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Urban schools that have narrowed the achievement gap: middle school math achievement in an urban setting

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Urban schools that have narrowed the achievement gap: middle school math achievement in an urban setting

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URBAN SCHOOLS THAT HAVE NARROWED THE ACHIEVEMENT GAP:
MIDDLE SCHOOL MATH ACHIEVEMENT IN AN URBAN SETTING
by
Theodore Sagun
____________________________________________________________________
A Dissertation Presented to the
FACULTY OF THE USC ROSSIER SCHOOL OF EDUCATION
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF EDUCATION
May 2010
Copyright 2010 Theodore Sagun

ii
DEDICATION
May all the glory and honor go to Jesus Christ, who makes all things possible.
My son, when you come to serve the Lord, prepare yourself for trials.
Be sincere of heart and steadfast, undisturbed in time of adversity.
Cling to him, forsake him not; thus will your future be great.
Accept whatever befalls you, in crushing misfortune be patient;
For in fire gold is tested, and worthy men in the crucible of humiliation.
Trust God and he will help you; make straight your ways and hope in him.
(Sirach 2:1-6)
First and foremost, to my brother, Gregory R. Sagun, because each time I see the
twinkle in another child’s eye, attempting to peer into their soul, I see an image of him.
Then, I am compelled to expend more energy to teach well.

iii
ACKNOWLEDGMENTS
My parents, Jesus and Pacifica, have been incredibly supportive to the nth degree.
Unknowingly, my mom provided my sister and me social capital in being the first in her
family obtain a college degree. My dad’s numerous anecdotes from his childhood
through his time at University of Philippines, Diliman, were constant reminders to seek a
calling and to sustain idealism. Furthermore, he did well by teaching us to love Christ.
Through modeling, my sister, Adele, set an extremely high bar and compelled me
to produce my best. My maximal capacity was only half her effort, but I am most
thankful that she supported me in this dissertation process.
To my students, “Nerd Patrol!” I hope that, through a sociocultural perspective, I
influenced each of them positively in the reciprocal manner you impacted my life and my
teaching practice. Serving them has been a humbling, rewarding experience.
The Panera Club deserves acknowledgement because of their support throughout
this grueling yet gratifying process. To Arleen and Rosalinda: Our meetings reflected
sociocultural theory in real time. Both of them contributed to any semblance of success I
garnered at USC. They are both God sent.
Dr. Hollins, Dr. Rachel Lotan, and Dr. Chang must be acknowledged. Dr.
Chang’s Theory of Probability class ignited concrete interest in applied mathematics.
Rachel was supportive and instrumental during my experience at Stanford’s Secondary
Teacher Education Program (STEP). Having Dr. Hollins for three classes defined my
perspective on urban education. Constantly, there was “something to think about” that

iv
positively impacted my instructional practice. I am blessed to enjoy math, to learn to
teach it with a sociocultural framework, and to learn about my students and their
community to instruct them effectively.
Mrs. Sena and Mrs. Ruiz were supportive throughout my studies and the
dissertation process. I can only hope to have served our students well.
Dr. Gothold set an ambitious timeline that was taxing, wearisome, but worthwhile
and meaningful. I am grateful to him for his leadership.
Dr. Fischer was instrumental in providing critical feedback and support. I thank
him for fueling my writing process.
To Ray Senesac and Ron Pirayoff: The long drives, inordinate emails, and
numerous phone conversations paid off. I thank both of them for their support,
dedication, and effort in contributing to the dissertation process.

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TABLE OF CONTENTS
Dedication ii
Acknowledgments iii
List of Tables viii
List of Figures ix
Abstract x
Chapter 1: Overview of the Study 1
Background of the Problem 2
Statement of the Problem 9
Purpose of the Study 9
Research Questions 10
Framework of the Study 11
Importance of the Study 13
Assumptions 13
Limitations of the Study 14
Delimitations of the Study 14
Definition of Terms 15
Organization of the Dissertation 22
Chapter 2: Literature Review 24
Historical Perspective on Student Performance 26
Changes in Assessment Practices 29
Accountability 32
Math Achievement Gap 34
Factors of the Achievement Gap 36
Critical Race Theory 37
Institutional Support 42
Poor Mathematics Teaching Quality 46
Achievement Gap Reduction 49
Leadership 51
Internal Accountability 53
Instruction 56
Quality of Instruction 59
Multicultural Education 62
Anecdotal Evidence 64
Sustainable Practices 69
Summary and Conclusions 72

vi
Chapter 3: Research Methodology 75
Sample and Population 78
District Level 79
School Level 80
Mathematics 82
Instrumentation 83
Document Review 83
Surveys 84
Interviews 85
Observations 86
Data Collection 87
Institutional Review Board 89
Data Analysis 89
Organizing and Preparing 90
Obtaining a General Sense 90
Coding 91
Generating Descriptions 91
Qualitative Narrative 91
Interpretation 91
Summary 92
Chapter 4: Results 93
Beacon Intermediate: Meet and Greet 93
Beacon Intermediate School: Physical Nature 96
Participants 99
Research Questions 100
Criteria 101
Findings for Research Question 1 102
Publicity of Student Work 102
Staff Collaboration 104
Shared Leadership 108
Findings for Research Question 2 119
CHAMPing 122
Student Engagement 123
Discrepancy Related to Student Engagement 125
Writing Across the Curriculum 127
Discrepancy in Writing Across the Curriculum 129
Having a Routine When There Is No Routine 130
Discrepancy in Routine 136
Summary 137
Findings for Research Question 3 138
Data Director 138
Grading Program 139
Two-Period Blocks of ELA/Math 141
Use of Spreadsheets to Collect and Disaggregate Student Data 143
Effect of Algebra 1 on Raising Student Achievement 144
Green Light 146
Sustainability 148
Discussion 153
Discussion of Emergent Themes 153

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Leader of Leaders 154
Teacher Collaboration 156
Data-Driven Culture 156
Algebra Curriculum 157
Chapter 5: Summary, Conclusions, and Recommendations 161
Summary of Findings 162
Implications for Practice 168
Recommendations for Teaching Staff 169
Recommendations for Administrators 170
Recommendations for the School District 171
Recommendations for Policy Makers 172
Recommendations for Research 173
Conclusion 175
References 177
Appendices
Appendix A: Document Review Master List, Categorized 185
Appendix B: Staff Input Survey 187
Appendix C: Interview Questions 192
Appendix D: Interview Follow-Up Questions 194
Appendix E: School Observation Form/Guide 195
Appendix F: Alignment of Data Needs, Sources, and Instrumentation 200
Appendix G: Research Questions/Survey Protocol Correlation Grid 203
Appendix H: Math Data Needs Data Sources 205

viii
LIST OF TABLES
Table 1: Responses to Survey Items 1-6 105
Table 2: Percentages of All Students Scoring Proficient or Advanced in
English-Language Arts: Three-Year Comparison 114
Table 3: Responses to Survey Items 7-16 115
Table 4: Percentages of Algebra 1 Students Ranked Proficient and Advanced
(P&A) on the California Standards Test 131
Table 5: Grading Program 140
Table 6: English-Language Arts (ELA) and Math Results for All Students:
Three-Year Comparison 145
Table 7: Academic Performance Index (API) Scores and Rankings for Beacon
Intermediate School, 2005-2009 149
Table 8: Beacon Intermediate School’s Percentages of Proficient and Advanced
Scores for Algebra 1 on the California Standards Test, 2004-2009 150
Table 9: Percentages of Students in English-Language Arts Who Scored
Proficient or Advanced on the California Standards Test at District
Schools, 2006-2009, by Grades 6, 7, and 8 152

ix
LIST OF FIGURES
Figure 1: Gap analysis model 50
Figure 2: Framework of the study based on Clark and Estes’s gap analysis 78

x
ABSTRACT
The achievement gap is a persistent academic disparity between White and Asian
students and ethnic minorities, English Language Learners, and low-income students.
The academic disparity exists within the realm of mathematics. Although many factors
are cited for contributing to the achievement gap, this study reviews institutional racism,
meager institutional support, and poor mathematics instruction as contributors to poor
academic achievement by historically poor or underperforming minority students. This
case study is one of nine doctoral dissertations focused on the theme of urban schools that
have narrowed the achievement gap with a focus on middle school algebra achievement.
This study focused on an urban school that experienced sustained academic achievement
in garnering at least 2 years of rising scores on the Academic Performance Index and the
California Standardized Test (CST) as well as 3 consecutive years of at least 80%
proficiency on the Algebra 1 CST. The author cites leadership, a collaborative
community, data-driven culture, and instruction focused on conceptual understanding of
standards to enhance student learning, especially in Algebra 1. This research raises
questions regarding the value of curricular autonomy as opposed to a strong attachment
to published curricula related to teaching subjects such as algebra.

1
CHAPTER 1
OVERVIEW OF THE STUDY
Historically, America’s urban youth have experienced persistently low academic
achievement. Sustained academic disparity between advantaged students and their poor
and minority peers has fueled legislation that holds adults and educators accountable for
student learning. The No Child Left Behind Act of 2001 (NCLB), which is the rede-
signed format of the Elementary and Secondary Education Act of 1965 (ESEA), was
initiated to ensure accountability. NCLB directed the spotlight on the academic perform-
ance of historically underperforming students by forcing schools to put more attention on
educating poor and minority students, as well as English Language Learners (ELL;
Haycock, 2006).
Low achievement by minority populations is prevalent in mathematics achieve-
ment. Underprivileged populations have historically been granted less access to better
teaching, better resources, and better schools (Byrnes, 2003; Peske & Haycock, 2006).
Constrained access to resources conducive to academic achievement has limited minority
students’ math achievement and performance. Therefore, unequal practices such as
tracking and limited access have created an achievement gap specific to math, limiting
opportunities for students to learn. Due to the “algebra-for-all eighth graders” decision
that is slowly sweeping through all middle schools (Kriegler, 2001), the limited access
and restricted opportunities to learn present a great issue for these historically under-
served populations to thrive in mathematics.

2
This study explored cultural norms, practices, and programs that were perceived
to have narrowed the achievement gap. The study was designed to determine models for
raising student achievement, specifically math achievement, in underprivileged students.
The desire was to contribute to literature on the achievement gap and to identify models
that could be valuable to urban schools with the potential for benchmarking. Reviewing
preexisting models offered in research to make comparisons is essential to this study.
Background of the Problem
The achievement gap is a persistent academic disparity between White and Asian
students and ethnic minorities, ELL, and low-income students. Valencia, Menchaca, and
Donato (2002) cited a history of inequality as the reason for the achievement gap between
Whites and Latinos. Ladson-Billings and Tate (1995) claimed that poor conditions in
schools, coupled with the limitations of poverty, are perceived as examples of institu-
tional racism that has inhibited student math achievement in African American communi-
ties. In essence, a history of segregated, inferior schooling conditions is the culprit
behind low academic progress by poor and minority students.
The National Assessment of Educational Progress (NAEP), widely known as the
Nation’s Report Card, paints a comprehensive view of academic discrepancies between
privileged students and their minority counterparts. The most recent publication of
NAEP shows that White-Hispanic and White-Black score gaps persisted between 1990
and 2009 (National Center for Education Statistics [NCES], 2009b). NAEP reported that
ELL students were far behind White students in math and reading in 2005 (Fry, 2007).
The Education Trust (2006) cited eighth-grade NAEP data from 2005 that showed that

3
only 6% of African Americans were performing at proficiency levels in math. This is in
clear contrast to 45% of Asian American students and 34% of White students. The
NCES reported that, from 1973 to 2008, the performance gap between Whites and their
African American and Latino counterparts fluctuated; from 2004 to 2008 gaps between
racial groups did not significantly improve (NCES, 2008). In 2009 the NCES reports
showed increased eighth-grade scores for White students, African American students, and
Hispanics coupled with trends that show no significant changes in White-Black score
gaps and White-Hispanic score gaps (NCES, 2009b).
The achievement gap reflects a history of inequitable practices in which minority
and underprivileged students have been granted less access to resources that promote
academic achievement. Historically, White students have been afforded greater access to
high-quality schools that offer more resources conducive to student achievement (Byrnes,
2003). Haycock (1998a, 1998b) stated that minority and poor students can experience
high levels of academic achievement if they are taught at the same level as their White
counterparts by teachers who have strong verbal and math skills, deep content knowl-
edge, and high standards. Peske and Haycock (2006) explained that hiring procedures
must change and urban schools in most need of quality teachers should be given the
choice to hire the most qualified teachers. Ladson-Billings and Tate (1995) referred to
exclusionary practices and segregation as means of separating Blacks and Whites through
complete denial from schools, through separation within schools, through White flight
and public funding of private schools, and through resegregation in the form of tracking
and creation of programs for gifted students. Peske and Haycock also asserted that, for

