually visits classes to share instructional knowledge for teaching and
learning, and the principal is to create professional development opportunities for
their faculty and staff to increase classroom performance for teachers and students.
A principal participating in the Colorado study said that when they gave the staff or
faculty a chance to participate in the leadership process, “unexpected leaders often
emerge” (p. 6). The principals involved in the study also created a list of nine items
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that they considered important for principals to know and perform to create shared
leadership which stems from instructional leadership:
1. Have the patience to lay a foundation of trust.
2. Take time to develop lasting relationships among faculty.
3. Take time to learn teachers’ strengths and focus on drawing on those
positive attributes, rather than working solely on their challenge areas.
4. Staff members must recognize through experience that if they are
given power, their decisions will be taken seriously.
5. Empower teachers early with decisions that result in “quick-fixes.”
6. Stay upbeat and positive, even in the face of difficulties. “My mood
sets the tone. I walk through the halls, smile and say, ‘Have a good
day.’” Says Houlihan.
7. Open your office door to anyone about anything. Listen and learn.
8. With support, ask teachers to facilitate team meetings.
9. Begin involving teachers in the touch decisions (e.g., professional
development, hiring, budget, school-wide curriculum decisions).
Mednick further examines instructional leadership with the Colorado
Leadership Model style of principalship that focuses on the aspect of principal as
facilitator. In Brighton, Colorado, the principals acted as facilitators: “Each school
has several lead teachers, a full-time in-house facilitator, and the principal, who
serves as coordinator and works to keep lines of communication open” (p. 5).
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Marzano (2003) also weighs in on the topic of what makes an effective
instructional leader. Marzano feels that there are four phases to creating successful
instructional leadership. The first phase is for the leader to familiarize his or herself
with the school culture. Second, is to perform a gap analysis to determine where the
school needs improvement or change. The third phase is creating a school that is
collaborative in its instructional leadership with the principal, through modeling,
showing the others how to be a successful instructional leader. Fourth phase is for
the instructional leader to have a guiding principal or purpose, and the last phase is
ensuring that the principal creates a dynamic and symbolic vision. Marzano feels
that instructional leadership is the essential essence to creating school reform and
increasing student achievement, and that there are three tenants of leadership:
1. Leadership for change is most effective when carried out by a small group of
educators with the principal functioning as a strong cohesive force.
2. The leadership team must operate in such a way as to provide strong guidance
while demonstrating respect for those on the team.
3. Effective leadership for change is characterized by specific behaviors that
enhance interpersonal relationships.
With the first principle, Marzano abolishes the belief that the principal is the
only instructional leader for the school. He emphasizes that instructional leadership
at the school should be shared: “...the intuitively appealing option of a strong
leadership team; the principal and other administrators operating as key players and
working with a dedicated group of classroom teachers” (p. 175). What is key in the
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second tenant is that instructional leaders have respect for those who are not part of
the instructional leadership team, while continuing interest but “not intrusive in the
daily lives of teachers” (p. 176). The last principle consists of the instructional
leader as one who is optimistic, honest, and considerate of all at the school.
Unlike earlier researchers that had many points that illustrate strong and
successful leadership, Davis et al. (2003) suggest that there are only two important
foci for school leadership: “Growing consensus on the attributes of effective school
principals shows that successful school leaders influence student achievement
through two important pathways—the support and development of effective teachers
and the implementation of effective organizational processes” (p. 2). However, even
Davis et al. like the before mentioned researchers believe that there still is not
enough evidence to “determine the impact and relative importance of leadership in
such key areas as curriculum, assessment, and adaptation to local contexts” (p. 2).
The reason why more research needs to be performed in these areas is because
today’s schools are relying on principals to be instructional leaders, and there is
lacking research in the most important areas of how leadership affects curriculum
and assessment in schools. Today’s schools are judged by the state and federal
governments on their curriculum and assessments, and if leadership significantly has
an impact on classroom performance, then schools and principals must have more
information on how to be effective instructional leaders.
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In the study, Davis et al. outline the problems facing today’s principals such
as the burgeoning list of duties that continues to grow daily and some of them
conflict with the interests and desires of the different stakeholders:
Principals are expected to be educational visionaries,
instructional and curriculum leaders, assessment experts,
disciplinarians, community builders, public
relations/communications experts, budget analysts, facility
managers, special programs administrators, as well as
guardians of various legal, contractual, and policy mandates
and initiatives. (p. 4)
With all these different responsibilities, Davis et al. state that the old way of creating
principals is no longer relevant and cannot compete with the current demands of the
job. Davis et al. stress that today’s educational leadership is under qualified, not
properly trained to meet today’s expectations, or qualified but choose to work in
suburbia. With all of these setbacks in installing qualified instructional leaders at
schools, the study stresses that there are three important factors that suggests that the
most important part of a principal’s job is to be an instructional leader:
1. developing a deep understanding of how to support teachers
2. managing the curriculum in ways that promote student learning and
3. developing the ability to transform schools into more effective organizations
that foster powerful teaching and learning for all students. (p. 6).
Knowing that the principal has such an impact on student performance and
achievement, it is important that principals not only be successful school leaders but
effective instructional leaders as well. This is the idea that Richard Dufour (2002)
puts forth in his article Beyond instructional leadership: The learning-centered
principal. Dufour reiterates the claims of the above researchers such as Marzano,
Houle, and Davis in that principals should be making sure that their staff is fully
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professionally developed: “Schools need leadership from principals who focus on
advancing student and staff learning” (webpage). However, he takes the concept of
instructional leader a step further by suggesting that principals are not focusing on
the proper section of being an instructional leader. He feels that instructional leaders
should change their focus from analyzing teaching to learning. He also stipulates
that principals should become learning leaders, not just instructional leaders:
When learning becomes the preoccupation of the school, when
all the school's educators examine the efforts and initiatives of
the school through the lens of their impact on learning, the
structure and culture of the school begin to change in
substantive ways. Principals foster this structural and cultural
transformation when they shift their emphasis from helping
individual teachers improve instruction to helping teams of
teachers ensure that students achieve the intended outcomes of
their schooling. (webpage)
He accomplished the feat of changing his school’s perspective from teaching to
learning through enabling his teachers to have collaborative time and making shared-
decisions. All members of the school focused on learning instead of teaching at the
meetings and in their discussions. He facilitated most of the meetings and gave his
teachers the crucial time to collaborate with each other. In his article, he lists all the
different needs that he provided for his teachers because he felt that a school could
not become a successful professional learning organization without the principal
fulfilling all the needs of the teachers to change the focus from teaching to learning:
They needed a process to follow and guiding questions to pursue.
They needed training, resources, and support to overcome
difficulties they encountered while developing common
outcomes, writing common assessments, and analyzing student
achievement data. They needed access to relevant, timely
information on their students' performance. They needed help
writing specific and measurable team improvement goals that
focused on student learning rather than on their team activities.
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They needed encouragement, recognition, and celebration as
they progressed. They needed someone to confront those
individuals or teams of teachers who failed to fulfill their
responsibilities. All of these tasks fell to me, the principal.
(webpage)
Through his article, Dufour extends the idea of an instructional leader to incorporate
the meaning of a leader of learning that creates a professional learning community at
the school through shifting a school’s focus from teaching to learning.
In Waters, Marzano, and McNulty’s paper Balanced Leadership (2003), they
performed a meta-analyses on how instructional leadership effects student
achievement. Waters et al. used 30 years of theoretical and quantitative research to
create a framework consisting of 21 leadership responsibilities that positively effect
student achievement: responsibilities, culture, order, discipline, resources,
curriculum/instruction/assessment, focus, knowledge of curriculum instruction
assessment, visibility, contingent awards, communication, outreach, input,
affirmation, relationship, change agent, optimizer, ideals/beliefs, monitors/evaluates,
flexibility, situational awareness, intellectual stimulation (p. 4).
Similarly to other researchers stated above, Waters et al. discovered that there
is a correlation between leadership and its impact on student performance and
achievement. What makes the paper interesting is that the researchers also
uncovered that as effective leadership has a positive effect on performance,
ineffective leadership has a negative effect on student achievement. Waters et al.
suggest that there are two factors that influence whether instructional leadership will
be effective or ineffective. The first factor is whether leaders properly identify
where change will be most effective for his or her school, and the second factor is
“whether leaders properly understand the magnitude or ‘order’ of change they are
leading and adjusting their leadership practices accordingly” (p. 5).
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Consequently, finding effective ideas and implementing them at the school
site level is a difficult task to accomplish because there continues to be in education a
national debate on how best to raise math achievement. Should we revise the math
standards? What math programs are the best for high school students? Are their
specialized mathematic techniques? Is reconstructing the school and the learning
environment enough to raise achievement, and does raising achievement lie in the
hands of school leaders such as lead teachers or the principal? Whatever school
leaders attempt to do at their school site to raise their students’ mathematic
performance, they will have to create new policy initiatives and designs specifically
for their school, and this is a difficult task to accomplish if the school leaders do not
have a pedagogical background in mathematics.
On the other hand, some leaders are all too willing to change their organization
with the educational flavor of the month and that can have adverse affects on
transformative schools:
The fundamental changes that are called for in education often
require leaders to question deeply held assumptions and long-
term practices. Nevertheless, in responding to adaptive
challenges, leaders must be careful not to change so rapidly
that their organizations lose something worthwhile. In the
past, education reformers often have bounced from fad to fad,
with little impact on student achievement. Thus, the challenge
for leaders is to carefully examine whether the changes they
are implementing are the best ones for their students in the
long run. (Gaddy, Goodwin, & Mayeski, 2001, p. 22)
Where are the proper guides and policies for leaders to determine which methods,
strategies, designs, and implementations are going to be effective for their school? It
is important that educational leaders and administrators have some sort of
information and guidance to help them deal with increasing their math scores
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through effective change. This is where policies, designs, methods, initiatives, and
strategies become imperative need to know knowledge for school leaders.
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CHAPTER 3
RESEARCH METHODOLOGY
This chapter illustrates the sample criteria and process, instrumentation, and
the data collection methodology and analysis. This study’s purpose examines how a
low performing school has increased student achievement in Mathematics using best
practices, mathematics interventions, policy and pedagogy, and through strong
educational leadership. The study also analyzes how educational leadership that do
not posses a background in mathematics still help to increase the school’s overall
mathematics growth. The study is guided by these research questions:
1. What was the pattern of Math achievement for various students at the
school?
2. What policy initiatives as well as curriculum, instruction and related
conditions seem to be related to improve math achievement at the school?
3. What change process did the school use to enhance its math program and
strategies to assist students in math?
4. To what extent was strong instructional leadership important in
improving: a) the math programs/strategies, and b) math achievement
among students?
5. How did leaders in the school resolve dilemmas about instructional
leadership?
The study uses a mixed methods approach; however, it has a strong qualitative base.
The qualitative approach is necessary for this study because this study requires the
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researcher to go in depth in discovering the reasons behind the school’s increase in
mathematics, which requires interviews with school stakeholders and a deep
understanding of the school’s culture and environment. The study uses the
quantitative approach in combination with the qualitative because the study requires
the use of multiple pieces of data such as school logistics, demographics,
mathematics scores, grades, and surveys to support and triangulate with the
qualitative information found at the school site.
The study ensures that triangulation occurred between the use of all data
information and procedures, research questions, and research instruments in order to
increase the reliability of the study. Conceptual frameworks were the basis of the
study’s investigative strategy. Information from the school site such as artifacts and
documents were triangulated with interviews to ensure reliability. The basis for the
instruments used in the study was designed using current educational research for
obtaining answers to the study’s research questions. Pseudonyms were given to all
information about the school, district, and stakeholders involved in the study in order
to guarantee discretion and privacy. In addition, none of the data and information
gathered during the research process will be shown to anyone outside of the
dissertation group.
Sampling Criteria and Process
Purposeful sampling was used in this study in order to examine how effective
schools provide mathematical education, interventions, and educational leadership to
increase effectively the students’ performances and scores in Mathematics. The one
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high school was purposively selected to gain a deeper understanding of how what
efforts the school undertook to create effective mathematical change. The study used
the following criteria to select the study’s school site:
1. Improvement in math achievement as evidenced by results on the California
Standards Test (CST) in Algebra I.
2. The school must have a student population of at least 1200 students with a
diverse population that includes more than 50% from traditional ethnic
minority groups.
3. The school must be a public comprehensive high school in the Southern
California region with grades 9-12.
4. The principal has been at the school for at least three years to ensure
leadership stability.
5. The school must have a minimum API of 600 or better and a statewide
overall rank of 5.
Dr. Marsh and the 11 cohort members met periodically to develop the
sampling criteria in order to develop a list of possible school sites for this study. The
school sample process began with the cohort members identifying schools that
qualify for our study through analysis of data and information available to the cohort
from the California Department of Education’s website. Each cohort member
researched 10 schools to help form a spreadsheet (Appendix J) with various schools’
CST Algebra 1 scores to create a list of potential schools.
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In the early stages of developing the sampling criteria, the group set the
portion of minority students that the school needs to have to be considered for our
research study at 65%. However, that number significantly limited the dissertation
group’s school selection choices, and so that group collectively decided to change
the sampling criteria minority number required for our study from 65% to 50%. The
second change of the criteria that the cohort made was to alter the statewide rank for
schools, originally set at six, is now set at five. With the more stringent criteria, the
sample was only 28, so the cohort altered some criteria to create a list of 110 schools
in the Southern California area that were eligible for the study.
To refine further the list of possible school sites for this study, the cohort
members examined the performance band scores of the school in regards to the CST
Algebra test for the years 2003-2005. The reason behind why the cohort chose
Algebra 1 CST scores for determining school site eligibility for this study is that
Algebra 1 is the gateway course into college and student future success. There are
five performance bands for the CST, and the cohort filtered the school site list by
examining whether schools had movement within bands. It was determined that only
school sites that had movement out of the bottom two bands of the CST that created
percentage increases in the school’s top two bands over a period of two years were
eligible for our study. Through analysis of school’s performance bands, the cohort
developed a smaller subset list of eligible school sites for the study that totaled 44.
The cohort then determined that for a school to remain eligible for our study,
it must have had a 0% decrease in the top two performance bands on the CST
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Algebra test, while continuing to have an increase of students scoring in the top
performance bands. This was a decision the group made because some schools on
the subset list had made gains in the top two performance bands; however, there was
also an increase in students scoring in the two lowest bands on the Algebra portion of
the CST. To be eligible to remain on the cohort’s school site list, the schools needed
to have zero change or a decrease in the lowest performance bands, while
simultaneously increasing the school’s two highest performance bands or having no
change in the top two bands. It was from this final list that a geographical
representation of eligible schools to study was created for the cohort members. Each
member then chose a school to study using this geographic map.
Once the cohort determined the research questions and frameworks, the
members decided upon which groups within the school site’s population sample that
they wanted to gather data and analyze for the study’s instrumentation. The cohort
identified the school stakeholders and population that would be beneficial to analyze
for the study such as key school leaders and teachers because they felt that they
would be able to give the cohort the most valuable information about how the school
was increasing their student’s mathematic achievement.
After IRB clearance, the cohort member made contact with the school. The
administrator over Mathematics instruction and the school principal gave the
researcher the proper authorization to begin the study at the school. Then, the
researcher proceeded to set up interview schedule dates with key leaders, teachers,
other staff members, and the questionnaire distribution methods. Through
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collaborative discussion, the cohort determined whom the stakeholders were at
school sites that needed to be interviewed and it was determined that the researcher
would interview the Assistant principal over mathematics instruction, the
mathematics coach, and other pertinent math teachers. The researcher interviewed
each participant one to three times to ensure reliability of the information collected
about the school. Each interview was approximately one half hour to one hour and
all interviews took place at the school site within school offices or teachers’ rooms.
The School District
The school selected for this study is located within beautiful South Beach
County. South Beach is composed of a conglomeration of several unified school
districts and cities. South Beach is nestled between the crevice of Los Angeles and
Orange County. The South Beach community is both simultaneously urban and
suburban with every city in South Beach containing an urban core surrounded by
several suburbs. Spacious beaches, panoramic views, and rolling hillsides surround
South Beach, and South Beach dwellers can see several Southern California
historical sites. The beaches give South Beach the air of a resort community with
metropolitan glamour. Many of the residents in South Beach have lived there for
generations, which give the community a feeling of the insularity of a small-town
bedroom community. Within the South Beach area there is a city called Malls.
Malls was incorporated in 1921, and is the largest city within South Beach.
Los Angeles County ranked Malls within the top 10 of its cities. Malls is a 25-square
mile city that has around 150,000 people. The property values in Malls are
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significantly above the average median home prices for Southern California because
Malls is known for its accessibility to beaches, safe community atmosphere, good
schools, and cosmopolitan shopping centers. Malls has its own police and fire
department, and also possess several hospitals and libraries. Malls thinks of itself as a
diverse city that is inclusive of all cultures with a strong global businesses market and
is a force in Los Angeles commerce market. Because of the many businesses in Malls,
the cities daytime population swells to around 200,000. Malls is one of the most
stratifying cities in South Beach because of its immense diversity and cultural pockets,
and strong pride the residents have within their different community sections of the
city.
Malls has its own school district called Directional Unified (DU) that was
established in 1947 and unified in 1948. DU’s school jurisdiction encompasses the
entire city of Malls, and has 17 elementary schools, eight middle schools, four
comprehensive high schools, one alternative school, three adult learning centers, and
one child development center. Where a student lives determines which school in DU
they attend. There are not many transfer rates between schools within DU, and
because DU’s school age population has been decreasing, there have been some
school closures within DU.
DU has a mission to ensure that every student within their school systems
succeeds to his or her potential, while continuing to be lifelong learners that
contribute to the international world. DU has five performance goals in which they
hold all school accountable. DU’s superintendent has served in many of the
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neighboring cities and has been a superintendent for almost two decades.
However, Malls just recently hired him last year. The DU school district is
composed of five board members, some of have not directly taught within the
educational system, but has consistently volunteered within educational boundaries
for over 20 years.
Selected School
The school site that was selected from within the DU system is North Pacific
High School (NPH). NPH opened in September 3, 1955 and is around 40 acres.
There are 21 buildings and 100 classrooms in NPH, and the school was extensively
remodeled in 1983. NPH is a comprehensive high school with 9-12 grades and
approximately around 2000 students. It has one principal, three Assistant principals,
and four counselors. The demographics for the school are 38.5% Asian, 1.6 Pacific
Islander, 3.1 Filipino, 21.6 Hispanic, 8.1 African American, and 30.1 White.
NPH receives their students from all the North residents of Malls. At one
time, many of the residents of North Malls were of an Asian background, but now
the demographics of North Malls are changing. North Malls is becoming more
Hispanic and the Asian students are going to West and South Pacific High Schools.
North Malls is not as fashionable of a place to live in as West or South Malls because
North Malls is farther away from the ocean. The housing prices are cheaper in North
Malls, and North Malls is considered by those in South Beach to be urban, while
West and South are considered suburban.
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Participants in the Study
The study triangulated several sources of data and information from NPH.
Triangulation of sources was necessary because the qualitative case study aspect of the
research needed support in order to increase the study’s reliability and validity. The
school shared several important documents with the researcher that helped give the
study valuable insight information as to school culture, process, and policy. These
documents also support information that was shared through the researcher’s interview
process with key educational school leaders.
The principal, the assistant principal over mathematic instruction, the
mathematics department chair, and several math teachers participated in the study. All
participants were very helpful in giving the researcher information about the school,
related to the research focus of the study.
School Site Administrators. The administrators at NPH are the principal and
two assistant principals. NPH’s principal is the educational head of the school and
determines the school’s overall vision and focus. However, the assistant principal over
mathematics instruction creates the school’s vision and focus for the math department
with the help of key instructional math leaders. The first interview was to inform the
assistant principal about the study and to ask preliminary research questions pertaining
to the school, the community, the district, and the principal’s background. The second
interview was more in-depth about aspects of the school, the mathematics programs,
the mathematics department, and a clarification of information that was or was not
presented in the first interview. The principal was also interviewed for the study. The
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principal’s assistant principals are invaluable members of her instructional
leadership team. The principal has given each of her assistant principals’ duties that
encompass not only instruction, but involve other school activities such as sports,
clubs, and daily school operations.
Teacher Leaders. The assistant principal over mathematics instruction was an
incredible source of information because he was able to introduce the researcher to
some of the key mathematical leaders at the school. NPH’s significant teacher leader
is the mathematics department chair, and she is an essential part of the instructional
leadership that helped raise their student’s achievement scores in Algebra 1 on the
CSTs. Another significant teacher leader is a mathematics teacher who previously was
an assistant principal for NPH.
Classroom Teachers. NPH also has some exceptional mathematics teachers
that are seen as instructional leaders for the school. The classroom teachers are also an
essential factor as to why the mathematics scores of the school are increasing. They
ensure that students are learning the curriculum, and they implement the school’s
educational policies. NPH’s math teachers are unique in that most of the teachers
teach both traditional and nontraditional math classes. These teachers were given
surveys because they are the closest to understanding the true reasons behind their
student’s successes in mathematics.
Instrumentation
Eleven doctoral education candidates, under the guidance of the dissertation
chair Dr. David Marsh, Associate Dean of the Rossier School of Education
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Academic Programs at the University of Southern California, developed the
instrumentation that is used in the study. The members split into four separate
teams, each working independently on a single piece of instrumentation for the
study. Before data collection began in the Fall of 2006, the team members debated
and refined the final instruments that were used for collecting the data from the
multiple school sites. The data instruments went through several variations through
the refining process. The data instrumentation and the research questions
relationships are represented within the matrix below in Table 1.
Table 1: Data Collection Instruments and Research Questions Relationships
RQ 1 RQ 2 RQ 3 RQ 4 RQ 5
School Profile X X
Leader
Interview
X X X X
Teacher
Interview
X X X X
Teacher
Questionnaire
X X X X
Frameworks for Instrument Design
The cohort created four conceptual frameworks that are the basis for the
group’s data collection for the school sites. The four conceptual frameworks are
illustrated in Appendices F through I. In a doctor of philosophy study, the
researcher develops the frameworks and then determines his or her research
questions from the analysis of the frameworks. However, in our problem of study,
it is more feasible for us to first determine our research questions and then proceed
to create the frameworks for the study. That is why our cohort members developed
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the study’s conceptual framework after determining the research questions.
There was a whole cohort discussion about what types of conceptual
frameworks the study needed. The cohort felt that four conceptual frameworks
were sufficient for this study, and broke into groups of three or four to decide upon
which educational research was necessary to develop the frameworks. Each
framework group made several revisions of the framework and then presented the
frameworks to the entire cohort. Instruments for data collection and conceptual
frameworks are discussed below.
Conceptual Framework A. The first conceptual framework is Figure 1 the
framework for effective school design (Appendix F). The framework for school
design encompasses both school design and a basis for analyzing math programs.
This framework is based upon the work of Marsh and Codding and their school
design model. The curriculum section of the model focuses is student-centered. The
curriculum of the school’s program is has a strong focus on student outcomes, so that
students are construction and creating their own learning. The elements of the
curriculum section of Marsh and Codding’s model are:
1. School-to-centered applications
2. Constructivist Knowledge
3. Based on student outcomes
The second part of Marsh and Codding’s model is school culture. Successful
school cultures are where positive and meaningful interactions are happening
between students, teachers, administrators, staff, and the community, and there is
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active learning and participation by all stakeholders involved with the school.
Meaningful and continuous professional development is also a significant factor in
creating a school culture that is successful because professional development affects
every area of learning and engagement between all stakeholders at the school. To
create a successful school culture, Marsh and Codding feel that these three elements
are taking place at the school site:
1. Ongoing professional development
2. Meaningful staff student reaction
3. Based on enhanced learning
The third section of Marsh and Codding’s model is learning activities. Marsh
and Codding have a constructivist view about learning activities, which is
represented in their curriculum section of the model. Marsh and Codding believe
that successful school designs have learning activities that create an environment in
which students are consistently pushed to think and function at their highest brain
levels, such as evaluation, judgment, and creation. Marsh and Codding stress that
problem-solving activities are a venue for students to use their higher order thinking
strategies, and that collaborating with others is a successful technique in learning
activities that bring out the highest thinking levels in students. There are also three
parts to the learning activities section:
1. Challenges student thinking
2. Collaborative
3. Student solve problems
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The final section on Marsh and Codding’s model is student performance
assessments. Student performance assessments are usually authentic and creative.
They are based on mastering a subject or topic. Student performance assessments
are usually not traditional or typical in nature, but created specifically so that
students can demonstrate their learning. There are three sections to the student
performance assessment portion of Marsh and Codding’s model:
1. Capture conceptual understanding
2. Capture problem-solving
3. Capture communication skills
Figure 1 – Framework for Effective School Design
School
Design
Curriculum Learning
Activities
Challenge
Students to
Think
Students
Solve
Problems
School
Culture
Based on
Enhanced
Learning
Meaningful
Staff-Student
Interactions
Ongoing
Professional
Development
Collaborative
School-to-Career
Applications
Constructivist
Knowledge
Based on
Student
Outcomes
Student Performance
Assessments
Capture
Conceptual
Understanding
Capture
Problem
Solving
Capture
Communication
Skills
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Conceptual Framework B. The second conceptual framework for the study
is effective math programs. The effective math program’s graphic is illustrated in
Figure 2 (Appendix G). Figure 2 illustrates that effective math programs have three
elements that make them successful and effective: standards-based instruction,
classroom practice, and curriculum design. Each of these elements has sub-sections
that go into further detail about the topic. The graphic begins with standards-based
instruction, which is essential to any successful math program. Due to the advent of
standards-based instruction and the NCLB requirements, the basis of every
mathematics programs must stem from standards. Within the standards-based
instruction section there are three sub-sections:
1. Assessments aligned to standards
2. Student achievement data drives instruction and decision
3. Common performances rubrics through collaboration
Most schools have developed a standards-based math program, but for it to
be effective, schools must have not only the classroom practice and assignments
aligned to standards, but the assessments must also be aligned. Successful schools
go one-step further than just aligning their assignments, assessments, and classroom
practices to standards, they take the data they receive from the assessments and use it
to inform their instruction and decision-making processes. It is crucial that schools
reflect on their data, and it is easier to do when the entire math department is in a
process of collaborating with each other through common performance rubrics,
assignments, and assessments. All three elements are important factors for
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successful schools; however, each element works in tandem with the other to
produce an effective mathematics program.
The second part of an effective math program is curriculum design. The
curriculum design section of the graphic has six elements:
1. Student-centered curriculum
2. Driven by learner outcomes
3. Emphasizes Conceptual
4. Focuses on problem-solving
5. Incorporates current learning theory
6. Scope and sequence is supported by learning theory
It has been discussed early that student-centered learning is important in
creating a successful curriculum, and that it should have a constructivist base focused
on learner outcomes. However, what has not yet been discussed as an important
element that makes math programs successful is that math programs should
emphasize concepts. Conceptual understanding of mathematics is crucial, and
effective math programs are designed to give student’s multiple opportunities in
various learning modalities chances to fully understand and comprehend
mathematical concepts. TIMSS illustrates this point in their comparison of
mathematics classrooms and programs in the United States versus those in Japan.
The Japanese students had significantly higher scores and achievement in
mathematics than American students and TIMSS believes that it is due to the idea
that the Japanese mathematics curriculum is built upon an emphasis of conceptual
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mathematics, while the American mathematics programs emphasize procedural
mathematics knowledge.
The third section of successful math design is classroom practices. There are
four elements of classroom practice:
1. Effective and coherent lesson design
2. Promotes high levels of student engagement
3. Makes use of prior knowledge
4. Cultural relevance
What makes an effective mathematics classroom is inherently what makes
any classroom effective. The teacher’s practice must be based upon theoretical and
pedagogical knowledge. The lesson plans must be standards-based, but effective in
the sense that students can follow and understand elements of the lessons. The
lessons must be built upon higher order thinking principals, and there should be
many problem-solving activities such as Marsh and Codding suggest. Marsh and
Codding and TIMSS emphasize that effective math programs have students
participating in collaborative projects that are real-world, authentic, and take into
account culturally relevant pedagogy.
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Figure 2 – Effective Math Programs
Conceptual Framework C. The third conceptual framework is Figure 3,
Bolman and Deal’s Four Frames (Appendix H). Figure 3 is from Bolman and Deal’s
Reframing Organizations (2003). Bolman and Deal’s frames are built to help leaders
understand and navigate through their intricate and complex workplace. The book
not only describes the four frames, but goes in-depth about how to work within your
current frame so that your workplace is effective and provides you with the
maximum benefits. The study transplants Bolman and Deal’s four frames structural,
human resources, political, and symbolic, and uses the fames as reflective tools to
understand the process by which the key instructional leaders at the school site
increased their student’s mathematics achievement.
Effectiv
e Math
Progra
Classroom Practices
ο Effective and
coherent lesson
design
ο Promotes high
levels of student
engagement
ο Makes use of prior
Curriculum Design
• Student-centered
curriculum
• Driven by learner
outcomes
• Emphasizes Conceptual
• Focuses on problem-
li
Standards Based
Instruction
ο Assessments
aligned to
standards
ο Student
achievement data
drives instruction
99
The first Bolman and Deal frame is the structural frame. The elements of
the structural frame are top down hierarchies, rules, policies, procedures, specialized
tasks, goals, and objectives. The structural frame is about consistency of
configuration and organization. Following the rules of procedure and policies are the
foundations of the structural frame. A structural leader is top down and hierarchical
similar to military structure. Everyone in the organization has their specific job and
task, and the delineation between supervisor and employee is clear and precise.
The second frame for Bolman and Deal is human resources. The name
human resources has evolved in recent history. In the past, human resources was just
the personnel department, but because it fulfills so many different roles now for
employees, the wording has changed to human resources or human relations. The
elements of human resources are employees as partners and family, people of the
organization, collaboration, groups, and self-actualization. A human resource leader
is one that sees his or her employees as being part of a team and family. Most
projects are collaborative, and the duties of the employees are not as task-specific as
the structural frame. There is a strong emphasis in this frame concerning
relationships. Maintaining positive and fulfilling relationships is the foundation of
the human resources frame.
The third frame is the political frame, which consists of elements such as
power, bargaining, competition, resources, and negotiations. The political frame can
be characterized by the current American political system. There are parties and
factions, and each group or person is attempting to subvert the other group in order
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to gain more resources and power for themselves or their party. The political
frame is encapsulated by the word power, in that the political frame is all about
power. A leader using the political frame is using their energy to gain as much
power as possible to control the organization through networking, access or denial of
resources, competition, and bargaining.
The fourth Bolman and Deal frame is the symbolic frame. The symbolic
frame has elements such as vision, belief, faith, and story telling. A leader using the
symbolic frame usually incorporates a lot of story telling when they are speaking to
their organization. They enter the organization with a vision, or they help the
organization create a new vision. The leader wants those in the organization to
believe in the entity and uses tools such as story telling to elicit faith from the
congregation. The symbolic leader can be seen as the preacher leader for the
organization, trying to get the organization to fulfill the created vision or ideal.
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Figure 3 – Bolman and Deal’s Four Frames
Frame Structural Human
Resources
Political Symbolic
Metaphor for
organization
Factory or
Machine
Family Jungle Carnival,
Temple,
Theater
Central
Concepts
Rules, Roles,
goals,
Policies,
Technology,
Environment
Needs, Skills,
Relationships
Power,
Conflict,
Competition,
Organizational
politics
Culture,
Meaning,
metaphor,
ritual,
ceremony,
stories, heroes
Image of
Leadership
Social
Architect
Empowerment Advocacy Inspiration
Basic
Leadership
Challenge
Attune
Structure to
task,
Technology,
environment
Align
Organizational
and human
needs
Develop
Agenda and
Power Base
Create Faith,
Beauty,
Meaning
Conceptual Framework D. The fourth conceptual framework is instructional
leadership. Figure 4 is the illustration of the instructional leadership concept
(Appendix I). This figure is based on the works of Blasé and Blasé (2004), Johnson
(2002) and Hessel (2002). It also combines some elements from the California
102
Department of Educations principal standards. There are five different elements
to the instructional leadership graphic:
1. Vision for learning
2. Supervision and monitoring instruction
3. Community and political
4. Culture of teaching and learning
5. Data driven decision-making analysis
Blasé and Blasé (2004) influences the instructional leadership graphic
because they discuss in their book ways in which instructional leaders have visions
for learning and supervision and monitoring instruction. Their book gives first hand
examples from teachers and staff members of ways in which the instructional leader
or principal was effective in communicating his or vision with the school, and
successful ways in which principals can monitor and supervise staff and teachers
without making the task seem contrite, meaningless, or demeaning. Some of the
ways Blasé et al. aims to create an environment of vision sharing, communication,
and how to properly supervise and monitor instruction is through collaborative works
between the instructional leader and teachers. They also suggest that the
instructional leader create a safe and positive culture and environment for teachers to
feel that they are a significant and appreciated part of the instructional learning
process. Blasé et al. also indicate that the instructional leader should create a
professional learning community at the school site. The professional learning
community will act as a support network for both the teachers and the instructional
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leader, in which the collaboration and communal efforts towards goals will take
place.
Johnson’s (2002) piece contributes to the figure by the data decision-making
and analysis component and the culture of teaching and learning. Johnson discusses
significantly in her book about how instructional leaders can find ways in which to
help their school begin using data to drive their decision-making process, and that
the data should be informing the teaching and learning processes at the school.
Johnson illustrates ways in which instructional leaders can create positive
environments in order to have the proper dialogues about data because she feels that
data is what instructional leaders should be focusing on in this day and age of
standards-based education. Johnson wants instructional leaders to understand how
data is a powerful tool they can use at their school site, and how they use data
informs school culture.
Framework for the First Research Question. The first research question is
“What was the pattern of math achievement for various students at the school?”
The school profile is the framework for the first research question. The school
profile illustrated the areas where students were achieving in mathematics. The
profile provides the researcher with a chance to see patterns within the school that
might not otherwise be seen if the data was not disaggregated to show student
increases in math.
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Figure 4 – Instructional Leadership Framework
Instructional Leadership Framework
What an effective leader must have knowledge of…
Vision for Learning Supervision and
monitoring of
instruction
Community and
Political
Culture of
Teaching and
Learning
Data Driven
Decision Making
Analysis
1.0--Facilitates the
development,
articulation,
implementation, and
stewardship of a vision
of learning that is
shared and supported
by the school
community.
A- Developing vision
B- Communicating
the vision
C- Implement the
vision
D- Monitor and
evaluate the vision
E- Addresses
obstacles to vision
implementation
and realization
Observes and
monitors
instructional
program. Provides
constructive
feedback in a
timely manner to
all teachers.
A-Classroom
observations
on a
daily/weekly
basis.
B- Allocates
resources
ensure
successful
teaching and
learning.
*time
*peer support
*materials
*professional
development
C- Supervision of
personnel
D- Hiring of
personnel that
supports the
learning goals
and vision of
the school
4.0--Collaborates
with families and
community
members, responds
to diverse
community
interests and needs,
and mobilizes
community
resources.
A- Understands
the value of
diversity
B- Understands
communities
needs
C- Involves
community in
the school
D- Provides
opportunity for
community
involvement
2.0 Advocates,
nurtures, and
sustains a school
culture and
instructional
program
A- Valuing of
students and
staff
B- Developing and
sustaining the
culture
C-Culture that is
inclusive of
and respectful
of diversity
D- Implements
practices for
culturally
relevant
teaching and
learning
E-Celebrates
students,
teachers and
staff
Uses data as a tool
for informing
instruction and
supporting student
learning
A- Utilizes
assessment data
to place
students
appropriately
B- Formative
benchmark
school site
assessments
C- Summative
standardized
assessment
D- Disaggregate
data by
students, classes
and cohorts
E- Use data to
guide and
improve
teachers
instructional
program
F- Use data to
create master
schedule
G- Using data to
inform and
improve pacing
instructional
plans
Framework for the Second Research Question. The second research question
is “What policy initiatives as well as curriculum, instruction and related conditions
seem to be related to improved math achievement at the school?” To answer this
research question, two frameworks were designed. The first framework is about
effective math programs, and so the effective math program graphic, Figure 2 was
developed. The second framework built to answer this question was the effective
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school design, Figure 1, based on Marsh and Codding’s model. The question is
two fold because it depends upon the school site whether it was the math curriculum,
the policy initiatives, the instruction, or all three that were increasing the student’s
math achievement.
Framework for the Third Research Question. The third research question is
“What change process did the school use to enhance its math program and strategies
to assist students in math?” The framework that was used to answer this question is
Bolman and Deal’s four frames (2003). The study is trying to determine what
change process occurred within the school for their student’s math scores to rise, and
the researchers felt, based upon Blasé et al. that change occurs through instructional
leadership. The researchers felt it necessary to understand how the school changed
by increasing the student’s mathematics achievement through the lens of the school’s
instructional leader(s). The frames help answer the research question by giving the
researchers the basis by which to analyze the instructional leaders processes or basis
for changing the school.
Framework for the Fourth Research Question. The fourth research question
is “To what extent was strong instructional leadership important in improving: a) the
math programs/strategies and b) math achievement among students?” To answer this
research question, the instructional leadership framework was developed. The
instructional leadership framework helps determine to how effective or successful
the instructional leader was in initiating and sustaining the change process that
increased the school’s mathematics achievement scores. The graphic provides the
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researchers with a basis for judging how effective the instructional leaders
policies and practices were at the school site. It helps the study determine whether
the change occurred due to the instructional leader, and if so, what did they do; it
also helps determine if the change occurred in spite of the instructional leader.
Framework for the Fifth Research Question. The fifth research question is
“How did leaders in the school resolve dilemmas about instructional leadership?”
The first framework for the fifth research question is the principal assessment
(Appendix K). The principal assessment determines how much the principal is
aware of the school’s math program and or do they possess an expertise in
mathematics. The graphic was developed using California’s standards for a highly
qualified teacher. The second framework to help answer the fifth research question
is Appendix L. This figure gives strategies and approaches based on educational
literature on how a leader unfamiliar with a subject matter can still be effective.
Data Collection Instruments
There are four data collection instruments for this study that were based upon
the conceptual frameworks. The instruments are the teacher questionnaire (parts A
and B), the key instructional leaders’ interview guide, the teacher interview, and the
school profile. The teacher questionnaire has two parts (Appendices A and B).
Instrument 1: Teacher Questionnaire. The first questionnaire (Appendix A)
is a scaled survey with 1 being strongly disagree and 5 being strongly agree. This
questionnaire has 25 questions and all of the teachers in the school. The second
teacher questionnaire (Appendix B) is also a scaled survey with 1 being strongly
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disagree and 5 being strongly agree. However, this questionnaire has 48
questions and goes more in-depth into the mathematics program at the school
because this questionnaire is specifically for the mathematics teachers at the school.