4
public education to prepare all students to meet the needs of an ever-changing global
economy, poor and minority students must not be taught by a disproportionate number of
inexperienced and underqualified teachers.
Synonymous with the issues of inequitable practice are those presented by
challenges spurred by unequal access to better resources and support afforded to more
privileged students. Ladson-Billings and Tate (1995) described the discrepancy in
intellectual property between urban students and their more privileged counterparts.
Essentially, schools serving poor students of color are less likely to offer access to
resources conducive to learning opportunities. Such learning opportunities are more
likely to exist in schools attended by more privileged students. Haycock (1998a)
predicted that the achievement gap would narrow simply if urban school children were
afforded equal teaching quality as that afford to students in affluent schools. Students
attending affluent schools have more learning opportunities because they are more likely
to be taught by experienced, qualified teachers; students in urban schools are more likely
to be taught by teachers lacking a major or minor in the subject that they are teaching
(Peske & Haycock, 2006).
Inequity and discriminatory practices developed in math through tracking
practices and denied access to more rigorous classes. Many poor and underprivileged
students have been kept in remedial classes (Snipes, V. T., & Waters, 2005) while more
privileged peers were granted access into gateway classes such as Algebra 1. Although
desegregation created a more diverse school setting, such tracking practices cultivated
“schools within schools” in which minority students filled lower-level and remedial

5
courses while privileged students enrolled in college preparatory classes (Wells, Holme,
Atanda, & Revilla, 2005).
A history of inequitable practices and mitigated access to resources for minorities
cultivated the achievement gap between White students and their underprivileged
counterparts. Tracing the long history of racial discrimination allows analysis to begin
with the court decision of Plessy v. Ferguson (1896) that provided separate but equal
facilities for Whites and minorities. This court decision impacted education as under-
privileged students, including Hispanics and Blacks, generally received less quality in
educational resources, curricula, and materials (Wells et al., 2005).
Prevalent segregation sparked the 1954 Brown v. Board of Education case that
declared the practice of segregation to be unconstitutional (Harris, D. N., & Harrington,
2006; Orfield, 2001). Fierce opposition to this decision was persistent resulting in the
Brown v. Board of Education II (1955) ruling that instructed states to act with “all
deliberate speed” in desegregating their public schools. Orfield explained that the
struggle to desegregate schools prevailed throughout the civil rights era and the passing
of the 1964 Civil Rights Act. As integration of minorities was encouraged, many schools
and districts were resilient in maintaining the status quo by tracking minority students
into lower-level courses and placing White students in college preparatory or advanced
classes. As a result, the 1966 Coleman Report reported racial inequality in test scores
(Lee, 2002). The academic disparity in student achievement between Whites and
minorities became more pronounced.

6
The narrowed academic disparity between White students and their Latino and
African American counterparts occurred between in the 1970s and 1980s (Lee, 2002).
In essence, the narrowed academic disparity occurred because minority students experi-
enced rising levels of educational achievement while White student achievement
remained constant. According to Lee, some researchers have attributed minority
students’ high performance to an emphasis on minimal competency, which had the direct
opposite effect to the gap’s widening trend when the focus of testing was placed on
higher learning standards.
A subplot that intertwined with the sustained achievement gap was a desire to
improve assessment practices. For instance, new curricula were developed after the Cold
War that stimulated creation of the National Defense Education Act (NDEA) in 1958 as a
response to the Soviet Union’s launching of Sputnik (Ed.Gov, 2009). Feeling the
pressure of falling behind in space exploration, the government sought human capital to
compete in science, mathematics, and technology. New curricula intended on enhancing
math and science skills, such as BSCS Biology, PSSC Physics, and CHEM study
chemistry, were created along with complementary assessments and evaluations of such
curricula (Haertel & Herman, 2005).
The theme of low academic achievement for poor and minority students was
dampened during the 1970s. This period was marked by the trend of minimum compe-
tency and the “back to the basics” movement. Such phenomena initiated a focus on basic
skills in math and reading (Haertel & Herman, 2005; Lee, 2002). Besides minimum
competency, education policies worked to narrow the achievement gap through school

7
desegregation and compensatory education (Lee, 2006). Larger percentages of under-
served populations were passing assessments due to diminished expectations and lowered
standards. Haertel and Herman (2005) explained that the proficiency level was lowered
so that acceptable passing rates would be achieved.
Decades later the theme of low student achievement persisted. A Nation At Risk
(National Commission on Excellence in Education [NCEE], 1983) sparked concern over
America’s superpower status that was perceivably challenged by other nations in addition
to the overall poor academic performance (Thomas & Brady, 2005). To address the
issues of low academic achievement in underperforming and underprivileged popula-
tions, the federal government emphasized test-based accountability. NCLB in 2001 was
the new incarnation of the ESEA of 1965. The original goal of ESEA was to provide
underserved populations high-quality education. NCLB, on the other hand, focused on
accountability and holding educators responsible for student learning outcomes.
The 1980s reflects an era of concerns regarding low academic achievement and
demands for more rigorous standards. For instance, as public concern brewed regarding
the poor quality of education in the 1950s, subsequent to Sputnik, U.S. concern over
international competitiveness emerged when A Nation at Risk was released. A Nation at
Risk not only helped to direct education away from the basic skills movement; it also
aided in propelling American education toward high academic standards and assessments
(Thomas & Brady, 2005), which were precursors to standards-based accountability.
The inception of federal education programs with ESEA experienced multiple
manifestations (Thomas & Brady, 2005) from 1965 to 2002. It was not until its most

8
current form, NCLB, was passed in January 2002 that legislation emphasized teacher
accountability based on student test performance. Some advocates have argued that, in
the past, educators were not held accountable for student learning (Stecher, Hamilton, &
Gonzalez, 2003). NCLB’s view of education was congruent to that of its original form,
ESEA, that student learning was insufficient. Also, as the theme of the achievement gap
emerged, another generality was exposed during the reauthorization of NCLB. Just as
the Sputnik launch and A Nation at Risk had called for higher standards in the spirit of
diminished international competitiveness, NCLB promoted elevated student outcomes in
the light of losing ground in global competitiveness.
Just as inequitable practices and constricted access to resources limited student
achievement for Latino and African American students, low student math achievement
for American students in general was a derivative of a fixation on practicing procedures
divergent from an emphasis on concepts and understanding (Stigler & Hiebert, 2004).
The mechanistic approach to teaching math in the United States has been characterized as
relatively unchallenging, procedurally oriented, and embedded in lessons that are
unnecessarily fragmented (Hiebert et al., 2005). Romberg and Kaput (1999) stated that
traditional math has failed to provide students a sense of math’s cultural and historical
importance, resulting in students’ aversion for the subject and their historical failure.
Furthermore, traditional math’s emphasis on computation and procedures has resulted in
limited student knowledge, stifling student opportunity to reason, think conceptually, and
think about math in ways that make sense (Stigler & Hiebert, 1999).

9
The achievement gap has pervaded American history. Its critical nature has made
it a topic of discussion and research during the last half-century. A parasite in the grand
context of education, it has stifled generations of underprivileged and poor minorities
who have been denied access and resources for academic success. Within the context of
math, the gap has prevented many urban and underserved minorities from math achieve-
ment by constricting access to critical courses such as Algebra 1. This is a major issue
because Americans educate only a small fraction of their citizens in math (Ball, 2004)
and, within mediocre math performance, score gaps persist between low-income
minorities and their White peers (Haycock, 2002).
Statement of the Problem
There is a persistent academic disparity between White and Asian students and
ethnic minority, ELL, and low-income students. Although the achievement gap has
fluctuated in scope, the gap has never fully closed. The issue of low academic achieve-
ment is manifested in the realm of mathematics in which minorities, particularly Latinos
and African American students, have historically been afforded fewer opportunities to
attain proficiency. This fact becomes more pronounced because math is most critical for
students in middle school, a period when students’ motivations toward math crystallize
into adulthood (Middleton & Spanias, 1999).
Purpose of the Study
A study of the practices of an urban middle school that has reduced the achieve-
ment gap is important for benchmarking, for creating models of practice, and for instill-
ing hope that the nation’s historically underserved students can succeed. The study can

10
contribute to an algebra research agenda offered by Ball (2003): analyses and comparison
of curriculum, instruction, and assessment; studies of relationships between teaching,
instructional materials, and learning; and studies of the impact of policy on equity and
student learning. The study of math is critical because algebra is considered to be a
gateway into higher education and successful participation in a democratic world (Ball,
2003; Edsource, 2009b; Kriegler, 2001). The purpose of the present study was to identify
programs, practices, and cultural norms employed by an urban middle school to narrow
the achievement gap and to display consistent elevated student performance in
mathematics.
As the country sustains interest in an “algebra for all” notion, analogous to
California’s decision to institute algebra as its eighth-grade-level math course (Kriegler,
2001), it is imperative to study schools that are experiencing success to determine
elements of practice that may be transferable to other schools. This study was one of
nine case studies by a cohort of doctoral students researching urban schools that have
closed the achievement gap. These researchers implemented qualitative case studies in
urban schools and schools that exhibited urban-like characteristics.
Research Questions
The study was guided by the following research questions:
1. What cultural norms, practiced within the school, are perceived to have
narrowed the achievement gap and sustained success?
2. What practices employed by the school are perceived to have narrowed the
achievement gap and sustained success?

11
3. What programs employed by the school are perceived to have narrowed the
achievement gap and sustained success?
Framework of the Study
This research applied the lens of critical race theory (CRT), a framework used to
theorize, examine, and challenge the ways in which racism impacts social structures,
including schools (Yosso, 2005). CRT has five main tenets: the centrality and inter-
sectionality of race and racism, the challenge to dominant society, the commitment to
social justice, the centrality of experiential knowledge, and the interdisciplinary per-
spective (Salorzano & Yosso, 2000).
The five tenets are summarized as follows. The centrality and intersectionality of
race and racism presents the view that CRT begins with the premise that race and racism
are endemic and permanent and a part of defining and explaining how U.S. society
functions (Bell, 1992; Russell, 1992). CRT views race and racism at their intersection
with other forms of subordination, such as gender and class discrimination (Crenshaw,
1989). The challenge to dominant society presents the view that CRT challenges White
privilege and refutes the traditional claims of the educational system and its institutions
regarding color and gender blindness, meritocracy, race neutrality, and equal opportunity.
The commitment to social justice explains that CRT is committed to social justice and
elimination of racism. In the struggle toward social justice in education, abolition of
racism is part of the goal to abolish other forms of subordination including gender, class,
and sexual orientation (Matusda, 1991; Wing, 1997). The centrality of experiential
knowledge explains that CRT recognizes that experiential knowledge of people of color is

12
critical to understanding, analyzing, and teaching about racial subordination within
education. CRT uses the lived experiences of people of color by including such methods
as storytelling, family histories, biographies, scenarios, parables, cuentos, testimonios,
chronicles, and narratives (Bell, 1987; Carrasco, 1996; Delgado, 1989; Montoya, 1994;
Olivas, 1990; Salorzano & Yosso, 2000). The transdisciplinary perspective explains that
CRT goes beyond disciplinary boundaries to analyze race and racism within both
historical and contemporary contexts, using scholarship from ethnic studies, women’s
studies, sociology, history, law, psychology, film, and other fields (Delgado, 1984;
Garcia, R., 1995; Harris, A., 1994; Olivas, 1990).
Another framework used as a lens in this study is the concept of institutional
support. According to Stanton-Salazar (1997), the existence of institutional support helps
students to become effective participants in mainstream institutional spheres, including
schools. Institutional support is derived from Bourdieu’s (1986) concept of social capital.
Institutional support takes various forms, such as provision of funds of knowledge associ-
ated with ascension within the educational system; bridging to gatekeepers, social net-
works, and opportunities for exploring mainstream institutions; role modeling; provision
of emotional and moral support; and provision of regular, personalized feedback that
incorporates the provision of funds of knowledge.
Another tool utilized in this study to understand the achievement gap is Clark and
Estes’s (2002) gap analysis framework. The achievement gap is essentially measured as
the difference between underperformance by poor and minority students and performance
by their more advantaged peers. By identifying human causes behind performance gaps,

13
schools can achieve desired student performance goals (Clark & Estes, 2002). Clark and
Estes’s gap analysis framework is used to close performance gaps and achieve business
goals. The gap analysis model can be employed to identify cultural norms, practices, and
programs that have supported student achievement and helped to narrow the achievement
gap.
Importance of the Study
Ball (2003) stated that the United States must improve the teaching and learning
of math in American schools because historical gaps in proficiency across societal groups
have not yet been eliminated. Thus, the importance of the study is to learn from success-
ful urban middle schools that have narrowed the achievement gap. The aim is to contri-
bute to literature by identifying a school that has narrowed the achievement gap and to
describe cultural norms, practices, and programs that have resulted in student achieve-
ment. Also, the study is intended to describe an exemplary model of middle school math
achievement in an urban setting to provide models of practice that can bolster district and
school practices to enhance student achievement. This case study is designed to extend
the body of knowledge regarding urban schools narrowing the achievement gap by
providing an example that has successfully commenced implementation of the algebra-
for-all mandate coupled with high student achievement in math.
Assumptions
Several assumptions were made in this qualitative study. First, it was assumed
interview participants were truthful and accurate in answering questions about teaching
practices, mathematics curricula, and effective school practices enhancing school and

14
mathematics achievement. Second, it was assumed that the school chosen for the case
study was a high-performing school. The researcher noted the school’s rising scores on
the Academic Performance Index (API) and the math California Standards Test (CST) for
a minimum of 2 consecutive school years. The researcher also took into consideration
the rising number of eighth-grade students enrolled in Algebra 1, coupled with sustained
eighth-grade Algebra 1 proficiency levels.
Limitations of the Study
A general limitation of the study was its case study nature. The case study
focused on one intermediate school with approximately 1,700 students. This limitation
prohibited generalization of findings. Another limitation was the number of participants
who joined the study, including teachers, administrators, and counselors. Also, given the
emphasis on mathematics achievement, the number of teachers in this department was a
subset of the entire staff. Another limitation was the inability to speak with all depart-
ment members at once. Although grade-level math teachers had common preparation
periods, opportunities to communicate with the entire department were challenging and
limited. Another limitation was potential unintended bias. The researcher is a mathe-
matics teacher with a particular passion for reform math. Perception of how math ought
to be taught was a challenge that had to be neutralized via triangulation.
Delimitations of the Study
Delimitations of the study were constructed by a group of nine doctoral students
researching urban schools that have closed the achievement gap. The selection criteria
included elements such as a significant (at least 15% of the school enrollment) minority

15
(Latino) population. Another was the presence of significant urban risk factors, such as
high populations of ELLs, economically disadvantaged students, at least 40% receiving
free or reduced-price lunches, and the presence of Title I. Another criterion was sustain-
ability, in that results showed a minimum of 2 consecutive years of increase on the API
or CST. This included subgroups meeting or exceeding state averages and displaying
significant progress toward an API score of 800. The group of researchers also stipulated
that case studies could not be focused on their own schools of employment to address
concerns regarding validity and reliability. Other delimitations included the range of
teachers participating in the study, coupled with the instrumentation generated to gather
data.
Definition of Terms
Unless cited, most of the following definitions were retrieved from Edsource’s
(2009a) web-based glossary of terms. These terms were specific to effective teaching
practices, the historical background of urban education, and mathematics pedagogy.
Academic Performance Index (API): A number used for school accountability
purposes to summarize the performance of a group of students, a school, or a district on
California’s standardized tests. A school’s number (or API score) is used to rank it
among schools of the same type (elementary, middle, high) and among the 100 schools of
the same type that are most similar in terms of students served, teacher qualifications, and
other factors. Schools and districts also receive separate API scores for “numerically
significant” student groups, including ethnic subgroups, socioeconomically disad-
vantaged students, ELL students, and students with disabilities.

16
Adequately Yearly Progress (AYP): A statewide accountability system mandated
by NCLB that requires each state to ensure that all schools and districts make adequate
yearly progress.
A Nation at Risk: The Imperative for Educational Reform (A Nation at Risk): A
report created by the NCEE defining problems in American education and providing
solutions to the addressed issues.
At risk: Descriptor of individuals or groups who are likely to fall into the lowest
quartile based on family stability, family violence, family income, child health and
development, and educational achievement (Garcia, G. E., 2002).
Brown v. Board of Education (1954): U.S. Supreme Court decision that reversed
the Plessy v. Ferguson (1896) ruling by stating that the doctrine of “separate but equal”
had no place in education. This landmark case held de jure public school segregation to
be unconstitutional (Grant & Ladson-Billings, 1997).
California Basic Educational Data System (CBEDS): An annual collection of
basic student and staff data from K-12 schools that includes data on student enrollment,
graduates, dropouts, course enrollment, enrollment in alternative education, gifted and
talented education programs, and more (Standardized Testing and Reporting [STAR],
2008).
California Standards Test (CST): Tests that are part of the STAR program and are
based on the state’s academic content standards regarding what teachers are expected to
teach and what students are expected to learn. The tests contain primarily multiple choice
items covering four subject areas: English Language Arts (ELA; Grades 2-11),

17
mathematics (Grades 2-11), history/social science (Grades 8, 10, and 11), and science
(Grades 5, 8, 10, and high school students who are taking specific subjects such as
biology, chemistry, or integrated science). CSTs are criterion-referenced tests; students
are scored as far below basic, below basic, basic, proficient, or advanced. The state goal
is for every student to score at proficient or above. Only California students take these
standards-based tests, so the results cannot be compared to test scores of students in other
states or nations.
Civil Rights Act: Legislation passed in 1964 that prohibits discrimination on the
basis of race or ethnicity by any program or activity that receives federal financial
assistance. This act was followed by Title IX of the Education Amendments of 1972,
Section 504 of the Rehabilitation Act of 1973, the Age Discrimination Act of 1975, and
Title II of the Americans With Disabilities Act of 1990, which included prohibitions on
discrimination on the basis of gender, disability, or age.
Classroom social norms: Principles that students cooperate to solve problems,
meaningful activity is valued over correct answers, persistence on solving challenging
problems is more important than completing a large number of activities, and partners
should reach agreements on the work of activities (Yackel, Cobb, & Wood, 1991).
Common assessment: An assessment typically created collaboratively by teachers
responsible for the same grade level or course to identify students who need support for
learning, teaching strategies most effective in helping students acquire knowledge,
program problems, and improvement goals for teachers and students (DuFour, DuFour,
Eaker, & Many, 2006).

18
Content knowledge: The body of knowledge comprising subject matter knowl-
edge and pedagogical content knowledge (Sherin, 2002; Shulman, 1986).
Culturally relevant pedagogy: An approach to teaching and learning that
empowers students intellectually, socially, emotionally, and politically through use of
cultural referents to disseminate knowledge, skills, and attitudes (Grant & Ladson-
Billings, 1997).
Culture: A way to describe core values, goals, beliefs, emotions, and processes
learned by people over time in family and work environments (Clark & Estes, 2002).
As a product, it embodies accumulated wisdom from predecessors; as a process, it is in
a constant state of flux as newcomers learn the old ways and become the conduits them-
selves (Bolman & Deal, 2003).
Elementary and Secondary Education Act of 1965 (ESEA): The principal federal
law affecting K-12 education. NCLB is the most recent reauthorization of the ESEA.
Originally enacted in 1965 as part of the War on Poverty, ESEA was created to support
the education of the country’s poorest children, and that remains its overarching purpose.
Congress must reauthorize the act every 6 years. Each reauthorization of ESEA has
involved some changes, but NCLB was the most dramatic revision of the act since its
creation. The provisions of NCLB represent a significant change in the federal govern-
ment’s influence in public schools and districts throughout the United States, particularly
in terms of assessment and teacher quality.
Emergency permits: Permission to teach granted to persons who do not qualify for
a credential or internship but meet minimum requirements. The permit holder completes

19
credential requirements through a college or university (California Department of
Education [CDE[, 2009).
English Language Learners (ELL): Students whose home language is not English
and who qualify for extra help. ELL students were formerly known as Limited English
Proficient (LEP).
Institutional agent: A person with the capacity and commitment to provide or
create opportunities to provide institutional resources and opportunities (Stanton-Salazar,
1997).
Institutional support: Key forms of social support that function to help school
children to become effective participants in mainstream institutional spheres, including
schools (Stanton-Salazar, 1997).
Internal accountability: The coherence and alignment of individuals’ perceptions
of their locus of responsibility and how their collective expectations at the organizational
level, and the processes by which people within the organization, account for what they
do (Elmore, 2005).
Minimum Competency Test (MCT): A criterion-referenced test commonly used
for mathematics and reading assessment that was required to earn a high school diploma
(Haertel & Herman, 2005).
National Assessment of Educational Progress (NAEP): A national test given to
specific grade levels in specific subjects every other year. A small sample of students
representative of all students in the state is tested. NAEP test scores can be compared to
national averages. California participates in NAEP, but not all states participate.

20
National Defense Education Act (NDEA): Law enacted during the Cold War as a
response to a perceived national threat subsequent to the Soviet Union’s launching of the
Sputnik I satellite. The NDEA funded science, engineering, and foreign language educa-
tion to reestablish the U.S. status as primary competitor within these areas (Flattau,
Bracken, Van Atta, de la Cruz, & Sullivan, 2006).
No Child Left Behind Act of 2001 (NCLB): The 2002 reauthorization of ESEA.
Originally passed in 1965, ESEA programs provide much of the federal funding for K-12
schools. NCLB’s provisions represent a significant change in the federal government’s
influence in public schools and districts throughout the United States, particularly in
terms of assessment, accountability, and teacher quality. NCLB increases the federal
focus on achievement by disadvantaged pupils, including English learners and students
who live in poverty; provides funding for “innovative programs” such as charter schools;
and supports the right of parents to transfer their children to another school if they
consider their current school to be low performing or unsafe.
Pedagogical content knowledge: Knowledge specifically for teaching a domain,
including the means by which to present concepts and their embedded factual elements to
facilitate understanding and mitigate misunderstanding by students (Sherin, 2002;
Shulman, 1986).
Performance level: Standard of performance on STAR tests based on the
student’s scale score. There are five performance levels: advanced, proficient, basic,
below basic, and far below basic. The goal in California is to have all students perform at
the proficient or advanced level (STAR, 2008).

21
Plessy v. Ferguson (1896): U.S. Supreme Court decision that promoted the
“separate but equal” notion by contending that “separate but equal” public railroad
facilities for diverse groups did not obstruct their rights to equal protection of the laws,
which were guaranteed by the Fourteenth Amendment. The decision became a precedent
for court cases in favor of segregation. The decision was reversed in Brown v. Board of
Education (Grant & Ladson-Billings, 1997).
Practice: Knowledge, skill, and values embodied in the behavior of people in an
organization (Elmore, 2005).
Professional development: The advancement of skills or expertise to succeed in a
particular profession, especially through continued education.
Program Improvement: An intervention program for schools and districts that fail
to make AYP for 2 consecutive years. The interventions become more severe if the
school/district continues to fail to reach AYP, to the point where some restructuring is
required.
Socioeconomic status (SES): A measure of an individual’s or family’s relative
economic and social ranking (NCES, 2009a).
Sociomathematical norms: An understanding of what counts as mathematically
different, mathematically sophisticated, mathematically efficient, and mathematically
elegant in math classrooms (Yackel & Cobb, 1996).
Standardized Testing and Reporting Program (STAR): California’s program of
standardized testing, consisting primarily of a battery of CSTs. These tests cover state-
adopted academic content standards in English, math, science, and history/social science.

22
Students in Grades 2-11 take various CSTs. Students in Grades 3 and 7 also take a short,
norm-referenced test in English and math that compares their scores to those of a national
sample. Certain Spanish-speaking English learners in Grades 2-11 take an additional test
in Spanish.
Subject matter knowledge: Understanding of facts and concepts within a particular
domain (Sherin, 2002; Shulman, 1986).
Tracking: Ability grouping to help teachers manage the variability in student
ability by allowing students to work with others who are similar in development and to
put students on paths that match their aspirations (Secada & Berman, 1999).
Organization of the Dissertation
Chapter 1 introduces the study’s background problem and presents the statement
of the problem, the purpose of the problem, and the research questions. The importance
of the study is stated, providing the impetus for this research. Descriptions of the
methodology, assumptions, delimitations, and limitations are presented to provide a
comprehensive view of beneficial and limiting aspects of the research.
Chapter 2 reviews literature specific to the achievement gap and mathematics
achievement. It includes the history of the achievement gap and the means by which
math achievement differed between more advantaged children and historically poor
minority students. The simultaneous progression toward standards-based instruction is
reviewed. Models of mathematics classrooms displaying high student achievement are
reviewed. This chapter highlights qualities of effective math classes.