The teacher questionnaires were developed for the study because the
researchers needed to have a tool in which to collect information pertinent to the
study’s research questions. The interviews were delivered to the teacher’s school
site, and teachers were asked to complete the questionnaires in a timely manner, so
that the researchers can learn about what factors teachers felt attributed to their
students’ mathematics achievement. The questionnaires were configured to ensure
that each of the research questions was addressed. The researchers developed the
questionnaire with the belief that it would take no longer than 30 minutes to
complete.
Instrument 2: Key Instructional Leader Interview Guide. The second
instrument for the study is the key instructional leaders’ interview guide (Appendix
D). This interview guide is specifically for the research interviewing the
instructional leader(s). Similar to the teacher questionnaires, the interview guide
leads the researcher through all the study’s research questions. The instructional
leaders’ interview guide can be used by the researcher for both administrators and
teachers. There may be instances in a school where the school has teacher leaders
such as mathematics coaches and department chairs, who are not administrators, but
qualify as instructional leaders. The cohort felt it necessary to create an interview
guide because it provides the researchers with more in-depth qualitative information
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than the other study’s instruments. The interview guide will give researchers the
true voices and perceptions of the school and its culture.
The instructional leaders’ interview guide is taken from Creswell’s (1998)
book. It is made up of open-ended questions, which each section of questions
relating to specific research questions for the study. The entire interview process
should take the researcher no more than 40 minutes. However, if the instructional
leader feels the need to elaborate on any of the questions, the interview is allowed to
take as much time as needed.
Instrument 3: The Teacher Interview Guide. The teacher interview guide is
the third instrument for the study (Appendix D). The teacher interview guide,
similar to the instructional leader guide is built to answer specific research questions
for the study. Teachers were interviewed with the interview guide to find out what
information they could share with the researchers to determine why the school was
having success in mathematics. The teacher interview guide is designed to take
approximately 30 minutes, with the interviewee answering several open-ended
questions. The interview process is allowed to take longer if the interviewee wants
to elaborate on any of the questions. Similarly to the instructional interview guide,
this interview guide is also based on Creswell.
Instrument 4: The School Profile. The school profile is the fourth instrument
for the study (Appendix J). The school profile was design to provide the cohort with
information about a school’s specific features and characteristics. Through
collaborative efforts, the cohort determined what characteristics of a school would be
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pertinent to the study, and these were put into the school profile. There were
three elements of the school profile: student performance, demographics, and
general school information. A significant part of the data for the school profile was
found on the California Department of Education’s website.
Data Collection
This study’s data was collected from September to November 2006 because
the cohort had not cleared Institutional Review Board (IRB) until September. There
were three rounds of data collection, so that all researchers were given ample time to
collect data in multiple rounds, review and analyze the collected data to ensure that
the collected data was accurate, and to maximize the number of participants for the
study. All study participants were afforded the opportunity to examine notes taken
from their interviews with the researcher to make certain that their words, responses,
and opinions were accurately portrayed in the study, and interviewees were once
again assured that the information gathered from them by the researcher would not be
shared with anyone outside of the cohort or those at their school site. In addition, the
extra rounds provided researchers with the opportunity to gain further understanding
about the school site, the reasons behind the success, and to triangulate all the data
and information.
The IRB process is one of the most important steps for the study’s data
collection because it affords the participants the great protection against undue harm
for their involvement with a study. IRB protects participants by setting up rigorous
tests for researchers that they must pass in order to begin their research at a specific
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site such as what are proper research methods, what is the methodology of the
study being conducted, and what are the proper data collection procedures, methods,
and policies. Then, the study’s methodology and data collecting processes were
presented to an IRB panel to await approval. Once approval was given to the study,
the researchers began the task of selecting a school sites in which to perform their
study from the qualified school sampling criteria list so that they could begin the data
collecting process. Once the sites were contacted by the researchers, they were given
the site approval form to sign and give back to the researcher. Participants were
again made aware that participating in the study was voluntary and an informational
leaflet was distributed to everyone at the site.
During the initial round of data collection, questionnaires were distributed to
participants in the study for them to complete and return to the researcher at a
designated date during the research window. Math teacher questionnaires were
distributed. It was during the initial round of data collection that interviews were
scheduled with specific participants. However, the first round of data collection is
where the first interview with the Assistant Principal took place. This first round is
where the researcher gained a preliminary overview of the school and its culture.
The second round of data collection involved picking up the math teacher
questionnaires and distributing the all teacher questionnaire. This is where the initial
interview with the Math Department chair took place, and a second brief interview
with the Assistant Principal took place. The researcher asked both participants how
they would characterize the school environment and culture, and the researcher
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received an information packet about the school developed by the school that
contained such items as school newsletters (current and past years), fliers, and
parental informational leaflets. Informational leaflets about the study were again
redistributed to all non-mathematics teachers and other non-mathematical related
staff, informing them about the study and that they had the right not to participate. In
this round, the researcher gained greater insight into the school operations,
functionality, procedures, atmosphere, and culture.
The third round of data collection involved the researcher returning to the
school for in-depth interviews with the Assistant Principal, the Math Department
chair, and two math teachers. The researcher continued to pick up math teacher
questionnaires, but also began collecting non-math teacher questionnaires. All
completed questionnaires retrieved by the researcher were compiled into a
spreadsheet database (see Appendix J). The purpose of this round of data collection
is the clarify information previously collected and to gain even further insight into
the school and its mathematical success.
The fourth round of data collection involved the researcher following-up with
the Assistant Principal, Math Department chair, and the first two math teachers
interviewed. This round is where the rest of the math teacher interviews were
completed and all the teacher questionnaires were retrieved. Brief interviews were
also conducted in this round with the clerical support staff of the Assistant Principal
and the Principal. This was the closing follow-up for the Math Department chair.
In the final round of data collection, the researcher performed the final
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closing follow-up with the Assistant Principal, the math teachers that were
interviewed in round four, and the clerical staff of the Assistant Principal and the
Principal. This concluding data collection round gave the researcher a chance to
clarify with the participants the following steps in the study, to ensure that their
statements are accurate, and to provide them contact information of the researcher in
case they determine that they want to alter any part of their interview with the
researcher in the future.
Data Analysis
The purpose of this study was to develop an understanding of how a school
effectively raised their students’ mathematic achievement through instructional
leadership. The cohort developed five research questions as the study’s guide.
Frameworks were created to align with the five research questions in order for the
researchers to correctly and accurately collect data and information from the school
sites with the data instruments.
IRB clearance was granted to the cohort, and data collection took place at the
school sites. The researcher used a computer to transcribe interviews with the
participants. All notes from these interviews were shown to the participants for
clarification and verification. Notes from the interviews were shown to the
participants, and questionnaires were collected by the researchers. During the follow-
up interviews with participants, the researcher asked questions pertaining to common
emerging themes from the interviews. All information gathered from the site is
correlated with the frameworks of the study. A spreadsheet was created for the
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questionnaire results and shared with the other researchers in the cohort. To ensure
reliability and validity common patterns in the data were then discussed and analyzed
by other cohort members.
Validity and Reliability
To ensure the study’s validity and reliability the cohort used various data
collection methods, approaches, and numerous informational sources were then
triangulated with other data sources derived from the school site and with other cohort
members. The data collection methods were also scrutinized by the cohort and
received IRB clearance. The information found in the questionnaires was compared
with the interviews. Participants had a significant period in which to check the validity
of their interview responses. The researcher also increased the validity and reliability
of the study by going to the school site several times to ensure the proper distribution
and collection of data, to perform all interviews, to ensure accuracy of the statements
given by the interviewees, retrieving multiple sources of data from all pertinent school
sources, triangulating all that data to share with fellow cohort researchers to minimize
researcher bias. However, it is important to note that due to the scope of the study,
generalizations of a larger scope are difficult to draw because the study focuses on
only one school site.
Conclusion
This chapter illustrated the sampling criteria and process, conceptual
frameworks, instrumentation, data collection, and data analysis performed in this
study. The chapter explains the research studies methodology. The cohort
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collaborated on every aspect of the study’s methodology—development,
processing, and review. Dr. Marsh oversaw every step of the methodology section,
and was the creative force behind the IRB approval for the cohort. IRB approved the
cohort’s study, and IRB approved the research study at North Pacific High. The data
was collected, analyzed, verified, and triangulated by the researcher, cohort, and Dr.
Marsh. Study findings are presented in Chapter 4.
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CHAPTER 4
FINDINGS, ANALYSIS, AND DISCUSSION
Chapter 4 presents the findings, analysis, and discussion of data that collected
for the research questions in this study. The five research questions, the conceptual
frameworks, and the study instruments aid in explanation of the findings of this case
study. The case study explored why the mathematic achievement scores at Pacific
North High (PNH), a diverse comprehensive high school, continued to rise, while
students’ math scores in Directional Unified (DU) and other nearby school districts
were stagnant or declining. To explore fully the change that took place within the
school that generated such an increase in math performance by the students, it is
helpful to understand the factors that produced the increase in scores. Furthermore,
an additional focus directed at discovering the role the leader played in the growth of
the students’ achievement, and how the leader accomplished the task of increasing
math scores when they do not possess an expertise in mathematics. The findings in
this study are from collected data using case study methodology, and five research
questions are used to present the findings in this chapter:
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 improve 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?
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4. To what extent was strong instructional leadership important in
improving a) the math programs/strategies and b) math achievement
among students?
5. How did leaders in the school resolve dilemmas about instructional
leadership?
The four instruments that were used to collect data from the school site were
detailed in Chapter 3: (1) The Teacher Questionnaire parts A & B (Appendix A &
B); (2) Teacher Interview Guide (Appendix C); (3) Key Leader Interview Guide
(Appendix D); (4) School Profile (Appendix J). There were multiple sources of data
collected from the school site for this study: such as interviews with three
instructional leaders, four mathematics teachers, one special education teacher, and
two classified staff that support the instructional leaders, teacher questionnaires,
informal observations, school site documents, documents from the district, artifacts,
and reports from the State and County websites.
After the data collection, the USC cohort exchanged their individual school
site data for analysis by other cohort members in order to ensure validity of the
research, and to gain further insight into the data such as common themes
represented throughout all cohort members’ data. The layout of this chapter is as
follows: the first section of the chapter presents the research findings through the
lens of the research questions; the second section of the chapter detailed the
discussion and analysis of the findings delineated by research question.
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Data Findings
Research Question 1: Patterns of Mathematics Achievement
Research question one was, “What was the pattern of Math achievement for
various students at the school?” In exploring the issue of Pacific North High’s
(PNH) pattern of math achievement, there arose two broad topics for analysis:
PNH’s overall mathematic demographics with a focus on PNH’s California
Standards Tests (CSTs) Algebra I scores and PNH’s California High School Exit
Exam (CAHSEE) math scores. In order to understand PNH’s patterns of math
achievement, it is imperative to examine subtopics that converge to compose PNH’s
math achievement patterns: PNH’s math scores in comparison to state averages and
like schools; the numbers of PNH students that take or pass the Advanced Placement
(AP) math exams; and the ethnic demographics of PNH’s math classes, passage
rates, and graduation rates.
PNH’s Overall Mathematic Demographics
In order to have a context upon which to understand PNH’s math
achievement, the study compares the state’s tests with PNH’s scores. California
judges schools using two calibers of measurement: the CST and the CAHSEE. Both
tests have median scores in which schools use as a standard for comparisons between
themselves and the state expectations or between themselves and other California
schools.
CST. The birth of the Standardized Testing and Reporting (STAR) began in
1997 with Governor Pete Wilson signing legislation that “required testing all
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students in grades two through eleven in English-language arts and mathematics,
grades two through eight in spelling, and grades nine through eleven in science and
history-social science” (CDE, 2006, p. 2). In 1998, testing turned into the Stanford
9, a national norm-reference test. In 1999, the test underwent modification to align it
with the California English and math standards. In 2003, all CST questions were
separated from the Stanford 9, and California students were only answering
standardized test questions that were derived from the California state standards.
Today, the CSTs have four components: the California Standardized Tests (CST),
the California Alternate Performance Assessment (CAPA), the California
Achievement Tests (CAT/6), and the Aprenda (CDE, 2006). Five distinct bands
represent students’ performance levels on the CST: far below basic, below basic,
basic, proficient, and advanced. For the purposes of this study, the study only
references one of the four CST components, the California Standardized Test.
CAHSEE. The CAHSEE is an exam that began in 1999 with a law that
requires all California public school students to pass the examination in order to
attain a diploma. The CDE states: “The purpose of the CAHSEE is to improve
student achievement in high school and to help ensure that students who graduate
from high school can demonstrate grade-level competency in reading, writing, and
mathematics” (CDE, 2006b, p. 1). There are two parts of the exam: ELA and math.
Both portions of the exam derive their questions from the California state standards.
The ELA portion of the exam is multiple-choice but also has a writing section. ELA
tenth grade standards and lower is the foundation of the exam. The Math portion of
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the exam is all multiple-choice: “It includes statistics, data analysis and
probability, number sense, measurement and geometry, algebra and functions,
mathematical reasoning, and Algebra I. Students must demonstrate computational
skills and a foundation in arithmetic, including working with decimals, fractions, and
percentages” (CDE, 2006b, p. 2). Students have several chances to pass both
portions of the exam, beginning with their first chance in tenth grade. Students must
pass both sections of the exam in order to qualify for a diploma.
State, County, and PNH CST Data. For the purposes of this study, anytime
the study referenced data, it is mathematical data, unless otherwise stated. It is also
important to note that due to the period of this study, the gathering of statistical data
is only from the years 2003 to 2005. Table 2 presents the statistical data from the
2003 to 2005 Mathematics section of the CST for the state of California, the County
of South Beach, and the high school Pacific North. The table shows the statistical
data of the state, South Beach County (SBC), and PNH in relation to the CST’s eight
elements: the number of students that took the math CST for that particular year; the
percentage of students’ enrolled at PNH, in the county of South Beach, and in the
state of California that took the test; the mean scaled score from tested students,
percentage of students that scored in the advanced, proficient, basic, below basic,
and far below basic categories on the CST for that year.
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Table 2: State, SBC, and PNH Ninth Grade Algebra 1 CSTs 2003-2005
2003 State SBC PNH
# Students Tested 187396 50357 176
% of Enrollment 37% 34% 33%
Mean Scaled
Score
306.1 297.3 292.4
% of Advanced 2% 1% 1%
% of Proficient 17% 13% 7%
% of Basic 32% 27% 33%
% of Below Basic 34% 38% 41%
% of Far Below
Basic
15% 20% 18%
2004 State SBC PNH
# Students Tested 222333 67479 194
% of Enrollment 43.1% 45.4% 33.5%
Mean Scaled
Score
301.2 292.1 291.6
% of Advanced 1% 1% 1%
% of Proficient 14% 10% 6%
% of Basic 29% 24% 30%
% of Below Basic 43% 47% 54%
% of Far Below
Basic
13% 18% 10%
2005 State SBC PNH
# Students Tested 248498 76174 210
% of Enrollment 46.4% 49.4% 36.5%
Mean Scaled
Score
304.2 294.3 302.1
% of Advanced 1% 1% 0%
% of Proficient 15% 11% 9%
% of Basic 33% 27% 39%
% of Below
Basic
37% 42% 45%
% of Far
Below Basic
14% 19% 7%
In 2004, PNH still had higher percentages of students placing in the basic
category than the state and SBC, but it also had the highest percentages of their
students placing in the below basic category as well. However, in 2004, PNH only
had the smallest number of students in the far below basic. PNH’s went from having
121
18% of the school’s students place in far below basic in 2003 to having only 10%
of students in the lowest quartile in 2004. This is a decrease of 8% of their far below
basic students in only one year. Whereas, the state and SBC had only a 2% decrease
in that category, PNH had 8% less students than the county of South Beach and 3%
less students than the state in the lowest quartile.
In 2005, even though PNH lost its 1% margin in the advanced category, the
school’s percentage points in the proficient category increased by 2%. Another
increase for PNH occurred in the basic category. From 2004 to 2005, the percentage
of PNH students scoring in the basic category increase by 9%, making the total
students scoring in the basic category 39% instead of 2004’s 30%. In the below
basic category, PNH’s percentages dropped from 54 to 45, a 9% decrease.
However, the most significant trend for PNH from 2003 to 2005 in Table 2 is
the significant gains the school made over the state and the county of South Beach in
the far below basic category. PNH has only 7% of its students in the far below basic
category in 2005; whereas, SBC has 19% and the state has 14% that means that PNH
has 12% less students than SBC and 7% less students than the state placing in far
below basic. In addition, PNH has the only far below basic percentages from 2003
to 2005 where the percentages have not increased in that quartile. From 2003 to
2005, PNH has had an 11% decrease in its far below basic students on the Algebra 1
Math CST.
CAHSEE State, County, and PNH Data. Tables 3 through 8 present the
CAHSEE data of the state, county, and PNH. Each year has two tables. Tables 3, 5,
122
and 7 have California, South Beach County, and Pacific North High School’s
information disaggregated by number of students tested and number of students that
passed the CAHSEE test with six classifications: all students, Special Education
students, English Language Learners (ELLs), Redesignated Fluent-English Proficient
(RFEPs), Socio-economically Disadvantaged (SED), and not Socio-economically
Disadvantaged NSED students. Tables 4, 6, and 8 have ethnic and gender
California, SBC, and PNH information disaggregated by number of students tested
and number of students that passed the CAHSEE test with ten classifications:
female, male, African American, American Indian, Filipino, Asian, Hispanic/Latino,
Pacific Islander, White not of Hispanic Origin, and Unknown students.
Table 3: State, County, School with CAHSEE Math Results 2003
Group All
Students
Special
Ed.
ELLs RFEPs SED NSED
State #Tested 725,123 76,300 157,811 74,763 264,279 444,496
Passed 314,540
(43%)
10,960
(14%)
35,170
(22%)
36,534
(49%)
81,695
(31%)
228,034
(51%)
South
Beach
#Tested 204,711 17,726 52,427 40,662 98,516 102,686
Passed 75,330
(37%)
1,853
(10%)
10,677
(20%)
17,872
(44%)
29,126
(30%)
45,350
(44%)
PNH #Tested 765 87 96 51 163 602
Passed 467
(61%)
16
(18%)
37 (39%) 44
(86%)
78
(48%)
389
(65%)
Table 4: State, County, School with Gender and Ethnic Designation 2003
State # Passed South
Beach #
Passed PNH # Passed
Female 362,228 155,627
(43%)
103,950 37,659
(36%)
388 231
(60%)
Male 360,913 158,389
(44%)
100,358 37,583
(37%)
373 234
(63%)
African
American
69,343 17,818
(26%)
26,247 5,919
(23%)
80 40 (50%)
American
Indian
6,249 2,558
(41%)
741 245
(33%)
6 ----
123
Table 4: Continued
Asian 52,723 36,794
(70%)
14,148 10,831
(77%)
215 174
(81%)
Filipino 19,223 11,332
(59%)
4,493 2,653
(59%)
27 18 (67%)
Hispanic/Latino 336,628 100,254
(30%)
122,723 34,302
(28%)
202 82 (41%)
Pacific Islander 5,212 2,158
(41%)
1,054 387
(37%)
14 8 (57%)
White not of
Hispanic Origin
221,200 139,272
(63%)
32,630 20,429
(63%)
214 141
(66%)
Unknown 14,545 4,354
(30%)
2,675 564
(21%)
7 ----
Table 5: State, County, School with CAHSEE Math Results 2004
Group All
Students
Special
Ed.
ELLs RFEP SED NSED
State #Tested 447,110 35,167 80,909 48,696 180,079 199,914
Passed 329,225
(74%)
10,441
(30%)
39,789
(49%)
40,338
(83%)
109,209
(61%)
170,090
(85%)
South
Beach
#Tested 118,339 9,080 30,554 20,681 63,175 38,923
Passed 80,055
(68%)
2,224
(24%)
14,810
(48%)
16,195
(78%)
36,922
(58%)
31,747
(82%)
PNH #Tested 522 35 54 57 113 321
Passed 465
(89%)
17
(49%)
40
(74%)
55
(96%)
90
(80%)
301 (94%)
Table 6: State, County, School with Gender and Ethnic Designation 2004
State # Passed South
Beach
#
Passed PNH # Passed
Female 220,499 163,806 (74%) 58,547 39,731 (68%) 266 239 (90%)
Male 226,569 165,247 (73%) 59,674 40,282 (68%) 256 226 (88%)
African
American
35,507 19,318 (54%) 12,863 7,858 (61%) 44 36 (82%)
American
Indian
4,017 2,778 (69%) 342 231 (68%) 4 ------
Asian 42,237 38,529 (91%) 11,835 11,153 (91%) 206 200 (97%)
Filipino 13,248 11,514 (87%) 3,157 2,730 (86%) 13 11 (85%)
Hispanic/
Latino
183,037 111,710 (61%) 65,544 38,270 (58%) 102 77 (75%)
Pacific
Islander
3,028 2,155 (71%) 608 417 (69%) 3 -----
White not
of
Hispanic
Origin
161,699 140,287 (87%) 23,167 20,291 (88%) 147 132 (90%)
Unknown 4,337 2,934 (68%) 850 468 (55%) 3 -----
124
Table 7: State, County, School with CAHSEE Math Results 2005
Group All
Students
Special
Ed.
ELLs RFEP SED NSED
State #Tested 639,860 73,534 142,251 66,326 120 273
Passed 402,151
(63%)
16,799
(23%)
56,601
(40%)
50,788
(77%)
93
(78%)
230
(84%)
South
Beach
#Tested 177,270 20,495 52,635 27,008 101,048 52,762
Passed 100,780
(57%)
3,820
(19%)
21,001
(40%)
19,518
(72%)
49,661
(49%)
38,245
(72%)
PNH #Tested 622 58 61 71 290,550 259,173
Passed 527
(85%)
26
(45%)
42
(69%)
67
(94%)
146,546
(50%)
199,891
(77%)
Table 8: State, County, School with Gender and Ethnic Designation 2005
State # Passed South
Beach #
Passed PNH # Passed
Female 314,124 198,913 (63%) 87,889 50,014 (57%) 306 257
(84%)
Male 325,377 203,104 (62%) 89,268 50,729 (57%) 316 260
(85%)
African
American
63,007 27,531 (44%) 23,311 9,234 (40%) 56 42
(75%)
American
Indian
5,831 3,428 (59%) 545 308 (57%) 2 ----
Asian 49,843 42,717 (86%) 13,342 12,030 (90%) 198 192
(97%)
Filipino 16,712 13,177 (79%) 4,008 3,156 (79%) 20 19
(95%)
Hispanic/
Latino
183,037 111,710 (61%) 65,544 38,270 (58%) 102 77
(75%)
Pacific
Islander
3,028 2,155 (71%) 608 417 (69%) 3 ----
White not
of
Hispanic
Origin
161,699 140,287 (87%) 23,167 20,291 (88%) 147 132
(90%)
Unknown 4,337 2,934 (68%) 850 468 (55%) 3 ----
From 2003 to 2005, in almost every instance where Pacific North High
(PNH) had quantifiable data, the school out-performed the state and South Beach
125
County. In only three instances, PNH did not out-perform the state: Table 7 with
the Filipino subgroup; and Table 6 with the SED and NSED subgroups.
PNH, SBC, and California Math Class Data. Table 9 and Table 10 both
show gender statistics for PNH from 2003 to 2005, the state and SBC. However,
Table 9 disaggregates the data by ethnicity and table 10 disaggregates the data by
course name and number. In Table 9 ethnicity information is categorized by male
and female data, and is sorted by math classes such as Intermediate Algebra,
Advanced Math, and 9-12 student enrollments.
Table 9: PNH, SBC, and State Math Class Data
Afr. Am 16 (23.9%) 5
(7.5%)
67 9 (10.8%) 8
(9.6%)
83 150
White 56 (18.5%) 64
(21.2%)
302 65 (19.1%) 51
(15%)
340 642
Mult./No
Resp.
0 0 0 0 0 0 0
School
Total
190 (18.8%) 239
(23.7%)
1,009 206 (19.2%) 216
(20.1%)
1,075 2,084
SBC
Total
35,107
(14.7%)
26,518
(11.1%)
239,055 30,539
(12.2%)
23,860
(9.5%)
250,251 489,306
State
Total
139,461
(15.6%)
114,108
(12.8%)
891,357 126,045
(13.4%)
106,196
(11.3%)
939,636 1,830,99
3
PNH
2004
Female Male
Ethnic
Group
Intermediate
Algebra
Adv.
Math
9-12
Enroll-
ment
Intermediate
Algebra
Adv.
Math
9-12
Enroll-
ment
Total 9-
12
Enrollm
ent
AM IND 1 (16.7%) 0 6 3 (23.1%) 0 13 19
Asian 105 (28.6%) 109
(29.7%)
367 100 (25.4%) 107
(27.2%)
393 760
Pac.
Island
2 (14.3%) 1(7.1%) 14 2 (12.5%) 1
(6.2%)
16 30
Filipino 8 (23.5%) 11
(32.4%)
34 7 (21.2%) 6
(18.2%)
33 67
Hispanic 44 (18.4%) 16
(6.7%)
239 24 (11.3%) 15
(7.0%)
213 452
Afr. Am 14 (17.7%) 6
(7.6%)
79 16 (20%) 6
(7.5%)
80 159
White 62 (18.9%) 34
(10.4%)
328 49 (14.3%) 43
(12.6%)
342 670
126
Table 9: Continued
Mult./No
Resp.
0 0 0 0 0 0 0
School
Total
236 (22.1%) 177
(16.6%)
1,067 201 (18.4%) 178
(16.3%)
1,090 2,157
SBC
Total
37,289
(15.2%)
27,585
(11.2%)
245,792 32,555
(12.6%)
24,432
(9.5%)
257,825 503,617
State
Total
146,230
(16%)
116,905
(12.8%)
913,827 131,312
(13.6%)
108,119
(11.2%)
963,109 1,876,93
6
PNH
2005
Female Male
Ethnic
Group
Intermediate
Algebra
Adv.
Math
9-12
Enroll-
ment
Intermediate
Algebra
Adv.
Math
9-12
Enroll-
ment
Total 9-
12
Enrollm
ent
AM IND 1 (20%) 0 5 1 (16.7%) 1
(16.7%)
6 11
Asian 73 (20.1%) 139
(38.3%)
363 82 (20.3%) 129
(31.9%)
404 767
Pac.
Island
3 (21.4%) 2
(14.3%)
14 2 (9.5%) 2
(9.5%)
32 35
Filipino 4 (12.2%) 10
(30.3%)
33 6 (16.7%) 4
(11.1%)
36 69
Hispanic 40 (15.9%) 29
(11.5%)
252 27 (12%) 16
(7.1%)
225 477
Afr. Am 10 (10.8%) 10
(10.8%)
93 13 (15.1%) 11
(12.8%)
86 179
White 66 (21%) 57
(18.2%)
315 49 (14%) 49
(14%)
349 664
Mult./No
Resp.
0 0 0 0 0 2 2
School
Total
197 (18.3%) 247
(23%)
1,075 180 (15.9%) 212
(18.8%)
1,129 2,204
SBC
Total
37,428
(14.7%)
29,926
(11.8%)
254,066 32,845
(12.3%)
26,415
(9.9%)
266,124 520,190
State
Total
156,022
(16.5%)
126,034
(13.3%)
944,212 141,604
(14.3%)
115,551
(11.6%)
992,802 1,937,01
4
In examining the data in Table 9 from 2003 to 2004, there are several
significant increases. PNH’s overall number totals in Intermediate Algebra for
females increased from 2003 to 2004 from 190 female students or 18.8% to 236
female students or 22.1%. This is an increase of 3.3% over the previous year. The
second increase occurs in the number of Asian female students taking Intermediate
Algebra; it went from 70 to 105. This is a 9.4% increase from the previous year.
127
Asian males slightly replicate this trend in Intermediate Algebra because only 5
more males that are Asian or 1.8% took Intermediate Algebra in 2004. The third
increase is with Hispanic students. Female Hispanics taking Intermediate Algebra
goes from 14.8% to 18.4%, which is a 3.6% increase from the year before. The
fourth increase is with African American females in advanced math, which increased
by 1 student from 2003 to 2004. In 2004, African American males also had an
increase but in the category of Intermediate Algebra. African American males went
from 10.8% to 20%. This was a 9.2% increase from the previous year. The fifth
increase in numbers from 2003 to 2004 is for Caucasian females in Intermediate
Math; they went from 56 to 62 students.
Even though most females’ numbers increased over 2003 to 2004, most male
PNH numbers decreased in Intermediate and advanced Algebra. Second, the total
percentage of students throughout the school in Intermediate or advanced math
dropped from 81.8% to 73.1%. Hispanic males and Caucasian male students’
numbers did not rise in Intermediate or advanced Algebra from 2003 to 2004. The
number of Asian male and females, Hispanic females, and Caucasian females’
percentages also decreased in Advanced Mathematics.
In examining the data from Table 9 from 2004 to 2005, the total school
number of female students in advanced math increased by 6.4% over the previous
year, and an increase of 2.5% happened for males in the advanced category.
Similarly, the total percentage of students taking either Intermediate or advanced
math in 2005 increased to 76%, which is 2.9% increase over the previous year.
128
In examining the subgroups for 2004 to 2005, the table indicates that
Asian females increased by 8.6% in advanced math over the previous year along
with an Asian male increase of in advanced math from 27.2% to 31.9%.
Furthermore, African American females continued their rise in advanced math with a
3.2% increase over the previous year. African American males also increased in
advanced math to 12.8%, which is a 5.3% increase over the previous year. In
addition, Hispanic females increased their numbers in advanced math from 6.7% to
11.5%. Caucasian male students also increased in the advanced math going from
12.6% to 14%, and Caucasian females increased in this category by 7.8%. In
Intermediate Algebra is where Hispanic males made gains, and they increased by 1
student in the advanced math category. Caucasian females continued their increases
in numbers in the Intermediate math category.
However, from 2004 to 2005, the total school number of female students in
Intermediate Algebra decreased along with the Asian female students’ numbers.
Asian males continued to decrease as well I this category. In addition, African
American males decreased in the Intermediate math category, and Hispanic females’
percentages decreased.
In Table 10, California, the county of South Beach, and Pacific North High
School’s math class information is sorted by course code and name with categorizes
such as male enrollment, female enrollment, total course enrollment, number of
classes, number of University of California and California State University
(UC/CSU) classes, Number of Full Time teachers (FTE) and average class size.
129
Table 10: PNH, SBC, and State Course Name Data with Gender 2003-2005
2003
Course
Code
Course Name Male
Enroll-
ment
Female
Enroll-
ment
Total
Course
Enrollment
Number of
Classes
Number
UC/CSU
Classes
Number
FTE
Teachers
Avg.
Class
Size
2400 Gen. Math 59 55 114 6 0 1.17 19
2403 Beg. Alg. 38 28 66 3 3 0.6 22
2404 Intermediate
Algebra
208 192 400 12 12 2.33 33.3
2405 Plane geometry 258 299 557 17 17 3.4 32.8
2409 Solid geo/trig. 160 164 324 10 10 2 32.4
2418 Indep Study 0 5 5 1 1 0.17 5
2421 Math b 18 9 27 3 3 0.75 9
2428 Beg. Alg. Part 1 (2
yr. course)
32 11 43 3 3 0.6 14.3
2429 Beg. Alg. Part 2 (2
yr. course)
117 95 212 12 12 2.4 17.7
Total Math 890 858 1,748 67 61 13.42 26.1
AP Math
2480 AP Cal. AB 16 13 29 1 1 0.2 29
2481 AP Cal. BC 13 36 49 2 2 0.4 24.5
2483 AP Stats 19 30 49 2 2 0.33 24.5
Total Math AP 48 79 127 5 5 0.93 25.4
SBC
Total
2,376,225 2,351,461 4,727,686 145,702 56,049 29,106.21 32.4
State
Total
8,090,896 7,986,988 16,077,884 536,660 202,976 104,461.18 30
2004
Course
Code
Course Name Male
Enroll-
ment
Female
Enroll-
ment
Total
Course
Enrollment
Number of
Classes
Number
UC/CSU
Classes
Number
FTE
Teachers
Avg.
Class
Size
2400 Gen. Math 58 43 101 5 0 1 20.2
2403 Beg. Alg. 37 32 69 3 3 0.57 23
2404 Intermediate
Algebra
203 234 437 14 14 2.69 31.2
2405 Plane geometry 256 253 509 16 16 3.2 31.8
2408 Intermediate. Alg.
& Trig.
35 37 72 3 3 0.6 24
2409 Solid geo/trig. 136 131 267 10 10 1.77 26.7
2410 Probability/Stats 19 21 40 2 2 0.4 20
2420 Math a 6 2 8 1 0 0.2 8
2421 Math b 21 21 42 3 0 0.7 14
2428 Beg. Alg. Part 1 (2
yr. course)
57 39 96 5 5 1 19.2
2429 Beg. Alg. Part 2 (2
yr. course)
92 62 154 7 7 1.28 22
Total Math 920 875 1,795 69 60 13.41 26
2480 AP Cal. AB 40 42 82 2 2 0.4 41
2481 AP Cal. BC 14 18 32 1 1 0.2 32
2483 AP Stats 21 12 33 1 1 0.2 33
Total AP Math 75 72 147 4 4 0.8 36.8
AP Math
2483 AP Stats 21 12 33 1 1 0.2 33
Total Math AP 75 72 147 4 4 0.8 36.8
SBC
Total
2,362,130 2,337,887 4,700,017 147,624 60,128 29,035.25 31.8
State
Total
8,213,465 9,091,795 16,305,260 525,625 213,223 104,430.9 31
2005
Course
Code
Course Name Male
Enroll-
ment
Female
Enroll-
ment
Total
Course
Enrollment
Number
of Classes
Number
UC/CSU
Classes
Number
FTE
Teachers
Avg.
Class
Size
2400 Gen. Math 71 54 125 7 0 1.4 17.9
130
Table 10: Continued
2403 Beg. Alg. 10 12 22 1 1 0.2 22
2404 Intermediate
Algebra
180 197 377 12 12 2.3 31.4
2405 Plane Geometry 264 279 543 16 16 3.2 33.9
2407 Trigonometry 37 45 82 3 3 0.5 27.3
2409 Solid geo/trig 107 136 243 14 14 1.4 17.4
2410 Prob./stats 30 18 48 2 2 0.4 24
2420 Math a 6 8 14 3 0 0.27 4.7
2421 Math b 10 9 19 5 0 0.86 3.8
2428 Beg. Alg. Part 1 (2
yr. course)
54 29 83 4 4 0.8 20.8
2429 Beg. Alg. Part 2 (2
yr. course)
136 107 243 13 13 2.6 18.7
Total Math 905 894 1,799 80 65 13.93 22.5
AP Math
2480 AP Cal. AB 41 52 93 3 3 0.4 31
2481 AP Cal. BC 20 8 28 3 3 0.4 9.3
2483 AP Stats 12 13 25 1 1 0.2 25
Total AP Math 73 73 146 7 7 1 20.9
SBC 2,415,026 2,385,086 4,800,112 150,870 61,586 29,613.06 31.8
State
Total
8,279,800 8,170,012 16,449,812 538,706 214,684 106,531.51 30.5
In Table 10 from 2003 to 2004, females in beginning algebra increased from
28 to 32, and in Intermediate Algebra female enrollment went from 192 to 234.
However, the total class size in Intermediate algebra decreased from 33.3 to 31.2.
The second increase for 2004 happened for both men and women in Advanced
Placement (AP) calculus AB. In this category, male numbers went from 16 in 2003
to 40 in 2004, and female numbers in this category went from 13 in 2003 to 42 in
2004. This increased the average class size to 41 from the previous year’s number of
29. AP calculus BC also had an increase of one male this year. The same trend for
AP calculus BC also happened for AP statistics. The number of men taking the class
increased, while the number of women taking the class decreased. The school also
had higher average AP class sizes in all AP classes than the state and county.
From 2003 to 2004, PNH added several math classes to its master schedule.
The school added 2408, which is an intermediate algebra and trigonometry class. In
addition, the school added 2410, a probability and statistics class to the schedule.
131
Math a, 2420 was added to the schedule by the teachers to compliment math b.
However, 2418, independent study of mathematics was taken out of the schedule in
2004.
In 2005, both male and female enrollment in general math increased
significantly from 58 to 71 male students and from 43 to 54 female students in the
course. The school also had to add two more classes of general math to its master
schedule. Even though the numbers of general math students increased in 2005, the
class average size of general math decreased from 20.2 to 17.9. This is the only year
in which plane geometry increased for both males and females at PNH, and the class
average size went to 33.9 from 31.8 the previous year.
In 2005, PNH added one more class to its master schedule, trigonometry. In
this year, the school beginning algebra part 1 and 2 saw an increase in its scores from
the previous years. In 2004, beginning algebra part 1 had 57 male students and 39
female students. In 2005, it lost 3 male students and 33 female students, making the
number of males 54 and females 29. In 2004, beginning algebra part 2 had only 57
male students and 39 female students. In 2005, it gained 79 males and 45 females,
making the number of males 136 and females 107. The school had to add 6 new
beginning algebra part 2 classes, but the average class size decreased from 22 to
18.7.
The AP calculus classes continued their growth in 2005. AP calculus AB had
1 more male than the previous year, but the women increased their numbers by 10 to
make it 52 women in AP calculus AB. The school added another class, and it
132
decreased by 10 students. Men saw growth again this year in AP calculus BC
from 14 to 20, but women lost 10 students from this category. However, the school
added two more classes of AP calculus BC to make the class average 9.3. This is
significantly lower than last years 32. In 2005, AP statistics saw a significant
decrease in its male students’ numbers, but not in its women students’ numbers.
There were 21 men in AP statistics in 2004, and in 2005, there were 12. In 2005,
women saw a gain of 1 student in AP statistics. Even though the school did not add
any AP statistic classes, the average class size dropped to 25 from 32. PNH’s
average class size for AP courses is significantly lower this year than the state’s
average class sizes, with 20.9 over the states 31.8.
The Gender data with course name and number does indicate that from 2003
to 2005, the total number of students in AP classes rose. It went from 7.2 in 2003
and stayed at 8.1 in 2004 and 2005. On the other hand, the number of students that
were not in higher-level math classes also rose from 2003 to 2005. In 2003, only
26% of PNH students were not in higher-level math class, but by 2005, 28.1% of
students were not in higher-level math classes.
Conclusion. Over the past few years, PNH underwent positive increases and
trends in its pattern of math achievement for various students. There were four
positive trends. The first trend is that the scores of the students continue to rise on
the math portion of the CST. In 2005, PNH had fewer students in the far below basic
category than the state and the county. In addition, this upward trend continued as
133
PNH’s students made great gains in other categories such as students moved from
the below basic category into the basic category and then into proficient.
A second trend of PNH’s math achievement happened with the CAHSEE.