23
Chapter 3 describes the methodology used in this case study, including the
research design, population, sampling procedures, instrumentation, and frameworks for
research questions.
Chapter 4 reports the findings of the case study, which was conducted in one
semester of first-hand research at Beacon Intermediate School.
Chapter 5 presents conclusions and recommendations for teachers, site
administrators, district administrators, policy makers, and researchers.

24
CHAPTER 2
LITERATURE REVIEW
This literature review focuses on the achievement gap and school practices con-
ducive to its reduction. An interest is also taken in determining school elements that have
not only narrowed the achievement gap, but have also enhanced student learning of
mathematics and elevated student math performance. The achievement gap is a per-
sistent academic disparity between White and Asian students and ethnic minorities,
ELLs, and low-income students. Many factors have been identified as contributing to the
achievement gap, such as poverty, low student motivation and effort for learning, poor
schooling conditions, and poor educational practices (Lee, 2002).
The existence of inequitable practices has been cited as the reason for the achieve-
ment gap between Whites and Latinos (Valencia et al., 2002). In essence, a history of
segregated, inferior schooling conditions are culprits behind low academic performance
by minorities. The 2008 NAEP reported that, although reading and mathematics scores
for White, African American, and Hispanic students had increased since 2008, White-
Hispanic and White-African American racial gaps remained (NCES, 2008). Ladson-
Billings and Tate (1995) identified institutional racism (namely, the poor conditions of
schools) along with the limitations of poverty as inhibitors of student math achievement
in African American communities. Thus, a theme of inferior schooling conditions
coupled with practices promoting segregation can be viewed as the culprit behind low
academic progress for poor and minorities (Orfield, 2001). Since the White-African
American and White-Hispanic score gaps are persistent in math, it will be helpful to

25
review the origins of those gaps and instructional practices in math that are conducive to
learning.
The academic disparity between White and Asian students and underperforming,
poor minorities is a critical topic for study, considering projected population trends in the
United States. According to the U.S. Department of Education, by 2026 approximately
70% of the U.S. student population will consist of Latino and non-White subgroups (as
cited in Garcia, G. E., 2002). Garcia reported that many educational initiatives target
such subgroups, carrying synonymous labels such as immigrant, at risk, underachieving,
and poor. The current trends in school and teacher accountability, coupled with test-
based accountability, were ignited as part of one of these educational initiatives (Stecher
et al., 2003). This literature review describes the most recent accountability measures
intended to address the achievement gap.
Exploring the areas relevant to the achievement gap and the more focused math
achievement gap requires discussion of certain elements to present a comprehensive
view. This review first addresses the historical perspective of the achievement gap and
the changes in federal legislation aimed at raising student achievement for underperform-
ing subgroups. Second, the review addresses the critical nature of mathematics education
and its relation to the achievement gap. Third, some theories used to conceptualize
inequitable practices in American education that present themselves as lenses into identi-
fying factors of the achievement gap are identified. Fourth, the review describes attempts
to reduce the achievement gap, including some existing practices that have narrowed the

26
gap. Fifth, sustainability of academic achievement and math achievement is discussed,
followed by the chapter summer and conclusion.
Historical Perspective on Student Performance
Viewing student performance from a historical standpoint reveals the achieve-
ment gap between White and Hispanic scores and between Black and White scores. This
historical perspective is critical to understanding the achievement gap’s origins. Looking
at the score gaps from a historical perspective highlights extensive effort by urban
schools to raise student achievement, which provides models of practice and benchmark-
ing opportunities for schools seeking to improve student outcomes.
A clear contributor to the achievement gap has been unequal access to education
for students. The 1896 Plessy v. Ferguson ruling allowed for separate but equal facilities
for Whites and their minority counterparts (Raffel, 1998). Although not specific to
schools, the Plessy v. Ferguson decision had a clear impact on education. Minority
students, including Hispanics and Blacks, were separated from their White peers and
generally received lower-quality educational resources, curricula, and materials (Wells et
al., 2005). For instance, besides attending dilapidated schools where decrepit facilities
were sometimes unsafe, it was common for minorities to receive materials and resources
handed down from their White counterparts (Snipes, V. T., & Waters, 2005). Segrega-
tion was prevalent and consistent in limiting Black and Latino students from access to
better resources and access points, thereby choking their pipeline to educational
achievement.

27
Eventually, the 1954 Brown v. Board of Education decision declared segregation
unconstitutional and reversed the Plessy v. Ferguson ruling (Harris, D. N., & Herrington,
2006; Orfield, 2001). However, stubborn opposition to the Court’s decision propelled
subsequent rulings, initiating Brown v. Board of Education II (Grant & Ladson-Billings,
1997). This decision instructed states to act with “all deliberate speed” in desegregating
their public schools, encouraging perpetual racism to seep into the micro-level of schools.
The struggle to desegregate schools was also highlighted by the 1964 Civil Rights Act
(Guryan, 2003). It was during the years following the enactment of the Civil Rights Act
that federal education officials, the Department of Justice, and the high courts exerted
pressure to achieve integration (Verdun, 2005). However, schools that were instructed to
integrate minorities with their White counterparts allowed persistent segregation by
tracking minority students into lower-level courses distanced from college preparatory
classes that were offered to White students only (Wells et al., 2005). In essence, status
quo prevailed as access remained undistributed to underserved and underprivileged
students who were in dire need of such resources.
The Coleman Report (Coleman et al., 1966) gave the federal government a picture
of persistent segregation in the United States 12 years after Brown v. Board of Education
(Guryan, 2003). The Coleman Report promoted racial integration of students in schools
to improve the education of African American students (Ladson-Billings, 2006). In fact,
the document reported that a decade after Brown the majority of Black students still
attended schools that were predominantly attended by Black students—the same students
who were behind White students in reading, verbal, and mathematics performance

28
(Raffel, 1998). Thus, the Coleman Report provided a clear view of the academic dis-
parity in student achievement between Whites and minorities. Also, educators were able
to determine factors that contributed to the achievement gap, including home, neighbor-
hood, and peer environments (Lee, 2002). Although attribution diverged from institu-
tional and classroom experiences, such as teacher effectiveness or lack of access to
resources and support, the Coleman Report contributed largely to efforts to spur
desegregation.
The narrowing academic disparity between White students and their Latino and
African American counterparts dates back to the 1970s and 1980s (Lee, 2006). NAEP,
dubbed the nation’s report card for student achievement, has documented the trends in the
achievement gap, from its decline in the 1970s and 1980s to its rise in the late 1980s to
the 1990s (Lee, 2002). Some researchers point to a relationship between the narrowing
trend and emphasis on basic skills and minimum competency (Haertel & Herman, 2005).
In essence, the narrowed academic disparity occurred because minority students per-
formed well as White student achievement remained constant. Lee explained that there is
also a view that the gap’s widening trend occurred as a result of White students’ better
performance when the focus of testing was placed on higher learning standards.
There is also a perspective that compensatory programs and funding, which were
lacking prior to the creation of ESEA, contributed to the narrowing achievement gap
(Lee, 2002). For instance, the Civil Rights movement, Brown v. Board of Education, and
improved access to K-12 education increased exposure of minorities to resources that had
long been available to White students only (Harris, D. N., & Herrington, 2006). Such

29
elements were cited as enhancing academic achievement for historically underperforming
students.
A history of inequitable practices and segregation has contributed to the achieve-
ment gap. As the minimum competency era led to a narrowed achievement gap, the
improvement in academic achievement by underperforming students was attributed to the
integration of compensatory funding. However, a concern regarding poor academic
standards remained, initiating educational reform aimed at enhancing performance by
historically underperforming and underserved students. Thus, examining the changes in
assessment practices is important to understanding the achievement gap’s widening and
narrowing effects. Furthermore, understanding instituted accountability measures is
important to understanding how the achievement gap impacts student performance and
instructional practices today.
Changes in Assessment Practices
Evident in 20th-century American education was a desire to improve assessment
practices by generations based on the shortcomings of their predecessors. The existing
low academic standards became an impetus for programs to improve student achievement
and quality of education in the United States (Haertel & Herman, 2005). The launching
of Sputnik resulted in various math and science curricula with the intentions of bolstering
American achievement in these areas (Ed.Gov, 2009; Schoenfeld, 2004). The NDEA
placed great emphasis on math and science curricula that commenced the “New Math
Movement” in the 1960s and 1970s (Snipes, V. T., & Waters, 2005). Eventually,
evaluations of such curricula were also developed.

30
The passing of ESEA popularized formal evaluations of educational programs
(Haertel & Herman, 2005). Evaluations of ESEA were used to measure the effectiveness
of Head Start, Follow Through, and other social and compensatory programs supple-
mented by the ESEA. According to Haertel and Herman (2005), these standardized tests
were sometimes deemed too challenging for the poor and disadvantaged students whom
Title I of ESEA targeted. Furthermore, abuses of ESEA funds, which were used in
general aid funds to all students rather than to targeted resources for the needs of educa-
tionally disadvantaged students, led to the amendment of ESEA four times in the 1960s
through the 1980s (Thomas & Brady, 2005).
The 1970s brought about a focus on minimum competency testing and a “back to
basics” movement (Lee, 2002; Schoenfeld, 2004), indicating the conclusion of the “New
Math Movement” (Schoenfeld, 2004). Discontent over compensatory education and the
already visible disparity in academic achievement fueled the movement. According to
Schoenfeld (2004), the curricula in this period resembled that of the pre-Sputnik years.
The MCT focused on basic skills, primarily in math and reading. Haertel and Herman
(2005) reported that passing was probably around the eighth-grade level or lower,
suggesting that a larger student population was passing. Eventually, such low standards
and minimal levels for passing resulted in low academic performance.
By the 1980s and the tenure of the Reagan administration, frustration over poor
academic performance sparked a move for higher academic standards (Thomas & Brady,
2005). The NCEE publicized America’s criticism of its educational system in A Nation
at Risk. A Nation at Risk propelled American education toward standards and

31
assessments, setting the stage for standards-based accountability. Eventually, frustration
resulted in the public’s demand for more rigorous and measurable standards, as well as
higher expectations for student academic performance. As it had been during the era of
Sputnik, U.S. concern over international competitiveness was openly expressed. Thus, it
was only a matter of time before divergence from basic skills and movement toward
higher-order thinking occurred.
In 1989 the National Council of Teachers of Mathematics (NCTM) and similar
organizations identified standards for subject matter that students must learn. By 1994
the Improving America’s School’s Act (IASA), the reauthorization of Title I, mandated
states to generate content and performance standards with aligned complementary assess-
ments (Haertel & Herman, 2005). The IASA also held states accountable for student
performance on these measures. To combat a history of low achievement by underper-
forming and underprivileged subgroups of students, the federal government emphasized
test-based accountability.
The era of accountability continued with the metamorphosis of ESEA (Thomas &
Brady, 2005). NCLB held educators primarily responsible for student learning outcomes.
NCLB’s predecessor, ESEA, had been enacted with the goal of providing poor and
underserved students with high-quality education. Title I of ESEA had provided funds
with the goal of raising academic achievement of children from low-income families.
NCLB was passed in January 2002 and strongly emphasized accountability based
on student test performance. Its justification mirrored that of its predecessor: Student
learning was insufficient. Also, similar to the sentiment found in A Nation at Risk, many

32
policy makers acknowledged the achievement gap as a serious deterrent to international
competitiveness.
The changes in assessment practices indicated the narrowing and widening of the
achievement gap. The launching of Sputnik, the release of A Nation at Risk, and the
reauthorization of ESEA as NCLB sparked changes in assessment practices that influ-
enced student performance. However, as Schoenfeld (2004) explained, the lesson learned
in the 1980s was that instruction had to be broader than just mastery of content and skills.
Accountability
In essence, NCLB focused on accountability (Williams et al., 2005). Prior to this
most recent reauthorization of ESEA, teachers and educators had not been held account-
able for student learning outcomes (Stecher et al., 2003). Although salaries increased
with longevity, teachers were not held responsible for learning outcomes within their
classrooms.
NCLB requires all state departments of education to adopt content standards
included in assessments that measure mastery of subject matter. California’s academic
standards have been considered the most rigorous in the nation (Williams et al., 2005).
Standards for the first four core subject areas—ELA, mathematics, social science, and
science—were completed in 1999. Currently, the CST is the primary assessment that
California uses to assess student learning on its academic content standards. All students
are required to score at least at the proficient level by 2013-2014 academic year (Thomas
& Brady, 2005). Overall, the intent of NCLB is to diminish inequalities that impact
underprivileged and poor students. This is another prevailing theme inherited from

33
ESEA. Thus, through NCLB, particular subgroups are monitored and NCLB is aimed at
measuring their progress.
In general, accountability flows from the federal level to the states and their
respective localities (Stecher et al., 2003). Each district has discretion over curricula,
materials, and resources to utilized with the goal of maximizing student learning. Thus,
with NCLB, federal funding is dependent on student performance. Sanctions may be
placed on districts that produce low test scores. In general, the aim of NCLB is to raise
academic achievement and bring equity by providing states and their localities
opportunities and challenges to devise methods of narrowing the achievement gap.
Under NCLB, schools are held accountable for testing 95% of their students in
each subgroup, as well as the entire school population (Williams et al., 2005). Schools
and the districts to which they belong must meet AYP for 2 consecutive years (Stecher et
al., 2003). Meeting AYP requires schools and their districts to meet a baseline expecta-
tion on the API or improve by a point.
The API is an annual summary of test scores on the CST (Williams et al., 2005).
One of its uses is to rank schools in California in deciles, indicating ranking compared to
all schools. Another ranking compares each school to 100 schools to which it is most
similar. Another element of the API is a score that falls between 200 and 1000.
Williams et al. (2005) explained that this score is used to provide the school a target
exceeding 800 and growing 5% between its current score and the state’s goal.
School accountability and the standards-based era emerged due to discontent over
low student performance and expectations. A goal of NCLB was to present states and

34
districts the challenge of determining methods for narrowing the achievement gap. All
schools were required to show that they were meeting AYP. As low student achievement
by minority students pervaded American education, the critical nature of mathematics
education was evident during various points in history. Thus, student learning was
questioned.
Math Achievement Gap
Mathematics education is rooted in the basic foundations of public education with
the goals of (a) generating responsible and informed citizens within a democracy
equipped with reasoning skills and quantitative understandings, (b) providing a wider
array of options and opportunities in career and life, and (c) promoting analytical tools
that are necessary in the disciplines of science and technology (Ball, 2003). In essence,
math is a tool for social access and social mobility (Schoenfeld, 2004). Thus, decisions
made by educators about the content and character of school math have consequences for
students and society (NCTM, 2000) because only a fraction of all students are educated
in math (Ball, 2004).
According to NCTM (2000), math is used in everyday life: in the workplace with
problem solving; as a tool for the scientific and technical community, namely the work
force within science, technology, engineering, and mathematics (STEM); as a part of
cultural heritage, which celebrates math as a cultural and intellectual achievement; and in
mathematics for life, which includes empowering quantitative skills to choose and decide
wisely on purchases. Within the math domain, algebra is emphasized because it is
essential to educational achievement and career opportunities (Ball, 2003). It is no

35
surprise that Algebra 1 has been a widely discussed topic as the 1998 California Mathe-
matics Framework established the content as its grade-level subject for eighth graders,
causing many districts to reevaluate expectations for student middle school enrollment in
algebra (Kriegler & Lee, 2007). The promotion of an “algebra for all” eighth-grade
curriculum is still a debated topic as data from the CDE still shows that many students
are unsuccessful in eighth-grade algebra (Kriegler, 2001). Since algebra is a contro-
versial topic and a focus of discourse, teaching of this mathematical domain must be
investigated.
Within the domain of math, the phenomenon of the achievement gap is perceived
to be a major concern as low achievement by rising numbers of minority students could
be detrimental to national productivity and global competitiveness (Ball, 2003). This
sentiment was prevalent in 1957, when the Soviet Union launched Sputnik into space and
thus displayed an advantage over the United States in space exploration (Ed.Gov, 2009).
Perception of falling behind in space exploration stirred concern over the quality of
American education, particularly U.S. competitiveness in math and the sciences (Flattau
et al., 2006). The result was the inception of the NDEA in 1958 and the development of
new math and sciences curricula sponsored by the National Science Foundation (Haertel
& Herman, 2005; Schoenfeld, 2004), along with other teacher-proof curricula created by
subject matter specialists (Lieberman & Miller, 1990). Math education plays a large part
in supplying the workforce with people who can contribute to national productivity.
Mathematics education has a large emphasis in global competitiveness in its
function of creating productive citizens. It has the function of cultivating citizens with

36
reasoning skills, providing a wider array of educational and career opportunities and
analytical thinking required for the sciences (Ball, 2003). However, problems remain due
to unequal proportions of African Americans and Latinos working in science, engineer-
ing, and technology (National Science Board, 2005). The National Science Board (2005)
reported that, although these subgroups comprised 10.3% and 9.2% of the 1997
American workforce, they contributed only 3.2% and 3.0%, respectively, to the science,
engineering, and technology work force. In essence, minority and historically under-
served students must be taught math effectively so they can contribute to these fields.
More important, all students must be taught well so they can become responsible, active
members of American society. Aversion toward math has become socially acceptable
and prevalent (Ball, 2004). Thus, seeking factors that narrow the achievement gap and
enhance student learning of math and algebra is a critical subject for research.
Factors of the Achievement Gap
The factors that contribute to the achievement gap are varied. Researchers have
cited socioeconomic and family conditions, youth culture and student behaviors, and
schooling conditions and practices (Lee, 2002). Other academics have cited language
barriers, low education levels upon arriving in the United States, and a lack of cultural
understanding between students and teachers as other deterrents of academic achievement
(Ream, 2003; White-Clark, 2005). NCTM (2000) reported that students who are poor,
considered nonnative speakers of English, disabled, female, or non-White have tradition-
ally been the victims of teachers’ low expectations, resulting in low achievement.

37
This section presents frameworks to discuss the achievement gap and describes
some of the factors that have contributed to the gap. Critical race theory is described to
measure racism’s impact on the educational system and schooling that has contributed to
practices such as institutional racism. Institutional support is a framework describing the
critical nature of teacher-student relationships to student academic success. Poor teach-
ing quality, specifically in math, is cited as a contributor to poor mathematics learning
and low student achievement in math.
Critical Race Theory
Critical race theory is a framework that can be used to theorize, examine, and
challenge the ways in which race and racism impact social structures, including schools
(Yosso, 2005). The achievement gap can be viewed through the lens of CRT, which
begins with the principle that racism is normal in American society and that civil rights
legislation has been more advantageous to Whites (Ladson-Billings, 1998). According to
Ladson-Billings and Tate (1995), understanding social inequity requires consideration of
three central notions: Race is a significant factor in determining inequity, American
society is based on property rights, and the intersection of race and property provides a
tool for understanding school inequity. CRT is herein defined and utilized to make sense
of the achievement gap’s origins, which provides an opportunity to view America’s
history of racial segregation, discrimination, and inequality.
Salorzano and Yosso (2000) asserted that CRT in education challenges the
dominant discourse on race and racism as related to education by viewing the means by
which educational theory, policy, and practice are used to oppress certain racial and

38
ethnic groups. Salorzano (1998) identified five tenets of CRT that can and should inform
theory, research, pedagogy, curriculum and policy in education: (a) the intercentricity of
race and racism, (b) the challenge to dominant ideology, (c) the commitment to social
justice, (d) the centrality of experiential knowledge, and (e) the utilization of interdisci-
plinary approaches.
The centrality and intersectionality of race and racism presents the view that CRT
begins with the premise that race and racism are endemic, permanent, and a part of
defining and explaining how U.S. society functions (Bell, 1992; Russell, 1992). CRT
views race and racism at their intersection with other forms of subordination, such as
gender and class discrimination (Crenshaw, 1989). The challenge to dominant society
presents the view that CRT challenges White privilege and refutes the traditional claims
of the educational system and its institutions regarding color and gender blindness,
meritocracy, race neutrality, and equal opportunity. The commitment to social justice
explains that CRT is committed to social justice and the elimination of racism. In the
struggle toward social justice in education, abolition of racism is part of the goal to
abolish other forms of subordination, including gender, class and sexual orientation
(Matusda, 1991; Wing, 1997). The centrality of experiential knowledge explains that
CRT recognizes that experiential knowledge of people of color is critical to understand-
ing, analyzing, and teaching about racial subordination within education. CRT uses the
lived experiences of people of color by including such methods as storytelling, family
histories, biographies, scenarios, parables, cuentos, testimonios, chronicles, and narratives
(Bell, 1987; Carrasco, 1996; Delgado, 1989; Olivas, 1990; Montoya, 1994; Salorzano &

39
Yosso, 2000). The transdisciplinary perspective explains that CRT goes beyond disci-
plinary boundaries to analyze race and racism within both historical and contemporary
contexts, using scholarship from ethnic studies, women’s studies, sociology, history, law,
psychology, film, and other fields (Delgado, 1984; Garcia, R., 1995; Harris, A., 1994;
Olivas, 1990).
As the achievement gap focused attention on segregation, CRT sheds light on the
idea that American society has become more segregated subsequent to the Brown deci-
sion (Ladson-Billings, 1995; Verdun, 2005). As Brown ignited commencement of inte-
gration, many White school and community leaders exerted their best efforts to maintain
the status quo (Wells et al., 2005). In essence, schools became a microcosm of culture
and the communities they served as they too became segregated. Public schools could
not fully implement desegregation policies because middle-class White citizens placed
pressure on policy makers and educators to maintain segregation. To reciprocate,
officials and leaders executed desegregation in a manner that was most acceptable to
White parents to prevent relocation of these White families. Thus, schools were able to
achieve only limited integration because White citizens held the majority of political and
leadership roles that affected educational policy. This is consistent with a CRT notion
that racism is a permanent element that pervades American society (Ladson-Billings,
1998).
Within CRT, Ladson-Billings and Tate (1995) included the proposition of
property rights—having the ability to define, possess, and own property—as an indicator
of power. Within education, CRT represents ownership of property as intellectual

40
property, and the quality and quantity of the curriculum can be viewed as property values
of the school (Snipes, V. T., & Waters, 2005). The notion of property rights provides a
lens for viewing the disparity between advantaged students and their underprivileged
peers.
Wells et al. (2005) used the term schools within schools to describe the phenome-
non of segregation that became prevalent in the 1970s and 1980s. Students shared a
common campus but attended classes with peers of the same race. The disparity in
classes in which students were enrolled provided the gap in rigor of instruction, college
placement, and quality of teaching. This suggests that intellectual property was available
only to students who had the best resources in such schools. According to Ladson-
Billings and Tate (1995), the access to intellectual property, called opportunity to learn,
was historically afforded mostly to White students.
V. T. Snipes and Waters (2005) documented the consistent practice of tracking:
minority students funneled into lower level mathematics courses such as consumer math
and general math and tracking their White peers into Algebra 1 courses during the fresh-
man year of high school. Such settings provided minimal opportunities to learn for
underserved students, since White students were generally more likely to be placed in
high-quality groups, gifted and talented programs, or college preparatory tracks (Byrnes,
2003). This choked opportunities for minority placement as they were placed in tradi-
tional course sequencing in high school, which was primarily set aside for the elite
students who were prepared for postsecondary education (Schoenfeld, 2004).