PNH’s upward momentum in math achievement from the CST also happened on the
CAHSEE for PNH students. In all but three instances, PNH’s students out-scored
the state and the county on the math portion of the CAHSEE exam in ethnic
subgroup data and other specific school categories such as Special Education and
English Language Learners.
When comparing the math class data of PNH with that of the county and the
state, the trend of female advancement in mathematics emerges. Math class data for
PNH from 2003 to 2005 illustrate that female students from all ethnic subgroups at
PNH are increasingly taking more Intermediate Algebra and advanced math classes.
In addition, female enrollment as well as male enrollment increased in advanced
placement math classes such as AP Calculus as well throughout the years.
The final trend for math achievement at PNH is the increase of math classes
at the school. The math curriculum changed significantly from 2003 to 2005
because of the addition of a variety of new advanced math classes for students. Over
the years, the PNH math curriculum evolved to include different types of advanced
math classes such as trigonometry and probability/statistics as options for students
who would not otherwise take an advanced math class if their only option for
advanced math was that they would be required to take AP Calculus.
134
Research Question 2: Policy, Curriculum, and Instruction
Research Question 2 is: “What policy initiatives as well as curriculum,
instruction and related conditions seem to be related to improved math achievement
at the school?” There were two frameworks used to analyze data findings for
research question 2. The first framework is based upon the work of Marsh and
Codding’s (1998) effective school design model (Appendix F). The framework
incorporates both school design and a foundation for effective math programs. The
components of the framework are curriculum, student performance assessments,
learning activities, and school culture. Each component has several elements that
compose the characteristics of the component. The second framework for research
question two is the effective math program graphic (Appendix G). The framework
has three main components: standards-based instruction, classroom practice, and
curriculum design. Similarly, to the Marsh and Codding model (1998), each
components of the effective math program graphic has several elements.
Policies
When asked if the federal and state policies had an impact on increasing the
achievement at PNH, Administrator B suggested that suggested, “That both the
federal and state policies had both positive and negative impacts.” Administrator B’s
demeanor was ambivalent because the administrator accepted and agreed with the
foundational tenets of the policies. However, administrator B saw that the enactment
and enforcement of the policies could sometimes be problematic for PNH or not
adequate meet the needs for the betterment of the school.
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NCLB. PNH, like most Californian schools, immediately tried to comply
with the mandates of NCLB. NCLB’s mission, such as the belief that all children
deserve quality education and the opportunity to go onto higher education, are parts
of PNH’s school principles. The administrators at the school went about ensuring
that their teachers were highly qualified and making sure that they were giving the
students opportunities to create academic success. In this way, the faculty, staff, and
administrators at PNH were committed to the ideals of NCLB.
On the other hand, both administrators at PNH felt that NCLB had a negative
impact on the school because some of its policies were restrictive and made
accomplishing some things at PNH more difficult. Administrator A admits that
NCLB is not a major concern for the school, and the math teacher questionnaire
reflects this same sentiment because only 62% of the math teachers felt that the main
external pressures for improved math achievement at PNH stemmed from NCLB.
The math and non-math teacher questionnaires reiterate similar feelings. On the
math teacher questionnaire, 57% of the math teachers felt that NCLB helped to
promote student achievement at PNH and on the non-math teacher questionnaire
54% of the teachers felt that NCLB helped to promote student achievement at PNH.
As an example of how NCLB limited PNH in its efforts to raise students’
achievement is through NCLB’s requirements of what NCLB deems as a highly
qualified teacher. Both administrators expressed concerns that NCLB limited them
in employing certain teachers at the school. During the interview, Administrator B
expressed the difficulty in hiring practices was due to NCLB’s mandate that all
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teachers hired at the school must be highly qualified, which in turn Administrator
B says means that they must have already possess a valid teaching credential in order
to be hired as a full time teacher. Administrator B states:
You have to have a highly qualified teacher to teach a subject.
This is the thing that bothers me, here I could have a teacher
that has all the potential. I can’t hire them because of NCLB
reasons or I am going backwards because this teacher doesn’t
have a teaching credential yet, he’d be an intern, or on an
internship, and so some of our best teachers right now, came
in on internships. This is one of the things I look at it and say
o.k. we want to grow the teacher in the direction we want
them to grow in to help our students. We had teachers that
have come in and the district says that they are really good
because they have a credential, and they are the worst teachers
we have ever had. Because they look at it as it is a paycheck
and I finally have a job.
The frustration administrator B has with NCLB is apparent during the interview.
However, it is mixed with respect and understanding of the underlying issues for
why a teacher hiring policy such as the one in NCLB is required, but the both
administrators are annoyed by the blanket handling of the policy affects the attempts
of PNH to create a faculty of teachers working towards creating student success.
PNH Response to NCLB. During their interviews, both administrators felt that
they continually try to comply with NCLB’s mandates. First, Administrator A
suggested that NCLB inadvertently reminds them to stay focused on increasing the
achievement of all students at PNH, so both teachers and administrators are looking
at data and are making more data driven decisions.
Second, Administrator B mentioned that the school has an innovative teacher
interview process in order to comply with NCLB highly qualified teacher mandates.
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Because of the limitation NCLB was putting on teacher hiring practice of PNH
administrators, Administrator B saw a need to make the PNH teacher hiring process
more selective. In order for PNH to hire highly qualified teachers that fit in with
PNH’s school culture, Administrator B felt that the hiring practice needed to be more
selective, while at the same time becoming more open. To accomplish this feat,
Administrator B, then a department chair, went to the Assistant Principal and
suggested that the school begin hiring teachers through departmental review.
Administrator B did not want a teacher hired by only an Assistant Principal’s and a
department chair’s interview because Administrator B felt, “if that person is going to
work with the rest of the department, I think it has to be a departmental interview. If
you bring the wrong person into the department it can destroy your department.”
Once the Assistant Principal and the department chair finish with the initial
screening of teacher applicants and they are down to around five viable teacher
candidates, the candidates then undergo a departmental interview. The departmental
interview consists of half or more of the department’s current teachers, the
department chair, and the administrator in overseeing the department. Then, the
departmental teachers ask the candidates questions about teaching methodology,
subject knowledge, instructional practices, and classroom management techniques.
Next, the departmental teachers, the department chair, and the administrator have a
closed session dialogue about the applicant to determine if the candidate will fit into
PNH’s school culture, departmental environment, and have the ability to teach
adequately the student population at PNH. Departmental teacher interviews began at
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PNH with the science department, then the math department, and now every
department at PNH hires teachers through this method. Administrator B states that
PNH uses departmental teacher interviews because part of PNH’s school culture is
for teachers to have strong sense of collaboration and to accomplish this goal PNH
needs new teachers with this collaborative motto:
The whole idea is if you want collaboration, the only way you
are going to get collaboration is if people feel comfortable
working with those other people [the new teachers that are
hired at PNH]. I am willing to help you, and you are willing
to help me, and we are not recreating the wheel every time you
bring a new teacher in because you are helping them. Many
times, those new teachers that bring in new ideas that you
want to share and vice versa. That’s one of the things I really
liked. Where it use to be the assistant principal and the
department chair, now they have departmental interviews due
to the fact that they see it working because if you want to have
a department that wants to work together, you have to build
that collegiality.
The most important factor of the departmental teacher interview is that it is working
for the school. PNH has been using this method, and both the administrators and the
teachers feel that it is successful and has helped raised their student achievement.
The belief that departmental interview is selection the right math teachers for the
department is represented in the math teacher questionnaire because 80% of the math
teachers felt that student need is a major consideration when making teacher
assignments at PNH. It has also had an effect on the faculty because they now feel a
part of the interview process as an important stakeholder. With this process, PNH is
finding that the new teachers they are hiring are satisfying the NCLB mandate, but
successfully complementing the school, instructional, and teacher culture at PNH.
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PSAA. Administrator A felt that NCLB did cause problems in the school’s
teacher hiring practices; however, Administrator A stipulates that state accountability
measures have over the past few years been more troublesome to the school:
The greatest impact NCLB has had is on the teachers I have
been allowed to hire at my school. However, I feel more
pressure to increase student achievement from Academic
Performance Index (API) reasons because the phase in for
NCLB hasn’t hit hard yet.
PNH has consistently met their Adequate Yearly Progress (AYP), and so
Administrator A is not as apprehensive about NCLB or feeling that NCLB is
influencing their efforts to raise student achievement at the school. What drives
PNH’s improvement in student achievement is that the school puts all their resources
and efforts into trying to meet the requirements of API and stay out of the school
improvement category of the PSAA. As the school met the PSAA mandates, the
state’s PSAA policy helped support further PNH’s programs and gave the school
more resources, which helped increase student achievement.
One way in which the state’s PSAA policies helped increase student
achievement at the school is in the area of teaching and instruction. Administrator A
states:
[The API] provided us a contact to have the conversation in
1998. As an administrator, I supervised the conversations.
We didn’t have the conversation around standards at first. It
took a lot of time and training to come around to common
ground and common conversations about teaching and
instruction. Then we went from where are our students, and
so what do we do to help them. Standards framed our
dialogues.
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The way in which the school went about increasing student achievement through
focusing on teaching and instruction is through several rounds of dialogue and
meetings. First, the state’s standards set the framework. Before the teachers at PNH
could have conversations about teaching and instruction in relation to the standards,
they began dialoguing within department meetings about student performance and
achievement at the school. It took several rounds of discourse on student
performance before teachers came up with a kind of consensus about issues
surrounding student achievement. Then, teachers began the next phase of exchanges
that entailed discussing methods of teaching and instruction pertaining to best
practices. Those conversations led teachers dialoguing about how to use the
successful teaching and instructional methods and practices to increase their
students’ achievement. So in reality, PNH teachers’ conversations about increasing
their students’ achievement stemmed from exchanges about performance, then best
practices, which led to standards, and then to meeting API requirements.
Administrator B thought that state policies such as standards helped focus teachers’
conversations around what instructional practices and methods successfully teach
state standards: “The positive effects I think is it primarily forces teachers to think
about their content and standards, and what they want students to improve on
because that is what is going to move student achievement.”
School Response to PSAA. To satisfy the requirements of California’s PSAA,
PNH created and instituted math committees, CPM, UCLA Math Project, and PNH
articulations with other high schools and the PNH middle school feeder. Because the
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PSAA is on the forefront of PNH administrators and teachers’ minds, the math
teachers created several math committees to comply with the PSAA and increase
PNH students’ achievements. There are math committees by grade, mathematical
subject, new teachers, and the entire mathematics department is a committee. For
several years now, Administrator B indicates that each committee has been
examining mathematical student assessment data from PNH but also from PNH’s
middle school feeder, in an attempt to determine how to increase PNH students’
math achievement and other mathematical trends.
The second way PNH copes with PSAA is through their CPM program. PNH
has several math teachers trained in how to provide CPM to students in various math
subjects. There are CPM classes for grades 9-12 and CPM Algebra 2, Geometry,
and Pre-Calculus classes. PNH chooses to offer students both traditional math
classes and CPM classes in most subjects because they are trying to ensure that they
are reaching all students learning modalities. PNH feels that CPM is what is helping
to increase their students’ math achievement. Both Teacher A and B feel it is the
reason why students of color or otherwise disadvantaged students math achievement
is increasing at PNH; they also indicate that CPM is the reason for students in the far
below basic and basic category are raising their scores.
The third response PNH has for PSAA is the partnership the PNH math
department has with the UCLA (University of California, Los Angeles) Math
Project. Teacher B explains that the UCLA Math Project provides PNH teachers
with professional development that works in the areas of strengthening the teachers’
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math content knowledge, instructional methods for teaching math, math research
opportunities, and classroom management skills for math classes. The UCLA Math
Project hosts conferences and classes that PNH teachers can attend. There is also a
mentoring aspect to UCLA’s Math Project. Administrator B indicates that the
UCLA Math project is “really good, and is really helping the teachers.”
Administrator B, Teacher A and Teacher B feel that the UCLA Math Project is an
influence in their rising math achievement at the school. During the interview,
Teacher B gives an example of how the UCLA Math Project helps teachers think
about math in unique ways, so that they can teach math to PNH students in a variety
of ways:
UCLA Math Project gave us a cow and chicken problem. You
have 10 heads and 28 feet. How many cows and how many
chickens do you have? Algebra teachers would go and set up
their system of equations, and then solve it, but a 2
nd
or 3
rd
grade teacher drew heads. She set up all the heads and feet
and made it really cute, and came up with four cows and 6
chickens, and I had the same. I looked at the problem that day
and said that was so much easier. My method works, and it
works every time, but sometimes there is such an easier way.
Sometimes you have to look at the problem different ways.
In addition, Teacher B mentions how the UCLA Math Project has helped key math
leaders’ dialogue with teachers about math and student performance, and this has
been a factor in the students’ increased math performance.
A final way in which PNH reacts to PSAA mandates is through articulation
between the PNH and the middle school feeder and other high schools.
Administrator B suggests that PNH “has more articulation from high school to high
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school” than with the middle school feeder. The high schools share with each
other by departments what they are doing to increase students’ achievement.
However, Administrator B does indicate that PNH has an articulation with the
middle school feeder once a quarter (every 10 weeks). PNH uses the middle school
articulations as time to connect with the feeder school to determine how to serve
better future PNH students that are coming from the feeder. PNH tries to determine
in advance what are the middle school feeder students math weaknesses, so that they
can develop future needs to meet those future students when the go to PNH.
CSR. PNH is a school that participates in California’s Morgan-Hart Class Size
Reduction Act (CSR). The CSR allows schools to create small class sizes for
English and one other core subject.
6
The classes are no more than 22 students.
Schools must apply to the program.
PNH Response to CSR. PNH decided that the entire ninth grade math classes
whether CPM Geometry, Traditional Geometry, or their two-year math program
would be a CSR class. Yearly, PNH has anywhere from 20 to 25 CSR math classes.
Teacher B felt that the CSR classes were making significant increases in students’
increases in math achievement. Teacher B indicates how important it was to keep
the CSR classes only for PNH’s ninth graders:
I have taught both the non-CSR and the CSR classes. They
[ninth graders] did so much better if they are all just ninth
graders. When you have, ninth who are on track doing well
6
All CSR information is from the CDE High School Class Size Reduction website:
www.cde.ca.gov/ls/cs/mh
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they can flourish. If they are with a lot of repeating
students that are 11
th
or 12
th
it ends up stifling them. It has
enabled our freshmen classes to rise up.
PNH math department felt that keeping only ninth graders in CSR classes would help
ninth graders focus more in crucial core classes, and would give PNH teachers the
ability to have more specialized time with students who needed extra mathematics
help.
CAHSEE. Another state policy that has a positive affect on PNH’s ability to
increase the school’s mathematic achievement is the CAHSEE. On the math teacher
questionnaire, when PNH math teachers were asked if the CAHSEE contributed to
the school’s effort to raise student achievement, 70% stipulated that it had an affect
and 71% of the non-math teachers affirmed the statement. These percentages
indicate that PNH teachers feel that the CAHSEE was one of the reasons for the
increase in students’ achievement at the school. Teacher C indicated that she knew
the school’s CAHSEE scores were good because of all the hard work that PNH
teachers have put into teaching to the standards upon which the CAHSEE focuses on
and doing whatever possible to help students meet these standards as well.
At first, PNH administrators did not agree with PNH teachers in their belief
that the CAHSEE has influenced the school’s efforts to increase math achievement.
Administrator A felt said, “I don’t think that CAHSEE has pushed us with the vast
majority of our students,” because Administrator A thinks about PNH’s math
achievement from an overall perspective. Administrator A sees the CAHSEE
requirement as being narrow because it centers mostly on 10
th
grade or a limited set
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of standards and requirements, and Administrator A focused more on trying to
improve all students at PNH’s math achievement and performance. Most of PNH’s
students have a high CAHSEE passage rate suggested Administrator A, and
Administrator B said, “That around 90% of their students pass the CAHSEE the first
time they take it.” Because of the school’s high passage rate, both administrators
suggest that the CAHSEE has not been as much of an area of concern for the school
as other areas.
However, as the interviews progressed, Administrator A does go on to mention
that the CAHSEE has been beneficial to PNH’s attempt to raise math achievement
through the means of “the CAHSEE has helped us reexamine how we deal with
students who aren’t being successful.” Administrator A did agree with the idea that
the CAHSEE assisted the school by helping the teachers and administrators at PNH
focus on student populations that might have otherwise been overlooked in the past
such as Special Education and English Language Learners and particular ethnic
subgroups at the school such as African Americans or Pacific Islanders. The
CASHEE helped PNH teachers and administrators target different populations for
specialized teaching and instructional emphasis that they might not have received in
the past, which is why the teachers at PNH felt the CAHSEE did help students at the
school increase in math.
School Response to CAHSEE: After the CAHSEE’s implementation across
California, PNH knew they needed an intervention for their students who did not
pass the exam, so they created the High School Math Class (HSM). HSM has three
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levels—HSM 1, 2, and 3. HSM 1 is what students receive if they do not pass the
CAHSEE in the 10
th
grade year. The class focuses specifically on mathematic
standards are tested on the CAHSEE. If students do not pass HSM 1, they take HSM
2 and then three. Both HSM two and three go over some of the same math standards
as HSM 1, but it does progress onto more advanced math. Administrator B, Teacher
B, and Teacher C feel that the HSM classes are benefiting the students who failed the
CAHSEE pass on the second or third attempt.
PNH also provides students that do not pass the CAHSEE with after school
tutoring. Administrator B asked the district to disperse to PNH money the state
designated for helping students pass the CAHSEE for the PNH’s after school math
tutoring: “We were doing it on our own until I asked the district for the state’s
money to fund our tutoring program because the district had taking away a lot of our
money over the past couple of years.” The district also gave PNH money for
CAHSEE books for the program. Tutoring happens two times a week for a few
hours after school. It is an optional program, but many students are taking advantage
of the opportunity.
DU’s API Policy. Directional Unified (DU) a few years ago decided to create
a mandate about API. Administrator B says, “One of the things is that our
superintendent has said that we will increase by 5 points per year, and that is a
mandate. It is part of our growth target for all the schools in the entire district.” The
DU API mandate came with the stipulation that you will increase or there will be
consequences. Both Administrators understand the necessity of setting high
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expectations for schools, teachers, and students. The school generally feels that
pressure is necessary to keep bettering itself and to stay focused on increasing
student achievement. In the way of high expectations, the teachers and
administrators feel the DU’s API policy helps them stay focused on the goals on
increasing student achievement.
DU’s Honors and AP Math Policy. Within the last few years, DU has decided
to create an open access policy for math. Any student that has fulfilled the
prerequisites to take honors math classes or AP math classes can take them.
Enrollment in honors and AP math classes across the district has increased. Student
enrollment in honors math classes and AP math classes at PNH has also increased.
For PNH, having more students in the advanced math classes is increasing student
achievement in those classes. Teacher B expresses that increasing access to advance
classes for students is a factor in the increased math achievement of students at PNH:
“What it says is if you allow students, many of them will rise up on their own,
whether you think they can do it or not. The AP numbers speak for themselves.”
PNH’s AP math numbers have significantly increased over the past few years, and
the math department is seeing more math students succeed than any year before.
DU’s CPM Policy. Since the early 1990s, DU has had a connection to College
Preparatory Math (CPM). Teacher A states: “We started CPM at PNH in 1991.”
However, it was not until years later that DU recognized the effect CPM was having
at PNH, and so it decided to mandate that all DU high schools would go from
teaching traditional math to using CPM. Teacher A says that DU was enthusiastic
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about using the program: “We got an initial support in the district to teach it.”
Teacher A then describes the fallout that occurred because the DU mandated that
CPM was to replace the traditional math system at all high schools:
It created a real issue. Not all teachers were in a place in their
life to teach a collaborative classroom [speaking of teachers
throughout the entire district, not particularly at PNH]. Not all
teachers knew the math well enough to spot what students
were doing wrong and help them. Teachers at other DU
schools took it to the community and the union.
Because of the controversy surrounding CPM, DU decided to make using the
program optional for its high schools. Eventually, it phased out of most high
schools, and now only PNH uses CPM.
PNH’s Response to DU’s Policies. Administrator B describes best PNH’s
response to all DU’s policies: “We are the law and order school. Whatever the
school or the board says to do we will do.” PNH is striving to meet the boards
mandate of increasing student performance and the school’s API by five points a
year through having various math interventions and math committees’ discussions
about students’ math performance data. PNH also continues to offer several CPM
classes to their students. Many PNH teachers voluntarily and without extra payment
stay after school and use their lunch breaks to tutor students who need extra math
assistance. Teachers A, B, C, and D all had various tutoring schedules for their
students in which they volunteer their services without payment from the district, and
they all said that almost all PNH teachers have some sort of volunteer tutoring
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service they provide to their students in order to meet DU student achievement
expectations.
School Design
PNH altered its school design as a means by which to increase the students’
math achievement at the school. The first feature of school design is student
performance assessments. Within student performance, assessments there are three
qualities: capture conceptual understanding, problem solving, and communication
skills. The second feature of school design is curriculum, which has three
components: school-to-career applications, constructivist knowledge, and are based
on student outcomes. The third feature of school design is learning activities, and it
has three characteristics: students solving problems, collaboration, and it must
challenge students to think.
Student Performance Assessments. PNH uses the state assessments such as the
CAHSEE and the CSTs as their base for student performance assessments. Some
districts, such as LAUSD, have district-wide student performance assessments in
core subjects. Unlike such school districts as LAUSD, PNH does not have uniform
district-wide or school wide mathematic student performance assessments. The
department also does not have departmental mathematic assessments. However,
each individual teacher in PNH’s math department has his or her own student
performance assessments. Teacher B refers to not having uniform departmental
assessments as “We’ll we do things similar [math assessments], but not that we are
grouped up [uniform departmental assessments by mathematic subject]; it is a free
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for all. We are open accessing for the teachers too.” Teacher B’s comment about
teachers having open access is about PNH teachers having the freedom to make
instructional, teaching, and learning decisions based on the needs of their individual
students. Students at PNH have the option to choose math classes that address their
individual learning style and modalities and still receiving the quality education that
they deserve. Even though, PNH math teachers do not have a formalized math
assessment, CPM teachers use the CPM curriculum, which does have culminating
tasks at the end of each unit. The CPM culminating tasks at the end of each unit are
as close to uniform student performance assessments that the PNH math department
uses.
The CPM unit assessment does capture whether the student has conceptual
understanding of math by having students write out how they solved the problem, so
the teacher can immediately see whether the student understands the mathematical
concept. The CPM unit assessment also incorporates problem solving because the
questions students are asked on the unit assessment are problem-solving type
questions. Finally, throughout the CPM course, students are continually using their
communication skills by explaining to each other how to solve problems.
Curriculum. The second component of school design is curriculum, and it has
three characteristics: school-to-career applications, constructivist knowledge, and
the curriculum is based on student outcomes. PNH does not have a school-to-career
applications program. However, the school does offer every student A-G
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requirement classes to ensure that every student who graduates from PNH has the
opportunity to go to a college or university if they so choose.
PNH’s math curriculum does offer constructivist classes such as the CPM math
classes. CPM offers students’ real-world math problems to solve that create an
environment of experimentation, so the students feel as if the class is a collaborative
math lab. The teacher is there as a facilitator or guide through the math labs
problems. The student and teacher are involved in the questioning and answer
solving process together.
In addition, student outcomes are the base of PNH’s curriculum. The belief
that student outcomes as the basis of PNH’s curriculum stems from the math teacher
questionnaire that indicates that 87% of the math teachers felt that student needs
were the basis of the school’s master schedule, and 76% of the non-math teachers
agreed. Because of student performance on standardized tests such as the CST and
the CAHSEE, PNH teachers and administrators added new math classes to the
master schedule. One was the HSM, which is an intervention for students who are
not passing the CAHSEE. The second class added to the schedule is a two-year
Algebra class for students who entered PNH from the middle school without the
sufficient skills needed to pass Algebra 1. Teacher C says of the program, “I think it
was a good program.” Teacher C goes onto say that the program worked. The
students’ knowledge of Algebra increased, and even if they did not pass the class,
they felt as if they were educationally moving in a more positive direction than if
they have just kept taking and failing Algebra 1 repeatedly. Teacher B also agreed
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with Teacher C that the students were prospering from the classes. The third
class added to the math master schedule is CPM classes for Algebra 2, Geometry,
and Pre-Calculus, or student can receive all classes from a traditional mathematical
teaching perspective. Administrators and teachers at PNH decided to add a
probability and statistics class for student that did not want to take Pre-Calculus.
There is a Trigonometry class for students that failed Algebra 2. The class goes over
similar concepts as Algebra 2, but from a different perspective.
Learning Activities. Learning activities must challenge student thinking, be
collaborative, and students must solve problems during the process. Teacher B
stipulates that PNH’s math teachers are committed to having authentic problem-
solving activities in every classroom. Teacher A indicates that the CPM curriculum
is very good at having students perform problem-solving questions that are
collaborative and challenging. In addition to CPM, Teacher C indicates that
students’ problem-solving and critically thinking is part of the HSM program, and
teachers try to make that class as collaborative as possible. Administrator B states
that it is because the math department is engages students in rigorous problem
solving that it is helping to raise PNH students’ math achievement.
School Culture. School culture has three distinct features: enhanced learning,
the staff and students have meaningful reactions, and there is ongoing professional
development is its base. PNH has a vibrant school culture based on enhanced
learning. Both teachers and students are committed to ensuring that all students
educationally succeed. A thought towards increasing student achievement and
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performance is the base design for all classes. The math teachers even created an
additional curriculum as an enhancement or supplement to the traditional math
textbooks to better accommodate PNH students learning styles. Keeping in mind
PNH students’ best interest is the way in which the math department makes all
decisions and teaches classes. In addition, teachers are making decisions about
curriculum, teaching, and instruction based upon students’ performance data.
The second element of school culture is that the staff and students have
meaningful interactions. An example of PNH teachers having meaningful
interactions with students is through homeroom. PNH faculty and staff decided that
on Wednesdays, teachers and students would have homeroom. The faculty and staff
specifically built into Wednesday’s schedule this period of the day, so the school bell
schedule changes from the normal school day schedule. In homeroom, teachers do
not have their regular students. They have students not from their regular classes,
but students that assigned to them since the ninth grade, and they have these students
until they graduate from PNH. This is a chance for students to interact with a neutral
adult. The class sizes for homeroom are around 24 to 25 students per teacher.
Administrator B describes the how the program builds relationships between
students and teachers:
Homeroom has teachers connect with students and students
connect with teachers or other adults that they don’t normally
have in their life. In other words, you have a student that is in
your homeroom, and you don’t necessarily give him a grade,
but you are trying to help that student have another adult that
they can connect to. Because a lot of times students don’t like
to be forthcoming and upfront when they have a problem in
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the classroom because they will say this teacher is going to
give me a grade X, Y, and Z, they are going to call my
parents. The teacher can intercede for them with that other
teacher without the student feeling penalized.
The administrators and the teachers feel that homeroom is having a positive impact
on student performance at the school. Administrator B personally attests to the fact
that homeroom is increasing the relationship bonds between teachers and students at
the school, which helps the PNH school climate remain positive.
Not only does homeroom add to the positive school culture at PNH, but
Teacher A suggests that PNH teachers have a stronger relationship with students
than most high schools because they spend more time interacting and talking with
their students. PNH teachers have more time because PNH math teachers decided
amongst themselves that it is imperative while they are teaching students to make a
personal effort to build solid relationships with students by communicating with
them as much as possible during the school day. Teacher A describes the
personalized relationships teachers have with students:
We have more observation than most schools to see kids who
are struggling. The kids talk to us more. The kids are more
open with us. We also pay more attention to the kids because
the only way we can keep them doing the work is if we have a
personal interest in the students.
Before school, during break, lunch, or after school the researcher saw students
getting tutoring help by teachers or teachers just having conversations with students.
During the interview, Teacher B describes the effect of the close relationships of
students and teachers at PNH: “It [PNH’s positive school climate] is an attribute of
the PNH campus. They feel safe here. They want to be here. The socio-economics
may not be skyrocketing here, but we have the mentality of a high socio-economic
campus.” Teacher D admits that often she has students in the class during lunch just
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to talk with her, and so she continually makes herself available for the students.
Both Teachers A and B suggested that the positive school culture at PNH is a
significant factor to why math test scores are rising.
Student-teacher interactions and relationships are not the only relationships
that help build a positive school climate. Teacher A suggests that the PNH
administration has always had good interactions with the teaching staff. Teacher A
and Teacher C feel that they can always rely on the administrator to provide
resources she needs to teach math, and Teacher B suggested that the administration
is always has time to communicate with the teachers. Teacher D suggested that the
administration really cares about math and makes math concerns a priority and both
Teachers A and B agreed.
The math teachers at PNH interact significantly with each other. Whether they
are participating in school or non-school functions, all PNH math teachers admit that
they have strong relational bonds to each other. Teacher B says, “The teachers for
the most part do a lot of things together. Every teacher [math] I have met is as if we
are a family. We do our picnics, faculty bowling, and our holiday parties. All the
[math] teachers get along.” Teacher D shared Teacher B’s sentiments that PNH
math teachers have close bonds of friendship and frequently help each other, “When
I was in the English department, no one even talked to me, but when I began in the
math department, everyone was really nice and helpful. I got to know everyone and
made a lot of friends.” Administrator B and Teacher A suggest that it is the close
ties the math department has with each other that is helping the students’ math scores
raise because of the PNH math teachers collegiality, cooperation, and sharing the
goal of really wanting to help students succeeded in math.
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The third characteristic of school culture is ongoing professional
development. Administrator A feels that professional development is important not
just to teachers, but to administrators as well:
We have to be the models for that [professional development],
it is important that the teachers see us growing professionally
and they take an interest one on one with teachers and a
personalized approach. They don’t all need the same kind of
things at the same time. We have some teachers thinking
about implementing more technology in the classes and work
and trying to support them in conferences and software
without forcing that on everything.
PNH has continuous professional development with the frequent articulation
meetings with other DU high schools and PNH’s middle school feeder. On the math
teacher questionnaire, 82% of PNH math teachers feel that their professional
development has helped increase their students’ math achievement. All of the
articulation meetings are by department, so the math department meets with the math
department of another DU high school or the math department of the PNH middle
school feeder. In addition, PNH’s math department has frequent committee
meetings. Teacher B stipulates that the Algebra math committee meets one to every
two weeks, and suggests that most math groups meet just as frequently.
Administrator B indicates that the math committees meet all the time, and that
administrators or the math department chair alternate supervision of those meetings.
At the math meetings, Teacher C indicates that there is always discussion of
students’ math achievement data, and what can PNH teacher do to increase students’
mathematic performances. Teacher D says, “The math department is always meeting
and having discussions about student work.” Teacher B stipulates that at the math
meetings have significant collaboration between participants, but general school
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meetings also are collegial: “We have a lot of collaboration within our whole
community, whether it is curricular or school wide planning.” Administrator B,
Teacher A, and Teacher B, indicate that they are not surprised that the math scores
are increasing because professional development of PNH’s math department focuses
on increasing student achievement through collaborative methods.
One PNH math key leader frequently participates in the UCLA Math Project
because it provides her with a lot of professional development. The teacher goes to
UCLA Math Project classes and conferences. Administrator B, Teacher A, and
Teacher B indicate that the math department is heavily involved with the
organization, and that the school receives continuous professional development from
UCLA’s Math Project.
Administrator B alludes to PNH undergoing several structural changes over
the past few years, and that those structural changes have added another level of
positive energy to the school culture at PNH. These structural changes are external
in nature such as teachers changing rooms to increase collegiality amongst the
teachers but also help build small support networks amongst teachers. Administrator
B describes how this all began with the rearrangement of the science department:
One of the things that has been ongoing because I did a long
time ago is that I put all the science teachers in the same
general area. We had science teachers on this side of the
school, and four teachers on this side. It doesn’t make sense
to have them separated by that distance because the
collegiality isn’t there. Right now, our science teachers are in
the same general vicinities. Typically, there is somebody next
to them that is a science teacher, so it makes it real nice
because if there is ever a problem you can always go to the
person next door. There is always a math teacher next door to
each other. When we have a new teacher, we try to put them
with a veteran teacher. So that way you know, we don’t have
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all the “newbies” right next to each other. All departments
do the same thing. They try to put them in pods of teachers.
By having the teachers clustered in pods by subject, PNH is creating immediate
support networks for teachers, so that teachers can build their own small professional
learning communities outside of the larger departmental learning community.
During the interview, Teacher D shares insights about how having the math teachers’
closer together increases collegiality: “Our math department has always been really
good about working together. If we have a new teacher, we want to make sure that
they know what they are doing and keep them informed and meet at lunch or
whatever.”
PNH also makes sure to put new teachers next to veteran teachers, so that
veteran teachers are more readily available to help the new teacher. The veteran
teacher becomes that new teachers mentor and the close proximity is beneficial for
both teachers. This idea of creating subject pods and pairing veterans with newer
teachers began in science but branched out into math, and then to all the other
departments. Administrator B suggested during the interview that everything begins
with the science department and then the math department follows. The
administrator suggests that there is a strong cooperative link between both
departments, which makes them the two strongest departments in the school.
Teacher A and Teacher B both mention how the pairing newer and veteran
teachers and grouping teachers by subject pods is helping to increase their
communication with each other, collegiality amongst the math department, and is a
factor in the increased math performance in their students. Teacher B notes that the
close proximity of teachers within the same subject helps teachers connect with each
other and share instructional ideas. The proximity increases student achievement
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because the teachers are able to have similar classes present to each other, work in
cooperative groups through cross-classes or even cross-curricularly. For example,
one Algebra 2 CPM class will enter the room of another teachers Algebra 2 CPM
class and the students will pair or group with students from another class to work on
math lab problems. Another example is that two teachers will have their second
period Algebra 2 CPM classes academically competing against one another for
prizes or on culminating units.
Math Program Design
PNH has a varied math program design to meet the needs of all PNH
students, and this is why the students’ math achievement at the school is increasing.
The effective math programs framework has three components: curriculum design,
classroom practices, and includes standards-based instruction. Curriculum design
has six elements: student-centered curriculum, driven by learner outcomes, there is
an emphasis on concepts, focuses on problem solving incorporates current learning
theory, and the scope and sequence is supported by learning theory. Classroom
practices have four features: effective and coherent lesson design, it promotes high
levels of student engagement, makes use of prior knowledge, and is culturally
relevant. The last component of math program design is standards-based instruction,
which has three characteristics: assessments aligned to standards, student
achievement data drives instruction and decisions, and common performance rubrics
created through collaboration.
Curriculum Design. PNH teachers have been altering the mathematics
curriculum design for various classes since the late 1980s. Teacher A remembers
that in the late 1980s and early 1990s, PNH math students were performing either
very poorly or very well and no one was in the middle. This was when the teachers
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in the math department realized that they needed to change their instructional
strategies, approaches, and curriculum because only a few students were succeeding
in math. The curriculum that the teachers found was CPM.
CPM’s curriculum satisfies all six elements of curriculum design. With
professors from UC Davis, California State University, Sacramento, and 90 middle
and high school math teachers created CPM.
7
Current mathematics learning theory
such as cooperative learning, problem-solving based learning, and spaced learning is
the basis of CPM. In addition, it relies heavily on this research for its scope and
sequence. It is models how Japanese students learned in the 1999 TIMSS study
videos. CPM is a student-centered curriculum. The teacher acts as a facilitator as
the students collaborate in groups or pairs to answer problem-solving questions. All
questions that students are given are problem-solving questions, which requires
students to write out the reasoning behind their answer in various ways. Not only do
the students have to write out the reason behind their answer, but they have to work
out the problem in different ways, and then recite how they solved the problem to
their partner(s). Students only receive a few questions a day to work on, so the
environment is more like science classes in the way that students must experiment
with the word problem like it is a math lab in order to solve the equations. Students
collaborate on only a few questions a day because CPM values conceptual
understanding versus memorizing mathematical procedures. In addition, students are
constantly revisiting previous concepts they learned because the program has
students continually reexamine old concepts but is presented in a new format and
always linked with a current concept. Teacher A illustrates how concepts in CPM
7
All CPM information was obtained from the CPM website: http://www.cpm.org/teachers/who.htm.
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are carried through from Algebra 1 to Pre-Calculus and instructionally taught the
same way throughout the program so students gain a sense of continuity: “In
Algebra 2, we teach functions a certain way, and when we get to Pre-Calculus we are
continuing to teach them the same way and the link lasts.” Figures 5 and 6
(Appendices Q and R) are examples of CPM problems.
8
Administrator B, Teachers A, B, and C feel that the CPM program has
significantly helped to increase students’ math achievement at PNH. Teacher A was
part of teacher coalition that wrote the course materials for CPM’s Geometry section.
Teacher A reflects upon how CPM came to PNH:
We started CPM at PNH in 1991. We began with geometry
and then we added within a year Algebra 1 to geometry.
Probably about the 3
rd
year, we brought in Algebra 2. Then,
we went into Pre-Calculus. Since 1995, we have had all four
programs.
Teacher A indicates that the CPM curriculum is work for both the students
and the teacher because the teacher is constantly moving about the room asking
students questions and making sure, they understand the material. The teachers are
there to guide students through their mathematical thought processes but not to do
the work for them: “As you move from person to person you learn who knows and
who doesn’t know,” (Teacher A). It is challenging for students because students not
only have to know how to solve the problem, but also have to reveal the process of
answering the question written on paper for the teacher and themselves and orally to
8
CPM permitted the researcher use of all sample questions.
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Figure 5: 1
st
CPM Sample Algebra 1 Question
163
Figure 6: 2
nd
CPM Sample Algebra 1 Question
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their partner(s). Teacher A says, “One of the fundamental concepts of this
curriculum is that everyone has to do it. The teacher has to have a better facility
through the room as the students work.” This requires teachers to have strong
classroom management skills and well-defined group or partner rules. Teacher A
indicates that when CPM teachers at the school have examined the CAHSEE scores,
students that have had CPM have the strongest math scores. In addition, Teacher A
says, “Students remember things they have learned in Geometry [CPM class] on
their SATs.” The most memorable phrase about CPM came from Teacher A about
the power of CPM in the classroom: “CPM has done well because it attracted
passionate people. People who have a true desire to make a difference in the
classroom make it work.”
Similarly, to Teacher A, Teacher B also teaches CPM classes. Teacher B feels
that the fact “that the school offers two distinct curriculums” is unique. She indicates
those students’ value choices and PNH provides students with the choice to have all
their classes in a traditional math style using Glencoe books or they can take CPM
classes throughout their high school experience. Teacher B strongly feels that CPM
is increasing math achievement for students of various learning styles because
students use so many learning modalities during CPM:
I have a lot of students who like to talk in my CPM, but that is
ok because we need them to talk and want them to talk. Then
we have those that really don’t talk that end up talking in this
class, and they kind of like that. I think CPM works because it
allows students to succeed in small doses without fully
understanding what they have done before or are doing now.
Teacher B indicates that she has seen students in her class stay working on difficult
math problems when students in traditional classes would have given up because the
program “gives them the feeling of success if they can start, and that’s something
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that helps to contribute to our kids’ successes in math.” Around half of the
students at PNH have chosen to take CPM classes.
One intervention curriculum that PNH offers to students is the two year
Algebra 1 program for students that came to PNH without the mathematical
knowledge to pass Algebra 1. The first year of the Algebra 1 class is Algebra 1x1,
and the second year of the class is Algebra 1x2. Most ninth grade students that did
not pass Algebra 1 in 8
th
grade enter Algebra 1x2. However, those students with
very low Algebraic knowledge take Algebra 1x1. Students who do pass Algebra 1x2
go into Geometry. Students that receive a D or F in Algebra 1x2 go into HSM 1.
Teacher B indicates that PNH provides these classes to students because “If you
[students] still don’t get it [Algebra 1], we can’t just force you into geometry.”
Teacher C teaches one of the two-year Algebra classes and feels that it is helping the
students who were behind when they entered PNH increase their math skills and
knowledge. The curriculum was a collaborative effort of several PNH teachers that
created an instructional manual for the classes. Teacher B says, “The Algebra 1
books were either too easy or too hard… [not] enough middle ground, and the
explanations weren’t that great either. We have had some teams over the years put a
lot of work into creating our own curriculum.” Students work in similar groups to
the CPM classes, and word problems make a significant portion of the work students
do in the class. Teacher C says that the problem is getting about 70% of the students
on track, and that “We are going to make sure 100% are on track next year.”
The two-year Algebra 1 curriculum is similar to CPM in many aspects such
as it is student-centered and problem solving is an important factor of the curriculum.
The teachers created the curriculum because the teachers saw that students coming to
them from their feeder did not possess the necessary skills to enter Geometry and be
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successful, so PNH teachers created a program that focuses on learner outcomes
by incorporating Algebra 1 skills while simultaneously preparing students to enter
Geometry. The curriculum focuses on Algebraic mathematical concepts but gives
the students fewer concepts than a traditional Algebra 1 class because these students
are in the intervention class because they already could not process all the concepts
in one year. The middle school feeder typically teaches the first year of the two-year
Algebra program. The first year involves students learning Algebraic concepts from
the first semester of Algebra 1. PNH usually teaches the second year of the program
in the ninth grade. Students learn Algebraic concepts from the second semester of
Algebra 1 in this year. The teaching and learning concepts such as the 1999 TIMSS
is the basis of the standards-based curriculum.
Another curriculum that PNH has is the High School Math (HSM)
curriculum, which is an intervention curriculum for students that did not pass the
CAHSEE. Teacher B states, “HSM began at PNH in 2002, when the math teachers’
could see the need from the CAHSEE.” There is HSM 1 for sophomores, HSM 2 for
juniors, and HSM 3 for seniors. Teacher C emphasizes that the purpose of the
interventions is to catch quickly them up on material they have yet mastered, while
still giving them the opportunity to go to college:
HSM 1 has two goals: get ready and pass the CAHSEE and
get ready and pass with a C or better to go onto Geometry in
their 11
th
grade year. Then, Algebra 2 their senior year and
you can onto a four-year college. We are always trying to
make sure they have that opportunity to go to a four-year
college.
The PNH math teachers saw that their students who were not passing the CAHSEE
needed an intervention to help them stay on track to graduating and going to college
is the reason for why they developed the HSM curriculum.
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The HSM curriculum is also similar to the two-year Algebra program
intervention and CPM in the instance that it is also student-centered curriculum and
focuses on problem-solving questions. However, the HSM curriculum only
emphasizes concepts that are on the CAHSEE. In addition, the scope and sequence
focuses on CAHSEE concepts and may support or not be supported by the learning
theory depending upon the PNH teacher teaching the class.
Teacher A also stresses that the PNH math department’s goal for all students is
that they should all have a pathway to Algebra 2, so that they can go to college.
Teacher A then goes onto describe the process by which intervention students can
still go through PNH’s various math curriculums and have the opportunity to go onto
college:
Our philosophy has to do with making sure there is a pathway
to Alg. 2. The pathway has detours to help strengthen you but
you can still make it through. If you come in as an Algebra 1
student, then you get Algebra 1, Geometry, and then Algebra
2. If you digress, it is HS math, Geometry, and then Algebra
2. If you go Algebra 1, Geometry, and then you fall down;
you can go to HS math class as a preparatory class for the
CAHSEE, and then go on to take Algebra 2.
The math department has made many avenues available to students to ensure
that they all have the ability to take an Algebra 2 class and pass because part of the
mission of PNH is to ensure that all students go have the opportunity to go to
college, and the math department at the school takes this belief seriously. This is
why on the math teacher questionnaire, 72% of the math teachers felt that support
classes such as HSM and the two-year Algebra courses added to the master schedule
improved student achievement.
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Classroom Practices. PNH math teachers use a multitude of classroom
instructional practices to teach mathematics. The math teacher questionnaires
indicates that 90% of the PNH math teachers feel that the department has helped
develop effective strategies that have increased the math achievement of students at
the school. Effective classroom practices have four components: effective and
coherent lesson design, promotes high levels of student engagement, is culturally
relevant, and makes use of students’ prior knowledge. PNH math teachers have
these elements as part of their instructional practices daily. The math teacher
questionnaire indicates that 87% of teachers at PNH use research-based instructional
strategies, which coincides with PNH math teachers’ belief that their classroom
practices have all four effective elements and 75% of non-math teachers agree.
Administrator B attests to the fact that when supervising math classrooms,
PNH math teachers are incorporating all of the four elements of effective classroom
practices, and his belief stems from the fact that students’ math achievement is rising
and that the math department is one of the two academically strongest departments
on the campus. Teacher A believes PNH math teachers have effective classroom
practices because the math curriculums they have created have effective and
coherent lessons based upon methodology that produces intense levels of student
engagement, and the teachers particularly try to make every lesson culturally
relevant. The curriculums not only build upon the students’ prior knowledge, but
also have connective mathematical links throughout different mathematical
curriculum subjects such as Geometry instructional techniques and procedures
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connect to Algebra 2, which connects with Pre-Calculus. Teacher B feels that
students’ math performances at PNH are increasing due to the emphasis that PNH
math teachers put on engaging all students in their classroom in math activities, and
the belief that if students have small successes in math, those will lead to bigger
accomplishments. Teacher B indicates that PNH math teachers classroom practices
stem from the conviction that all students can learn and be successful at PNH if
given the opportunity.
The interviewed teachers do provide the researcher with examples of what they
feel is their techniques for effective math classroom practices, and reasons they point
to why they believe PNH students’ are increasing their math achievement. One thing
the researcher noticed about every math classroom had students’ desks and chair set
up in groups. The researcher also noticed that in PNH math classes, students were
working in groups and discussing math problems in groups. Teacher D says about
groups that “if there is an assignment that could be done in groups, I let them decide
if they want to work in groups because there are some kids who like to work in
groups and some who don’t.” During each interview, PNH math teachers
continually expressed their belief in the importance of providing PNH students with
options. Other PNH teachers also felt that part of their classroom practice was to
provide their math students with options.
The researcher also noticed that in PNH math classes, students were highly
engaged, and teachers were walking about the room as facilitators not lecturing in
the front of the room. Students were using many different types of manipulatives
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from food, to paper, to blocks, and every room was equipped with several boards,
an overhead, and calculators. Teacher B classroom practice methodology stems
from the University of Michigan and the UCLA Math Project, which she says are
similar because they both believe in math classes having high levels of student
engagement. In addition, she says that both organizations rely “A lot of conceptual
understanding and problem solving was a big push.” Teacher B indicates that her
classroom practices is also heavily based on having students do problem solve, and
she focuses constantly on “having students, even if they were wrong, to explain their
answers.” Teacher B’s classroom practice philosophy is “I try to look at math from
different approaches, and I gained a lot more from that,” and this is how she
approaches her teaching math in her classroom. Teacher B tries to ensure that
students view math from as many perspectives as possible, so she teaches the
mathematical concepts using as many different methods to ensure that all students
are learning. Teacher B believes that most PNH teachers use a multitude of
techniques to teach PNH students, and this is why the math achievement of the
students at the school is increasing.
Teacher C indicates that she also attempts to use many different teaching
methods in her classroom practices in order to reach every student’s different
learning style. For visual students, Teacher C says, “I use the overhead a lot.” She
models for her student how to do the problems, but Teacher C also recites to the
students her thought processes of how she is solving the equation, while modeling
how to find the answer:
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What I would do is put up the worksheet that they are
looking at. When I am telling them how to do something.
They are seeing it. I think my demand in that they take notes
helps. When I write they write.
During her lessons, Teacher C makes sure that she is always verbally explaining her
thought process through the problems, while students can see the visual
manifestation her solving the problems. Teacher C also believes that note taking
during math classes are essential because she is trying to appeal to students that have
stronger linguistic intelligence. Not only do students take notes, but also while in
pairs, one student orally tells the other student how to solve an equation and while
the one student is telling how to solve the problem, other student is taking notes.
Then the student telling the other student how to solve the problem writes his or her
own notes on how to solve the equation. Then, Teacher C has the students reverse
roles: “If I understand it [the problem], and I am telling you what to write. If I am
writing it down [too], I’m learning how to do it [too].” Similarly, to the other
teachers, Teacher C has students working in groups or pairs, but she likes to have
students learn mathematics through games: “We play games where they can work in
pairs. They have whiteboards, and they decide together if that is the answer, they
want to put up there.” Even though PNH math teachers have different teaching
styles, they all have similar classroom practices that follow the four elements of
effective math classrooms. Teacher C believes the variety to learning that she brings
to her classroom practice is what increasing students’ math achievement at PNH is.
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Teacher A also incorporates all the four elements of effective mathematics
classrooms in her classroom practices, but she describes to the researcher how she
feels it is her relationship with the students and the belief that all students can
succeed in math that makes her use all the veteran techniques she knows in her
classroom practice. Teacher A feels that part of her classroom practice is to make
special connections with them, making sure she talks daily to all students, and being
very observant. She feels that teachers learn a lot about their students from just
watching and listening to them interact in the classroom, but it is important hear their
needs and concerns while talking with them. Building an effective rapport with her
students is an essential technique in her classroom practice toolkit, and Teacher A
believes this is why PNH math students are increasing their achievement.
Standards-Based Instruction. Standards-based instruction is the last element
of effective math programs. It has three characteristics: assessments are aligned to
standards, student achievement data drives instruction and decisions, and common
performance rubrics that were created through collaboration. All PNH math teachers
and administrators stipulate that the math teachers teach to the California state
standards and have standards-based lessons and curriculums, and that the entire math
department feels that state content standards are important. This math questionnaire
illustrates the belief because 85% of the math teachers indicate that the
implementation of standards has served as a foundation for the increase in math
achievement for PNH’s students. The math teacher questionnaire indicates that 87%
of PNH math teachers believe that teachers at our school teach standards-based
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lessons, while only 77% of the non-math teachers feel that the teachers at PNH
teach to the standards. Ten percent more math teachers believe that teachers at the
school are teaching to the standards than the non-math teachers at PNH.
All assessments tied to curriculum such as HSM, CPM, and the two-year
Algebra courses aligned with state standards. All math teachers and administrators
feel that student achievement data drives all math instruction and decisions. This
fact has been proven by PNH’s math department using student performance data to
create new standards-based curriculums to better meet the needs of their students
such as HSM, the two-year Algebra course, and brining in the CPM classes. The
PNH math department does not have common performance rubrics such as the entire
math department has created an Algebra 2 performance assessment and rubric.
However, the PNH math teachers do use performance rubrics that they
collaboratively created for the HSM curriculum and the two-year Algebra course.
On the other hand, PNH math teachers do use the common performance rubrics that
are in the CPM manuals. However, they did not collaboratively create those rubric,
but Teacher A did help to create the Geometry performance rubric with other
teachers outside of PNH.
Conclusion. The mandates of federal, state, and school district policies such
as NCLB, PSAA, and DU’s math policies have had an effect on PNH’s math
curriculum, instruction, practices, and design. The school has made changes in order
to comply with many of these policies, and these responsive changes to policy have
helped to increase PNH math students’ achievement at the school.
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In general, the policies of the federal, state, and DU have led to PNH’s
teachers and administrators focus their efforts to increase students’ math
achievement by examining school data in order to make data driven decision.
Federal, state, and school district policies have driven PNH to create a new method
of hiring teachers, which the terms deem as the departmental interview process. In
attempting to meet the policies, PNH also created new math curriculums, classes,
programs, committees, and relationships with other educational entities. In addition
to adhering and responding to policies in order to raise students’ math achievement
at the school, PNH also changed its school design through rearranging teacher
locations, classroom practices, and school schedules. All of these activities helped to
amplify the positive school culture and math environment at the school, which also
led to increasing students’ math achievement.
Research Question 3: Change Process
Research Question 3 is: “What change process did the school use to enhance
its math program and strategies to assist students in math?” Bolman and Deal’s
(2003) Four Frames of Leadership and the Concerns Based Adoption Model
(CBAM) are lenses by which to examine the change process that led to Pacific North
High’s (PNH) students increase in mathematics achievement. First, this section
begins by describing the historical background surrounding PNH’s secondary reform
movement. Secondly, CBAM is discussed in relation to PNH’s change process.
Third, the section examines the actions of PNH’s administrators and key math
leaders through the lens of Bolman and Deal’s Four Frames. At the time of the
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school’s reform, one of PNH’s current administrators that was interviewed
stipulated that they did not use the Bolman and Deal framework as the basis for their
leadership actions and decisions. However, during his interview, the researcher
asked him to recall the story of the reformation using the Bolman and Deal
framework. On the other hand, the principal of PNH purposely used Bolman and
Deal’s leadership framework during the school’s reform process and continues to use
Bolman and Deal as a primary tool of leadership. Consequently, in matters
concerning PNH math teachers, teacher leadership, or when the principal that began
PNH’s reformation process is mentioned in this chapter in connection with the Four
Frames, the researcher is using the framework as a guide to understanding and
analysis of former leadership decisions made during the reform process at PNH.
Historical Background
Fifteen years ago, the community around PNH was slowly changing. PNH is
located in the Northern part of Malls, and the 1990s signaled a change in the
ethnicities of the families moving into the neighborhood. Northern Malls had been
predominantly Caucasian and then more Asian and Hispanic families moved into the
district. African Americans have relatively remained a small part of the community
from then until the present.
The principal at PNH at the time foresaw that the new population moving into
the area that PNH serviced implied that the student population at PNH was to change
in the near future. For that reason, she began using professional developments to
prepare the teachers for this new influx of students, while she kept searching for new
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and innovative ways that teachers can instruct students. She shared her vision for
the school with the faculty and staff, and described to them that the school was about
to undergo a change process
The faculty at PNH had never had much turn over, and when teachers began
teaching at the school, they eventually would end up teaching 20 to 30 years and
retiring from PNH. This meant that many of the instructional practices of PNH
teachers were outdated and needed a refresher, so when the new students came to
PNH, they did not perform as well as teachers and administrators hoped because
most teachers were just doing teaching as usual. This was just about the time when
the federal government and the state started making proclamations about
accountability and closing the achievement gap was first and foremost in everyone’s
mind. Professional standards for teachers and state content standards for teachers
were coming to schools, and California was creating new standards-based content
accountability tests. PNH teachers and administrator realized that their students had
new ways of learning and teachers needed new methodology and techniques to teach
them.
The state was starting to hold schools accountable for ensuring that all
students would pass accountability tests, graduate from high school, and have the
opportunity to go onto college. PNH administrators and teachers knew that their
school’s test scores were showing that while some students were succeeding at their
school, a significant number of students were not. With this realization, the teachers
and administrators at PNH made a commitment to themselves, the students, and the
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parents in the community that they would change school curriculum, instructional
practices, staffing, and school design to ensure that all students at PNH would have
the opportunity to succeed.
The first thing to change was staffing. The administrators saw to it that for
those teachers that did not commit to making these changing, they would not be
working any longer at PNH. There were also modifications made in the arena of
administration. Then, PNH administrators and teachers looked at their school
performance data to determine how and what ways they needed to change to raise
student achievement, and they concluded that they needed to alter the school
curriculum, school design, classroom practices, and provide different professional
development.
Because of the needs of PNH’s student population, the teachers and
administrators put into place a variety of classes, curriculums, committees, altered
the school’s design, had various staff changes, and are providing continuous
professional development for both teachers and key leadership. PNH has now
become a school committed to the success of all students, but is struggling to keep
ahead of the state accountability measures, abreast of the newest instructional
practices, and the changing politics and policies of the Directional Unified (DU)
school district.
Change Process through CBAM
CBAM. There are seven levels in the Concerns-Based Adoption Model by
Loucks and Hall (1979). The zero level, Awareness, is where the person or group
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has no concern for the about the topic or the change process. Informational is the
first level of CBAM, and the person or persons is beginning to have interest in the
topic or the change process. The second level of CBAM is Personal. The person or
persons wonder how the topic or change process will affect them. In level three,
Management, the person, or persons are organizing and planning for the topic or the
change process. The fourth level of CBAM is Consequence, and the person or
persons are in a routine with the topic, in the habit of using the curriculum, or
pondering how their use of the item is affecting others. Collaboration is the fifth
level of CBAM. The person or persons are working in partnership with others on the
topic or the change process. The final level of CBAM is Refocusing. In this stage,
person or persons modify the topic or the change process in order to make it more
effective or create different options for its use.
The CBAM levels act as a framework for the changes that took place at PNH
as the school attempted to raise students’ achievement. Particularly, this section of
the dissertation will focus on how the overall change processes of the school led to
the increase of specifically students increasing their performance and achievement in
mathematics.
CBAM Level 0. Around, fifteen years ago, PNH was in the zero stage of
CBAM development. The teachers and administration had no awareness of the
change process that the principal was about provoke. At the time, PNH was a school
filled predominantly with Caucasian students. There were only a small number of
students of color, and they were mostly Japanese and African American. Both
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administrators at PNH today stipulate that, not until recently, has the PNH
teachers and faculty had changes or significant turnover. At that time, the school
would go seven to ten years without receiving a new teacher. PNH was the model of
stability, and no teachers or administrators other than the principal were pondering
on the upcoming changes they would see within the next few years.
CBAM Level 1. It was the principal around fifteen years ago that announced to
PNH teachers and staff that the school would have to transform in order to
effectively serve the new student population shortly to enter the school, that made
the teachers and administration aware of the modifications that were shortly going to
have to be made at PNH. Administrator B called the former principal a visionary,
and so the faculty and staff were thrust into CBAM level one with the principal
saying, “the demographics are going to change and we need to put things in place.”
It was then that she shared her vision with the school and went over the new changes
that were going to take place at PNH.
PNH’s teachers were just beginning to receive information from the
administration about state mandates, standards, and new district policies that
stemmed from the state accountability measures. A new wave of reform was
permeating the discussions of PNH teachers. In addition, the math department was
receiving information about new mathematics techniques and methods such as the
TIMSS reports and CPM.
CBAM Level 2. The second level of CBAM is the Personal stage. Once the
principal made PNH aware that the school had to alter its instructional practices,
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teachers began to wonder how modifying instruction would affect their teaching.
Administrators were pondering how the changes in teaching would affect their
supervision, professional developments, and hiring practices. Math teachers were
asking administration about how the reform process would affect them, and
administrators were working with key math leaders to bring back answers to PNH
math teachers’ questions from the DU and the state.
The math department began to wonder how the new students would affect
math teaches methods of instruction, and how PNH math teacher would have to alter
classroom practices to meet the needs of these students. Teachers that did not
approve of the idea of changing their teaching methods were beginning to whisper
their discontent about the belief that PNH needed to alter their instructional practices.
Fear of the unknown and change about the changing role of the teacher in the
classroom was affecting some teachers (Teacher A).
CBAM Level 3. The Management level of CBAM for PNH teachers,
administrators, and staff took years because PNH administrators and teachers
implemented many changes and programs to PNH’s school design, programs,
curricula, and classes. During this time, PNH’s key math leaders instituted programs
such as CPM, HSM, the two-year Algebra courses, homeroom, open-math policy,
and the departmental interview process. The programs were implemented gradual
stages starting with CPM in 1991, two-year Algebra courses, HSM, homeroom, and
then the open-math policy (Teacher B). Each program implementation required
implementation by math teachers of new classroom practices and methods.
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Teachers A and C recall during the Management level most teachers during
this period were involved in some aspect of creating one or more curriculums or
were on one math committee, and that implementation of the programs was
performed with the help of all the PNH math teachers.
During this stage, PNH student performance data also suggested that all PNH
math teachers needed to alter their instructional methods, and this belief stemmed
from the facts of the TIMSS reports. At this time, they also began forming subject
specific math committees. Math committees were dialoguing about students’ low
mathematic data and what were curriculums needed in order to raise PNH students’
math achievement.
In one instance during this stage, Teacher A describes that when the transition
to standards occurred, as part of the changes PNH was making to ensure that all
students succeed, some teachers were adverse to teaching to the standards and using
the standards as a base for their instruction and curriculum. They refused to make
the changes to their instructional practice and classroom methodology. Teacher A
stipulates that those that refused to utilize standards in their classroom instruction the
administration asked them to leave. Administrator B says they took early retirement,
and Administrator A indicates that there was no place for them at PNH. However,
the number of teachers that did not implement the reform changes, and there were
only a few, the administration asked them to leave.
The incorporation of the new math curriculums were significant changes that
occurred during this level of CBAM. First, the math teachers began the CPM
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curriculum at PNH. It took several years of implementation until the school had
CPM Algebra 2, Geometry, and Pre-Calculus. Teacher C felt that the teachers were
excited about implementing CPM because they enjoyed the program, and believed it
would help PNH students. Teacher A knew that implementation of CPM is what the
students at PNH needed in order to raise their math performances. Several teachers
also enjoyed seeing the execution of math curriculums such as the HSM and the two-
year Algebra course. Math committees were also busy during this stage, ensuring
that the PNH math teachers and students were transitioning well into the new math
curriculum and system. In addition, teachers were to begin using research-based
instructional strategies in all math classes. Administrator B attests that it took
several years, but things at PNH began to change.
CBAM Level 4. Level four of CBAM is Consequence, and it involves the math
teachers at PNH implementing the transitional changes in math that took place at the
school, and that they are now accustomed to working within the new changes that
happened at PNH. This level is similar to CBAM level 3 in that it also took years for
the PNH math teachers to feel comfortable with the new reforms made at the school.
In this level, PNH teachers wondered how the implemented changes at PNH affected
the students. The administrators would question how the changes they institute are
affecting the teachers. Administrator A feels that the school is still in this stage with
many of the programs and curriculums used at the school. Teacher B admits that
many of the PNH math teachers feel very comfortable with certain math programs
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that they have been using at the school for awhile such as CPM and the two-year
algebra courses.
CBAM Level 5. The fifth level of CBAM is Collaboration. In this stage,
PNH teachers are working in teams and the administration is collaborating with the
teachers. Teachers A, B, C, and Administrator B felt that this level is a continual
state of existence for PNH teachers and administrators. The math teachers, during
their math meetings are examining ways in which they teach the curriculum and
programs in order to share best practices and PNH students’ math achievement data.
This is the time that math teachers share instructional and classroom practices. In
addition, the math teachers share issues and concerns about curriculum, instruction,
and programs. Not only do they share these concerns, but also the math teachers
look for solutions to their collective problems. Administrator B thinks about
collaboration and remembers the past:
The biggest thing that has happened here is that teachers don’t
work in isolation anymore. Ten or 15 years ago, it use to be
let’s close the doors and they basically you were king of the
castle. That’s not the way it should be. If you look at it that
way, you are not going to grow as a person or as a teacher.
PNH teachers used the meetings to collaborate and discuss ideas about instructional
practice, math methods, and used the time to plan professional developments and
programs for PNH students. Administrator B says that collaboration has always
been part of the PNH school culture: “Part of this [collaboration] has always been
the norm here.” In addition, the questionnaire also stipulates that 87% of the
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teachers feel that collaboration has played a key role in increasing student
achievement at PNH.
In addition, Teacher A feels that the collaborative efforts of the PNH math
teachers extend into having collaborative relationships with students in the math
classrooms during math labs and projects. The belief in collaboration that PNH math
teachers demonstrate with each other translated into classroom activities because
many PNH math teachers require high levels of collaboration from their students
during math class.
Another example of the math department’s collaborative nature is that it has
aligned itself very closely to the science department. Administrator B indicated that
whether the science department led, the math department would soon follow. The
PNH math teachers’ collaboration with the science teachers has led to both
departments becoming the two most important and foremost departments on campus.
With the advent of the PSAA, the PNH math department knows exactly where they
want to take their students, and all teachers interviewed felt that they had a clear
sense of how the department was going to achieve that success.
CBAM Level 6. Refocusing is the sixth level of CBAM. The teachers modify
the PNH math curriculum, programs, or instructional practice for alternative uses or
for more effectiveness during this stage. This stage is also continuous for PNH math
teachers and administrators. The math teachers are always examining their
curriculum and program for ways to enhance it to better serve PNH students and
make them more successful in mathematics. PNH math teachers continually refocus
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their efforts in order to find better instructional methods or find different ways to
use old instructional methods.
PNH teachers would use meetings to reflect upon how the implementation of
the math curriculum, programs, and new instructional techniques were progressing,
but also to determine in which ways they needed to alter the programs to be more
effective for the students. This is what happened with the HSM program. Teacher C
indicated that the teachers felt that they needed to alter the program to make it more
effective, so they changed the curriculum to meet the needs of their students.
Something similar occurred with the Pre-Calculus class. Teacher A indicated that
PNH math teachers discovered that some PNH students did not want to take Pre-
Calculus, but were still willing to take another math class, so the math department
created the Probability and Statistics class. Teacher B indicated that this same idea
of creating a class as an alternative math class for students happened with
Trigonometry. PNH math teachers created a Trigonometry class for students that did
not pass Algebra 2, but the students are still learning similar math concepts to
Algebra 2 but in a different style. Teacher B remarked during the interview that this
is the stage when teachers find new ways to teach mathematics or they revamp old
ways for different purposes. Administrator B suggests this is the period where PNH
math teachers reflect upon instructional practices and curriculum.
Administrators during refocusing are revisiting math department plans from
the past. They are trying to make judgments about the math curriculum and
programs effectiveness. They are balancing resources and funding to continue
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supporting the math curriculums and programs. They are negotiating with the
DU for resources and funds for the school. Administrators are also negotiating with
parents when any change or modification occurs to their child’s curriculum or
program. Just lately in the refocusing phase, Administrator A suggests that PNH has
been hiring a significant number of teachers. Administrator B says PNH has been
hiring more teachers because their staff was stable with no turnover so long, and now
those teachers are retiring and a new set is taking their place. Administrator A
stipulates recently, PNH has been hiring more teachers from Michigan: “Even when
we lost solid people, they have been replaced by solid people. If they are weak, they
haven’t really stayed.”
Change Process through Four Frames
Another framework used as a lens in which to analyze the findings produced
by PNH during the study is Bolman and Deal’s (2003) Four Frames. The Four
Frames are structural, political, human resources, and symbolic. There are several
different attributes associated with each frame. The attributes associated with the
structural frame is that the leader is strong in hierarchies, rules, polices, and
procedures. The features of the human resources frame are that the leader has
strength in dealing with personnel, collaboration, and groups. In the political frame,
the leader is strong in bargaining, garnering resources, and negotiations. A leader
strong in the symbolic frame employs elements of vision, belief, and storytelling.
Leaders utilize one or more of these styles regularly because most leaders are
dominant in one of more of these frames. Bolman and Deal’s four frames act as a
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guide through the leadership processes of PNH’s administration, while the school
attempted to alter itself by raising student achievement.
When asked by the researcher where Administrator A views the PNH staff on
the CBAM continuum, she said that the school was either implementation or
collaboration. However, Administrator A did note, “the math department was real
comfortable with change, but wanted to have a voice.” Administrator B felt the
school was at collaboration or refocusing. However, many different stakeholders at
the school depending on what is the topic can view what CBAM level PNH is in
many different ways. During the interview, Teacher A felt similarly to
Administrator B in the respect that the math department was alternating between
Collaboration and Refocusing. Teacher B felt the math department was in the
Collaborating stage and Teacher C felt the department was in Refocusing. Teacher
D was not sure what stage the department was in, but did say that the department
does a lot of collaborating.
Story of PNH’s Secondary School Reform through Four Frames. Around
fifteen years ago, PNH’s principal saw the need for PNH to reform its educational
practices to meet better the needs of changing population in the school’s community
as well as the larger scale changes taking place within the political and social context
of education. Administrator B recalls that at that time, the current principal was very
high in the symbolic frame, even though the principal was not intentionally using
this frame of leadership. The principal knew the educational direction in which PNH
needed to go, and explained the idea to the faculty and staff. Administrator B called
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the former principal a visionary, and remembers the principal’s words as she
addressed the faculty and staff about the reform movement that was to take place at
the school: “the demographics are going to change and we need to put things in
place.”
It was during this time that the principal shared her vision with the school and
went over the new changes that were going to take place at PNH. Administrator B
stipulated to the researcher that he recalled the principal to be high in symbolism
because she already envisioned the change-taking place at PNH. He states, “She was
a visionary because she saw the change and prepared us for change, and what you
have to do to address the change and adapt to different cultures.”
Information gathered from the interviews suggested to the researcher that in
the beginning of PNH’s secondary reform, PNH’s administrators and teachers were
working within high levels of the structural frame. Nothing had changed in years,
and everyone knew his or her organizational roles. This suggested to the researcher
that the principal had created a state of stability at PNH, which indicates that she was
strong in structure, but she made those working for her feel appreciated and valued
(Teacher A), and that suggest that she was also strong in relationships. The
researcher feels that what speaks to the former principal’s sense of human resources
is that the staff was stable, and there had not been much instability or change
amongst teachers and staff. The school culture was positive.
In preparing for PNH’s educational transformation, the researcher believes that
the principal significantly used the political frame to begin initially gathering
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educational resources for the school in expectation of the change. She had to
clear all reform decisions, not only with her faculty and staff, but also with the
district office. PNH was one of DU’s first high schools to try to accomplish such
wide-ranging educational reforms, and this is why the principal at the time was keen
on being politically perceptive. She had to get resources such as proper professional
development for her teachers and funds for the new programs, curriculums,
textbooks.
In addition to the changes in the school’s student demographics, there were
other educational changes about to take place at PNH. Standards and accountability
were educational hot topics, and the political climate at the time was putting more
stress on schools to produce students that could compete within the international
arena with other industrial countries. The federal and state governments were
beginning to require that schools prepare all students as if they are going to college
and graduating from high school, and all teachers were being required to use content
standards as the base of their instruction. The principal was savvy in that she
foresaw these changes in the educational climate, and had already began preparing
PNH teachers and administrators for these changes.
It is during this time of standards and accountability that Teacher A indicates
that PNH began to see an influx of students of color, and the achievement for some
of these students was low, especially in mathematics. The researcher believes that
this is when the math teachers exhibited that they were high in structure, and they
began to collaborate in order to create curriculums and programs such as CPM, the
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two-year Algebra course, and HSM. Teachers A and C recall that most teachers
during this period were involved in some aspect of creating one or more curriculums
or were on one math committee. During the creation of these programs and
curriculums, the math teachers set goals for themselves and their students.
In addition to structure, the researcher stipulates the math teachers must also
have been working highly in symbolism because they saw the need of the students,
and had the belief that they could provide PNH students with better methods and
practices for teaching math. The teachers had student data performance that proved
the need for mathematics interventions and alternative methods and the need to
change math instructional practice. In order to fulfill the vision of raising students’
math achievement at PNH, teachers began forming subject specific math
committees. The committees mapped out math reform strategies, curriculum, and
practices based on students’ math performance data in order to increase PNH
students’ math achievement.
The researcher suggested that many of the PNH math teachers were in the
human resources frame because they truly cared about what they were trying to
accomplish for students as well as caring about their fellow teachers, as stipulated by
all those interviewed. Many math teachers volunteered to teach the new reform
classes because they wanted students to succeed in math. In addition, they felt it
necessary to make sure to train all teachers in new instructional techniques, in the
new curriculums, had a voice in the new curriculums, and encouraged new
classroom practices.
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During the implementation stage of PNH’s secondary reform process, the
researcher believes the administration was working within the structural frame in that
they were finding time for math teachers to meet with each other to plan the new
curriculum and instructional ideas. Administrators needed to ensure that the school
met and accomplished its goals and timelines. The researcher also sees the
administrators as working in the political frame during this stage because they were
asking DU for resources and going outside of the district to find support for the work
their teachers were doing on the math curriculums and program design. In addition,
the views the reorganization of the math master schedule, the math teacher
assignments, the school’s bell schedule, and the school’s organizational design as a
function of the human resources frame. Teacher A recalls the administration
supporting the teachers in their work to ensure that all students succeed at PNH, and
Teacher C remembers how willing the administration was to find the necessary
resources for the math teachers to continue their work on the curriculums and
instructional practices. Finally, the researcher stipulates that the administration must
also have been high in symbolism because they continually reminded teachers of the
reformation vision of the school, and they also communicated to the teachers how
the new state accountability system (PSAA) and NCLB would affect the school if
they did not meet the standards of the state or federal government.
Several years elapsed during the beginning of the reform process and the end
of the implementation period. Administrator B and Teacher A suggested that during
this period, several changes in the administration occurred, and this signified to the
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researcher that the school underwent a shift in its human resources frame. The
school began the reform process with one principal but went through a few by the
end of the implementation stage. In addition, the school had also had many assistant
principals during this time. However, by the end of the implementation period, the
school did not have a principal or assistant principals with a background in
mathematics, even though, in the past, the school did have administrators that had a
math background. Administrator A admits that new administrators had to learn the
school culture, politics, and had to continue the visionary reform plan started at the
school before their arrival.
In the implementation stage, Administrator B suggests that the PNH
administrators worked within the structural frame by making sure the master
schedules were properly organized, and that they had put the right students within
the classes. Students needing intervention would be receiving the two-year Algebra
course or the HSM curriculum. Students that wished to go into CPM would be in
those classes as well as those students that choose to stay in traditional classes.
Administrator B indicates that this is the stage that administrators would reorganize
teachers room locations to enhance collegiality and ensure that new teachers were
receiving support from a veteran math teacher. Administrators would still be
scheduling the math committee meeting times, and would ensure that those
schedules did not conflict with other meetings at the school.
The implementation stage is where the researcher feels the administration
became active in the political frame because the administrators had to negotiate with
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DU to receive assurances that the district would fund the math curriculums and
programs at the school such as the CAHSEE after school math tutoring program and
supply the program with books. In addition, the researchers feel that during this time
the administration used this frame in order to let teachers go that would not properly
implement the changes that all math stakeholders had agreed upon: “And for awhile
there, I think we had some teachers who were like, it’s a job. It’s a paycheck”
(Administrator B). Those were the teachers that Administrator A said were asked to
leave the school because they were not willing to be an effective member of the PNH
staff working towards increasing students mathematic achievement. However there
was only a tiny number of teacher asked to leave, most complied.
During this period, the researcher feels that the administrators were letting the
teachers shape the symbolic vision of the new math department with its new
curriculums and programs. Administrator B felt that the administrators were aware
that the symbolic frame is more than visionary; it is also a chance for administrators
to reward teachers on the difficult job of implementing curriculums and programs.
Administrator B felt that the teachers wanted the ability to shape their own idea of
the math department’s implementation of the curriculum and programs without much
interference from administration.
After implementation, the teachers began to reflect upon whether the reform
measures were increasing PNH students’ math achievement. During this stage, the
researcher believes that PNH math teachers were high in human resources because
they collaborated with each other often. Not only did they collaborate with each
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other, but also with students and parents to ensure that they were reaching all
students with their curriculums and programs, and that all PNH students had the
opportunity to succeed in math. The math teacher questionnaire indicates that 95%
of the PNH math teachers feels that teachers collaborate to develop common
assessments and rubrics, but the teachers also indicate in interviews that it is not so
much common rubrics and assessments as it is curriculum and mathematics student
performance data of all kinds; it is not restricted to just assessments and rubrics.
When interviewed, Teacher D indicated that PNH math teachers have always
been high in the human resources frame because it is one of the friendliest
departments on campus, and Teacher B suggests that the PNH math department is
just like a family. Teacher A also indicated to the researcher that PNH math teachers
are extremely high in human resources because she remembers collaborating often
with teachers all throughout her 20-year teaching career at PNH, and she mentions
how still continues to collaborate often with other math teachers about curriculum
and instructional practices. In addition, Teacher A feels that the collaborative efforts
of the PNH math teachers extend into having collaborative relationships with
students in the math classrooms during math labs and projects. This is another
indication of the PNH math teachers are working within high levels of the human
resources framework.
The researcher indicates that PNH math teachers worked within the structural
frame in the sense that they extensively collaborated with each other to refine the
reform programs, curriculum, and instructional methods. The teachers exhibited
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good communication and planning skills in order to manage all the collaborative
meetings between themselves, the administrators, the parents, and the students. The
math department is structural in the sense that each math teacher knows math policy,
procedure, and chain of command.
In addition, during this time, the researcher believes that PNH math teachers
are frequently high in the political frame because they use their resources wisely to
give themselves collaborative time. The fact that math is a core subject, and that
PNH teachers know how to use this clout to their advantage, suggests that math key
leaders at PNH are fully aware of how to employ the political framework.
Furthermore, Teacher A and Teacher B indicated to the researcher that the
administration attempted to make sure that parents understood the symbolic vision of
what was happening in the math department at the school, and how best parents
could collaborate with the department and the administration to ensure their child’s
success. This frame also involves administrators reassuring and praising teachers
that work well together for the betterment of the school. Administrator B says that
teacher and administrators have collaborated so much that “The teachers feel free to
just ask the principal and say ‘hey there is a problem’ we see something happening
and how do we address it.”
The current administration began during the last stage of implementation and
the being stage of PNH’s reflective period. After implementation, the researcher
indicated that the PNH’s administrators have many attributes associated with the
symbolic lens because administrators must have plans months in advance, but the
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flexibility to change when needs arise. During the reflective period at PNH,
administrators continue to reward the PNH teachers’ efforts, but keep encouraging
teacher to keep perfecting their curriculums and programs to make it even more
effective for all stakeholders. Administrator B suggests that it is important that
teachers know understand that they are appreciated. In addition, he says, “I think
now we are getting more teachers that are saying I can make a difference and really
believing it.” Administrator A explains that this is why administrators must
continually discuss the vision of where the school is going during every frame, but
especially in refocusing.