41
In general, many minority students have historically been tracked into lower-level
classes (Snipes, V. T., & Waters, 2005). This prevents Latino and African American
students from enrollment in high-level and college preparatory classes necessary for
educational achievement. According to Ladson-Billings and Tate (1995), the absolute
right to exclude in schooling was portrayed through the following phenomena: the denial
of Blacks in schools, the creation of separate schools, White flight and public funding of
private schools and insistence on vouchers, resegregation through tracking, and the
creation of gifted, honors, and placement programs.
An example of institutional racism is the aforementioned placement of minority
students into general and consumer math upon entrance to high school. Such practices
often provided White students higher-tracked classes such as Algebra 1 (Wells et al.,
2005). According to Lubienski, McGraw, and Strutchens (2004), access to advanced
math in middle school (e.g., Algebra 1) determines whether minority students have
access to higher-level mathematics such as trigonometry and calculus in high school.
Schoenfeld (2004) explained that students who found the college track “inhospitable”
were offered classes such as business math or shop math. Thus, Algebra 1 is considered
to be a gateway class because it is a determinant of student success or consideration of
engineering and other technical fields (Ball, 2003).
V. T. Snipes and Waters (2005) cited examples of institutionalized racism such as
tracking, lack of exposure to better teachers, less access to technology, and disconnect of
the curriculum to the home environment. Although schools took steps to end segregation
through the Brown decision, a verifiable and consistent achievement gap was persistent

42
as schools perpetuated the variance in resources afforded to students attending the same
schools (Snipes, V. T., & Waters, 2005; Wells et al., 2005). Furthermore, although
performance and achievement are factors in access to higher-level classes (Berry, 2008),
access and success are also influenced by an understanding of fairness and objectivity,
which is inconsistent in the enrollment of Latinos and African Americans in higher-level
mathematics, as reported by the NCES (2008).
CRT challenges the dominant view on race and racism as related to education by
viewing how educational theory, policy, and practice are used to oppress certain ethnic
groups (Salorzano, 1998). Examples of subordination include institutional racism and
tracking practices that bar historically underperforming students from higher-level classes
that they need for school achievement. CRT is utilized in this study to examine practices
at an urban school to examine the ways that race and racism impact cultural norms,
practices, and programs.
Institutional Support
The framework of social capital, derived from the work of Bourdieu (1986) and
Coleman (1988), can be utilized to view inequitable practices in education. Something
has social capital when social interactions between stakeholders have potential value in
attaining certain interests (Bourdieu, 1986). Within the perspective of the achievement
gap, educators and teachers working as institutional agents have potential for social
capital because they have the capacity to provide access, resources, and opportunities that
students may not necessarily receive from family members (Stanton-Salazar, 1997). This

43
section reviews institutional support and the critical access provided by institutional
agents.
The concept of social capital identifies laws of social structure that are used by
individuals to attain certain interests (Stanton-Salazar, 1997). In essence, student
relationships with institutional agents contain social capital if there is potential for student
learning, emotional support, opportunities to attain academic success, and mentorship.
Stanton-Salazar (1997) explained that institutional agents are important because they
have the capacity to provide or negotiate transmission of resources and opportunities to
poor and underserved students. Historically, since low-income and minority children
were provided limited access to quality education and effective teaching (Peske &
Haycock, 2006), these underprivileged and underserved students were granted less access
to sources of social capital and resources critical to academic success.
Stanton-Salazar (1997) identified six key forms of institutional support and
described them as key components of academic success and social integration: (a) pro-
vision of various funds of knowledge that promote success in the educational system;
(b) bridging to provide access to gatekeepers, social networks, and opportunities for
exploring mainstream institutions; (c) advocacy and other forms of personalized inter-
vention; (d) role modeling; (e) provision of emotional and moral support; and (f) pro-
vision of regular, personalized evaluative feedback and guidance. Stanton-Salazar also
offered seven forms of institutionally based funds of knowledge. The first is institu-
tionally sanctioned discourses, which are described as socially acceptable ways of
communicating. The second is academic task specific knowledge, which includes subject

44
area knowledge. The third is organizational/bureaucratic funds of knowledge, which is
described as knowledge of how bureaucracies operate and their chains of command. The
fourth is network development, which includes knowledge that leads to skillful network-
ing behavior that includes knowledge of how to negotiate with various institutional
agents within and outside of school, as well as how to form ties with peers who are
integrated into the school’s high-status academic spheres. The fifth is technical funds of
knowledge, including computer literacy, study skills, test-taking skills, time management
skills, and decision-making skills. The sixth is knowledge of labor and educational
markets, including job and educational opportunities, requisites and barriers to admission,
and how to fulfill requisites for admission. The seventh is problem-solving knowledge,
including knowing how to integrate the first six knowledge forms for the purpose of
solving school-related problems, making sound decisions, and reaching personal goals.
According to Bourdieu (1986), the laws concerning the exchange of economic
capital are applicable to human social relations, thus defining social capital as cumu-
lative, having the function of producing social benefits, functioning as other forms of
capital, and possessing the capacity to reproduce itself. Limited access to social capital
and institutional support can be likened to the ideas offered by CRT that underprivileged
students’ property rights are restricted, thereby limiting intellectual property and the
opportunity to learn (Snipes, V. T., & Waters, 2005).
As segregation became a barrier to social capital and institutional support (Wells
et al., 2005), critical access to college preparatory subject matter and gateway courses
was also limited. At a much deeper level, absence of college preparatory courses

45
removed the potential for teacher-student relationships that contain potential for social
capital as institutional support provides social supports that help students to function
within the school system (Stanton-Salazar, 1997). Rapport with such an institutional
agent may provide access to critical knowledge, including subject matter knowledge, as
well as understanding about acquisition of resources and supports conducive to educa-
tional achievement.
The notions of CRT and social capital are still charged in mathematics education.
In mathematics, it is during the middle grades when students’ motivations toward mathe-
matics are formed and are then carried into adulthood (Middleton & Spanias, 1999).
Thus, when the opportunity to learn is restricted, the aims of teaching math are broken:
the ability to reason, the expansion of options available for a career, and the ability to
develop analytical thought (Ball, 2003). When minority students lack institutional sup-
port, they enter sub-algebra courses, such as consumer math, having already experienced
repeated failure, and they expect more failure (Boaler & Staples, 2008). However, as
NCLB placed teacher accountability in the spotlight, math teaching requires discussion in
its contribution to the achievement gap.
Institutional support refers to key forms of social support that function to help
students to become effective participants in the educational system (Stanton-Salazar,
1997). Institutional support is a lens that helps to make sense of the impact of social
capital within school spheres for students who have underperformed historically. This
concept will be used to identify factors within an urban school that have helped to narrow
the achievement gap and raise student academic success.

46
Poor Mathematics Teaching Quality
In general, math classrooms in the United States have lacked quality of teaching
as teachers have maintained ineffective practices of instructing students to follow rules
and practice procedures (Stigler & Hiebert, 1999) that are relatively unchallenging and
contained within unnecessarily fragmented lessons (Hiebert et al., 2005). This subsection
reviews the levels and importance of quality of teaching.
According to Stigler and Hiebert (1999), a perspective of American math instruc-
tion has been documented in the Third International Math and Science Study (TIMSS),
which has been in existence for more than 30 years. TIMSS has compared math and
science student achievement in 41 nations. One component included a video study with a
goal of analyzing eighth-grade mathematics instruction in the United States, Germany,
and Japan. Researchers have sought to learn about the way American teachers view
reform and whether they are teaching reform-oriented math.
One of the main findings presented in the TIMSS video studies highlights teach-
ing as a cultural activity marked by commonalities in instruction within the participating
countries (Stigler & Hiebert, 1999, 2004). Reviewing the TIMSS data, Stigler and
Hiebert noted that American math teaching was limited, focusing narrowly on procedural
skills, adopting the motto “learning terms and practicing procedures.” The researchers
discovered that students in U.S. classrooms spent 95.8% of seatwork practicing problems,
as opposed to applying knowledge or even inventing or developing mathematical pro-
cesses. Hiebert et al. (2005) reported that U.S. students spent 91% of the time working
on problems using “procedures only or displaying results only” while only performing

47
1% of the problems as “making connections.” Stigler and Hiebert explained that this was
consistent with the perception of math instruction in the United States in which math is
viewed as procedural, coupled with an assumption that learning occurs as more exercises
are practiced.
The pattern of mathematics instruction is a generalized activity commonly known
as a segmented lesson consisting of the following activities: (a) review of the previous
day’s material through homework check or warm-up, (b) demonstrating how to solve
problems for the day, (c) practicing problems, and (d) correcting seatwork and assigning
homework (Romberg & Kaput, 1999; Stigler & Hiebert, 1999). According to Kersaint,
Thompson, and Petkova (2009), students who are loaded with computational routines and
not provided opportunities to engage in meaningful and challenging tasks lack opportuni-
ties to make sense of math. Thus, the fact that only a small percentage of students reach
proficiency levels makes sense due to the prevalence of such instructional practices that
focus on rules of thumb, along with definitions and procedures (Ball, 2004). Stigler and
Hiebert highlighted this deficiency in U.S. math instruction where teachers habitually
demonstrate procedures for students before assigning problems. In fact, when the curri-
culum contains potentially rich problems, American teachers revert to traditional prac-
tices and transform the approach from “making connections” to using “procedures only,”
thereby reducing instructional potential (Stigler & Hiebert, 2004).
Romberg and Kaput (1999) noted that it should not be surprising that many
students do not like traditional mathematics because the approach has failed to bring
cultural or historical relevance of mathematics, much less its usefulness. This dislike is

48
likely to occur when a strong focus on usage of curriculum materials exists and overlooks
teacher discretion in the use of curriculum regarding pieces to emphasize, omit, and aug-
ment for student needs (Ball, 2004). Therefore, “teacher-proof” curricula are promising
but Ball noted the absence of adaptation between students and teachers that is required by
effective instruction. Furthermore, in Algebra, students are usually made to memorize
procedures that they understand only as strings of symbols, are required to solve prob-
lems absent of meaning, and are graded on the production of correct symbol strings
absent of reflection or articulation, rather than conceptual knowledge and mathematical
reasoning (Kaput, 1999). Simply stated, Stigler and Hiebert (2004) reported that low
math achievement in the United States cannot be explained by an emphasis on concepts
and understanding when most American eighth graders expend most of their effort in
practicing mathematical procedures.
Studying mathematics instruction exposes poor mathematics teaching in the
United States that has affected not only impoverished and minority students but all
students situated within American classrooms. This, along with CRT and institutional
supports, offer lenses into viewing inequitable and poor practices that have contributed to
the achievement gap. Unequal access to quality education, poor instruction, assignment
of students into academic tracks, and disconnects between institutional agents and
students are just some elements that explain ethnic differences in mathematics achiev-
ement (Byrnes, 2003). As it is necessary to identify elements that contribute to the
achievement gap, it is also equally imperative to identify factors that lead to its reduction.

49
Studying math instruction and viewing the quality of teaching is an integral part of this
study.
Achievement Gap Reduction
The achievement gap is essentially measured as the difference between underper-
formance by poor and minority students and performance by their more advantaged
peers. By identifying human causes behind performance gaps, organizations such as
schools can achieve desired performance goals (Clark & Estes, 2002). Clark and Estes’s
gap analysis framework is used to close performance gaps and achieve business goals.
The gap analysis model can be employed to identify cultural norms, practices, and pro-
grams that have supported student achievement and helped to narrow the achievement
gap. Clark and Estes stated that identification of performance gaps is the necessary
primary step in closing the gaps. See Figure 1.
The gap analysis model consists of six steps: (a) identification of business goals;
(b) identification of performance goals; (c) identification of performance gaps; (d) analy-
sis of those gaps to determine causes; (e) naming knowledge/skill solutions, motivation
solutions, organizational solutions, and evaluation of results; and (f) revision of goals
(Clark & Estes, 2002). The gap analysis model was modified for the present study and
framed within the process of analysis that lists the process entailed for an urban school to
narrow the achievement gap and sustain academic success. Thus, rather than identifying
business goals, step 1 of the modified model includes identification of an urban school
that has experienced academic success. In step 2, rather than find individual performance
goals, the modified process includes identification of student subgroups’ academic

50

Figure 1. Gap analysis model. Source: Turning Research Into Results: A Guide to Select-
ing the Right Performance Solutions, by R. E. Clark and F. F. Estes, 2002, Atlanta: CEP
Press.

achievement. Thus, the modified model is framed around a school organization as
opposed to a business.
In public education, each individual school can essentially measure its own
performance gaps to create the opportunity to utilize gap analysis for enhanced student
achievement. According to Clark and Estes (2002), the most critical factors contributing
to performance gaps are knowledge and skills of members, motivation to achieve a goal,

51
and organizational barriers stifling performance. Since the achievement gap is situated in
American education, knowledge and skills of educators, their motivations to achieve high
student outcomes, and the performance of students within schools that they serve can be
examined through the gap analysis model.
Leadership
The role of leadership is critical because a highly effective school leader can
create a dramatic impact on overall academic achievement by students (Marzano, Waters,
& McNulty, 2005). Instructional leadership is one of the characteristics of successful
schools (Waters, Marzano, & McNulty, 2003). Marzano et al. identified 21 categories or
responsibilities of a school leader related to principal leadership. These responsibilities
encapsulate the definition of effective leadership (Waters, Marzano, &McNulty, 2004).
Although the responsibilities are interrelated, they are reported as distinct areas of
leadership. The responsibilities are as follows: affirmation, change agent, contingent
rewards, communication, culture, discipline, flexibility, focus, ideals/beliefs, input,
intellectual stimulation, involvement in curriculum, instruction, and assessment, knowl-
edge of curriculum instruction, and assessment, monitoring/evaluating, optimizer, order,
outreach, relationships, resources, situational awareness, and visibility. To provide focus
in the present study, the responsibilities for communication, culture, input, and visibility
are examined.
Marzano et al. (2005) described communication as the extent to which a school
leader establishes solid lines of communication between teachers and their colleagues and
between teachers and the principal, and maintains accessible dialogue with staff. They

52
also stated that communication is established between teachers and students. Clark and
Estes (2002) cited communication as a type of support necessary for effective perform-
ance enhancement processes.
According to Waters et al. (2004), culture is the responsibility that fosters shared
beliefs, generates a sense of collaboration, and builds community. Marzano et al. (2005)
explained that creating an effective school culture that creates student achievement is the
primary tool with which a leader can foster change. Culture is a critical aspect of leader-
ship to be explored because it can reside in the environment, among groups of people,
and in individuals (Clark & Estes, 2002).
Input is the responsibility that involves teachers in the design of policies and
implementation of important decisions (Waters et al., 2004). Marzano et al. (2005) cited
using leadership teams in decision making as an example.
Visibility is the principal’s high-quality contact with teachers and students (Waters
et al., 2004). Some examples are frequent classroom observations and visitations and
visibility and contact with parents, students, and teachers (Marzano et al., 2005).
Clark and Estes (2002) cited organizational barriers as a cause of performance
gaps. They described organizational barriers as missing equipment, inadequate facilities,
or faulty processes that can inhibit or stifle work. Leadership is a critical aspect of urban
schools that have narrowed the achievement gap because school leaders have oversight to
identify organizational barriers. Waters et al. (2004) identified responsibilities of
effective school leaders in effective schools. These are leadership characteristics on

53
which to focus when studying an urban school that has produced high student outcomes
and narrowed the achievement gap.
Internal Accountability
The achievement gap highlights a need for leadership that functions to create an
environment conducive to learning and promotes conditions that result in improvement of
practices. Elmore (2006) identified characteristics of high-performing poverty schools
that reflect a sense of accountability. In such organizations, leaders clearly articulate
expectations for student learning coupled with a sense of urgency about improvement.
Teachers hold themselves accountable for student learning and thereby examine practices
critically. School leaders are open to classroom observations for analysis of practices.
According to Clark and Estes (2002), knowledge and skills are necessary to achieve per-
formance goals; motivation influences choosing to work toward a goal, persisting until
the goal is reached, and expending effort to accomplish the goal. Thus, accountability
requires teachers’ adequate knowledge and skills as well as motivation to fuel improve-
ment within a school.
Elmore (2003) described the notion of low internal accountability, a characteristic
lacking in low-performing schools. Internal accountability is a quality in effective
organizations and the result of alignment of individual and collective values, which are
reinforced by the processes of accountability (Elmore, 2005). Elmore explained that
these schools are missing a common understanding regarding expectations for student
learning among their educators. Thus, classroom practices are not influenced in positive
ways that would result in student learning.

54
High internal accountability leads to observable gains in student learning (Elmore,
2003). When improvement occurs, it becomes a process of individual and organizational
learning in a developmental progression (Elmore, 2005). Elmore explained that
improvement is a technical and social emotional process involving learning and adapting
to new instructional practices and developing internal accountability with the emotional
component of internalizing responsibility for student learning.
The process of school improvement includes various phases: problem recognition,
low-hanging fruit, stagnation, external help, barrier resolution, impossible work, trans-
formed organization, and self-management of improvement (Elmore, 2003). Problem
recognition occurs when the organization recognizes and internalizes problems of per-
formance and chooses a performance target on which to focus their work. Low-hanging
fruit is a phase that develops when schools succeed in choosing the right target and
develop initial skills in educators and students to meet that target, resulting in increased
student performance. Usually, the initial decisions consist of low-level changes, such as
aligning tests to standards or identification of focus students to monitor so performances
can improve easily. Stagnation is marked by short-term disappointing effects when the
school attempts to implement a more ambitious kind of instructional improvement.
External help is sought when schools attempt to identify new practices through external
help, support, and professional development when performance has stagnated again. In
barrier resolution, the school chooses the next problem to face based on analysis of the
barriers to continued improvement. Impossible work is characterized by the period in
which existing instructional practices and existing organizational norms become more

55
direct and challenging; in this situation, the conditions for future improvement are present
in the school but the capacity to make improvements is not present. A transformed
organization occurs when teachers and administrators understand that they have changed
the way in which instruction occurs and have changed their own capacity to take
responsibility for student performance. Self-management of improvement is a stage in
which teachers, administrators, and students take responsibility for managing their own
improvement process and learning.
Clark and Estes (2002) cited lack of knowledge and skills and low motivation as
elements that cause performance gaps, which are equivalent to student achievement gaps.
The development of internal accountability, which resides in effective schools where
individual and collective values have aligned and leads to student learning (Elmore,
2003), can help to combat a dearth in knowledge and skills and a lack of motivation.
Elmore described the process of school improvement, including attaining expertise about
problems of student learning and instructional practice in the impossible work phase, in
addition to acquiring external help, both addressing the challenge of enhancing knowl-
edge and skills of educators. Also in the transformed organization phase, schools are
generally stronger and more coherent, have distributed responsibilities and display higher
morale among staff to address low motivation within members. Based on this review,
internal accountability and aspects of improving schools were monitored in the present
study.

56
Instruction
A major issue exposed by the achievement gap is that many poor or minority
students do not have the knowledge and skills necessary for academic achievement
because their teachers do not have adequate skills to teach (Peske & Haycock, 2006).
Part of the issue is teacher effectiveness: Teachers do not have the knowledge and skills
to teach their subject. Another issue is the quality of teaching: Students are relegated to
learn rote, procedural skills absent of conceptual understanding or a coherent structure of
knowledge to be learned (Carpenter et al., 2004). If teachers do not have adequate
knowledge and skills, it is reasonable to conclude that students will most likely not have
the knowledge and skills either, which is a contributing factor to performance gaps (Clark
& Estes, 2002).
Teacher effectiveness. Reducing the achievement gap requires, in part, deter-
mining which teachers are most effective (Peske & Haycock, 2006). Some researchers
report impressive results of assigning students to teachers considered to be most effective
or those with the most adequate knowledge and skills. When students are placed under
the supervision of the most effective teachers, they can gain up to 5 percentile points
within 2 years and outperform students assigned to least effective teachers by 50 per-
centile points or higher (Carey, 2004; Gordon, Kane, & Staiger, 2006). Clark and Estes
(2002) described a lack of knowledge and skills as one of the three major causes of
performance gaps. Thus, a lack of teacher knowledge and skills can be detrimental to the
performance of students.

57
Assignment of teachers to minority and underserved students in most need of
quality teaching would result in a reduction of the achievement gap. Carey (2004)
claimed that education under an effective teacher may even offset the disadvantage of
low socioeconomic status in elementary school, a cardinal issue for many disadvantaged
minority students. The usefulness of the Tennessee Value-Added Assessment System
(TVAAS), used to determine the amount of learning a student accrues under the super-
vision of specific teachers on an annual basis, is pronounced. Identifying such teachers
would be critical for education of students who would otherwise receive less quality
instruction.
TVAAS provides researchers tools to gather data about teacher effectiveness.
Although the design is imperfect, it can assist in assignment of effective teachers to
students who are in most need of their services. Many outstanding teachers are
commonly found in classrooms of advantaged students rather than in classrooms of low-
income or minority students (Carey, 2004; Peske & Haycock, 2006). This is important
because research has commonly identified the impact of teacher effectiveness, which is
more pronounced than other influences of achievement such as race, poverty, or parent
involvement (Carey, 2004; Lee, 2002). Perhaps there can be a more assertive effort to
place these teachers with students who need them most.
The achievement gap exposes a need for high-quality instruction. Some
researchers have claimed that teacher quality is a critical influence on student achieve-
ment (Hollins & Torres Guzman, 2005; Rivkin, Hanushek, & Kain, 2005). This high-
lights the pronounced need for teachers with concrete subject matter knowledge and solid

58
pedagogical knowledge and skills to teach successfully. In mathematics, for example,
some research indicates that approximately 70% of eighth graders are taught by teachers
who have majored or minored in mathematics or mathematics education (Wenglinsky,
2000). Although this number may seem adequate for America’s youth, this does not
focus on the subset of students originating from low socioeconomic status areas and
representing disadvantaged students. Peske and Haycock (2006) reported that nearly half
of students taking secondary mathematics and living in high-minority areas and attending
and high-poverty schools were taught by teachers who had not earned at least a minor in
mathematics. This is supported by Ladson-Billings (2006), whose studies indicated that
children in high poverty schools were more than likely than other students to be taught by
teachers lacking even a minor in the subjects that they taught. Thus, institutional support
for math achievement is diverted from this population of students. This suggests that
students in most need of highly qualified teachers are the least to be granted this support.
Researchers have offered various strategies for enhancing student performance.
For instance, Wenglinsky (2002) and Ladson-Billings (2006) spoke to the critical nature
of a rigorous curriculum and teachers with sufficient understanding of their subject matter
to teach the curriculum. This elevates the need for concrete subject matter knowledge
and pedagogical knowledge. Without these elements for teaching, a rigorous curriculum
is pointless, as teachers are unable to adapt to the ways in which students learn best. In
addition, teachers have a higher likelihood of lacking flexibility in teaching for depth if
their knowledge is limited. In essence, a highly qualified teacher—one who has knowl-
edge and skills to teach students effectively—is needed.

59
Acquiring effective teachers is a critical aspect of narrowing the achievement gap
(Peske & Haycock, 2006). In the pre-K through Grade 12 levels, acquisition of highly
qualified teachers is critical because teachers who major or minor in the subject matter
will have more tools to meet the needs of students. Having subject matter knowledge,
which is a deep understanding of the topic, balanced with pedagogical content knowl-
edge, which is an understanding of strategies to facilitate understandings of the subject
(Sherin, 2002), is necessary for teaching math effectively. Teachers who have studied
mathematics more deeply should have a higher likelihood of developing solid subject
matter knowledge and pedagogical subject matter knowledge.
Quality of Instruction
The trend in mathematics teaching in the United States can be characterized as
relatively unchallenging, where familiar problems are practiced in routines with no
attempt to inspire mathematical reasoning (Hiebert et al., 2005). Stigler and Hiebert
(1999) claimed that the main ingredient in promoting student learning is quality of teach-
ing, which requires that teachers cease the utilization of the same traditional instructional
methods. Haycock (2002) explained that teachers of math must have strong background
knowledge because those with this content knowledge are more effective in raising
student achievement. Ball (2004) noted that, to teach math well, teachers must be able to
use mathematical knowledge in a flexible manner to help students to understand math.
Thus, a lack of knowledge and skills to teach math in a flexible manner can lead to
performance gaps between students who are commonly taught by more knowledgeable
teachers and those who are taught by teachers with inadequate skills. This is essentially

60
the deficiency in skills that Clark and Estes (2002) described as producing performance
gaps.
Some researchers propose connecting prior knowledge to what students will learn,
constructing a coherent structure for the knowledge to be learned rather than discon-
nected ideas and skills, engaging students in inquiry and problem solving, and taking
responsibility for ideas students offer and their procedures (Carpenter et al., 2004).
Stigler and Hiebert (2004) claimed that a focus on such elements of teaching and instruc-
tion will yield greater gains than focusing on the more superficial aspects of teaching,
such as organization, textbook, and curriculum content. Since these researchers have
posited that teaching is a cultural practice, they have promoted the notion of analysis of
practice as a lens into cultural routines of teaching to evaluate and improve instruction.
Other researchers have proposed parallel ideas regarding the ways in which
mathematical understanding is constructed. Carpenter and Lehrer (1999) claimed that
classrooms where learning with understanding occurs invite students to construct
relationships between new ideas and processes already understood; extend and apply
mathematical knowledge less susceptible to forgetfulness; reflect about learning experi-
ences to reorganize knowledge in coherent ways; articulate understanding verbally,
through writing, and through pictures and diagrams; and make knowledge one’s own to
develop a personal investment in learning. This approach is consistent with ideas offered
by Romberg and Kaput (1999) that school mathematics should be perceived as a human
activity in which students determine why algorithms and techniques work, help in
developing new techniques, and explain and justify thinking.