PNH’s Current Administrators through Four Frames. When discussing the
four frames with the administrators and the teachers, Administrator B stated to the
researcher that he believed that he operated in more of a structural frame. However,
the researcher feels that his position often makes him rely on the human resources
frame because he frequently has to observe and evaluate teachers at PNH. In
addition, he is often providing advice to newer teachers about instruction: “As older
teachers you have that bag of trick…to get kids engaged, and you don’t have to think
about using those things, I tell them [the tricks] to help the younger teachers, and let
them try it.” On the other hand, Administrator B did not seem to realize during the
interview, but he told the researcher over ten different stories. His language was full
of metaphors and he is an apt storyteller, but when asked what he thought his
strongest four frames were, he did not say symbolism. However, other interviewed
teachers stipulated to the researcher that Administrator B is a good organizer, but the
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researcher feels that where he draws his most strength and passion is from the
symbolic frame.
Teachers indicated to the researcher that they believe that Administrator A is
very high in the political frame. One of the most frequented comments the
interviewed teachers had to say about Administrator A is that she would tell the math
teachers, “Whatever you need, I will get it.” When the researched asked
Administrator A what structural changes she did to influence the students increase on
math achievement, she believed that getting more school funding for professional
development for the teachers was significant. Even though organizing professional
development is structural, the researcher believes that Administrator A is heavily
working in the political frame because she saw the ability to tap into resources to get
the math teachers increased funding. The significant element that kept professional
development going for the math teachers was money and knowing how to
manipulate resources. When the researcher asked Administrator A how she
negotiates the political aspects associated with the change process she says, “I am
comfortable in the politics arena.” Administrator A believes that it is easier for her
to use relationships in order to gather resources for the school because she has been
in the district for 20 years and has a long history of building relationships with
others. Building relationships to gain resources is the method by which
Administrator A feels is how she negotiates political aspects at all levels—the site,
the district, the community.
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When Administrator A was asked what she did symbolically to support and
engage in the change process implemented at PNH to improve the math
achievement, she indicates says, “I think its honoring the past and those who have
contributed to make the values of the school what it is and being visible at all
events.” PNH has had a long history, and some of the math teachers have been
working over 20 years to increase PNH students’ success in mathematics, so
honoring their work from the past to the present is important. All teachers
interviewed expressed to the researcher that they felt the administration, especially
Administrator A, worked highly within the symbolic frame to encourage, inspire,
and recognize their accomplishments. Teacher E stipulates that the DU has not
given PNH any type of recognition for the work they have done in raising
achievement at the school.
Conclusion. When examining the change processes that PNH used to enhance
its math program and strategies to assist students in math, Bolman and Deal’s Four
Frames and CBAM were used to understand PNH’s secondary reform
transformations. PNH took over fifteen years to complete its CBAM transformation,
and it continually shifts back and forth between CBAM’s Management and
Refocusing levels because every time PNH math teachers find ways in which to
modify their reform effort they go back into CBAM’s Management level through to
Reformation. The CBAM model of change is continuous for the teachers and
administrators at PNH, and the stages repeat, not necessarily simultaneously for each
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reformation program, curriculum, and instructional practice that the teachers have
put in place at the school.
In using the Four Frames to examine the actions of PNH’s administrators, key
math leaders, and math teachers, it is apparent to the researcher that at the beginning
of the reform movement, PNH’s administrators were high in the symbolic frame. As
time went on, the political frame and structural was more in the forefront, but human
resources was also an underlying style for the administrators. However, in the
reflective stage symbolic again reemerged as a readily used style of leadership for
PNH administrators. Currently at PNH, the administrators’ exhibited to the
researcher attributes from both the symbolic and the political frame, mainly because
of the political climate of the district and the personalities of the PNH administrators.
Interestingly, all four frames are and were evidently used by different key math
leaders at PNH from pre-reformation to post-reformation, and continue to be
exhibited in PNH’s current math key leaders.
Research Question 4: Instructional Leadership
Research Question 4 is: “To what extent was strong instructional leadership
important in improving a) the math programs/strategies and b) math achievement
among students?” In order to answer research question four, the researcher uses the
instructional leadership framework that is based on Johnson (2002), Hessel and
Holloway (2002), and the principal standards from the California Department of
Education. The instructional leadership framework consists of five components:
vision for learning, supervision and monitoring of instruction, community and
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political, culture of teaching and learning, and data driven decision-making
analysis. Vision for learning is the first component of the instructional leadership
framework, and leaders in this component acts as a facilitator for the
implementation, communication, and planning for the vision for the school.
There are five characteristics of vision for learning: developing vision,
communicating the vision, implementation of the vision, and monitoring and
evaluation of the vision, and addressing obstacles to implementation and realization
of the vision. Supervision and monitoring of instruction is the second component,
and it involves leaders monitoring and observing the school’s instructional program
and curriculum and providing teachers with effective, helpful, and timely feedback.
There are four characteristics to the supervision and monitoring of instruction:
classroom monitoring on a daily/weekly basis distributes resources to ensure
successful teaching and learning, supervises personnel, and hiring of personnel that
supports the learning goals and vision of the school. The third component of the
instructional leadership framework is community and politics, which indicates that
leaders in this frame collaborate with community and parental stakeholders to
respond to the needs of both parties to musters the community resources. This
component has four elements: the leader understands the value of diversity,
recognizes community’s needs, engages the community in the school, and provides
opportunity for the community to be involved with the school. The fourth
component of the instructional leadership framework is culture of teaching and
learning. Leaders in this frame sponsor, cultivate, and maintain the school’s culture
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and instructional program. Five characteristics compose this frame: valuing of
students and staff, create and maintain the school’s culture, culture that is inclusive
and respectful of diversity, implements practices for culturally relevant teaching and
learning, and celebrates students, teachers, and staff. In the Data driven decision-
making frame, leaders use data as a tool for informing instruction and supporting
student learning. This component has seven characteristics: the leader utilizes
assessment data to place students appropriately; uses formative benchmark school
site assessments, has summative standardized assessment, disaggregates data by
students, classes, and cohorts, uses data to guide and improve teachers instructional
program, uses data to guide and improve teachers instructional program, uses data to
create master schedule, and uses data to inform and improve pacing instructional
plans.
Vision for Learning
PNH has had a history of strong instructional leadership at the school,
especially in the frame of vision and learning. Both administrators and teachers
recognized the former principal to be high in the symbolic frame because of her
vision and ability to translate that vision to her staff. PNH’s current instructional
leaders honor the past efforts of PNH’s leaders from before, but they also add their
own instructional leadership abilities that have contributed to the increase in math
achievement amongst PNH’s students.
Developing the Vision. Similar, to the past instructional leaders at PNH, the
school’s current leaders are high in several elements of vision and learning.
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Administrator B has been a key part of vision and learning’s first characteristic,
developing vision. His natural leadership style is symbolic, and he has helped to
create PNH’s vision of a successful math department with students increasing in
their mathematic performances. Administrator B’s philosophy has been that “I
didn’t want anything to come from the top down.” He saw a math department in
which the power for improving students’ achievement was in their hands. He helped
develop the vision through inspiring the math teachers at PNH to create their own
vision of how they were going to improve their department’s curriculum and
programs. Administrator B strongly believed that if change was to happen, it must
come from the teachers because they were going to be the ones to implement the
changes in the classroom and at the school. It was the vision of Administrator B to
change the school’s design so that the math teachers would be in pods, and new
teacher would have a veteran math teacher next door to them.
Administrator A was also another force at PNH that helped develop the math
department’s vision of success. She laid the foundation for the math teachers’
success through giving them clear expectations of what the federal and state
governments expected, what the district expected of the school and teachers, and
what the administration at PNH expected of the math department. Administrator A’s
clarity of goals and outcomes for teachers and students enabled the math department
to understand the rubric by which they were being judged, and they knew what goals
and outcomes stakeholders expected of them.
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Another key instructional leader that was essential in the development of
the vision and learning that led to the math teachers and students’ success is Teacher
A. Teacher A has been involved in PNH’s change process since it began, and has
led the department into its current success with students increasing their math
performances. She was instrumental in helping the math department determine in
which direction they were to go with curriculum. Teacher A also helped the math
department develop the intervention programs and the new math department design.
Teacher B is another key instructional leader that helped PNH develop the
vision of collaborating with entities outside the school like the UCLA Math Project
and recruiting new math teachers that had innovative ways of teaching mathematics.
She also is key in developing the various math committees at the school, and making
sure the department is getting effective professional developments.
Communicating the Vision. Several instructional leaders are responsible for
communicating the math department’s vision because PNH has had a history of
collaboration. The structure of PNH is unique in that the math department has
several key instructional leaders, and each leader is responsible for communicating
their part of the math department’s vision. Administrator A communicates the to the
math department the school’s general and overall vision, while simultaneously
conveying important information from the state and district that might affect the
department’s vision. Because Administrator A, in the beginning, clearly conveyed
the expectations from the state, district, and the PNH administration, the vision of the
math department’s curriculum and programs is clear to all stakeholders.
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Administrator B communicates the vision through personal conversation
with both teachers and administrators. He visits the math department meetings and
math teachers’ classrooms. He uses a lot of metaphor and storytelling to get across
the vision. He is the central communicator or the vehicle by which the other
instructional leaders convey messages to each other. In addition, Administrator B
conveys messages about the math teachers’ vision of curriculums and programs to
parents.
Both key instructional leaders that are teachers convey messages directly to
other teachers and to Administrator B. Teacher B conveys messages about the math
department’s vision for curriculum and programs to other departments at PNH, but
also to parents. She also uses technology such as email and phone messages to talk
to teachers. Teacher A communicates with the teachers within her specific
committees, but also with parents and students. Teacher A feels it is imperative that
she frequently discusses the math department’s vision for curriculum, programs, and
instructional practices with students at PNH.
Implementing the Vision. The implementation of the vision was again the
responsibility of all four key school instructional leaders. Teacher A implemented
the math department vision of the CPM curriculum, and significantly helped with the
planning of the intervention programs HSM and the two-year Algebra course.
Teacher B helped implement the math department’s vision of multiple committees
and the UCLA Math Project. Both teachers helped implement the new math classes
in the math curriculum such as the Trigonometry and Statistics/Probability classes.
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In addition, both teachers helped implement the vision of new classroom practices
in the PNH math department.
The administrators at the school helped implement the math teachers’ vision of
curriculum, programs, and classroom practice through finding funding and resources
to help support the vision. In addition, the administrators helped ensure that
implementation of the math department’s programs, curriculum, and classroom
practices were properly organized, arrange, and direct the installation at PNH. The
administrators also made sure that the district office approved of the implementation
of the vision PNH’s math teachers had for the department. During the
implementation, the administrators ensured that all school design measures were
enacted in order to help facilitate the math department vision.
Monitor and Evaluate the Vision. The administrators at PNH help monitor the
math department’s vision of curriculum, programs, and classroom practices through
classroom observations, discussions with teachers, dialogues with other key math
instructional leaders, and dialogues with the district office. PNH math teacher
instructional leaders also help monitor and evaluate the vision through dialogues
with teachers, administrators, parents, and students. The teachers analyzed students’
performance data with administrators and fellow PNH teachers. Both teachers also
visited classes to see if the vision is effectively being instituted. Communication
with all stakeholders and all key leaders is the way in which both administrators and
PNH math teacher leaders monitor and evaluate the curriculum, programs, and
classroom practices vision of the math department.
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Addresses Obstacles to Vision Implementation and Realization. All four
key leaders address obstacles to the realization and implementation of the
curriculum, programs, and classroom practices of PNH’s math department. The
math key instructional leaders are the first to addresses implementation or realization
issues with teachers, parents, or students. Then, the teachers would communicate
these problems to the administration. The administration would look further into the
situation, or they would allow the key math instructional leaders to address and
resolve the situation. If the teachers could not resolve, then, the administrators
would intervene.
Supervision and Monitoring of Instruction and Personnel
PNH has a self-policing policy about supervision and monitoring of
mathematics instruction. Most math teachers collaborate with each other, so it
creates an environment of self-monitoring. Because of collaboration, math teachers
are monitoring each other on a weekly basis. In addition to self-monitoring, the key
math instructional leaders do go out into the classrooms to observe teachers on a
weekly basis. The administrators observe the teachers more infrequently because
they have so many other teachers to observe at the school. However, Administrator
B does monitor classes on a weekly basis. Up until recently, Administrator B was
visiting classes daily.
Allocation of Resources. Most math teachers in the school are first to
acknowledge that Administrator A immediately allocates resources that are
necessary to ensure successful teaching and learning of math at PNH. Teachers A
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and B both remark that she can always rely on Administrator A to provide for the
math departments needs such as materials, professional development, and
collaboration time. Teacher A retells a story of when she asked Administrator A to
get graphic calculators for the math department, and shortly after the discussion,
Administrator A found the money to supply not only the department with calculators,
but she got so many that all math classes were supplied. Administrator A comments
that she tries to individualize the resources she provides to the PNH math teachers
because she stipulates that not all teachers need the same resources. However, it
should be noted that the math key instructional leaders are also very resourceful in
providing the math department with items in which they are in need.
Hiring of Personnel. The hiring of personnel is a collaborative effort.
Personnel are hired by Administrator A and Administrator B. Once the candidates
for new math teachers at PNH are chosen, the administrators narrow down the
candidate pool until there are only five candidates left. Then, the administration
opens up the hiring and interview process to the math department, so that the
candidate will have a departmental interview. The administrators require that at each
interview, at least half of the math department must be in attendance to ask
curriculum, classroom practices, and instructional methodology of the candidates.
Next, the department and the administrators have a meeting to discuss each
candidate. Then, the selection for the new math teacher is made. Administrator B
wanted teachers to have more involvement in the process because he stipulates that
the new teacher candidate must acculturate well with the other teachers for the
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department to continue to be effective. Administrator B developed this process of
departmental hiring at PNH.
Community and Political
Administrator A is the key instructional leader that relies heavily on the
political frame because she says she is particularly comfortable in that arena. She
continually gathers resources for the math department through political means.
Administrator A’s philosophy is to use her relationships with those in and outside of
the district to provide for her school. Administrator A signifies that she deals
constantly with politics within the community. Administrator A fulfills all elements
of the community and political component. Her motto is to be seen in the
community as much as possible in order to build relationships to help the school
succeed. Being that Administrator A grew up in the district, she values the diversity
of the community, so she tries to get the community as involved as possible with the
school. She knows the communities needs because she is always in the community
building relationships. She makes sure that students at the school are active in the
community and has students outwardly in their actions and voices display
community pride.
Culture of Teaching and Learning
PNH is a diverse school surrounded by a diverse community. The
administrators at the school are diverse, and each value the diversity of PNH’s
teachers, students, and community. The teachers at PNH describe the math
department as a family, and the administrators feel just the same. The belief of PNH
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as a family of people extends from the administrators, to the teachers, to the staff,
to the students, to the community. This respect for diversity has been a part of the
PNH school culture for some time, and the recently added diversity of even more
varied student population only increases these feelings.
The development of valuing students and teachers cultures has always been a
part of PNH, but the principal from 15 years ago really brought it to the forefront of
teachers and students minds. From past administrators to the present, they have all
cultivated a feeling of acceptance, respect, and tolerance at PNH for diversity.
Administrators have always encouraged culturally relevant teaching in the
classroom, and the math department has emphasized it as one of their departmental
classroom practices. This culture was easy for PNH administrators to sustain
because the school put on events throughout the year to engage students and teachers
in dialogues and activities centered on diversity and culture. For example, one such
event involves the incoming freshman to PNH. Administrator B retells the story that
began a couple of years ago. The district was having several fights on campuses and
they asked PNH what were they doing because students were not having cultural
problems on this campus. Administrator B says, this was because PNH had
developed a program called Human Relations with a Human Relations committee.
This is a committee where students and teachers discuss cultural and diversity issues
on campus. Administrator B explains that all PNH incoming freshmen have a week
where they get to experience what it is like to have a disability or be someone of a
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different culture, or they experience what it is like to be a student at PNH of a
different culture:
For example, we have a plate on one kid like you are a foreign
language student speaking in a different language. The other
kids turn away from them and ignore them, and they say why
is this happening to me? We’ll turn the plate over, and the
student finds that they were a foreign language student
speaking in a different language, so no one knew what you
were saying. You get to feel what it is like for that other
person. It helps kids see some other issues that others face.
We have a vision and Life skills with the county. For all the
freshmen, all have to go to orientation for a week. They have
to pretend to be a student with a disability and try to continue
to function as before. The next to last day there is a panel
where people with disabilities talk to the students.
Administrator B boasts that a lot of time, PNH will see what culturally needs to be
done before the district, and the district adopted PNH’s idea of a Human Relations
committee for campuses.
Data Driven Decision-Making Analysis
What prompted PNH to initiate and implement the change process in the math
department is because of mathematics statistical performance data that came from
PNH students on standardized tests and through students performing poorly in PNH
math classes. The PNH math teachers were seeing their students fail exams, quizzes,
test, and not complete assignments. The student performance data coming from the
PNH math teachers, classrooms were grim, which was only reinforced by the
mathematics data from the state’s standardized tests. It is from this data that PNH
math teachers and administrators decided to initiate change process procedures to
increase PNH students’ math achievement.
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PNH does not have formative benchmark school site assessments, nor does
it have common summative standardized assessments. The closest thing the school
does have to common assessments is the CPM program has unit assessments and
course closure activities. In math committees, the teachers at the school
continuously analyze student performance data from math classes and standardized
test data from the state. The data is disaggregated by ethnicity, gender, and grade
level. The PNH teachers and administration have been using the data to make
decisions about student placement in math classes. They also utilize the data that the
middle school feeder provides to place students in the correct math classes. Both
teachers and administrators at PNH are continually using data to update the master
schedule and improve the department’s instructional program.
Conclusion. Strong instructional leadership was important in improving PNH
students’ math achievement, programs, and strategies. PNH has continuously had
administrators that were strong in symbolism, storytelling, and vision. PNH’s
current administrators also typify these same elements of vision and learning. In
addition to having strong features of vision and learning, PNH’s administrators and
key math leaders share responsibility for communicating the vision, implementing
the vision, and monitoring the it between themselves and other stakeholders such as
the PNH math teachers. PNH administrators and key math leaders also share
supervising and monitoring of instruction and personnel between each other and the
teachers. Another point on which key math leaders and PNH administrators
collaborate with the teachers is hiring of new teachers through departmental
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overview. The last way in which PNH administrators and key math leaders
collaborate is on the culture of teaching and learning at the school. What makes
PNH’s administrators and math key leaders so effective in increasing students’ math
achievement, math programs, and math strategies is that they so often work with
teachers and other school stakeholders to improve academics at the school.
Research Question 5: Resolving Instructional Leadership Dilemmas
Research Question 5 is: “How did leaders in the school resolve dilemmas
about instructional leadership?” In an attempt to examine the fifth research question,
two frameworks were used. The first framework is the principal assessment. It
helps determine how aware they are of the school’s math program and if they
possess an expertise in mathematics. This framework was developed by California’s
state highly qualified teacher standards. The second framework that answers
research question 5 is the strategy and the approach template. It matches leadership
strategies with research-based educational literature. This template helps the
researcher determine, which effective strategies the leader has been using to increase
students’ math achievement.
There are 12 strategies that help administrators resolve instructional
leadership dilemmas: the delegation approach (Northouse, 2001), teacher leadership
(Gabriel, 2005), action research (Stringer, 1999), human resources frame (Bolman &
Deal, 2003), and supplemental services (NCLB, 2001). Marzano (2003) has seven
strategies on the list: meaningful staff development activities, instructional
strategies, student engagement, guaranteed and viable curriculum dealing with
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strategies emphasizing articulation with feeder schools, challenging goals and
effective feedback, guaranteed and viable curriculum pertaining to a revised course
scope and sequence and/or curriculum, and meaningful staff development activities.
PNH’s administration used two of the strategies to resolve their instructional
dilemmas: the delegation approach (Northouse, 2001) and teacher leader (Gabriel,
2005). In delegation of leadership, the leader entrusts the subordinate with the power
to carry out the task or duty. The second strategy that PNH administrators employ is
the teacher leadership by Gabriel (2005). This strategy involves the leader
empowering teachers to become school leaders themselves.
Principal’s Expertise Framework
In the assessment of principal’s expertise framework (Appendix K), the
researcher is able to use the framework to determine the math expertise of the
principal at PNH. In step 1 of the framework, the principal is asked if he or she is
Highly Qualified Teacher (HQT) compliant in mathematics. The principal of PNH is
not HQT compliant. The second step asks does the principal have a credential or a
major in mathematics. No, is the answer to step two. In step three, the principal is
asked if he or she has a minor or taught math. The answer to step three is no. The
principal expertise framework implies that the principal at PNH has a low expertise
in mathematics.
Lack of Subject Matter Competency Strategies
Using the assessment of principal’s expertise framework, the researcher
determined that the principal of PNH has a low expertise in mathematics. Even
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though the principal has low expertise in math, the students at PNH continued to
increase their mathematics achievement. Even without math expertise, mathematic
programs, curriculum, interventions, and instructional practices were designed and
implemented, and school design changes to place to make mathematics more effect
for students and teachers at PNH. The mathematics change process occurred at PNH
without a principal high in math expertise. Consequently, all of this was organized,
implemented, and maintained due to one strategy the principal uses to overcome her
lack of math competency to continue PNH’s success. The strategy the principal uses
is delegation of leadership to an assistant with higher math expertise (Northouse,
2001).
Delegation of Leadership. PNH’s principal uses Northouse’s delegation of
leadership strategy (2001) to resolve school dilemmas about mathematical
instructional leadership. The delegation strategy of leadership involves the leader
giving the subordinate with the expertise the ability the power and resources to
accomplish the given task. Usually, in delegation leadership, the leader delegates to
someone that has a high expertise in the topic and willingness to complete the tasks.
PNH’s principal delegates instructional math leadership to Administrator B.
Administrator B admits that it is his job to oversee and evaluate the math department
at PNH.
Once the principal has delegated leadership to Administrator B, she also uses
delegation leadership with the teachers in the math department such as the
department chair and other key mathematical instructional leaders because he does
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not have mathematical competency as determined by the assessment of
principal’s expertise framework. The math teachers at the school have a high level
of math competence and expertise, which is a characteristic for delegation
leadership. During the change process, Administrator B did not just delegate to the
mathematic instructional key leaders, he continued to provide them with resources,
support, and guidance.
Teacher Leader. Administrator B also uses another strategy from the lack of
subject competency framework, the teacher leader strategy by Gabriel (2005). The
teacher leader strategy involves six elements: organizational leadership, strategic
leadership, interpersonal leadership, adaptive leadership, motivational leadership,
and instructional leadership. In addition, Administrator B is a very democratic
leader, which he uses in conjunction with his teacher leadership techniques. He is a
democratic leader because he is always involving the math teachers in the in all
aspects of the change process that took place at PNH that increased the math
students’ achievement.
PNH has a history of administrators using the teacher leader method,
especially concerning the math department at the school because the department has
consistently been high in expertise. Once again, Administrator B uses the teacher
leader method because of his lack of math competency, so he relied on the teacher
leader style during the change process. First, he nurtured the math teachers at the
school by using his ability to be high in the symbolic and structural frames. He
always encouraged the teachers to find their own solutions to the math problems
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happening at the school. Teacher A remembers Administrator B being very
supportive in getting the department to energized to resolve the problems that were
occurring at the school in math. He used his structural frame to organize meetings
for the teachers to have time to communicate and collaborate with each other on the
math situation at PNH. He changed teacher classrooms and created smaller math
communities within the bigger math department community, so teachers could have
closer relationships and build more collegiality.
The second element of the teacher leader style is strategic leadership, and
Administrator B got the other key math teachers involved to assemble several math
teams throughout the change process. He relied heavily on the math department
chair and other key math teachers in determining what teams were needed and the
delegation of duties within the teams. The teams created math curriculum, programs,
classroom practices, and even interview new math teacher applicants.
Interpersonal leadership is the third element of the teacher leader style, and
Administrator B is very high in communicating with the math teachers. Frequently
throughout the change process, he was visiting teachers and classrooms. He is adept
in emailing, and did not hesitate to call key math teachers about the change process.
Administrator B has very high interpersonal skills due to his symbolic style of story-
telling, acknowledgement of teachers work and efforts, and his human resource
belief of treating teachers at PNH as though they were family. All interviewed math
teachers said the department felt as though it was a family, and this is due to two
reasons: the teachers themselves have a high level of collegiality and the
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administrators at the school make the teachers feel appreciated, respected, and
value their thoughts and opinions.
The fourth characteristic of teacher leadership is adaptive leadership. This is
where Administrator B’s democratic sensibility lies. He is always willing to include
teachers into the discussions about change, and share responsibility with them.
Administrator B is a shared-decision making type of person, and because of his high
organizational skills, he makes it easy and systematic for teachers to adapt to change.
Because the teachers are in control of the change process, change for the math
teachers is efficient and quick.
Motivational leadership is the fifth element of teacher leadership, and PNH
has always had a climate of closeness, community, and caring. The administrators at
PNH inherited a positive school climate in the math department, and it continues to
thrive due to the key math leaders personalities but also that of the Administrators A
and B. In addition, Administrator B works with key math teachers to keep a climate
of collaboration and communication going at the school.
The final characteristic of teacher leadership is instructional leadership.
Administrator A has always been very clear about classroom expectations for
teachers and students. Administrator B, often with key math leaders, discusses
student and teacher improvement with the PNH math teachers. Almost all math
meetings focus on student achievement and how to increase students’ achievement in
math at the school. Math teachers at the school are always looking at ways to
improve their current math curriculum, programs, and classroom practices.
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Specific Instructional Dilemmas. Whenever PNH has specific
instructional dilemmas, the principal says, “If they feel they have a concern, I am
available to listen. I think I try to put things back on them, so they grow as leaders. I
…think it out with them.” Administrator B indicates that he also has the teachers try
to solve their own problems because he does not want things to seem as if it is top
down. If they come up with a valid solution, he will tell them to try it. If they do not
come up with a solution, he will coach them until they feel comfortable enough to
resolve the problem on their own.
Administrator A explains a current instructional dilemma that the school is
undergoing. It pertains to the CPM program. The district made CPM optional for
high schools in the district years ago. However, PNH is the only high school that
continues to have CPM as an option for their students. The district is making the
choice of PNH offering CPM as a math curriculum more difficult. Administrator A
explains “The school district left us alone, but the last few years, it has been hard to
sustain because of textbook adoptions, and CPM students phasing out in middle
school for Algebra 1.” In an attempt to resolve this dilemma Administrator A has
tried to use her relationships within the district to keep CPM at PNH. In addition,
Teacher B stipulates that the math teachers at PNH have open forum sessions with
freshmen entering PNH, in order to explain the CPM classes and format. This gives
students an opportunity to ask their fellow students about the classes.
One instructional dilemma at PNH is the school took a study that compared
Advanced Placement exam scores with those of the CSTs. The students are passing
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the Advanced Placement exams with fours and fives but “they got below
proficient on the STAR, and we are like what is the deal. They were like, the STAR
isn’t important to us (Administrator B).” However, he stipulates that the students
know the CAHSEE is important to them, and so they give their best performance on
that test. To resolve this situation, Administrator B indicates that the school is going
to try to make a better connection with the students about trying on the CSTs because
it is important to the school, not for you, but “that it matters to you’re brothers and
sisters that will eventually come here.” Administrator B goes on to say that the
school needs to make it clear to the students the importance of the CSTs and why
they need the students to give their best on those exams. The school is formulating
some plan about how to get students more involved with the CSTs, and they are
talking to all the stakeholders.
Conclusion. The principal’s expertise framework indicates that the PNH
administrators do not possess expertise in math. To compensate for the lack of math
expertise, the PNH administrators use two out of the 12 strategies to resolve
dilemmas about instructional leadership. The first strategy is Northouse’s (2001)
delegation of leadership, and the second strategy is Gabriel’s (2005) teacher leader.
Because PNH only has three administrators, the principal delegates leadership to
Administrator B who then delegates the responsibility to the key math leaders.
PNH’s administrators also use teacher leadership because the school has a history of
relying on its teachers for opinions, resolution of problems, and implementation of
programs. Not only is delegation of leadership and teacher leader strategies
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complementary, but what makes the way in which PNH’s administrators uses of
the two strategies special is that the school has dedicated, reliable, high in math
expertise, and require little supervision. In addition, teacher leadership works well
with the symbolic leadership style of Administrator B who is in charge of the math
department at PNH because he acts as a supportive facilitator and resource provider
for the math teachers. Math achievement for PNH’s students has increased over the
years because the administrators use the complimentary instructional leadership
strategies such as delegation and teacher leadership.
Discussion
The research questions and conceptual frameworks facilitate the discussion of
the data findings. Key elements of data were analyzed by each research question in
order to understand issues and common themes taking place within Pacific North
High School (PNH). The discussion explores the key findings of the study in order
to determine what they imply about PNH students’ increase in math achievement,
and what role the school’s leadership played in the school’s success.
Research Question 1: Patterns of Mathematics Achievement
For several years now, the students at Pacific North High School’s (PNH)
mathematics achievement on standardized tests has continued to rise steadily. The
PNH math teachers feel that this increase stems from their efforts to provide a
mathematics curriculum that meets the needs of all PNH students by providing them
with a variety of math classes such as CPM, targeted math intervention classes,
altering classroom practices, and after school tutoring. From 2003 to 2005, PNH
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students’ math achievement has made great gains, and in several instances, the
students performed better than South Beach county and the state of California.
PNH Patterns of Math Achievement
CST. On the math portion of the Algebra 1 CST from 2003 to 2005, PNH
had important gains, but the school also had some setbacks. One important decrease
is in the far below basic category. From 2003 to 2005, both the state and county had
increases in this category in 2004. In this category, only PNH has continued
consistently to decrease its far below basic percentages during those years. PNH’s
far below basic category on the math portion of the Algebra 1 CST went from 18%
to 7%, which is 12% less students than the county and 7% less students in the
category than the state.
This 11% decrease is due to the math teachers’ focus on providing targeted
intervention for the far below basic and below basic PNH math students through the
two-year Algebra course. The two-year Algebra course is students that come into
PNH with a history of scoring in the lowest two quartiles. Because the program
extends the Algebra 1 concepts over two years, students have a longer chance and
more opportunity to grasp fully the Algebraic concepts. The added conceptual time
and focus on fewer Algebraic standards increases student performance on the math
section of the CST, and this is indicated in the decrease of far below basic category
students for PNH.
The second sign of increased math achievement for PNH on the math portion
of the CST are in the below basic and basic category. The 2003 to 2005 statistics
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indicate that PNH students had continued upward mobility from the below basic
to the basic category. Over the years, Table 2 shows that students in the far below
basic category have swelled the ranks of the below basic category, which has in turn
increased students in the basic category. This increase is also due to the two-year
Algebra program.
Even with the CST statistical data that indicates that PNH students’ scores
are on the rise, the percentage of students scoring in the advance section of the CST
has decreased from 2003 to 2005. However, the students’ percentages have
increased in the proficient category. The decrease of scores in the advance category
is due to PNH math teacher’s intense focus on raising the far below basic and below
basic students’ scores, and trying to ensure that basic students are striving towards
proficiency in Algebra 1. The focal point of the PNH math teachers has not been on
students that are proficient or advanced, so most of their energies and newly
developed classroom practices have focused on targeting and improving the far
below and below basic student because upward movement for students in those two
categories increases PNH’s API more significantly than if the basic or proficient
students’ scores increased.
CAHSEE. On the CAHSEE exam from 2003 to 2005, PNH repeatedly
outscored the state and the county by consistently having more students pass the
exam from the following school-wide designations: all students, Special Ed., ELLs,
RFEPs, SED, and NSED. In addition, PNH students from almost all ethnicities also
had more students pass the exam than the state and the county. However, there are
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three instances in which the school did not have more students than the pass the
CAHSEE than the state and or the county: the Filipino subgroup of students in 2004,
the SED subgroup in 2005, and the NSED subgroup in 2005.
The success the school has seen on the CAHSEE exam is due to two factors:
the CSR mandated classes for ninth grade and the HSM classes. The CSR classes
are a significant contributor to the high CAHSEE passage rate because PNH math
teachers felt that ninth grade was an essential year, and so wanted to give their ninth
graders the best opportunity to be not disturbed while studying math. All ninth grade
math classes are using the CSR restriction because the PNH math teachers believe
that ninth graders will focus more in math with fewer students per class. No
upperclassmen are allowed in these math classes. The low class numbers is a way
for the teachers to provide more individualized and differentiated instruction to their
ninth graders. This focus on achieving as idealized as possible conditions for ninth
graders to learn math is a priority for PNH math teachers.
The second class that has helped with the highest CAHSEE passage rate by
PNH students is the HSM classes. There are two HSM classes, level one, and level
two. If you do not pass the CAHSEE, you take level one, and take the test again. If
you still do not pass the CAHSEE, you take level two. PNH has very little students
that take HSM level two. The reason the classes work is that the classes expressly
target standards that are on the CAHSEE, and the classes are taught in a similar vein
to CPM classes. This means that PNH math teachers are using strategies such as a
heavy emphasis on problem-solving, discussing problem with other students using
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the math lab techniques, and students write out their math processes to how they
answered a question. In addition, the class is focuses on mathematical concepts
found on the CAHSEE and less focused with procedure.
Even with all the success PNH has had on the CAHSEE exam, the math
teachers at the school still have significant work to accomplish with the Special
Education and Socio-economically Disadvantaged (SED) students. Only 45% of the
Special Education students and 50% of the SED students are passing the
mathematics portion of the CAHSEE. There are two reasons why the two subgroup
populations have half or less than half of their population passing the math section of
the CAHSEE. The reason why the Special Education students are not highly
performing on the CAHSEE is that most of the interventions to help
underperforming students have been focused on regular math students that are not
receiving Special Education services. Special Education has been its own entity for
many years, and is just now coming under the fold of regular education. Teacher B
states, “Special Education uses their own materials in addition to what we use for
HSM and Algebra 1.” Special Education teachers have the option of using the
regular math curricula, but they do have their own materials and curriculum. Before
the PSAA, Special Education students had been ignored by many schools, and the
PSAA shone light onto making sure that all students in a school are well-served by
teachers. Because Special Education students’ scores affect the PSAA, PNH is just
now communicating with Special Education teachers on how to uplift math
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performance and achievement. PNH still has a lot to do with Special Education
before the Special Education students’ math scores rise.
The SED students’ math performance has always been lower than the non
Socio-economically Disadvantaged (NSED) students’ scores. However, there has
not always been so many SEDs at PNH up until recently when the socio-economics
within the community began to change. Within the last fifteen years, there has been
an influx of the SED student, which the PNH math teacher was not yet prepared to
teach. It has only been recently through PSAA pressures and new professional
development that PNH teachers have began developing new instructional practices to
meet the needs of these students.
PNH Math Classes. In examining the math classes that PNH students took
from 2003 to 2005, there are some interesting results. Females taking math at PNH
in 2004 increased their numbers in Intermediate Algebra from the previous year.
Then, in 2005, there was an increase in the number of females taking Advanced
math. This indicates that overall female math achievement at PNH is on the rise
because more females are taking Intermediate Algebra and advanced math.
From 2003-2005, students from ethnic subgroups increased their math
achievement at PNH. The groups that raised their math achievement are Asian
females, Asian males, and African American females. Each of these groups had
numbers in advanced math category increase because numbers were decreasing in
the Intermediate Algebra category.
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By 2005, Pacific Islander females, Filipino females, Hispanic females, and
African American males had increased their numbers in advanced math. On the
other hand, in some instances, some of these subgroups experienced a decrease of
numbers in the advanced category for 2004. This same trend happened for the total
overall percentage of students taking Intermediate Algebra or advanced math at
PNH. The total number dropped in 2004, but increased in 2005. The numbers
dropped because the number of male students taking Intermediate Algebra or
advanced math decreased.
Even though PNH is having success in increasing their students’ math
achievement as is signified by the math portion of the CST and the CAHSEE exam,
when examining the school’s math class data, it is apparent that there are significant
populations of students at PNH not taking Intermediate Algebra or advanced math
classes. Out of the total male population at PNH, 65% are not taking Intermediate
Algebra or advanced math classes. Out of the total female population at PNH, 59%
are not taking Intermediate Algebra or advanced math classes. This data indicates
that a significant number of more males in PNH are in lower level math classes.
When examining the ethnicity class data for PNH, the percentages of specific ethnic
subgroups indicate that PNH still has a lot of work to do in the area of getting certain
groups into higher-level math classes. Four significant PNH ethnic student
subgroups have higher than 50% of their students that are not in Intermediate
Algebra or advanced math, and only one subgroup has less than 50% of students in
higher-level math classes: 77% of Hispanics, 75% of African Americans, 67%
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White, and 65% Filipino students are not in Intermediate Algebra or advanced
math, whereas only 45% Asian students are not in Intermediate Algebra or advanced
math classes. For all PNH’s success in raising math achievement at the school, the
math teachers still have historically underrepresented student populations such as
Hispanics and African Americans with substantial numbers of those students not in
Intermediate Algebra or advanced math classes.
The increase that PNH has seen in by 2005 of students taking Intermediate
Algebra and advance math classes are due to two factors: CPM and the math
teachers adding more math classes to the curriculum. CPM helped increase the
number of students in Intermediate Algebra and advanced math classes because
students in that enjoy CPM classes have the opportunity to take Intermediate Algebra
and advanced CPM classes. In addition, the PNH math teachers indicate that CPM is
raising student achievement in their classrooms, so students understand mathematics
more than before. If this is true, then students are taking higher levels of
mathematics because they now understand the concepts more fully, and so it means
that more PNH students are taking Intermediate and advanced math classes.
The second reason for the increase in Intermediate Algebra and advanced
math is the PNH math teachers adding more math classes to the curriculum such as
Trigonometry and Probability/Statistics. These are classes that PNH students can
take instead of Pre-Calculus or if they did not pass Algebra 2. The alternative
classes give PNH students who would not have taken advanced math classes a
chance to take a nontraditional advanced math class.
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PNH Gender Data by Course Name. There were two significant number
increases in students taking math classes at PNH when examining gender data by
course name: Intermediate Algebra and AP Calculus. In 2004, Intermediate Algebra
had a gain of female enrollment from 192 to 234. The second increase is in the
number of students that took AP Calculus in 2004, and this growth continued
through 2005. However, AP statistics decreased in 2004, which is due to the
opening of new classes such as Probability/Statistics, which is an alternative for
students not wanting to take Calculus. Once again, the growth of these classes can
be attributed to CPM and the addition of new math classes to the master schedule.
However, the AP calculus increase can also be attributed to the DU policy of open
enrollment in honors and AP classes. Students that meet the prerequisites to take an
honors or AP classes is allowed to take them. Open enrollment has more students
throughout the district taking honors and AP math classes. However, Teacher B
stipulates “That the district began the open enrollment policy in 2005 to 2006, but
PNH had it before-hand.”
It is important to note that in the gender math data by course number and
name, student numbers in AP classes continued to increase, student numbers in
general math classes and students not in higher-level math classes also continued to
increase. This is due to the PNH teachers’ insistence on not pushing students into
advanced math classes in which they feel the students would not succeed. However,
the increase of students taking lower-level math classes could also stem from the fact
that PNH’s middle school feeder is sending the high school more students who need
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lower-level math classes. For example, in 2005, there was a significant increase
of students in the part two section of the two-year Algebra program because these
students were in the middle school feeder’s part one of the two-year Algebra
program. Only 96 of the 243 part two Algebra students in the two-year Algebra
program were in PNH’s section one of the two-year Algebra program. In addition,
the increase of students needing lower level math classes can stem from the fact that
the middle school feeder is not using the CPM curriculum any longer. The
curriculum could have been reaching students in the middle school feeder that were
not being properly serviced by the traditional math classes.
Research Question 2: Policy, Curriculum, and Instruction
Policies
NCLB. Several policy, curriculum, and instructional issues led to PNH
increasing students’ mathematics achievement. The ubiquitous NCLB policy is one
of the most significant forces behind school’s focusing on increased accountability to
ensure that all students succeed in school. However, for PNH, NCLB was not such
an oppressive mandate because PNH’s school culture has always been to ensure that
all students at the school graduate and have the opportunity to go to college. The
administrators and teachers at the school fully admit that they had no problems
complying with NCLB requirements, but the policy has made them increase their
efforts to make data driven decisions.
One important product of NCLB at PNH is the departmental teacher
interview, and it is significant because it is working. Teachers from the math
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department interview prospective new teacher candidates to determine if the
candidate fits well with the PNH culture. This process gives teachers an opportunity
to partake in the interview process, which gives them a sense of power over the
process. It is on their recommendations whether a candidate is hired. Since the
process has been in place, the department has felt more satisfied with their quality of
teacher that is being hired at PNH. In addition, the process has increased the feeling
of collegiality amongst the math teachers, which in turn has increased collaboration
efforts. Teacher collaboration at PNH has led to the increase in students’ math
achievement. The process has also increased the department’s self image in a
positive way because the new hires have fit well into the culture of the PNH math
department. This process began in the science department, and then went into the
math department. Now, the process has changed the entire school’s hiring practices
because now all PNH departments have departmental interview for new teacher
candidates.
PSAA. Unlike NCLB, the stringent mandates of the PSAA have worried the
teachers and administrators at PNH. The math department was worried because it
knew that not all students’ math needs were being served by the PNH math
curriculum. Because the API requirements of the PSAA indicate that a school’s
score is affected by how well student subgroup populations are performing on
standards-based assessments, PNH knew that their API score might be affected if
they did not meet the math needs of specific subgroups such as students of color.
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In order to comply with the PSAA mandates, PNH created math
committees, new curriculum, and has a professional development contract with
UCLA. The math committees were a significant feature of PNH’s response to the
PSAA because it is from these committees that programs such as CPM and HSM
were developed and implemented. Because of the variety of math committee’s grade
level and by math subject, teachers have a chance to participate in the math
department on a smaller scale. The smaller size of the committees makes the
atmosphere more collegial, which has increased math teacher’s collaboration on
projects such as CPM, HSM, classroom instructional practices. This collegiality and
collaboration then lead to the raise achievement shown by the PNH students in
mathematics. The smaller committees have also helped to increase the PNH’s math
achievement by providing teachers with an opportunity to explore student math
performance data in-depth. Teachers analyze student data based upon the special
expertise of the committee, and then they collectively share that information with the
larger group after they have had time to go thoroughly through the data. The
teachers expressed that they liked the smaller committees, and that they know they
are working due to the current student success in math, and it also helps the teachers
have a chance to communicate with each other about best practices that specifically
relate to their math committees specialized topic.
With the PSAA as a continued source of pressure on the school, determined
to meet their API, the school looked for ways in which to increase all of their
students’ math achievement. The answer was to find CPM and create curriculums
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such as HSM and the two-year Algebra course. The math teachers used their
committee meetings to plan and implement the curriculums. The planning stage for
CPM was not as complicated as the two-year Algebra course and HSM because this
curriculum was already created by the CPM organization. However, the two-year
Algebra and HSM courses took significantly longer to create because the math
teachers at PNH were creating these programs themselves. The two-year Algebra
program had to be created with the feeder middle school math teachers because the
feeder school math teachers are the ones that teach the first level of the program, so
collaboration and articulation between the high school and the middle school was
essential and difficult work. Once created, the programs were implemented.
Implementing the program was not as difficult for the PNH math teachers as was
modifying the program after implementation. As the math teachers foresaw the
needs of their students change, they attempted to adjust the two programs to
students’ needs. Teacher C mentions that it seemed as if the 10
th
grade math
curriculum was constantly changing. Not only are the math teachers at PNH
continually making alterations and adjustments to the two math curriculums because
of student needs, but also because of changes in the district’s math policies.
PNH’s third response to meeting the mandates of the PSAA was for the math
teachers to receive professional development from the UCLA Math Project. The
math key instructional leaders at PNH felt that the math department needed outside
guidance to increase their students’ math achievement and to use professional
development and time effectively. The math project key math leaders’ research-
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based instructional practices for math, but also classroom management techniques
that got students more engaged in mathematics to increase student learning that they
could share with other PNH math teachers. In addition, the math project gave math
leaders new conceptual models of mathematics and lesson plans and information on
best mathematical leadership practices. Furthermore, the key leaders received
training in how they can provide productive professional developments for their
math teachers, but also how to lead math discussions with teachers centered on
student mathematical achievement. Teachers and administrators at PNH believed the
UCLA Math Project was another resource for the school that helped increase
students’ math achievement, but provided them and their students with new ways to
view and understand mathematics. Because the UCLA Math Project’s professional
development was aimed at both math teachers and key instructional math leaders and
providers, it gave the PNH teachers a common language and understanding that
centered the math teachers’ dialogues. The instructional classroom practices and
techniques complimented the CPM curriculum that the math teachers were already
doing, so it helped enhance the PNH math curriculum and classroom practices. Even
though not all PNH math teachers were involved with the UCLA Project, the project
influenced most PNH math teachers’ instructional techniques and practices in their
classrooms because a PNH key math leader was involved with the project. Not all
PNH math teachers partake in the UCLA Math Project because of the distance it
takes to get to the UCLA campus or other school obligations. The changes PNH
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math teachers made to ensure that they met the PSAA requirements also helped
them increase all of their students’ math achievement.
BTSA. California state’s Beginning Teacher and Support (BTSA) program
was created to support newly credentialed and beginning teachers. Teachers attend
BTSA classes to improve their classroom practices and instructional techniques, and
they receive mentors. The purpose of BTSA is to ensure that new teachers receive
enough advice and guidance to get them through the difficult first years of teaching.
The program is suppose to make certain that all new teachers are receiving a
standardized set of information to enhance their teaching performance, and the new
teachers are evaluated based upon the same standardized criteria. BTSA is supposed
to alleviate from the school district and the school the responsibility of training and
acquainting new teachers to the system of education. The program reinforces the
NCLB requirements for new teachers, and is expected to produce higher quality
teachers that are equipped to use instructional methods that raise student
achievement.
However, PNH administrators feel that the program does not fulfill its
premise of supporting new teachers. They feel that the state’s program is more of a
hindrance to the PNH’s efforts to increase the student achievement at the school,
especially in the area of mathematics. Teacher A, a veteran teacher of over 20 years
and once a BTSA mentor, stipulates that BTSA hinders PNH’s effort to improve
student achievement because of how the program works. Teacher A feels that the
quality of support that the program provides new teachers is not sufficient, and that
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the complex procedures within the program that give new teachers support make
the program inadequate to carry out PNH math teachers’ mission of increasing all
students’ mathematics achievement at the school:
I think as far as [BTSA] creating teachers, as far as I can tell,
this is a real issue. We in no way support the teaching staff
with this [BTSA] philosophy [meaning the state’s BTSA
program does not properly support new teachers and the PNH
staff]. When you are a brand new teacher, you have so many
more issues than just teaching. The way BTSA is set up to
help other teachers is unrealistic. A math teacher needs a
math mentor/provider, not one interested in just checking off
boxes.
Teacher A then goes on to explain that the BTSA program does not support the
teachers at PNH because not only do they not give PNH’s new math teachers math
mentors or coaches, they do not provide for the total well-being of the new teacher.
Teacher A feels that BTSA is only concerned with making sure the new teacher
fulfills all the teacher-credentialing requirements, but does not provide them with
help outside of the arena of credentialing. For example, help such as how to create
good standard based lesson plans within your field of study, how to get students
engaged and work in groups in math class, and how do you differentiate for math
students. Teacher A also complains that new teachers are so busy fulfilling BTSA
requirements that they do not have time to participate in mentoring programs or
collaborative teams with teachers at PNH. PNH math teachers do a significant
amount of collaboration on math committees and teams. What is happening is that
new math teachers are finding it difficult to participate in the math committee and
team activities because of BTSA commitments. This affects the new math teachers’
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acculturation to the PNH math teacher culture. PNH veteran math teachers are
finding it difficult, because of time restraints and BTSA commitments, to educate the
new math teachers in PNH math curriculum and procedures. Without this training,
new PNH math teachers are not as effective teachers of math as they could be which
in turn affects the achievement of PNH students in math.
In addition to Teacher A’s complaints about BTSA, during the interview,
Administrator B also expressed similar concerns about the BTSA program as a
hindrance in the schools efforts to increase achievement. Administrator B states:
To be honest with you, the BTSA stuff has hurt us more than
it has helped us. Because we use to have a mentor program
here that really focused on teacher-to-teacher help, rather than
here is the paper work and fill out the paperwork. Our
teachers are spending so much time doing the 42 different
competencies. Yes, the competencies are important, but the
focus should not be the paperwork, but the focus should be
what is actually happening in the classroom.
Administrator B suggests that too many of the new PNH teachers are feeling
enormous pressures from programs such as BTSA that require extra amounts of their
time, which Administrator B feels that time should be going into better use such as
for new teacher mentoring and PNH school culture teacher and instructional
conditioning on the campus. The administrator tells of the instance where a would-
be math teacher chose not to enter the profession due to what the would-be teacher
referred to as “all the extras” such as BTSA, paperwork, added time, and extra
energy. Administrator B says, “We want good teachers, but we don’t want to make
it so that when we have someone good, it is impossible for them to want to continue
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because that first year is probably the most critical year.” Administrator B feels
similar to Teacher A in the respect that they feel the program is not working properly
in that it causes new PNH teachers extra unnecessary stress and pressure and that it
does not provide them with the quality training and indoctrination the PNH teacher
mentoring program use to provide.
PNH math teachers and administrators feel because of issues associated with
BTSA, that the state program is hampering the school’s student achievement efforts.
The program affects PNH teachers negatively in these ways: the school is not able to
indoctrinate properly the new teachers into the school; the BTSA program takes
them away from school, so the school cannot utilize the new teachers in different
professional developments; because of BTSA, the school lost their own teacher
mentoring program; and the extra pressures are causing more new teachers to leave
the profession early and others who would enter the profession decide not to enter
because of all the extras. BTSA is counteracting the efforts of PNH to increase
student mathematic achievement and PNH math teachers and administrators are not
quite sure how to offset the negative effect BTSA is having on the math department,
which thus translates into an affect on math achievement of PNH students. Up until
recently, PNH had not had much teacher turn over in the math department, so BTSA
requirements and obligations did not have much of an affect on math achievement
for students. However, with the math department beginning to get more new
teachers, BTSA issues have become a new developing problem for the school,
student math achievement, and teacher morale.
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CSR. One important implication of CSR that helped the school raise their
mathematics achievement is that they made sure that all ninth grade math classes
were CSR classes. This policy of only having no more than around 20 students per
math class kept the number of students taking math classes small, which gave PNH
math teachers the ability to give student personalized math attention and help. In
addition, teachers were able to recognize more quickly a student that was struggling
in the class, faster than before all ninth grade classes were CSR. CSR also made
math classes more manageable for the math teachers; in areas such as classroom
management, grouping and pairing, math labs, and math games. Because the policy
made it so that teachers had less students in class, there were less papers, tests, and
examines to grade. This enabled teachers to be more available to students for
tutoring hours before and after school or during breaks. In addition, less students
meant that teachers had a chance to really get to know their students and make
personal connections. In turn, this not only gave teachers the ability to more
personalize and tailor math assignments, but it also made collaborating with other
teachers easier because teachers really knew their students mathematical strengths
and weaknesses, so when PNH math teachers talked with other teachers, they could
really see similarities and make comparisons with other teachers about their students.
These similarities and comparisons of students were discussed during math meetings
and helped create needs assessments, interventions, and new math programs at PNH.
CAHSEE. The CAHSEE’s affect on PNH students increasing their math
achievement is significant. Because the CAHSEE passage rate has the ability to
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affect the school’s API in both positive and negative ways determined by how
well various school subgroups perform on the exam, so PNH has paid special
attention to ensuring that students at the school were ensuring that all groups were
passing the CAHSEE. This is one of the reasons why PNH has had a CAHSEE
passage rate around 85%. To ensure that all subgroups are passing the CAHSEE,
PNH math teachers created a CAHSEE math intervention class for students that did
not pass the CAHSEE after the first try. The class is called HSM. HSM has a level
one and a level two. The program helps a lot of the lower-level math students pass
the exam, so that they have a chance to graduate from PNH. The mandate that all
students have to pass the CAHSEE or it affects a school’s API, which in turn affects
their AYP, is so strong that most of the PNH math teachers make it mandatory for
students that did not pass the CAHSEE to go right into HSM. The exam has
increased the school’s math achievement because not only do the teacher’s care
about test passage, but so do PNH students. In addition, the CAHSEE sheds lights
on subgroups that might have failed and been ignored by PNH math teachers in the
past. Now, PNH math teachers ensure that they are preparing all students to pass the
exam, which in turn is an attempt at closing the achievement gap. The CAHSEE
made PNH teachers more aware of the existence of the achievement gap at their
school, and the CAHSEE forces them to try to minimize the gap.
DU’s Policies. Directional Unified (DU) had three policies that helped to
increase students’ math achievement at PNH: the API policy, open math policy, and
CPM policy. DU’s API policy required that PNH increase their API score by 5
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points each year. This policy helps math teachers at PNH keep their focus on
increasing math achievement, so they continue to try to find better math classroom
instructional practices, take more mathematics professional development, making
data driven decisions, and to continue the dialogues about student performance. In
addition, PNH teachers go especially out of the way to provide students opportunities
for tutoring. Many PNH teachers help their students in math during breaks, lunch,
before school, and after school.
However, DU’s growth target policy is beginning to cause the PNH some
problems. Administrator B alludes to the fact the policy is already a concern for the
school because it is a blanket mandate that all school’s must increase student
achievement by 5 points each year, while not considering the policy on a school by
school basis throughout DU. The reason Administrator B is concerned about the
policy creating dissention between them, the district, and other DU high schools is
because PNH has the lowest socio-economic community population amongst DU
schools. In addition, PNH has more ethnic diversity within its school, and
Administrator B suggests that this brings about other concerns and considerations for
PNH than other DU schools. Administrator B explains that the demographics of the
student population that PNH serves increases its difficulty in meeting the district’s
growth target policy:
…[it is] kind of unfortunate or disheartening sometimes to be
honest with you. When you look at the scores, you go ‘oh we
are not as good.’ But when you look at our base population
and our resources, our scores are way better than their scores
in comparison to them [other DU high schools], and things
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that a lot of people don’t look at is, if we had their kids, we
would probably be twice as good. That is the thing that no
one ever sees, except the staff that is here. If you are starting
here [low hand movement], and you go up this much [raises
hand to a high level], but if you are starting already here
[raises hand to a high level], and you go up that much [moves
hand a little higher than before], what difference did you
make? That is the thing that really bothers us in a way.
Administrator B implies that DU has some inequities amongst the high schools, and
it is not appropriate to deem that all high schools in DU should rise to meet
unrealistic expectations; at least not unless DU examined more closely the
inequalities between the high schools, and taking that achievement gap into
consideration when setting appropriate achievement goals for each high school. This
feeling of unfairness by DU onto PNH math teachers has made some teachers feel as
though the district is penalizing them without considering how difficult it was for
them to get the students to progress this far, and that DU needs to recognize the
accomplishment they have already performed because it is already affecting the
morale of the math teachers at the school.
The second policy is DU’s open math policy. This policy allows students that
meet all the prerequisites to mathematics honor and AP classes can take the classes.
Open math enrollment has increased the number of PNH students taking higher-level
math classes such as AP and honor classes. The teachers like the idea that more
students will try to take honors and AP classes, and that it is already happening at
PNH. However, the math teachers are worried that some students are taking
advanced math classes such as AP statistics and AP calculus and that they are not
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prepared to succeed in those classes. On the other hand, PNH math teachers do
not want to discourage students from trying to challenge themselves in mathematics,
but they do not want students to fail the class and have a diminished sense of their
mathematical skills or be negatively affected by not performing well in the class. It
is a fine line that the PNH math teachers are walking with the open math policy, and
they do not want negative performances in honors or AP math classes to decrease the
morale of the mathematics student and teacher community at the school.
The last DU policy is about CPM. DU has allowed their high schools to
choose whether to have CPM in the math curriculum or master schedule. This has
made PNH the only high school in DU still teaching CPM to their students. This has
put significant pressure on PNH because the school has felt pressure from the district
to take CPM away as an option for students. DU has put pressure on PNH not to
continue having the CPM option for their students is through by not letting middle
schools use the CPM curriculum. PNH’s middle school feeder use to teach the
Algebra 1 portion of CPM to its 8
th
grade students, so by the time those students
arrived at PNH, they were already familiar with CPM. This made it easier for PNH
to keep their CPM enrollment numbers high because students were already use to the
program and how it worked. Now, PNH is finding it more difficult to convince
students to take CPM classes because the format is so new to them; it is different
from any other math class they have taken in their school careers. PNH teachers’
stipulate than some students are just afraid to try a new math class, and this impacts
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the CPM enrollment numbers at PNH that have steadily decreased since the
district said that no middle school can use CPM.
School Design
Student Performance Assessments. Student performance assessments such as
the CAHSEE and the CSTs were significant in helping PNH math teachers to
examine their classroom and instructional practices, making data-driven decisions,
and using the data to reconstruct their math curriculum. The teachers continually
analyzed the data from the performance assessments in math committees and
meetings as a method to increasing their students’ math achievement.
However, what is significant about how PNH math teachers increased the
students’ math achievement at the school, is that they did not use district or school
performance assessments like large school district such as LAUSD. Marsh and
Codding indicate that highly effective school designs include student performance
assessments that capture conceptual understanding, problem solving, and
communication skills. What makes PNH special is that the school does not have
standardized departmental student performance assessments, but the math teachers
each give their own student performance assessments that meet Marsh and
Codding’s requirements of effective student performance assessments. Because of
the math department’s instructional practices and curriculum, authentic student
performance assessments are given, but each teacher gives their own. The idea of
not having standardized departmental math student performance assessments gives
PNH math teachers the ability to tailor their assessments to their students. The
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teachers are pleased with having this freedom, and feel the autonomy they have
over their student performance assessments is helping to increase the school’s math
achievement.
The closest the PNH math department has to standardized departmental student
performance assessments is the CPM curriculum unit assessments. Because most
PNH math teachers teach a CPM class, these assessments are similar. However,
CPM unit assessments meet all the Marsh and Codding requirements for effective
student performance assessments. The PNH math teachers do enjoy the CPM
program, and do feel the unit assessments are effective in demonstrating to the
teacher the students’ mathematical skills and understanding in the subject. Because
the CPM student performance assessments are so effective, it helps the teachers
increase their students’ mathematics achievement because they know exactly what
mathematical concepts to work on with their students.
Curriculum. The math curriculum at PNH is an important factor in why PNH
has increased its students’ math achievement. The curriculum has all three
components of what Marsh and Codding determine is a successful math curriculum.
PNH’s math curriculum was created by the math teachers at the school because of
their need to ensure that all students were to succeed in math, and because the
teachers recognized that their student outcome data indicated that the math
curriculum needed to change if they were fulfill their mission. The teachers went out
and brought in the CPM, which is a constructivist math curriculum. In addition, they
altered the math curriculum to include more math classes and options for their
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students to meet all their students’ mathematical conceptual needs. The PNH
math teachers also felt it essential to provide their students with math interventions
for students that were not passing vital math classes or exams such as Algebra 1 or
the CAHSEE. PNH math teachers understood that students not passing Algebra 1
meant that they were not going to succeed in other math classes at PNH, and
possibly not graduate from PNH or have the opportunity to go to college. PNH math
teachers provided many avenues within their math curriculum for mathematical
success for their students, which helped increase the school’s math achievement.
CPM is embedded at PNH because of the school’s commitment to student learning.
Learning Activities. PNH has a variety of learning activities in math that hold
student interest and meet Marsh and Codding’s guidelines for effectual learning
activities at a school. The PNH math teachers are dedicated to providing their
students options in the math curriculum, and this belief extends into the learning
activities that take place within the classroom. The math teachers’ philosophy is to
have a variety of learning activities during the lessons, with a focus on having a high
engagement of participation during the lessons. Most of PNH math teachers have
students working in collaborative groups or pairs to figure out math problems or for
using manipulatives. The programs such as CPM and the curriculum HSM are very
collaborative and challenge student thinking through problem-solving activities that
are real-world based, so the founding premise of these PNH classes meet the
expectations of effective learning activities for students. What has been effective for
PNH math teachers in increasing the math achievement of their students is the fact
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that across the department the teachers subscribe to mathematical philosophy and
methodology of having instructional techniques that meet the standards of Marsh and
Codding’s learning activities principles. Even for classes that do not have these
learning activity elements built into the program such as the traditional classrooms,
the teachers still use effective learning activity techniques for students that are
similar to those presented in the TIMSS videos of the Japanese classroom.
School Culture. One significant asset of PNH’s math department that helped
increase the math achievement at the school is PNH’s strong school culture and
sense of identity. What makes the culture of PNH’s math department so noteworthy
is the department’s belief in enhanced learning, not only for the students but for
themselves as well. The mission statement of PNH includes many outcomes that
relate to student learning, and so enhancing student learning and growth is a
foundational principle of the school that is the motivational purpose of all PNH
teachers. When the school first began transforming itself, the math department at
PNH strongly believed in meeting the needs of all of their students. The principal
foresaw that her staff would need professional development for the change occurring
at the school educationally, politically, and in the community. Before the change
process began, the math teachers were positive in their desire to learn the best
instructional techniques and methodologies in raising students’ achievement in
mathematics. PNH is unique in that the school has had a history of principals
dedicated to supporting a school culture committed to diversity, openness, and
learning for students, staff, and teachers.
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During the change process, the math teachers saw the need to alter the math
curriculum in order to serve better their student population and increase math
performance, and so the department sought out mathematics programs such as CPM.
Because of the math department’s commitment to student learning, the PNH math
teachers determined that it was necessary to add math interventions to the curriculum
because the school’s mathematical student performance data indicated that students
were not performing well in certain areas. To compensate for students that did not
pass certain math requirements, programs such as HSM and the two-year Algebra
program were formed. These programs were created to support students that were
not meeting PNH math teachers’ expectations, and the PNH math teachers care
enough about their students to create programs to boost students’ mathematical skills
to provide opportunities for the students to succeed in math at PNH.
After the addition of these new programs to the math curriculum, the PNH
teachers continue to enhance their learning as well as the learning of their students
by continuing their professional developments on how to teach innovatively math
and through continuing all the changes they have made in the math curriculum. In
addition, the math teachers continue to analyze student performance data to
determine if what needs PNH math students have and how to mathematical serve
better the student population at the school, especially the historically
underrepresented groups. So far, the PNH math teachers have succeeded in focusing
on enhancing student learning at the school because the math scores and
achievement continue to rise for most ethnic subgroups and special populations at
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the school as well as the school’s performance on standardized mathematical
exams. What makes the PNH focus on enhancing student learning in mathematics so
special is that all PNH math teachers make all curriculum and instructional decisions
based upon how those decisions positively influences their students’ mathematical
achievement.
The second element of school culture is meaningful interactions between
students and the staff. PNH’s math teachers have a special connection with their
students, that is shown throughout the department. Most PNH math teachers try to
make sure that meaningful interactions between teacher and student happen during
instructional time. For example, that the teacher speaks and listens to students’
concerns, problems whether it be with math or personal, and ensure that students
know that the teacher is an avenue for support, access, and networking. PNH math
teachers pride themselves on the fact that they try to personalize lessons to garner the
most student engagement during instructional time, and that most PNH math
teachers feel that it is essential that PNH students know that their teachers care about
them academically and personally. The unofficial motto or creed of the math
department is how can they teach a student and have that student learn, unless they
have taken the personal time to know that student. What was interesting about PNH
is that most of the teachers spent most of their free time during the day such as
before and after school, lunch, and break tutoring, mentoring, or just conversing with
their students. During lunch and after school, the researcher saw that most
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classrooms were open and building relationships with their students through
conversations or academic interventions.
The conversations between students and teachers are explored further through
a special program that is instituted throughout the entire school. The entire faculty at
PNH serves as mentors to various students because every Wednesday PNH students
have a homeroom session with a teacher. In this session, the students are free to
discuss issues, problems, or just talk with the teacher. The teacher can intercede on
his or her behalf if the student is having a problem with another teacher. This is also
the time where the teacher asks questions of the student and guides them on their
educational path. This personal relationship between the student and teacher is built
upon over four years from the time the student is in the ninth to the twelfth grade,
and the teachers never have their own students, so the students feel free to have open
and honest conversations with the teachers. In addition, it is a time where the
teachers can gauge from the students what is effective or not effective at the school,
and how to alter the school to better serve student needs.
Another reason that PNH has a uniquely strong school culture, particularly the
math department, is because of the interactions the math teachers have with the
administration and other math teachers. PNH math teachers have always felt that the
administration at the school supports them and wants them to succeed. The
administration has always been open and honest with the math department, and in
turn the math department feels that they can trust and communicate well with the
administration. This is all due to the fact that the administration and the math
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teachers have the common goal of raising PNH students’ mathematical
achievement, and that finding the necessary resources for both students and teachers
is essential to creating that success. This belief and mutual respect both parties have
with each other in all areas of communication has led to positive relationships
between the administration and the math teachers at PNH, and the increased
cooperation between the groups has led to the increase in students’ mathematical
achievement.
The interactions the teachers within the math department have with each other
is also another important factor to the success the school has been seeing in the
mathematics achievement of students at PNH. The math teachers at PNH have a
close bond and community. When describing the school culture of the math
department, all teachers and administrators interviewed suggested that the
department was more like a family. The math teachers are socially and academically
active with each other. They have many collaboration activities, teams, and
committees together. The teachers are in groups or pods around the school so all
math teachers have someone next door in which to collaborate with, share lessons, or
discuss issues or concerns. What is special about the PNH math teacher pod set-up
is that all new teachers receive a veteran math teacher next door to mentor and
monitor their progress as a teacher. This creates an atmosphere in which the teachers
are supporting each other and helping each other succeed so that administration is
not the only responsible party in making sure that teachers are successfully
performing their duties. In addition, the math teachers spend time outside of school
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with each other. They have picnics, parties, and sport activities, all of which
strengthen their connection with each other. However, what connects the teachers
the most is each math teachers’ desire and commitment to helping their students
succeed at PNH and beyond.
Effective professional development is the last feature of school culture. PNH’s
administrators do not hesitate to provide their math teachers with professional
development, but not just uniform professional development. The PNH
administrators make particular efforts to personalize professional development for
each math teacher, and frequently encourage and support math teachers progress
towards searching for professional developments that the teacher feels will
personally help them be better teachers or instructional leaders. The development
that the administrators and key instructional math leaders provide for their math
teachers are also of high quality, and collaborating on ways to improve student
achievement in math is always a priority at the professional developments. What is
making PNH math teachers successful in raising students’ math achievement is that
the teachers are constantly focusing during professional developments on what are
the best instructional methods, practices, and knowledge to increase students’
mathematical performance and achievement. This belief sets a precedent before any
other concerns that the teachers might have about matters pertaining to themselves
because the PNH math departments conviction is that ensuring that all students
succeed at PNH in math goes before everything else because educating the PNH
students are the math teachers highest priority.
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Math Program Design
It is not only the math program design that has helped PNH math teachers
increase math achievement at the school, but how the math teachers at PNH have
insisted on having as much variety in the math program. The math teachers believed
that providing students with options for different math classes, having many different
types of math classes, and creating interventions within the math curriculum that still
gave students opportunities for mathematical success and access to an opportunity
for college as a necessary dimension of the math curriculum is why the PNH math
program design is helping the students raise their mathematical achievement.
Curriculum Design. CPM is one of the school’s most unique and challenging
math curriculums at PNH that has led to the increase of student achievement in
mathematics for the school. PNH math teachers brought CPM into the school as an
options for students to take instead of traditional mathematics because they saw that
not all their students were performing well in traditional classes. The math teachers
knew that they needed an alternative to traditional classes for students that were not
succeeding in math, and so the teachers brought CPM into the PNH math curriculum
design.
The curriculum is effective because it fulfills all the six elements of curriculum
design. In addition, it is researched-based and uses current mathematics learning and
instructional methodology. What makes the program unique and challenging is that
the teacher acts as facilitator while students solve math-lab type problems. The
teacher must go from group to group ensuring that students are understanding the
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concepts and having personal interactions with the students to get students to
make the mathematical connections, but the teacher is not allowed to solve the
problem for the students. In addition, students cooperatively only solve a few word
problems per day, and the focus is not on mathematical procedure but on
mathematical conceptual knowledge and mastery. The problems that the students
are solving are also real-world problems that draw upon students’ prior mathematical
knowledge.
The curriculum has been successful for PNH in helping to raise students’ math
achievement because the PNH math teachers believe in the program’s instructional
methods. PNH math teachers feel that students should be cooperating or
collaborating with each other during class to solve math problems, and that it is
essential that PNH students master mathematical concepts instead of procedure. In
addition, PNH math teachers feel that solving word problems is a vital and universal
concept that goes beyond math into adulthood. Teachers also feel the program is
adding to the success of their students in math achievement because the program
enables the teacher to move around room more and determine which students
understand or do not understand the concept. This gives the teacher the ability to
alter the lesson, reinforce some concepts over others, or to know better when to
intervene with students who are struggling in their classroom. The close interaction
the teachers have with the students gives teachers the ability to intercede with a
student and understand how to effectively help the student succeed in math in the
classroom.
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Even though the math teachers at PNH believe that CPM plays a significant
role in the successes their students have had in math, the PNH math teachers are
continually fighting with DU and others to ensure that CPM remains in the math
curriculum at the school. PNH was the first school in DU to institute CPM as an
optional math curriculum for students. Because of PNH’s success with the program,
DU decided that all DU schools must implement the program at their schools. This
mandate was not taken well at most DU schools because the math teachers at other
DU schools did not like the CPM curriculum because it made teaching math more
difficult for the teacher. CPM requires the math teacher to act as facilitator during
instructional time. The classroom is set-up as an instructional math lab class with
students working in groups mastering mathematical concepts and not procedures.
For many math teachers at other DU schools, the curriculum add too much stress
because it required teachers to change their instructional classroom practices and
methods, extend their math preparation class time, alter classroom management
techniques because students were in groups, and run the class as a scientific math
lab. Several of the math teachers at other DU schools complained to the teacher’s
union, the community, and the district. Because of the negativity associated with
CPM from other DU schools, DU made teaching the CPM curriculum at high
schools optional. As the years went by, most DU high schools choose not to have
CPM in their math curriculum, and PNH is the only DU school left that teaches CPM
classes to their students.
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PNH math teachers believe that DU high schools lost out on an excellent
program because the teachers were not willing to change their instructional methods
and practices. Because PNH is the last high school in DU that uses CPM in their
math curriculum, PNH math teachers and administrators feel pressured by the district
to discard the program, which is exactly opposite of what the math department and
administration at PNH want. PNH math teachers and administrators love the CPM
program and feel that it is one of the significant factors that is causing the increase in
math achievement that is happening with their students. However, the district’s
optional CPM policy, and the fact that the district has taken CPM out of middle
schools, is making finding students who want to take CPM classes at PNH more
difficult than in past years.
Before, a significant number of middle school students would have CPM
Algebra 1 classes, so by the time they arrived at PNH; they were already accustomed
to CPM instructional methodology and practices. This made it easier for PNH math
teachers to convince entering freshman to take CPM classes. The PNH math
teachers know that most students that take CPM classes like them, do well in them,
and continue to take them throughout the rest of their high school careers. With
CPM not being in the middle school and it being option for high schools, PNH math
teachers are finding it more difficult to get students to take CPM classes, even
though the PNH teachers are enthusiastic about teaching the classes. Even with all
the issues surrounding CPM in the district, PNH math teachers are still getting about
half of the student population at PNH to take CPM math classes, but the resistant
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from the district towards the PNH math teachers about teaching CPM math
classes is disheartening to them and is lowering their morale. The PNH teachers feel
as if the district is persecuting them for trying non-traditional mathematical methods
of instruction to increase their student achievement. The feelings of resentment and
rejection of their instructional methods by the district is affecting the school culture
at PNH because the PNH math department is one of the two strongest and most
respected departments at the school. If they are being slighted or pressured by the
district, the entire school feels as if they are being rebuffed and spurned as well. It
does not encourage other departments at PNH to take risks to help improve students’
performance and achievement in other subjects. If the PNH math teachers feel that
DU has negative suppositions about them, this influences PNH math teacher morale,
which in turn affects instructional practices, teacher performance, and student
achievement. PNH math teachers are concerned that the district is going to remove a
math program from their curriculum that the teachers and administration deem as
valuable and essential in raising students’ math achievement and performance.
Another math program that PNH math teachers see as helping to raise
students’ math achievement is the two-year Algebra 1 program. This program was
created with the help of PNH’s middle school feeder math teachers. The PNH math
teachers realized that the students that were coming from the middle school feeder
that were not successful in Algebra 1 were not succeeding in PNH higher-level math
classes. The PNH teachers determined that an intervention needed to happen for
those students, if they were to be successful in math at PNH, so the PNH math
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teachers and those of the middle school feeder created the two-year Algebra 1
program. It is two years because students study the first semester of Algebraic
concepts in the first year of the program.
Most of the first year of the program is taught at the middle school feeder, but
PNH has a limited few of the first year Algebra 1 courses. In the second year of the
program, the students study the second semester of Algebra 1 concepts. Both
schools’ teachers felt that the program needed to be two years because the Algebra 1
concepts are a gateway to all the other higher-level math concepts at PNH, and they
wanted students to have a higher chance and opportunity to take and pass the higher-
level math classes at PNH. The PNH teachers also knew that if the students gained a
strong sense of Algebra 1 concepts that those students would have a higher chance of
passing the CAHSEE exam and go on to take higher-level math classes that would
lead to the opportunity of going to college. PNH teachers feel that the intervention
classes are working to increase the achievement of their lower-level math students at
a much faster rate than in the past. They see more students progressing in math and
taking more higher level math classes as well as having better performance on
standardized mathematic exams.
Another math curriculum that PNH teachers created to combat low math
achievement is the HSM math program. The program is an intervention curriculum
for students that do not pass the CAHSEE exam. The classes focus on standards that
are specifically addressed on the CAHSEE. PNH math teachers have seen the
success of this program through their high CAHSEE passage rate, more historically
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represented students passing the CAHSEE, and other special designated groups at
the school such as the RFEPs and Special Education students passing the CAHSEE.
Since the initiation of the program, the school has seen an increase in math
achievement from all students that needed the CAHSEE intervention classes at PNH.
The reason that math curriculums at PNH are helping to increase students’
math achievement at the school stems from the idea that the programs were created
to improve students’ math performance and knowledge. The PNH math teachers
have developed many avenues in which their students can receive necessary
mathematical intervention, but continue on a college opportunity track. The PNH
math curriculum was designed by the teachers with the thoughts of helping their
students succeed to the best of their ability, but the curriculum also provides enough
variety to interest students in math who might find the traditional curriculum
unappealing. PNH has shown that providing mathematical variety and targeted
intervention classes for students raises students’ math achievement and performance.
The PNH teachers stipulated to the researcher that the math curriculum was designed
with the student and not the teacher in mind.
Classroom Practices. PNH math teachers use many classroom instructional
practices to teach mathematics, and they use all of the four elements effective
strategies and math curriculum practices. However, the most important strategies
that they all use is to provide students with high levels of student engagement and
discussion about math problems, grouping students together, giving several word
problem that are real-life based and connect to a student’s prior knowledge, and
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letting students know that the math teacher cares about them personally and
academically. What was most notable in all math classrooms at PNH is that students
are highly engaged, collaborative groups are taking place during instructional
lessons, a significant amount of writing about math or during math classes took
place, and teachers were acting as facilitators during math lessons. The PNH math
teachers love teaching math to their students, and it is illustrated through their
classroom practice. The energetic spark and love for math is what is translating to
the PNH students, and the PNH teachers always try to provide PNH students
opportunities for big and small math success in class. Celebrating mathematic
accomplishments is important for both PNH teachers and students, and creates a
positive math climate at the school that converts to higher math achievement gains
by students.
Standards-Based Instruction. Since the inception of mathematical standards
in California, PNH math teachers have used them to guide their instruction. In
addition, all lessons and curriculums at PNH are standards-based. However,
standards are not the impetus for PNH to increase students’ math achievement. PNH
math teachers use standards as tool, but they do not drive the belief system of PNH
math teachers. Standards are important to the PNH math teachers, and they use them
effectively but they always try to teach their math classes above the minimum
standards-based requirements.
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Research Question 3: Change Process
Change Process using Four Frames and CBAM
PNH’s math department, math teachers, and administrators underwent
considerable changes in their curriculum, instruction, policies, and leadership
capacities during the long change process to improve PNH students’ math
achievement and performance. In examining these significant changes, CBAM and
Bolman and Deal’s four frames were lenses through which PNH’s change process is
illustrated.
Symbolism. One important factor during the change process that began
launched the change process at PNH to improve student achievement at the school
happened in CBAM’s Levels 0 and 1. Levels 0 and 1 of CBAM is the beginning
awareness and brainstorming phases of the change process and what was so
significant in this section is that vision and foresight of the principal fifteen years ago
initiated PNH’s attempt at improving students’ achievement.
The principal of PNH 15 years ago was incredibly strong in symbolism, and
she foresaw that PNH was soon to change of the student population within PNH.
The change of student population would create an alteration of classroom
instructional practices, methodology, and techniques for PNH teachers. PNH
teachers would need professional development to cope with the new changes, and the
teachers at the school would have to be properly prepared for the changes that were
to occur at the school. The principal of PNH, at the time, alerted the school to the
changes that were about to occur, and through her leadership and insight began to
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slowly change PNH school culture in preparation of the change process that was
to occur in the near future. Because of the principal’s vision and leadership skills,
PNH teachers were ready to undergo the change that occurred at the school. In
addition, it was because of the principal’s leadership that transformation at PNH
went well and led to an increase of students’ mathematical achievement.
The symbolic frame for the PNH instructional leaders were also key in CBAM
level 6—Refocusing. The refocusing phase is the phase in which the PNH math
teachers reexamine the changes they have made in the change process and modify
the curriculum, programs, or instructional practices to make them more effective or
use them in alternate ways. This is the level in which the current key instructional
math leaders used the symbolic frame to alter PNH’s mathematical vision.
PNH’s key instructional math leaders refocused the math teachers into
determining how to make the current math curriculums, programs, and instructional
practices more effective to continue raising students’ math achievement and
performance. This was accomplished by the key instructional leaders reiterating
PNH’s mission of helping all students succeed, and celebrating the educational
successes of the PNH math department. In addition, PNH key instructional math
leaders used storytelling throughout the refocusing phase to illustrate to the PNH
math teachers new goals and outcomes for the math department pertaining to student
achievement.
What makes the symbolic frame a significant factor in increasing PNH
students’ math achievement is the ability of the PNH key instructional math leaders
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to use symbolism to get PNH math teachers to be more self-reliant in that the
math teachers are now creating their own visions of the math department. Not only
are the math teachers creating their own visions of the math department, but of the
curriculum, programs, instructional practices, professional developments and
methods to increasing PNH students’ math achievement. PNH math teachers now
rely on themselves to create their own symbolic visions, instead of needing the PNH
administration.
Political. The political frame for key instructional leaders at PNH also helped
to raise PNH students’ math achievement. Several of the PNH administrators
throughout the change process years were strong in the political frame, and the
current principal of PNH is also effective at using the political framework. PNH
administrators and key instructional math leaders knew how to use resources,
alliances, and relationships for the benefit of the PNH math department.
In level 2 of CBAM, PNH math teachers were wondering how the changes
they would have to make in their instructional practices and curriculum would affect
them and their teaching. This is the level in which the key instructional math leaders
used the political frame to gather educational resources such as professional
development and money in preparation of the change at PNH. The PNH key
instructional math leaders got assurances from DU to ensure that the math
department would be allowed to make necessary changes to the math curriculum and
design such as adding program options and new classes.
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The political framework was also used during this phase of CBAM to quell
the negative voices that did not understand the need for PNH’s math department to
change its instructional practices, curriculum, and programs. Key instructional math
leaders used politics to bring these people on board with the new vision in the PNH’s
math department or to ask those dissenters to find a different place of employment.
The political frame was also highly used in CBAM level 3 by both
instructional math leaders and math teachers. Both parties attempted to find the
resources and support for the changes they were trying to create at the school. The
key instructional leaders supported the teachers in going outside of the DU to find
resources to support the school, and this is how key math leaders at PNH united with
the UCLA Math Project for professional development.
Teacher A recalls the administration supporting the teachers in their work to
ensure that all students succeed at PNH, and Teacher C remembers how willing the
administration was to find the necessary resources for the math teachers to continue
their work on the curriculums and instructional practices. The administration was
also strong in symbolism because they laid out the plans for the teachers how the
new state accountability system (PSAA) and NCLB would affect the school if they
did not meet the standards of the state or federal government.
Human Resources. The human resource frame helped increase PNH
students’ math achievement through empowerment of the math teachers. The key
instructional math leaders at the school empowered the math teachers to take
ownership in the management, organization, and implementation of the change
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process. In every step of the CBAM levels, the key instructional math leaders
sought input from the math department and encouraged many math teachers to
become key instructional math leaders throughout the process.
The sense of empowerment that most math teachers at PNH felt influenced the
math department’s school culture. The school culture surrounding the change
process was positive and supportive. The teachers took felt a sense of autonomy to
make decisions about the programs, curriculum, and instructional practices that they
wanted included during the change process. The PNH math department saw itself as
a family, and continues to see itself the same way today. What is significant about
the human resources frame for PNH during the change process is that the math
teachers did not see the change as coming from top-down but from bottom-up.
CBAM level 4 is where the key instructional math leaders made sure that the
teachers were properly trained in the new curriculum, programs, and classes that
were to occur at PNH. The math leaders sought out various professional
developments to give the math teachers to ensure that they were ready to use
properly the new techniques and methodologies. In addition, the key instructional
math leaders used this level to have the math teachers with expertise in certain
curricula to provide professional development to other PNH math teachers.
However, one of the most crucial CBAM levels for when key instructional
leaders and math teachers used the human resources frame was during level 5—
Collaboration. The collaborating phase of CBAM at PNH saw both key instructional
leaders and math teachers collaborating with each other on the change process at
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PNH. Key math leaders and math teachers frequently worked together in teams
and shared ideas. What makes PNH’s collaboration special is the fact that it is part
of the math department’s culture at PNH to collaborate, not only with administration,
but parents, students, and other schools. The change process at PNH was such a
success because the PNH math teachers and key leaders were so willing to
collaborate together in order to raise students’ math achievement.
Structural. The Management stage, or Level 3 of CBAM was highly
structural for key instructional math leaders. This was the level in which the leaders
had to organize meetings and time for the math teachers to meet and plan the
implementation that was to take place at the school. The leaders needed to know
each teachers’ assignment, tasks, and obligations to the school. They needed to
know when the meetings were occurring and that they did not overlap. In addition,
the key math leaders understood how to structurally change the outlay of the school
to make it more effective for both teachers and students.
The changing of the structure of PNH also occurred in CBAM level 4. CBAM
level 4 is the stage in which many of the transitional and implementation changes
occurred at PNH, and it is also a time in which key instructional leaders used the
structural frame. The key instructional math leaders used the structural frame to
determine which math teachers would teach which new math curriculum, programs,
and classes. The new curriculum, classes, programs, and instructional had to be
organized by the key instructional leaders. However, the key instructional math
leaders created ways in which the math teachers would help in the development and
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implementation of the new curriculums, programs, and classes at PNH. A
significant portion of the structural changes that occurred in CBAM level 4 stemmed
from the collaboration of the key instructional math leaders with the math teachers.
Current Administrator and CBAM Levels and Four Frames. What is
important to note about the current administration at PNH is that each administrator
are strong in different Bolman and Deal frames, but the frames in which they are in
are complimentary to their positions and add to the success of students’ increasing
their math achievement. Administrator B is high in the symbolic and human
resources frames. Administrator B is always quick with a story or a compliment for
math teachers. His vibrant personality is so warm that it positively influences the
culture of the math department. Administrator B is continually empowering math
teachers to become teacher leaders and encouraging ownership in decision
concerning the math department. This makes the math teachers feel as if
Administrator B is confident in their abilities as educators to make wise
mathematical decisions pertaining to their students, which in turn influences
students’ math achievement.
Administrator A is strong in the political frame. Anything the math
department needs she will immediately procure. Through her political connections,
she is able to gather resources and funds for the math teachers that they would not
otherwise be able to access. Administrator A knows how to use her relationships
within and without of the district to personalize professional developments for the
math teachers and she works very closely with teacher leaders to ensure the math
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department’s success. Administrator A is very successful in using politics to the
advantage of PNH math teachers, and this has made the math teachers feel as though
they can always count on her to provide them with the necessary tools to increase
PNH students’ math achievement. They rely heavily on Administrator A for
resources, and have the confidence in her that they feel free to ask for anything that
might help improves PNH students’ math achievement.
Research Question 4: Instructional Leadership
Strong instructional leadership was indeed a significant factor in improving the
students’ mathematical achievement at PNH. Throughout its years of transformation
to advance student achievement, PNH has consistently had visionary and politically
savvy instructional leaders. Five components of instructional leadership created with
the works of Johnson (2002), Hessel and Holloway (2002), and the California
Department of Education is used to examine the affect PNH’s instructional
leadership has had on PNH students’ math achievement.
Vision for Learning
The administration at PNH has continually foresaw the need for improving
instruction to meet the needs of their diverse student population, and this new wave
of PNH transformation began with the principal at that time recognizing that the
community around PNH was changing and therefore so would instruction at the
school. At that time, the principal led the reform movement at the school by
informing the teachers and staff about how instructional practices and curriculum at
PNH needed to change, but also informing the teachers and staff about the changing
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political climate in education. This PNH administrator prepared both the teachers
and staff to undergo the beginning stages of the instructional reform at PNH.
The impetus for PNH’s secondary reform movement in mathematics began
over fifteen years ago, but several alterations to the mathematics instructional
curriculum and design have happened more recently under the current PNH
administration. It was soon after the student population at PNH began to change that
the instructional leadership at the school and in the math department began to look
for new instructional practices and curriculums to meet the needs of the new
population. In addition, several administrators at PNH at the time were from math
backgrounds, and so they understood the changes that were needed in order to meet
the demands of the new student population but also those of the new state mandates
and requirements.
The new secondary reform of standards-based curriculum and instruction was
taking hold across the state of California, and PNH’s administrators and key math
instructional leaders looked for math programs and curriculums that would address
the new demands put upon the school by standards and standardized tests. It was
key instructional math leaders with the support of PNH’s administration that sought
out CPM and brought it to the school as a new alternative curriculum for students.
CPM was chosen because it not only accommodated diverse, multi-sensory, and
multiple learning styles, but the program fit the state’s mandate that all curriculum be
standards-based and research tested.
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The PSAA provided its own challenges for the school, and PNH
administrators and key instructional math leaders. To ensure that PNH met their API
requirements in mathematics, key instructional math leaders created programs that
sought to address the needs of students that were struggling in Algebra 1. At the
time, PNH key instructional math leaders and administrators recognized the fact that
Algebra 1 is the entryway into advanced or higher-level mathematics. Some students
entering PNH did not have the knowledge and skill required to pass Algebra 1 and
successfully go into higher-level math classes at PNH. Students who did not possess
the ability to pass Algebra 1 would lower PNH’s API scores, and so instructional
math leaders and administrators collaborated with the school’s current math teachers
and those of the middle school feeder to create a program in which raise PNH’s and
the middle school feeders 8
th
grade students Algebra 1 achievement. The program
that was created is the two-year Algebra 1 curriculum.
Then, with the advent of the CAHSEE, PNH’s key instructional math leaders
and administrators identified students that did not pass the CAHSEE. Again, with
the collaboration of PNH’s math teachers, the HSM CAHSEE intervention program
was created in 2002 to address the needs of students that were not passing the
CAHSEE. The program deliberately targeted standards that were on the CAHSEE in
a format that was different from traditional math classes because the instructional
math leaders understood that students not passing the CAHSEE were those that were
also failing in traditional math classes at PNH. In order for those students to pass the
CAHSEE, they need alternative mathematics techniques and curriculum, and PNH’s
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administrators and key instructional math leaders sought to provide PNH’s
students with a math program that specifically addressed their needs but gave them
avenues of opportunity to still go onto college.
Throughout PNH’s mathematics reform movement, the PNH administrators
and key instructional math leaders were always supportive of PNH math teachers
trying new instructional techniques, curriculum, and programs. They supported the
PNH math teachers with funds and resources to ensure that the programs would
succeed. The administrators and key instructional math leaders made sure that
effective professional development was provided to the math teachers about
instruction and curriculum. In addition, the vision that administrators and key
instructional math leaders had for PNH was always positive not punitive. Clear
expectations about goals and outcomes for students, staff, and teachers were clearly
stated by the administration, and frequently the administrators and key math leaders
would dialogue with math teachers while analyzing students’ math performances and
scores how to improve students’ math achievement. All through the years of PNH’s
mathematics reform, there has been a continual vision of how to improve PNH
students’ math achievement, and the administration and math key leaders helped
develop, implement, and refocus the plan throughout the years so that all
stakeholders involved in the process knew how to evaluate the progress of the plan.
Even though today’s administrators at PNH do not possess a mathematics
background, the school continues to raise its math achievement and this is due to the
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commitment that today’s PNH math leaders have to the plan of increasing
students’ math achievement at PNH.
Developing the Vision. What is unique about how PNH’s administrators and
key instructional math leaders have developed the current mathematics reformation
vision is because throughout the years, PNH has continually had instructional leaders
high in symbolism. The vision of PNH’s transformation for improving student
achievement began with a PNH principal fifteen years ago and has steadily been
transmitted by other administrators and instructional leaders high in symbolism.
However, it is not just that these administrators and key math leaders have had the
ability to foresee and develop PNH’s mathematical vision, but these same
administrators and math key leaders have the ability to articulate the vision to all
stakeholders.
Communicating the Vision. PNH’s administrators and key instructional math
leaders did not have a problem communicating the vision of reform to PNH math
teachers because PNH administrators and key math leaders were clear and articulate
about the developing the plan, implementing the plan, and refocusing the plan when
needed. Because of PNH’s positive school culture and climate, especially in the
math department being that it is one of the strongest departments on the PNH
campus, the math teachers collaborated easily through frequent dialogues with each
other and the key math leaders and administrators on PNH’s mathematics secondary
reform. What the administrators and key math leaders did that was pertinent to
communicating the vision to all stakeholders was by clearly explaining the reasons
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behind why the school needed to reform mathematics, what was the purposes
behind the reformation, and the process and means by which the math department
would reform.
However, while communicating the vision and mathematics reformation plan
went well with the school’s stakeholders, it has not bode so well with the district
office. For a while now, DU has been in conflict with PNH about the need for
programs such as CPM and the two-year Algebra 1 program at the school. DU sees
no need for the CPM program and would rather the school stop using it as an
alternative curriculum for students, and has required it taken out of their middle
school and has let it be taken out of all the other DU high schools. In addition, DU
also does not want PNH to continue using the two-year Algebra 1 program because
of how the program affects the high school’s CST scores. Teacher C indicated that
DU has been putting stress on the PNH administrators and key math leaders to
discontinue the two-year Algebra 1 course because it cannot be tested by the CSTs
because the classes Algebra 1x1 and Algebra 1x2 are not classified by CSTs as an
Algebra 1 class. As a result, any PNH student that is taking Algebra 1x1 or 1x2 is
automatically labeled in the below basic or far below basic category of the
mathematics portion of the CST. PNH’s administrators and key math leaders are
having difficulties communicating to DU the value and important roles these math
programs play at improving students’ math achievement at PNH, and so DU
continues to try to force PNH to remove these programs from their math curriculum.
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Implement the Vision. What is distinctive about how PNH’s administrators
and key instructional math leaders implemented the vision is that it was done
collaboratively with significant input from PNH math teachers. Each phase of the
implementation on every program, curriculum, and instructional practices was
discussed with math teachers, and implemented by various PNH math teachers.
PNH’s administrators and key math leaders gave PNH math teachers autonomy to
take ownership in the implementation process of the curriculums, programs, and
instructional practices.
Monitor and Evaluate the Vision. The administrators at PNH, key math
leaders, and math teachers all help monitor and evaluate the math reform vision at
the school. Even the students help monitor and evaluate math programs and
curriculum through input during homeroom and through the analysis of students’
math scores and performances within classes. Because the atmosphere at PNH is
one of openness and honesty, the math teachers feel compelled to discuss any issues
and problems they are having with PNH’s math curriculum, programs, and
instructional practices with the administration and key math leaders. The
instructional leaders foster this type of candid discussion in order to ensure that they
are providing PNH students with the best possible mathematics curriculum that
meets all their needs.
However, PNH’s problem lies not in how the school’s stakeholders evaluate
and monitor the success or achievement of the math programs, curriculums, and
instructional practices but in how the DU and the state evaluates and monitors them.
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Currently, because of state and DU requirements such as how the state classifies
math classes and categories student achievement, PNH’s monitoring and evaluation
of math programs, curriculum, and instructional practices is at odds with DU. DU
evaluates any math program at PNH that is not recognized or is in opposition to state
assessments such as CSTs is seen as not valuable. On the other hand, PNH’s math
teachers, key math leaders, and administrators see alternative math programs,
curriculums, and instructional practices as valuable to PNH students because they
have been proven to raise students’ math achievement, whether they follow the
state’s standardized guidelines and categories or not. Both DU and PNH are looking
at evaluation of the math programs, curriculum, and instructional practices from
different viewpoints and philosophies. At the present, DU has the power to make its
philosophy and point of view supersede that of PNH’s math teachers, administrators,
and key math leaders.
Addresses Obstacles to Vision Implementation and Realization. Each PNH
administrator and key math leaders address obstacles to the vision’s implementation
and realization in different ways. The key leaders of the past would make significant
attempts to pacify stakeholders that opposed the vision and its plan. Great effort was
made by the instructional leaders at that time to be all-inclusive about the plan, and
would try to bring as many voices into the conversation about improving students’
math achievement as possible. The administrators and key leaders would mainly use
their symbolic and human resources skills to address obstacles to the vision.
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However, today’s PNH administrators and key math leaders are not so
quick to placate those that do not agree or present obstacles to further realizing the
plan because implementation of the plan has already occurred. In addition, the
implementation of the plan was successful and PNH is seeing great progress in math
achievement being made by their students because of the vision and plan, so those
who now oppose the plan, mainly DU, the administration and key math leaders do
not try to mollify their discontent. The PNH administrators and key math leaders
now use the political frame to deal with barriers to their vision.
Supervision and Monitoring of Instruction and Personnel
What is special about how PNH’s math teachers, administrators, and key math
leaders supervise and monitor instruction and personnel at the school, is by how it is
done in such a collaborative method. Because PNH’s math department has such as
strong collaborative school culture, most math teachers self-monitor or supervise
each other’s classrooms. The administration has grouped the math teachers together
in such a way that it is convenient for math teachers to work together in teams or
pairs and know what is going on in each others’ math classrooms. Instructional
practice and students’ performances in math is frequently discussed in meetings,
PNH’s math teachers continually monitor and evaluate their own students’ math
progress but those in other classrooms because PNH math teachers have open and
honest communications with each other about math instruction and curriculum.
Hiring of Personnel. The hiring of personnel at PNH is rather distinctive. The
principal or assistant administrators hire math teachers’ at most traditional high
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schools. However, PNH has a departmental hiring process. Once a small
selected number of math candidates are chosen by the administration and math key
leaders, the math candidate then has an interview with the half or more of PNH’s
math department. In addition, it is the math department that determines whether the
candidate is a good fit with the PNH math community or whether they should not be
hired at PNH. This process gives the PNH math department ownership in the hiring
process, but also has helped to create the positive math teacher culture at the school.
Administrators and teachers at PNH cite the hiring process as one factor in why the
scores for students at PNH in math achievement have risen.
Community and Political
The PNH instructional math leaders and administrators have always relied
heavily on building community and political relationships. In order to implement the
mathematics secondary reform vision took several stages of dialoguing with the
community and other DU political sources. PNH’s current administration is adept at
communicating with the community through newsletters, emails, school events, and
city meetings because the dictum of the current administration is that it pays for
PNH’s administrators to be everywhere promoting and informing the PNH
community about what is happening at the school. PNH’s administrators were very
visible on and off campus campaigning for the school. Building relationships with
the community is of the PNH administration’s highest priority, especially when the
school is having conflicts over the math curriculum, programs, and instructional
practices with the district.
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Culture of Teaching and Learning
PNH’s administrators and key math leaders have always endorsed a positive
atmosphere for teaching and learning for PNH math teachers. However, the school’s
mission is built upon ensuring that all students learn and succeed while at PNH, and
this is the message that the administrators and key math leaders emphasize and
promote to the math teachers at PNH in order to sustain the school’s positive
environment for teaching and learning. Not only do the administrators at PNH
emphasize a constructive school culture for teaching and learning, but they reinforce
it by giving teachers respect, ownership in school decisions, and constant
collaboration and communication with them.
The administrators at PNH in collaboration with PNH teachers created
programs that reinforce the idea of welcoming and understanding diversity at their
school. Diversity is one of the centerpieces around which many events and programs
are focused around at PNH, and the administrators and teachers at the school feel
that this focus enhances teaching and learning at the school.
Research Question 5: Resolving Instructional Leadership Dilemmas
Principal’s Expertise Framework
The principal’s expertise framework indicated that the PNH administrators in
charge of mathematics instruction at PNH had no expertise in math, and the
framework labels them as not Highly Qualified Teacher (HQT) compliant. This is a
change from PNH’s past where as several PNH’s administrators over the math
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department had a background in math. PNH’s current administration has no math
expertise and has to rely strongly on key math leaders. However, even with the
disadvantage of not having a mathematics background, PNH’s current administrators
have seen the students’ math achievement at PNH continue to progress and advance
each year.
Lack of Subject Matter Competency Strategies
Delegation of Leadership. Delegation of leadership from Northouse (2001)
is a strategy that the PNH administrators use in order to cope with their lack of math
expertise. The PNH administrators are forced into using the delegation of leadership
strategy because they have no experience teaching or creating math curriculum, and
they need to be able to monitor, evaluate, implement, and refocus the mathematics
efforts taking place at the school. In order to accomplish all these particular tasks
within the realm of math, the PNH administrators that lack math expertise must rely
on the math key leaders and math teachers’ expertise in the subject. This takes
significant trust on the part of the administrator to give subordinates at PNH the
power , authority, and resources necessary to accomplish the secondary mathematics
reform developments and implementations. In addition, the administrators give
power and authority to the subordinates to refocus, evaluate, and monitor the
progress of the reformation plan.
What is interesting about the PNH’s delegation of leadership strategy by the
administrators to the math key leaders and math teachers is the fact that the power,
authority, and resources are delegated twice. The principal of PNH delegates power
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to the assistant principal, who because of his lack of math competency then
delegates authority to the math key leaders and math teachers. Because the math
department at the school is strong and very competent, the double delegation of
authority works. In addition, there is a clear chain of command for the delegation to
the math key leaders and teachers so that no faculty or staff is confused about whom
to go to ask questions concerning math curriculum, programs, instruction, and
resources. Also, not all power and authority is delegated to the same key math
leaders and teachers. Because PNH has such a collaborative group of math teachers,
many of the teachers share power and authority over instruction, curriculum, and
resources. Each math teacher has ownership and an involvement concerning PNH’s
math curriculum, programs, instruction, and resources.
Teacher Leader. The second strategy used by the administrators at PNH is
the teacher leader strategy by Gabriel (2005). This strategy involves the creation of
key teacher leaders in the school. The key leaders lessen the burden of responsibility
for administrators at the school, while increasing teacher input, participation, and
ownership. The reason that PNH administrators use the teacher leader method is not
only due to the administrators lack of math competency, but because the
administrators use the delegation of leadership method. Once the delegation of
leadership method runs its course at PNH, it becomes the teacher leader strategy.
The PNH administrators have delegated leadership to PNH math teachers, who have
then taken ownership in math curriculum at the school. Much of the transformative
work that has occurred at PNH is due to the school’s teacher leaders and their work
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with the math teachers at PNH because PNH has committed and independent
math teacher leaders.
What makes the PNH’s administrators use of the teacher leader strategy so
successful is that one of the teacher leaders at PNH use to be a former administrator
at the school and at other schools in DU. This former administrator, now teacher, is
a math teacher with a high expertise in math. This teacher is the confidante and
advisor for the PNH administrators on math at the school and also advises the current
math department chair at PNH about math matters. This former administrator, now
math teacher, has been the cornerstone of the math department at PNH for decades
and helped create many of the successful programs, curriculum, and instructional
practices that are used at PNH today. This math teacher leader, along with other
independent, creative, and driven math teacher leaders at PNH significantly helped to
mold the framework by which students’ math achievement increasing at PNH is
directly linked to their efforts.
Specific Instructional Dilemmas. Whenever PNH has specific instructional
dilemmas, the administrators feel comfortable relying on the strong math teacher
leaders at the school. The PNH administrators stress that teachers be self-reliant and
try to solve their own mathematical dilemmas, but they do stipulate to the teachers
that they will whole-heartedly support them and give them any resources necessary
to resolve the problem. This tactic of the administrators works because the PNH
math department has teachers that are independent and committed to the principal
that everything they do is for the benefit of increasing PNH students’ math
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achievement. The approach of having the math teachers or their key instructional
leaders solve specific instructional dilemmas stems from PNH’s history of having an
independent and self-reliant teaching staff and culture devoted to ownership of the
school, its curriculum, and its problems.
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CHAPTER 5
SUMMARY, CONCLUSIONS, AND IMPLICATIONS
For several decades, American high school students’ academic performances
continued to trail behind those of other industrialized nations on international
comparative studies such as the TIMSS. Furthermore, American high school
students’ academic achievement on national objective standards is declining or
stagnant as well, especially in the area of mathematics. American students’ poor
mathematical achievement is causing the nation to undergo an achievement gap,
between not only Caucasian students and students of color but also between
Americans and other industrialized countries. A Nation at Risk (1983) further
reinforces the belief that America faces a serious national challenge to find ways in
which to resolve American students’ inadequacies in mathematics.
The performance gap in math represents an especially important problem in
many respects because statistics indicate that performance in high school
mathematics predetermines students’ future successes in high school and beyond
(Rose & Betts, 2001; Murnane, Willet, & Levy, 1995). If math predetermines a
students’ future socio-economic status, a performance gap between Caucasians and
students of color in America only perpetuates the cycle of poverty for students that
do not achievement mathematical success in high school. This is why math
achievement is especially important for urban youth.
There have been state and national efforts to improve math achievement in
high schools that have focused on state standards, improved curriculum and
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instruction, better-prepared teachers, and related reform efforts. As a response to
public pressure to increase students’ math achievement, the federal government has
created policies such as No Child Left Behind (NCLB), and California enacted the
Public School’s Accountability Act (PSAA) in 1999. In an attempt to restore equity
within and minimize the achievement gap within schools, NCLB required states to
have core content standards, so that everyone would know what knowledge and
skills students should know in each grade level. In addition, NCLB advocated for
ways in which to better-prepare teachers and defined for states and school districts
who is a highly qualified teacher because schools are mandated to have highly
qualified teachers teaching students within their school.
Consequently, from these reform efforts, such as the PSAA, have come new
school designs that focus on student achievement and related school features. In
order to comply with the national and state reform efforts, schools have instituted
new school designs such as Small Learning Communities (SLCs) (Gates Foundation,
2005), Career Academies, and Comprehensive School Reform (CSR). The objective
of these school reforms is to provide students with a more personalized school going
experience, in which teachers have deeper relationships with students and a better
grasp of their needs (Pluker, Zapf & Spradin, 2004). In addition to restructuring
reforms such as SLCs, schools have also established Professional Learning
Communities (PLCs) as a secondary school reform to increase students’ academic
achievement (Dufour, 2004). However, with new school reforms to increase
students’ achievement, schools needed to build local capacity for improvement in
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order to deal with the new policies, initiatives, and designs. This meant that
schools needed to find the capability not just to institute these reforms but also to
sustain the implementation. In order to build local capacity for school improvement
schools and districts have created new policies and initiatives within the prevue of
state and national initiatives in an attempt to increase their students’ achievement.
For some schools it meant retraining teachers or creating teacher leaders, and in
other schools, it meant a new form of shared leadership between all school
stakeholders. It has been difficult for some schools and districts to create this
capacity, and Californian schools demonstrate that building local capacity for
improvement is difficult by how many schools were labeled as Program
Improvement (PI) schools because they could not meet the rigid standards of NCLB
or the PSAA. Furthermore, some California school districts are now PI districts
because a significant number of their schools are not meeting state and national
standards.
Additionally, instructional leadership is a key feature in cultivating effective
policies and initiatives that increase students’ achievement, especially in
mathematics. Providentially, considerable research has been performed in order to
identify features of effective instructional leadership in this context such as Marzano
(2003), Blasé et al. (2004), and Datnow (2003). Today’s educational scholars
maintain that today’s schools require transformative leaders in order to sustain
reform policies and initiatives for increasing students’ achievement. However, being
an instructional leader versus a leader focused solely on operations and management
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of a school is a new feature to today’s principals. Finally, strong instructional
leaders are important to ensuring that secondary school reforms are implemented
effectively and successful maintained.
Purpose of the Study
The purpose of this study was to examine how an urban California high
school effectively increased its students’ mathematic achievement through secondary
school reform methods such as creating new math programs and interventions,
altering the mathematics curriculum, and rearranging the school’s design. In
addition, the study explored how instructional leaders without mathematical
expertise, implemented policies, curriculum, and school reforms that helped increase
the students’ math achievement.
Research Questions
Five research questions guided the examination and parameters of the study:
10. What was the pattern of math achievement for various students at the
school?
11. What policy initiatives as well as curriculum, instruction and related
conditions seem to be related to improve math achievement at the
school?
12. What change process did the school use to enhance its math program
and strategies to assist students in math?
13. To what extent was strong instructional leadership important in
improving a) the math programs/strategies and b) math achievement
among students?
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14. How did instructional leaders respond in academic areas in which
they were not experts?
Methodology
This case study employed principally qualitative methods to examine how a
high school increased its students’ achievement in mathematics over several years.
All data collected for the study was triangulated with other members of Dr. Marsh’s
doctoral cohort. In addition, all qualitative data was cross-referenced with
quantitative data such as reports from the California Department of Education in
order to ensure validity and reliability. Four conceptual frameworks form the basis
of the four instruments used to collect data intended to answer each of the five
research questions. At the University of Southern California, with the supervision of
Dr. David Marsh, Associate Dean of the Rossier School of Education Academic
Programs, eleven doctoral students in the summer of 2006 developed the research-
based conceptual frameworks and instrumentation for the study.
Sample
The unit of analysis purposively selected for the study was a Southern
California high school in order to understand better, how a school increases its
students’ mathematical achievement over several years. The selected school for the
study is a comprehensive high school with an ethnically diverse student population
and a principal that has been at the school for over three years. For the last three
years, the school had increased its students’ mathematical achievement.
Data Collection and Analysis
Data collection for the study happened in fall of 2006. The basis for the
instrumentation used in the study was four conceptual frameworks. The first
conceptual framework is the effective school design (Appendix F) based upon Marsh
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and Codding’s (1998) school design model. The framework has four distinct
components: curriculum, school culture, learning activities, and student
performance. Each of these components has three features.
The second conceptual framework examines elements of effective math
programs (Appendix G). The framework emphasizes three areas that make math
programs at schools effective: standards-based instruction, classroom practice, and
curriculum design. Each component has several elements that define characteristics
for each component.
The third conceptual framework is Bolman and Deal’s Four Frames (1997)
(Appendix H). The framework helps detail leaders roles within the school setting.
There are four frames: structural, human resources, political, and symbolic. Each
frame is composed of several characteristics. The structural frame deals with
organization. The human resources frame deals with personnel. The political frames
deals with the controlling of resources, and the symbolic frame deals with vision.
The fourth conceptual framework is the instructional leadership graphic based
on the works of Blasé et al. (2004), Johnson (2002), Hessel (2002), and the
California Department of Educations principal standards. The framework has five
components: vision for learning, supervision and monitoring instruction, community
and political, community and political, culture of teaching and learning, and data
driven decision-making analysis.
The basis for the collection and analysis of data are the four data collection
instruments:
1. The first data collection instrument is the teacher questionnaire (Appendix A
and B). The teacher questionnaire has two parts: the math teacher
questionnaire and the non-math teacher questionnaire. The math teacher
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questionnaire goes more in-depth than the non-math teacher questionnaire
about the math programs and interventions the school underwent to increase
its students’ math achievement. The instrument is an efficient tool to collect
relevant information that answered the research questions.
2. The second data collection instrument is the key instructional leader interview
guide (Appendix D) from Creswell’s book (1998). Both administrators and
key math leaders that are teachers are interviewed with the guide. The guide
offers more detailed qualitative answers to the research questions than the
teacher questionnaires.
3. The third data collection instrument is the teacher interview guide (Appendix
D). Similarly to the key instructional leader interview guide, the teacher
interview guide is based upon Creswell’s book.
4. The fourth data collection instrument is the school profile (Appendix J). The
school profile had three features: student performance, demographics, and
general school information. Information for the profile was collected from
the California Department of Education’s website.
Summary of Findings
The data collected from the four data collection instruments operated in
conjunction to portray a representation of Pacific North High School (PNH) that
exemplify several findings that contributed to the students’ mathematical
achievement increases over the past few years. In the section below, reviewed by
research question is each significant finding.
Research Question 1: Patterns of Mathematics Achievement
The first research question asked, “What was the pattern of math achievement
for various students at the school?” In analysis of this question, data were collected
289
from the California Department of Education reports such as the California
Standards Test (CST), California High School Exit Exam (CAHSEE), PNH math
class data, and gender and ethnicity math data by course name and number. In
examining the collected data, the researcher discovered there were nine significant
patterns of math achievement for PNH:
1. In the far below basic category on the math portion of the CST from 2003-
2005, PNH decreased its percentage of students within this category until its
percentages of students within the category was lower than the state and the
county. This is due to PNH’s math teachers providing the far below basic
students targeted intervention classes such as the two-year Algebra course.
2. PNH has had an upward progression of its students on the math portion of
the CST from 2003 to 2005 with students moving from the far below basic
category to the below basic category and those in below basic moving to the
basic category. This upward progression of the school’s students into higher
categories on the math CST is also due to the targeted two-year Algebra
program.
3. PNH’s student on the math portion of the CST from 2003 to 2005 have
decreased in the advance category, but have increased in the proficient
category. This is due to the math teacher’s focus on intervention for students
scoring in the lower quartiles on the test.
4. From 2003 to 2005 on the CAHSEE, PNH continually outscored the state and
county on almost all school-wide designated categories and ethnic
designations as well. However, PNH did not outscore the state and county on
the CAHSEE in three designated categories: for Filipinos in 2004, Socio-
economic disadvantaged (SED) in 2005, Not socio-economically
290
disadvantaged (NSED) in 2005. The school’s success on the CAHSEE is
due to the High School Math (HSM) classes and the mandated
Comprehensive School Reform (CSR) for ninth grade students.
5. Even though PNH has seen success on the CAHSEE, only half or less than
half of the Special Education students and SED students are passing the
exam. This is due to Special Education teachers using their own curriculum,
and there has recently been an increase of SED students at PNH and they are
finding new strategies for teaching math to SED students.
6. There have been significant increases of female PNH students taking high
lever math classes such as Intermediate Algebra, advanced math, and
Advanced Placement (AP) math, especially in students of color but also for
Caucasian females.
7. More males are in lower level math classes than females from 2003 to 2005.
8. In examining the math gender data by course name and number from 2003 to
2005, more PNH students are taking Intermediate Algebra and AP Calculus
classes. This is due to the open enrollment math policy.
9. The 2003 to 2005 gender data by course name and number also indicate that
more students are general math classes at PNH. This is due to the middle
school feeder sending PNH more students requiring general math classes
because they are no longer using the CPM curriculum.
Research Question 2: Policy, Curriculum, and Instruction
The second research question asked, “What policy initiatives as well as
curriculum, instruction and related conditions seem to be related to improve math
achievement at the school?” In analysis of this question, data were collected from
math and non-math teacher questionnaires and interview. In examining the collected
291
data, the researcher discovered there were ten significant findings that were
related to improving Pacific North High School’s (PNH) math achievement:
1. The math department interview process is an important product derived from
PNH’s adaptation to the NCLB highly qualified teacher mandate.
2. The PNH math department created new math classes, curriculum, and
programs in order to meet the requirements of the Public School
Accountability Act (PSAA).
3. In addition, PNH math teachers created new math committees to comply with
the PSAA.
4. A key instructional math leader also uses the resources of the UCLA Math
Project to facilitate her in helping PNH’s math teachers fulfill the PSAA’s
objectives.
5. The administrators and key instructional leaders at PNH feel that the
Beginning Teacher and Support (BTSA) program that PNH’s new teachers
are mandated to participate does not fulfill its premise of supporting new
teachers.
6. PNH has ensured that all ninth grade math classes are under the
Comprehensive School Reform (CSR) mandate, and it has helped to raise the
students’ math achievement.
7. The California High School Exit Exam (CAHSEE) has helped increase the
students’ math achievement at PNH because PNH math teachers have created
the High School Math (HSM) intervention classes to help students pass the
exam, and the exam also helps PNH’s math teachers focus on the best
strategies to meet the math needs of students from historically
underrepresented groups, so that they pass the exam.
292
8. Direction Unified (DU) had three policies that helped PNH increase their
students’ math achievement: the Academic Performance Index (API) policy,
open math policy, and College Preparatory Math (CPM).
9. PNH’s math curriculum exudes all of Marsh and Codding’s components for
successful math curriculums.
10. PNH has a unique school culture and identity that is positive, independent,
focused on diversity, concerned exceptionally with building teacher and
student relationships, and improving student achievement.
Research Question 3: Change Process
The third research question asked, “What change process did the school use to
enhance its math program and strategies to assist students in math?” In examining
the collected data, the researcher discovered thee were four significant findings
related to the change process, the school underwent to improve its math program and
strategies and increase its students’ math achievement:
1. The former and current PNH administrators were strong in the symbolic and
political frame.
2. The PNH math teachers and key instructional math leaders that were teachers
were strong in structure and human resources.
3. PNH had strong administrative instructional leadership during the first,
second, and third phases of the Concerns Based Adoption Model (CBAM)
process.
4. The math department went through all levels of CBAM, but continually
analyze the effectiveness of the programs they have implemented, and
refocus those programs that they see need alteration to improve effectiveness
for students.
293
Research Question 4: Instructional Leadership
The fourth research question asked, “To what extent was strong instructional
leadership important in improving a) the math programs/strategies and b) math
achievement among students? In examining the collected data, the researcher
discovered thee were five significant findings related to the extent that strong
instructional was a factor in improving Pacific North High’s (PNH) math
programs/strategies and math achievement among its students:
1. PNH’s administrators had a clear vision with explicitly stated expectations
that they communicated to math teachers about student achievement that was
implemented effectively.
2. There was continuous collaboration between the administration, the key math
leaders, and the math teachers in attempting to raise students’ math
achievement at the school.
3. The administration was supportive of the new instructional techniques,
curriculum, and classes that the math teachers created.
4. The key math instructional leaders with the math teachers take the lead role in
monitoring and evaluating the math department’s implementation of vision
for improving students’ math achievement at the school.
5. There is a discrepancy between how the district and state monitor and
evaluate the progress of student achievement at the school, and how the
school evaluates and monitors students’ progress.
Research Question 5: Resolving Instructional Leadership Dilemmas
The fifth research question asked, “How did instructional leaders respond in
academic areas in which they were not experts?” In examining the collected data,
the researcher discovered thee were four significant findings related to how
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instructional leaders resolved problems in areas of which they did not possess
expertise:
1. Because the PNH administrators lacked math expertise, they compensated by
using two complementary leadership approaches: delegation of leadership by
Northouse (2001) and teacher leadership by Gabriel (2005).
2. One of the current math teachers at PNH used to be an administrator, and the
PNH administration and key math instructional leaders rely heavily on her for
guidance on math issues.
3. The PNH math teachers are independent and self-reliant.
4. The administration expediently provided the math department with any
necessary resources to accomplish the vision of raising students’ math
achievement.
Recommendations for Future Research
Based on the findings indicated through the data collection and analysis,
recommendations were made regarding future research in these areas:
1. The school of study was an urban comprehensive high school. It is
suggested that this study be simulated in suburban and rural high schools or
in high schools with smaller or larger student populations to determine if
school type affected the research findings. In addition, it replication should
happen in urban comprehensive high schools that are not in a unified district
to see if the effect of having no district policies affect the school’s secondary
math reforms.
2. To provide a more comprehensive picture of secondary school reform for
high school’s in Directional Unified (DU), a study can be performed that
incorporates all the high schools in DU.
295
3. The study of Pacific North High School (PNH) is a qualitative study.
However, a quantitative study of other DU high schools can provide valuable
information about DU’s secondary school reforms in relation to raising
students’ math achievement through policies, programs, school design, and
instructional leadership.
4. PNH’s mathematics secondary school reform focused on altering math
curriculum to increase its students’ math achievement without much
changing of school structure, hierarchies, or school-wide initiatives. PNH’s
reforms were more departmental, but a study can be performed that focuses
on a high school that raises its math achievement through other means such
as altering its school design through Small Learning Communities (SLC) or
Professional Learning Communities (PLC) to gain further insight into
secondary school reformation.
5. Because PNH had such mathematical success with programs such as College
Preparatory Math (CPM), High School Math (HSM), and the two-year
Algebra course, a study can be performed to examine a school increasing its
students’ math achievement through other math programs such as Cognitive
Tutor and Integrated Math to determine the most effective math programs for
secondary school math reform.
6. Since PNH did not rely heavily on outside forces and resources in order to
implement its secondary school reform in mathematics, a study can be
performed on a school that relies heavily on outside organizations such as the
Gates Foundation or 21
st
Century to control its secondary school reform in
math that raises students’ achievement in order to see which method is most
effective for reforming schools.
296
7. A significant part of PNH’s success in increasing achievement for its
students in math is due to the school’s independent and self-reliant math
department. Further research can be performed in how a school without a
strong math department increases its math achievement in order to discover
the effect a math department has on secondary school reform in mathematics.
8. PNH’s administrative leaders were high in the symbolic and political frames,
whereas the math teachers were high in human resources and structural.
Further studies can be performed on school’s that increased their students’
math achievement where the administrative leaders or teachers were high in
other Bolman and Deal’s frames to determine if certain combinations of
Bolman and Deal’s frames are more effective for increasing achievement
than others.
9. PNH’s administrators used the teacher leader and the delegation strategies
because they did not have math expertise. Studies can be performed on other
high schools that increased students’ math achievement where leaders use
other leadership strategies in order to discover which strategies are most
influential.
10. At PNH, the community and parents were not a significant factor in
increasing the students’ achievement in math. Further studies can be
performed, where schools increased their students’ math achievement
through community and parental effort to determine the amount of influence
the community or parental support has on a school’s secondary school reform
in math.
297
Implications for Practice
The analysis of the findings led to implications for practice. Implications for
practitioners are presented below by topic of accountability:
School Boards and Key District Leaders
1. Due to the district’s blanket policy that all high schools within their district
must have a five-point academic achievement growth on their Academic
Performance Index (API) each year, PNH’s school culture and teacher morale
is waning. PNH teachers and administrators feel that the district’s policy is
unfair because it does not take into account the individual needs and
challenges associated with PNH in raising their achievement levels. The
school feels as though the district is singling them out for punishment
because it is harder for them, with their diverse population to meet the
district’s five point required growth versus other schools in the district that do
not have such a diverse population or as many low socio-economically
disadvantaged students. PNH’s administrators feel that it is easier for other
district high schools that do not possess PNH’s population challenges to meet
the district’s mandate. Due to the fact that PNH sees the district’s growth
policy as unjust, the districts need to have achievable individualize academic
student growth achievement policies for each school within their district that
correctly gauges the needs of each school and compensates for school
deficiencies and challenges with sufficient resources and guidance. This
means that district offices have a system in place to correctly estimate the
needs of a school in order for it to reach the district’s growth rate targets.
The district must provide resources and funds expediently, and not rely on the
school to ask for support. The district office must also be proactive in
298
developing policies that help school administrators understand how the
district is going to support them in achieving district goals. In addition, the
district office needs to more than just punitive measures but supportive
structures, policies, and a program in place for when a school is does not
meet the district’s goals.
2. Recently, Directional Unified (DU) has decided to take away programs from
middle schools that were functionally connected and tied to high schools such
as the College Preparatory Math (CPM) program. Students at the middle
school would receive the Algebra I portion of the program, and then when
they entered PNH, they would be familiar with CPM methods and take the
Algebra 2, Geometry, and other CPM classes. Because the district disbanded
CPM in PNH’s middle school feeder, PNH has had a much more difficult
time in acquiring students for their CPM classes. In addition, the district now
requires that Algebra 1 be taught in 8
th
grade only. This destroys the work
that PNH math teachers have done with their middle school feeder on the
two-year Algebra 1 intervention program for students that failed Algebra 1 in
the middle school. This was a program that connected the middle school and
feeder and encouraged collaboration between both schools. No longer will
students receive the Algebra 1 intervention at PNH if they fail Algebra 1 at
the middle school feeder. This leaves a section of students that PNH serves
underserved. Due to these examples, it is imperative that districts understand
and better analyze the organizational flow of students from a middle school
feeder to a high school because changing programs at the middle school
feeder affects the programs within a high school. Districts can perform a
study that examines the effect of high school programs when programs
299
change at the school’s middle school feeder. The district office must also
keep in mind that high schools and middle schools have articulations, and
that when changes occur, more communication between the schools is needed
to resolve issues or change methods and strategies between the schools. In
addition, when problems do arise between the middle school and high school
because of a change of program stemming from a district mandate, it is
important for the district to provide each school with adequate time, proper
resources, and guidance or a plan from the district office on how to comply
with the new policy.
3. DU has decided this year to not allow PNH’s math teachers to teach the two-
year Algebra 1 program or Algebra 1 on the campus, they are also pressuring
the school to stop using the CPM program because they feel it is not
effective. Even though PNH’s math teachers and administrators all feel that
their increase in students’ math achievement is due to CPM. However, the
district still wants the program abolished, even though, it has not provided the
school with a policy or information on how the district deems programs
effective or not effective. Districts need to acknowledge and repair
discrepancies of monitoring and evaluating programs and curriculums
between the district and the school. It is a district’s responsibility to provide
a school’s administrators with information regarding how the district
monitors and evaluates programs and deems them effective or not effective.
Explicit policy statements, plans, and procedures need to be made by districts
in order to demonstrate to school’s the qualifications upon which the district
bases its evaluations of a school’s programs and curriculums. The district
must then have adequate professional development for the school’s
300
administration and key instructional leaders about the district’s
qualifications of evaluating a program or curriculum. In addition, the district
must give the school adequate time to meet the districts requirements.
4. DU distributes evenly distributes funds to each high school in a one-size fits
all fashion, similarly to its growth mandate, and so other district high schools
receive the same funds as PNH. Even though PNH has different needs and
challenges that, it faces than the other high schools within the district.
Districts need to remember that each school is unique and should have
individualized evaluations of each school within their district. Not every
school within a district is equal, so having providing the same resources,
materials, and funds to every school is inequitable. A district should yearly
perform a needs assessment on each school to determine how much each
school within the district will need to adequate meet the mandates and
policies of the district, and so the district can determine how they can fairly
and adequately support each school.
School Site Administrators
1. When school site administrators realize that a state policy such as BTSA is
not adequately providing teachers with the support they need, it is up to the
school to implement effective programs to compensate for the lack of
support. School site administrators must make the district aware of the
inadequacy of the policy, and then ask for assistance from the district in
rectifying the situation through resources, funds, and professional
development. The administrator must demonstrate to the district in what
way they need help, and how the implementation will be beneficial for the
teachers.
301
2. PNH, like many other schools, has increasingly put their efforts over the
past years into focusing on raising the student achievement of the students
in the lowest two quartiles—below basics and far below basics. PNH has
not created any programs, interventions, or reviewed instructional methods
for increasing the achievement of students that are not in the lower two
quartiles such as the basic or proficient students. PNH is not the only
school to have such a focus, and so school site administrators need to work
with teachers on developing plans for increasing student achievement in the
higher quartiles and not just having teachers focus on the lowest quartiles.
It is important for administrators to acknowledge that it is imperative to
move students out of the lowest two quartiles, but the goal is for students to
be proficient in subjects. Site administrators must remember that schools
serve all students, and there must be programs, curriculum, and resources
that move students from the basic category into proficient and advanced.
Schools that only focus on the lowest quartiles are leaving children behind
that are not reaching their potential in the basic category that have the
ability to progress into the proficient or advanced category. Administrators
can research programs that are for advancing the middle quartile students
such as Advancement Via Individual Determination (AVID), and
partnership with organizations in order to increase achievement of average
students.
3. DU is pressuring PNH to stop using its CPM program and has forbidden
PNH math teachers to teach the two-year Algebra 1 program, and PNH felt
that both programs are effective and essentially the reason why their
student achievement has increased over recent years. In recognition of
302
PNH’s situation with its district office, it is the responsibility of the
school site administrators that when a program or curriculum is effective at
the school to make sure that the district understands the importance and
significant of the program to the school. The administrator must provide
substantial statistical evidence and documentation that the program is
raising student achievement. Administrators should disaggregate the
information by school classifications and ethnic subgroups to indicate its
effect on particular groups at the school. If the district wants to eliminate
the program or curriculum, it is the administrators that can galvanize the
community and the teachers, with the proper evidence of the program or
curriculums effective on student achievement, to put up a strong defense
for keeping it at the school.
303
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Appendix A: Teacher Questionnaire A—All Teachers
Thank you for taking the time to complete this survey. It is hoped that the
results will serve as a rich source of data that may serve to better inform schools
seeking to improve in math achievement. Please return the survey to the principal’s
secretary by November 6, 2006. Once again, your assistance is greatly appreciated.
Directions: Please rate each item on the following scale by circling the
response of your choice:
5= Strongly Agree
4 = Agree Somewhat
3= Neutral
2 = Disagree Somewhat
1= Disagree Strongly
1. The No Child Left Behind Legislation has promoted increased student achievement
at our school.
1 2 3 4 5
2. The requirement that students pass the CAHSEE to earn a high school diploma has
contributed to the school’s effort to improve student achievement.
1 2 3 4 5
3. Board Policies in our district have contributed to improved math achievement in
our school.
1 2 3 4 5
4. Our school has successfully implemented common assessments that support
increased student achievement.
1 2 3 4 5
316
5. Teachers at our school teach standards-based lessons.
1 2 3 4 5
6. The master schedule at our school is built based on student need.
1 2 3 4 5
7. Teachers at our school use researched-based instructional strategies to increase
student achievement
1 2 3 4 5
8. Periodic benchmark assessments provide useful data that our teachers use to drive
instruction
1 2 3 4 5
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.
1 2 3 4 5
10. In an effort to improve instruction on our campus, our school has focused on
personnel issues including hiring quality teachers and fostering a positive working
environment amongst peers on campus.
1 2 3 4 5
11. In an effort to improve instruction on our campus, our school has focused on
overcoming political obstacles and gaining the necessary support to move the
school forward.
1 2 3 4 5
12. In an effort to improve instruction on our campus, our school has focused on
motivating students and staff as well as celebrating successes.
1 2 3 4 5
317
13. There is a shared vision for increased student achievement at our school.
1 2 3 4 5
14. Our school had a clear strategic plan to improve student achievement.
1 2 3 4 5
15. Student achievement is a priority when the school allocates its financial resources.
1 2 3 4 5
16. Professional development offerings at our site are based on student achievement
data
1 2 3 4 5
17. The principal works to gain the support of the community for the school’s
academic efforts.
1 2 3 4 5
18. The school leadership works to establish and maintain a respect for cultural
diversity
1 2 3 4 5
19. Students and staff are valued and their successes celebrated.
1 2 3 4 5
20. The school leaders used data-driven information to address problems/issues
related to student achievement.
1 2 3 4 5
21. The principal works hard to monitor and supervise instruction in the classroom
1 2 3 4 5
22. The principal makes effective use of the department chairs and relies on their
expertise when making important curricular decisions.
1 2 3 4 5
318
23. The principal has delegated some curricular authority to an assistant principal
with greater expertise in curriculum and instruction.
1 2 3 4 5
24. Outside experts have been used to promote greater capacity in the area of
instruction.
1 2 3 4 5
25. Site leadership fosters a culture of inquiry and collaborative problem solving.
1 2 3 4 5
26. The school’s leaders emphasize the importance of quality instruction as a primary
mission of the school.
1 2 3 4 5
27. Site leaders emphasize having high expectations for student achievement.
1 2 3 4 5
28. Quality interventions have been implemented on our site to help students at risk of
failing academically.
1 2 3 4 5
29. Professional Development has been a key tool used by site leaders in our effort to
improve instruction on our campus.
1 2 3 4 5
30. Teacher assignments are made strategically and with student need in mind.
1 2 3 4 5
319
Appendix B: Teacher Questionnaire B—Math Teachers
Thank you for taking the time to complete this survey. It is hoped that the
results will serve as a rich source of data that may serve to better inform schools
seeking to improve in math achievement. Please return the survey to the principal’s
secretary by October 15, 2006. Once again, your assistance is greatly appreciated.
Directions: Please rate each item on the following scale by circling the
response of your choice:
5= Strongly Agree
4 = Agree Somewhat
3= Neutral
2 = Disagree Somewhat
1= Disagree Strongly
1. The No Child Left Behind Legislation has promoted increased student achievement
at our school.
1 2 3 4 5
2. The requirement that students pass the CAHSEE to earn a high school diploma has
contributed to the school’s effort to improve student achievement.
1 2 3 4 5
3. Board Policies in our district have contributed to improved math achievement in
our school.
1 2 3 4 5
320
4. Our school has successfully implemented common assessments that support
increased student achievement.
1 2 3 4 5
5. Teachers at our school teach standards-based lessons.
1 2 3 4 5
6. The master schedule at our school is built based on student need.
1 2 3 4 5
7. Teachers at our school use researched-based instructional strategies to increase
student achievement
1 2 3 4 5
8. Periodic benchmark assessments provide useful data that our teachers use to drive
instruction
1 2 3 4 5
9. Student need is a major consideration when making teacher assignments in math at
our school.
1 2 3 4 5
10. The NCLB Act has been one of the main external pressures for improved math
achievement at this school.
1 2 3 4 5
11. The requirement that students pass the CAHSEE in math in order to earn a high
school diploma has contributed to the school’s effort to improve math
achievement.
1 2 3 4 5
321
12. Our school’s effort to improve student achievement in math instruction had
nothing to do with external accountability such as NCLB regulations and the
CAHSEE requirement.
1 2 3 4 5
13. Support classes have been included in our master schedule to improve student
achievement in math.
1 2 3 4 5
14. The implementation of standards-based instruction has served as an important
foundation in improving student achievement in math.
1 2 3 4 5
15. Our school has added the use of math coaches or experts to assist in the effort to
improve student achievement in math.
1 2 3 4 5
16. Teachers collaborate to develop common assessments and rubrics.
1 2 3 4 5
17. Professional development offerings at our site are based on student achievement
data.
1 2 3 4 5
18. Teachers have helped develop strategies used at our school to improve
instructional practice in math.
1 2 3 4 5
19. The principal has served as a “change agent” for improved student achievement in
math.
1 2 3 4 5
322
20. Student achievement in math was made a priority as the school allocated its
financial resources.
1 2 3 4 5
21. Our school had a clear strategic plan to improve student achievement in math.
1 2 3 4 5
22. Professional Development has played a key role in increasing student
achievement in math
1 2 3 4 5
23. Teacher collaboration has played a key role in increasing student achievement in
math.
1 2 3 4 5
24. Changes in the curriculum have played a key role in increasing student
achievement in math.
1 2 3 4 5
25. Our school has implemented effective intervention strategies for students having
difficulty in math
1 2 3 4 5
26. My district supports teachers with effective staff development in Mathematics
Instruction.
1 2 3 4 5
27. My principal actively supports opportunities for staff members to collaborate and
plan Mathematics lessons and units.
1 2 3 4 5
323
28. Teachers learn by watching each other teach and discussing best practices.
1 2 3 4 5
29. Our school has effective strategies to support students of various learning
modalities
1 2 3 4 5
30. Our school uses math coaches to help teachers become more reflective with their
math instruction
1 2 3 4 5
31. I have gained valuable resources from math coaches/instructional leaders that
have improved the quality of my math instruction.
1 2 3 4 5
32. My school's instructional leader provides professional development resources that
I use in my mathematics instruction.
1 2 3 4 5
33. The school leader is aware of the mathematics instruction and academic progress
of the students in my class.
1 2 3 4 5
34. The school leader provides opportunities for faculty members to discuss
mathematics instruction.
1 2 3 4 5
35. The school instructional leader encourages faculty members to discuss effective
math instructional strategies.
1 2 3 4 5
324
36. My school's math instructional practices are developed from evidence-based
strategies.
1 2 3 4 5
37. I have regular support from proven instructional leaders in math instruction.
1 2 3 4 5
38. The math achievement goals and measures for my school were clearly articulated
and easy to understand.
1 2 3 4 5
39. I received coaching and mentoring from instructional leaders or peer coaches.
1 2 3 4 5
41. The district personnel, school leaders and teachers all have a shared vision for
increased math achievement.
1 2 3 4 5
42. My district and school leaders seem knowledgeable about instructionally effective
math practices and assessment strategies.
1 2 3 4 5
43. The Math Department Chair has been entrusted with and is empowered to make
important curricular decisions.
1 2 3 4 5
44. Outside experts have been used to promote greater capacity in the area of math
instruction.
1 2 3 4 5
45. The school’s leaders emphasize the importance of quality instruction as a primary
mission of the school.
1 2 3 4 5
325
46. Professional Development in math has been a key tool used by site leaders in
our effort to improve instruction on our campus.
1 2 3 4 5
47. Site leaders emphasize having high expectations for student achievement in math.
1 2 3 4 5
48. Quality interventions in math have been implemented on our site to help students
at risk of failing academically.
1 2 3 4 5
49. Our site leaders emphasize a culture of collaboration as a means of improving
instruction at our site.
1 2 3 4 5
50. Teacher assignments in the math department are made strategically and with
student need in mind.
1 2 3 4 5
326
Appendix C: Teacher Interview Guide
1. What is your current position?
2. Describe your educational background, credentials held, years of experience
and any specialized training you have had in math instruction.
3. What policy initiatives and/or curricular programs do you feel have contributed
to improved student achievement in math?
4. What teaching strategies, methods and/or instructional materials do you feel
have contributed to improved student achievement in math?
5. Over the past few years, what changes, if any do you feel have made a
significant impact on student achievement in math? How were they
implemented?
6. What role did school leaders (administrators, department chair, lead teachers,
math coaches) play in the development and implementation of the math
program?
7. What actions taken by school leaders most directly affected student
achievement in math?
327
Appendix D: Key Leader Interview
Key Leader Interview Guide
Research Question Two: What Policy initiatives as well as curriculum,
instruction and related conditions seem to be related to improved math
achievement in the school?
Directions to Interviewer:
Describe the purpose of the interview, expected timeline, and
introduce each topic as the RQ changes. For this section,:
“The first part of our interview, I will be asking you to describe your
perceptions about how policy issues have affected your efforts to improve student
achievement in math. Specifically, we will cover policy issues related to:
POLICIES
NCLB- AYP/HQT
District
State Policies/API
CAHSEE
Are you ready?
1. How do you perceive NCLB as having influenced your efforts to increase student
achievement?
AYP?
HQT?
2. What board policies and/or practices (if any) are in place that support increased
student achievement in math?
Benchmarks assessments
Financial resources
Additional Staffing / CSR
328
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?
CHANGE PROCESS
Research Question 3: What change process did the school use to enhance
its math program and strategies to assist students in math?
“Let’s turn our attention to how you handled the change process related
to your efforts to improve student achievement in math. Specifically, I will be
asking you about different aspects of the change process as described in Bolman
and Deal’s Four frames, as well as the Concerns Based Adoption Model (CBAM).
In case you are not familiar with either of these models, here is a copy of the
frameworks for your reference and clarification. (give the frameworks to the
interviewee). OK, so I will be asking you about:”
Structural changes (school design, leadership, use of facilities, etc. )
HR – Key Personal Changes
o Teacher assignments and master schedule
Political issues related to the changes made at your schools
o How did you negotiate the political aspects associated with you
change process
Symbolic Methods used to add meaning and importance to your initiatives
such as:
o Vision/mission
o Culture/climate
o Ceremonies/ awards/recognition
CBAM
o Ask to describe where their staff is and how they got there
329
1. What structural changes have you made that you feel have contributed to
improved math achievement?
o School design
o Leadership
o Facilities
o CSR
2. What personnel changes have been implemented that has positively influenced the
math achievement?
o Teacher assignments
o Leadership roles
3. How did you negotiate the political aspects associated with the change process?
o Site level
o District level
o Community level
4. What did you do symbolically to support and engage in the change process that has
been implemented to improve math achievement?
o Vision/mission
o Culture climate
o Ceremonial/awards
5. Where do you view your staff on the CBAM continuum (Concerns Based Adoption
Model)? And, how did they get there?
Leadership Instrument RQ 4
Research Question 4: To what extent was strong instructional leadership
important in improving (a) the math programs/strategies and (b) math
achievement among students?
“I would now like to ask you about issues specifically related to the role of
instructional leadership in your efforts to improve student achievement in math.
Specifically, I will be asking about the roles leaders played and issued related to
the development of a professional learning community on your campus.”
330
1. Who were the leaders on your campus who helped bring about the
improved achievement in math?
a. What were there roles?
2. How was the professional growth of the math teachers supported?
3. To what degree was teacher collaboration and/or reflection fostered and
encouraged?
4. How has the school leadership worked to implement a professional
community on you campus?
a. Teacher empowerment
b. Teacher leadership
c. Peer collaboration
d. Reflection
5. In what ways have site leaders attempted to make the focus on student learning
and results?
Leadership Questionnaire RQ5
Research Question 5: How did leaders in the school resolve dilemmas
about instructional leadership?
“Now let’s talk a little about how the site leadership went about
overcoming any obstacles you may have faced as you worked to improve student
achievement in math.” You may find it useful to refer to the frameworks on
change that I provided to you earlier.
1. What particular obstacles did you school face in the implementation of you
changes related to improved achievement in math?
2. How did the site leadership work to overcome these obstacles?
a. Structural Changes / Solutions
b. Human Resource Changes / Solutions
c. Political Changes / Solutions
d. Symbolic Changes / Solutions
331
Appendix E: Evaluation Chart Design
Evaluation Design Chart
Evaluation
Questions
Data Needs Data Sources Instrumentation
RQ-1
What was the pattern
of math achievement
for various students
at the school?
Test Scores
- CAHSEE, STAR,
AP, DWA
Grade Distributions
Remedial enrollment
SIS
Hard Copy Test
Reports
CDE Web Site
School Profile
RQ-2
What policy
initiatives as well as
curriculum,
instruction/and
related conditions
are related to
improved math
achievement at the
school?
Board Policies
Curriculum
Frameworks
Instructional Strategies
Instructional Materials
School climate &
Culture Data
Course scope &
sequence
course outlines
pacing calendars
Board Policies
grad requirements
Textbook list
Teacher Questionnaire
Key Leader Interview
Guide
Teacher Interview
Guide
RQ-3
What change process
did the school use to
enhance the math
program and
strategies?
• Professional develop
plan
• Administration
• Teachers
Policies - District/Site
Instructional model
• Master schedule,
Teaming, PLC
Instructional
materials/strategies
Site Plan
personnel chart
job descriptions
master schedule
categorical budget
Teacher Questionnaire
Key Leader Interview
Guide
Teacher Interview
Guide
RQ-4
How was
instructional
leadership important
in improving a) the
math
programs/strategies
and b) math
achievement among
students?
Leaders names and
positions
Specific math
programs used
Strategies for staff
dev.
Conventions /
committees developed
Resources available to
leader
Stakeholder
perceptions
Leadership Roles-
formal / informal
Teachers
Administrators
Support Personnel
Test Score Reports
CDE Web Site
Teacher Questionnaire
Key Leader Interview
Guide
Teacher Interview
Guide
RQ-5
How did
instructional leaders
respond in academic
areas in which they
were not experts ?
Strategies
(prioritization)
Resources
Professional
development
Technology
Administrators
Teacher Leaders
Support Personnel
Teacher Questionnaire
Key Leader Interview
Guide
Teacher Interview
Guide
332
Appendix F: School Design Framework
School
Design
Curriculum Learning
Activities
Challenge
Students to
Think
Students
Solve
Problems
School
Culture
Based on
Enhanced
Learning
Meaningful
Staff-Student
Interactions
Ongoing
Professional
Development
Collaborative
School-to-Career
Applications
Constructivist
Knowledge
Based on
Student
Outcomes
Student Performance
Assessments
Capture
Conceptual
Understanding
Capture
Problem
Solving
Capture
Communication
Skills
333
Appendix G: Effective Math Programs
Effectiv
e Math
Progra
Classroom Practices
ο Effective and
coherent lesson
design
ο Promotes high
levels of student
engagement
ο Makes use of
i
Curriculum Design
• Student-centered
curriculum
• Driven by learner
outcomes
• Emphasizes Conceptual
• Focuses on problem-
solving
Standards Based
Instruction
ο Assessments
aligned to
standards
ο Student
achievement
data drives
it ti d
334
Appendix H: Bolman and Deal’s Four Frames
Frame Structural Human
Resources
Political Symbolic
Metaphor for
organization
Factory or
Machine
Family Jungle Carnival,
Temple,
Theater
Central
Concepts
Rules, Roles,
goals,
Policies,
Technology,
Environment
Needs, Skills,
Relationships
Power,
Conflict,
Competition,
Organizational
politics
Culture,
Meaning,
metaphor,
ritual,
ceremony,
stories, heroes
Image of
Leadership
Social
Architect
Empowerment Advocacy Inspiration
Basic
Leadership
Challenge
Attune
Structure to
task,
Technology,
environment
Align
Organizational
and human
needs
Develop
Agenda and
Power Base
Create Faith,
Beauty,
Meaning
335
Appendix I: Instructional Leadership
Frame Structural Human
Resources
Political Symbolic
Metaphor for
organization
Factory or
Machine
Family Jungle Carnival,
Temple,
Theater
Central
Concepts
Rules, Roles,
goals,
Policies,
Technology,
Environment
Needs, Skills,
Relationships
Power,
Conflict,
Competition,
Organizational
politics
Culture,
Meaning,
metaphor,
ritual,
ceremony,
stories, heroes
Image of
Leadership
Social
Architect
Empowerment Advocacy Inspiration
Basic
Leadership
Challenge
Attune
Structure to
task,
Technology,
environment
Align
Organizational
and human
needs
Develop
Agenda and
Power Base
Create Faith,
Beauty,
Meaning
336
Appendix J: School Profile Spreadsheet
Algebra 1
School
Increase in
Top two
Quintiles
Decrease in
Bottom Two
Quintiles
Algebra I
Total Gains
District
Schurr High 4% -67% 71% Montebello Unified
Mark Keppel High 22% -28% 50% Alhambra Unified
Escondido High 15% -32% 47% Escondido Union High
Western High 21% -26% 47% Anaheim Union High
Brawley High 9% -31% 40% Brawley Union High
Oxnard High 13% -17% 30% Oxnard Union High
San Gabriel High 11% -17% 28% Alhambra Unified
El Rancho High 4% -22% 26% El Rancho Unified
Palm Springs High 9% -17% 26% Palm Springs Unified
Townsend (Robert O.) 17% -7% 24% Chino Valley Unified
Loara High 11% -13% 24% Anaheim Union High
Gabrielino High 6% -17% 23% San Gabriel Unified
Whittier High 4% -16% 20% Whittier Union High
Serra Senior High 4% -15% 19% San Diego Unified
Los Angeles Center 7% -11% 18% Los Angeles Unified
Alhambra High 6% -11% 17% Alhambra Unified
University High 10% -7% 17% Irvine Unified
Point Loma Senior 4% -13% 17% San Diego Unified
337
Mira Mesa High 2% -13% 15% San Diego Unified
Central High 4% -11% 15% Central Union High
Arcadia High 3% -12% 15% Arcadia Unified
San Diego Creative 9% -6% 15% San Diego Unified
Southwest High 4% -11% 15% Central Union High
Arlington High 2% -12% 14% Riverside Unified
Monte Vista High 5% -8% 13% Grossmont Union
La Serna High 5% -8% 13% Whittier Union High
Diamond Bar High 10% -2% 12% Walnut Valley Unified
North High 2% -10% 12% Torrance Unified
El Camino High 2% -10% 12% Oceanside Unified
Taft (William Howard) 6% -5% 11% Los Angeles Unified
John F. Kennedy High 0% -11% 11% Anaheim Union High
Hilltop Senior High 4% -7% 11% Sweetwater Union
Charter Oak High 0% -10% 10% FALSE
Tustin High -1% -10% 9% Tustin Unified
Bonita Vista Senior 4% -5% 9% Sweetwater Union
Burroughs High 7% -2% 9% Burbank Unified
Eastlake High 3% -6% 9% Sweetwater Union
King/Drew Med. Mag. 2% -6% 8% Los Angeles Unified
Polytechnic High 4% -4% 8% Long Beach Unified
Bravo Medical Magnet 3% -5% 8% Los Angeles Unified
Valencia High 2% -6% 8% Placentia-Yorba Linda
Polytechnic High -1% -8% 7% Riverside Unified
338
Millikan Senior High 2% -5% 7% Long Beach Unified
Hamilton (Alexander) 0% -6% 6% Los Angeles Unified
Gahr (Richard) High 1% -5% 6% ABC Unified
University City High 1% -5% 6% San Diego Unified
Westminster High 0% -6% 6% Huntington Beach
Ramona High 0% -4% 4% Riverside Unified
Diamond Ranch High 1% -2% 3% Pomona Unified
Santiago High 1% -1% 2% Corona-Norco Unified
West High -10% -12% 2% Torrance Unified
Pasadena High -2% -4% 2% Pasadena Unified
North (John W.) High -1% -3% 2% Riverside Unified
Rancho Verde High -2% -3% 1% Val Verde Unified
Morse Senior High -1% -2% 1% San Diego Unified
Henry Senior High -1% -2% 1% San Diego Unified
Walnut High 1% 0% 1% Walnut Valley Unified
Ayala (Ruben S.) High -3% -3% 0% Chino Valley Unified
Culver City Senior -1% -1% 0% Culver City Unified
Wilson (Glen A.) High -2% -1% -1% Hacienda la Puente
Fallbrook High -2% -1% -1% Fallbrook Union High
Warren High -1% 0% -1% Downey Unified
Rio Mesa High -3% -2% -1% Oxnard Union High
Torrance High -3% -1% -2% Torrance Unified
Rowland (John A.) -2% 0% -2% Rowland Unified
West Covina High -1% 1% -2% West Covina Unified
339
La Mirada High 1% 3% -2% Norwalk-La Mirada
Marshall Fundamental -1% 3% -4% Pasadena Unified
Corona Senior High -3% 2% -5% Corona-Norco Unified
Orange Glen High -2% 4% -6% Escondido Union High
Costa Mesa High -2% 4% -6% Newport-Mesa Unified
Vista High -1% 5% -6% Vista Unified
Centennial High 0% 7% -7% Corona-Norco Unified
Irvine High -2% 5% -7% Irvine Unified
Eagle Rock High -4% 4% -8% Los Angeles Unified
Otay Ranch Senior -8% 0% -8% Sweetwater Union
Orange High -5% 4% -9% Orange Unified
Lakewood High -6% 4% -10% Long Beach Unified
Sunny Hills High -5% 5% -10% Fullerton Joint Union
Rancho Cucamonga -2% 8% -10% Chaffey Joint Union
Wilson High -5% 7% -12% Long Beach Unified
La Sierra High -6% 7% -13% Alvord Unified
Temple City High -8% 5% -13% Temple City Unified
Highland High -6% 10% -16% Antelope Valley Union
Redlands Senior High -6% 12% -18% Redlands Unified
La Habra High -12% 9% -21% Fullerton Joint Union
Chino Hills High -10% 11% -21% Chino Valley Unified
Chatsworth High -9% 12% -21% Los Angeles Unified
La Quinta High -5% 16% -21% Desert Sands Unified
Colony High -5% 16% -21% Chaffey Joint Union
340
Fountain Valley High -21% 1% -22% Huntington Beach
Mayfair High -9% 13% -22% Bellflower Unified
Alta Loma High -6% 17% -23% Chaffey Joint Union
Upland High -13% 11% -24% Upland Unified
Monrovia High -8% 17% -25% Monrovia Unified
Santa Barbara High -9% 17% -26% Santa Barbara High
Sonora High -10% 18% -28% Fullerton Joint Union
Rancho Alamitos High -14% 14% -28% Garden Grove Unified
West Valley High -12% 17% -29% Hemet Unified
South Hills High -15% 19% -34% Covina-Valley Unified
Cerritos High -20% 16% -36% ABC Unified
La Quinta High -20% 16% -36% Garden Grove Unified
Sherman Oaks Ctr. -21% 17% -38% Los Angeles Unified
Fullerton High -10% 28% -38% Fullerton Joint Union
Los Altos High -18% 21% -39% Hacienda la Puente
Etiwanda High -17% 23% -40% Chaffey Joint Union
Cleveland High -17% 24% -41% Los Angeles Unified
Garden Grove High -30% 12% -42% Garden Grove Unified
Troy High -17% 30% -47% Fullerton Joint Union
Los Amigos High -33% 27% -60% Garden Grove Unified
California High -60% 51% -111% Whittier Union High
Avg Growth/Decline -2.36% -0.46% -1.90%
341
Appendix K: Assessment of Principal’s Expertise in Math
Assessment of Principal’s Expertise in Math
Step 1
Is the Principal
HQT Compliant?
Yes No
High
Expertise
Step 2
Does the
Principal have a
credential or
major in math?
Yes No
Medium
Expertise
Does the Principal
have a minor or
taught math?
Yes No
Medium
Expertise
Low
Expertise
342
Appendix L: Strategies to Overcome a Lack of Subject Matter Competency
Item
Strategy Approach/Source
1 Delegate Leadership to Assistant with greater expertise
Delegation Approach
(Northouse, 2001 p. 58)
2 Empower Department Chair
Teacher Leadership (Gabriel, 2005)
3 Bring in Outside Expertise
Meaningful Staff
Development Activities
(Marzano, 2003 pp. 65-66)
4 Emphasize inquiry and problem solving
Action Research
(Stringer 1999)
5 Emphasize quality instruction
Instructional Strategies
(Marzano, 2003 pp. 78-87)
6
Emphasize strategies to engage students in the learning
process
Student Engagement
(Marzano, 2003 pp. 149-150)
7 Emphasize articulation with feeder schools
Guaranteed, Viable Curriculum (Marzano, 2003
pp. 22-34)
8 Emphasize raised expectations
Challenging Goals and Effective Feedback
(Marzano, 2003 pp. 35-46)
9 Emphasize Strategic Teacher Assignments
HR Frame
(Bolman & Deal, 2003)
10
Emphasize Revised Course Scope and Sequence and/ or
Curriculum
Guaranteed, Viable Curriculum (Marzano, 2003
pp. 22-34)
11 Emphasize Interventions for lower performing students
Supplemental Services
(NCLB, 2001)
12 Emphasize Professional Development
Meaningful Staff
Development Activities
(Marzano, 2003 pp. 65-66)
343
Appendix M: Math Teacher Questionnaire Spreadsheet Database
Math Teacher Questionnaire Results
# of Questionnaires 8
Research Question 2
(note 2.2 and 2.11 = same question)
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13
# 1 2 3 4 5 6 7 8 9 10 11 12 13
2.88 3.50 2.75 3.50 4.38 4.38 4.38 3.63 4.00 3.13 3.50 2.88 3.63
Research Question 3
(note 3.9 and 3.12 = same question)
3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13
# 14 15 16 17 18 19 20 21 22 23 24 25
4.25 2.50 4.75 4.13 4.50 3.88 3.00 3.38 3.50 4.38 3.25 3.75
3.14 3.15 3.16 3.17
# 26 27 28 29
4.13 4.00 3.25 3.75
Research Question 4
(note there is no number 40 in the questionnaire)
4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12
# 30 31 32 33 34 35 36 37 38 39 40 41 42
2.13 2.25 3.38 3.38 3.25 3.63 3.50 3.50 3.88 4.38 3.63 3.88
Research Question 5
5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8
# 43 44 45 46 47 48 49 50
3.63 3.75 4.13 3.38 4.63 4.00 3.25 3.88
344
Appendix N: Non-Math Teacher Questionnaire Spreadsheet
Non-Math Teacher Questionnaire
# of Questions 45
Research Question 2
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8
# 1 2 3 4 5 6 7 8
2.69 3.58 3.29 3.56 3.87 3.82 3.76 3.56
Research Question 3
3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8
# 9 10 11 12 13 14 15 16
3.80 3.78 3.82 3.78 3.78 3.67 3.67 3.58
Research Question 4
4.1 4.2 4.3 4.4 4.5
# 17 18 19 20 21
3.82 3.89 3.98 3.87 3.51
Research Question 5
5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8
# 22 23 24 25 26 27 28 29
3.60 3.67 3.09 3.56 3.91 3.89 3.89 3.51
5.9
# 30
3.76
345
Appendix O CPM Sample Algebra 1 Question
346
Appendix P CPM Sample Question 2
Abstract (if available)
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Asset Metadata
Creator
Nichols, Jahnell Jones
(author)
Core Title
A story of achievement in areas where others fail: a case study of secondary school reform in mathematics at Pacific North High School
School
Rossier School of Education
Degree
Doctor of Education
Degree Program
Education (Leadership)
Publication Date
07/10/2007
Defense Date
05/21/2007
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
High School,mathematics,OAI-PMH Harvest,Secondary,secondary school reform
Place Name
California
(states),
USA
(countries)
Language
English
Advisor
Marsh, David D. (
committee chair
), Olsen, Carlye (
committee member
), Rousseau, Sylvia G. (
committee member
)
Creator Email
jahnell.jones@lausd.net
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-m603
Unique identifier
UC1323452
Identifier
etd-Nichols-20070710 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-520597 (legacy record id),usctheses-m603 (legacy record id)
Legacy Identifier
etd-Nichols-20070710.pdf
Dmrecord
520597
Document Type
Dissertation
Rights
Nichols, Jahnell Jones
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Repository Name
Libraries, University of Southern California
Repository Location
Los Angeles, California
Repository Email
cisadmin@lib.usc.edu
Tags
secondary school reform