61
Effective mathematics teaching diverges from traditional mathematics practices
and the three-part lesson approach. In fact, effective teaching requires teacher under-
standing of student comprehension levels and uses it as a baseline for teaching (Ball,
2004). This requires reflection on what students are learning and continued efforts for
improvement (NCTM, 2000). NCTM posited that effectiveness requires teachers to
know and understand mathematics deeply, understand and be committed to students as
learners of math by drawing from their knowledge to utilize a variety of pedagogical
tools and assessment methods. In general, NCTM stated that effective teaching is incon-
gruous with traditional methods because teaching is centered on students—observing
their learning and listening to their explanations—which reduces the incidence of
teacher-dominated classrooms and redirects focus on supporting student learning that is
conducive to making precise instructional decisions.
Narrowing the achievement gap requires that historically underperforming
students be provided knowledge and skills to experience academic success. It also
requires that well-equipped teachers be assigned to teach poor and minority students. In
math, teachers with a strong subject matter background are more effective in producing
student achievement (Haycock, 2002). To address the issue of knowledge and skills that
Clark and Estes (2002) claimed contribute to performance gaps, teachers must have the
necessary tools to be successful in teaching urban youth. Therefore, teacher effectiveness
and quality of instruction are focal points in this research.

62
Multicultural Education
Teachers should be able to work well with and teach diverse sets of learners.
Since motivation is one of the three main causes of performance gaps (Clark & Estes,
2002), it would be informative to determine whether employment of a culturally relevant
curriculum and establishment of positive student-teacher relationships are conducive to
student motivation, learning, and academic achievement. Teachers must be able to teach
minority and low-income students effectively because the majority-minority phenomenon
is a reality; the U.S. Department of Education has predicted that the U.S. population will
soon consist of mostly Latino and non-White groups (as cited in G. E. Garcia, 2002). Lee
(2002) noted that the achievement gap has a lifetime of consequences for poor and his-
torically underserved students. Haycock (2001) reported that in 1999 African American
and Latino students, at the end of high school, were displaying reading and math skills
comparable to eighth-grade White students.
Researchers have noted that curricula should tap into students’ cultural experi-
ences (Nelson-Barber, 1999). Furthermore, teachers must develop trusting relationships
with students, promoting institutional support that is conducive to student educational
attainment and success. According to P. R. Snipes and Snipes (2005), elements framed
within African American student achievement in math and science are historical aware-
ness of Black education, teacher expectations and beliefs, cultural awareness, testing,
equity in the classroom, and career selections. Berry (2008) listed broad factors that
contribute to African American boys’ success in math: positive rapport from caring
teachers, previous exposure to rigorous math instruction, standards-based instruction,

63
positive academic and social interactions, and a positive self-image regarding math and
school.
Culturally relevant pedagogy. A one-size-fits-all curriculum would be sufficient
if all students experienced sustained educational success. Extensive research has identi-
fied culturally responsive curricula as necessary to meet the needs of diverse students.
This fact calls for teachers to understand the culture that students bring into the class-
room. In essence, teachers must use student culture as a vehicle to guide learning
(Ladson-Billings, 1995). This implies a flexible use of cultural knowledge to create an
environment conducive to student learning.
An underlying assumption is that ample teacher subject matter knowledge and
pedagogical understanding are necessary to incorporate into the curriculum ideas that
students bring to class. Students must be able to use their ways of understanding subjects
such as math. In this regard, teachers must be able to extract and use students’ prior
knowledge to guide lessons and build concepts on prior understandings that students
bring to class.
Student-teacher relationship. The notion of social capital is critical in the
relationship of teaching and student achievement. Since the interaction between teacher
and student has potential to contain social capital (Katz, 1999), a common understanding
between students and teachers is critical for student success. This is especially important
when the teacher work force is steadily becoming more White and the students that they
teach are becoming more diverse (Garcia, G. E., 2002).

64
The interaction between teachers and students is valuable because it has immense
potential for social capital and institutional support. In general, these relationships
between minority students and school personnel may hold great potential for students
who may not necessarily have information through family about access and resources that
could bolster educational achievement (Stanton-Salazar, 1997). Obtaining critical sup-
port from teachers, who assume the role of institutional agent, creates great potential for
academic success as minority students receive instruction by participating within the
social sphere of schools.
Clark and Estes (2002) included lack of motivation as one of the primary causes
of performance gaps. One of the reasons the achievement gap exists is ineffective
teachers who have insufficient knowledge and skills to teach poor and minority students
(Ladson-Billings, 2006). A culturally relevant pedagogy provides a means of using
student culture to provide a context for teaching (Ladson-Billings, 1995) and teacher-
student relationships have potential for institutional support with access to resources that
have potential for academic achievement (Stanton-Salazar, 1997). The existence of a
culturally relevant pedagogy and teacher-student relationships are focal points in the
present study and were reviewed to determine any effects in student performance.
Anecdotal Evidence
Citing examples of schools that have narrowed the achievement gap provides
models for practice. Furthermore, since the achievement gap is essentially a performance
gap between White and Asian students and their poor or minority counterparts, it is
important to review the knowledge and skills and motivational and organizational

65
elements at these schools to analyze the means by which they have raised student
achievement and ultimately narrowed the achievement gap.
The University Park Campus School (UPCS) is an urban school serving Grades 7
through 12 in Massachusetts (Goldberger & Bayerl, 2008). Although UPCS is not a
California school, its challenges are similar to those faced by many California urban
schools with historically low test scores and underperforming students. Upon entering
the school, UPCS’s students generally have low achievement levels in math, reading, and
writing, and approximately 64% of the students are designated English as a Second
Language (ESL) students. Despite all of the challenges that UPCS faces with consist-
ently low levels of incoming students, nearly two thirds of UPCS students scored at the
advanced level of the Grade 10 high school graduation examination. According to
Golberger and Bayerl, 85% of these Grade 10 students have scored at least at proficient
on the same math exam during the past 6 years and 95% of UPCS’s five graduating
classes during that time continued to college.
Mathematics classrooms at UPCS are described as containing a rigorous course
sequence coupled with a cultural norm of approaching tough problems with confidence
(Goldberger & Bayerl, 2008). Teachers are amenable to multiple ways of solving
problems, in contrast to a one-size-fits-all approach to learning. Teachers at UPCS relish
the challenge of teaching, emphasizing depth over breath and providing student oppor-
tunities to explain mathematical thinking orally and in writing. Therefore, these students
leave with knowledge and skills to perform well. This is important because knowledge
and skills gaps are one of the main causes of performance gaps (Clark & Estes, 2002).

66
The research report on UPCS stated that closing the achievement gap in math
requires attention to a combination of a rigorous college preparatory curriculum and the
supportive, personalized attention that students need to become successful. Thus,
students are provided the knowledge and skills to become successful, as well as the
motivation to perform via consistent support. This is consistent with factors cited by
Berry (2008) that contribute to mathematical success for Black students. According to
Berry, positive caring teachers who assume the role of institutional agents are needed,
along with a rigorous math curriculum. This is critical for students whose motivations
toward math could already be declining when they enter middle school. In essence, this
setting demonstrates that teacher-student relationships contain extensive social capital.
As student effort is reinforced and student confidence is enhanced by a cultural norm of
encouraging adults who provide institutional support, achievement in math is more likely
to improve.
The Stanford Mathematics Teaching and Learning Study generated longitudinal
data highlighting Railside School (Boaler & Staples, 2008), an urban school in
California, capturing the plight of urban schools that have worked arduously to serve the
needs of minority students. To ameliorate student disenchantment with mathematics,
Railside’s math department emphasized certain characteristics in their program designed
to fuel student achievement. These elements included creating heterogeneous classes,
collaborative learning and shared responsibility, departmental collaboration, and block
scheduling (Boaler, 2002). Another critical aspect in math student achievement was
Railside’s selectiveness in hiring teachers. Railside sought reform-minded teachers who

67
valued equitable practices (Boaler, 2006). Railside contained organizational elements
that supported student performance through its teachers. This is important because Clark
and Estes (2002) cited organizational factors as a main contributor to performance gaps.
The Railside study included two other high schools that were similar in size.
Contrasts between Railside and the other high schools, Greendale and Hilltop, were that
Railside contained a larger low-socioeconomic population, higher numbers of ELL
students, and lower percentages of parents with educational attainment (Boaler, 2006).
Similar to UPCS, Railside students experienced success in math that is less common in
most urban schools. The study reported 41% of the students were enrolled in advanced
math classes of precalculus and calculus, as compared to 27% of the students from the
two other schools in the longitudinal study (Boaler & Staples, 2008). Both UPCS and
Railside campuses exhibited qualities conducive to sustainable student success.
According to Boaler and Staples (2008), math programs that supported student
learning varied at the school sites. The more advantaged schools in the study, Greendale
and Hilltop, used traditional curricula, including Interactive Mathematics Program (IMP).
The math program developed by Railside teachers through practice of collaboration was
not specific to any text. In fact, Boaler reported that teachers cooperatively gathered
materials from various curricula, such as College Preparatory Mathematics (CPM) and
IMP and designed their own curriculum. Through the cultural norm of collaboration,
teachers shared teaching practices and ways of enacting their devised curriculum.
Boaler reported that this collaboration impacted teacher practices. Specifically, teacher
collaboration resulted in more conceptual problems for students through group work and

68
classroom elements that were not carefully designed into the curricula of the more
traditional schools.
Some elements of the teaching practices were most pertinent to student math
achievement. Termed relational equity by Boaler (2006), such elements included respect
for different backgrounds, learning to treat each other equitably, and learning to work
together. According to Yackel et al. (1991), cooperative learning is a component of
general classroom norms that also include an emphasis on meaningful activity over
correct answers, persistence in challenging inquiries, and explaining solutions to others.
This approach is broader then sociomathematical norms that are understandings about
what is mathematically different, mathematically sophisticated, mathematically efficient,
and mathematically elegant (Yackel & Cobb, 1996).
Through cooperative learning, developing mutual respect, and learning to treat
each other equitably, students developed academic success in math. Boaler (2006)
reported that, at Railside, teachers were mindful of developing sociomathematical and
general social norms in their classes, nurturing classroom qualities that promote student
understanding. In broader terms, a culturally relevant pedagogy fueled teacher practices
that generated classrooms where students learned to work cooperatively and respectfully,
enhancing student math achievement.
The examples provided by UCPS and Railside paint an image of schools that have
narrowed the achievement gap through leadership and instruction. Since Clark and Estes
(2002) described knowledge and skills, motivation, and organizational gaps as the lead-
ing contributors to performance gaps, these are the units of analysis by which to measure

69
UCPS’s and Railside’s success. At UCPS, a cultural norm of caring for students encour-
aged teachers to provide support to students to do well academically and emphasized
depth of learning and thus limited organizational, motivational, and knowledge and skill
gaps that had deterred student performance. At Railside, school administrators carefully
hired teachers who shared similar philosophies about student learning. Furthermore,
teachers emphasized collaboration, both at the teacher level and the student level, as well
as conceptual mathematics. Railside teachers were motivated to work together and
utilize knowledge and skills to generate a curriculum to promote student learning. These
are important details because knowledge and skills, as well as motivational gaps, are
large contributors to performance gaps (Clark & Estes, 2002).
Sustainable Practices
Reviewing literature on schools that have narrowed the achievement gap brings to
light the question of sustainability in academic success. The topic of sustainability is
important for measuring long-term success and identifying practices conducive to that
success. In order to address knowledge and skills, motivational, and organizational gaps
at schools with a desire to narrow the achievement gap, it is beneficial to review practices
that have been fruitful for other organizations and those provided in literature.
High-performing poverty schools contain leaders who clearly articulate expecta-
tions for student learning, along with a sense of urgency about improvement (Elmore,
2006). Internal accountability permeates the organization in that individual and collect-
ive values are aligned and reinforced by the process of accountability (Elmore, 2005).
Furthermore, in the process of improvement, the school undergoes a transformational

70
process whereby staff members take responsibility for student learning and outcomes
(Elmore, 2003).
Schools that have a critical mass of active teachers can help students to achieve
higher levels of academic performance than those students would normally reach. Plac-
ing highly qualified teachers with students who need them most would help to narrow the
achievement gap, as shown by the TVAAS study (Carey, 2004). Selectiveness in the
hiring process would filter out teachers whose visions do not mirror those of the school,
as shown in Railside. Furthermore, assigning minority students to teachers who have
more subject matter knowledge and pedagogical knowledge would place them in class-
rooms that are more likely to be equipped with tools to meet their wider range of needs.
Some schools that create a culture of confident and committed learners with an
emphasis on effort and create environments with a love for learning have narrowed the
achievement gap. Boaler and Staples (2008) and Goldberger and Bayerl (2008) con-
sistently reported the value of preaching effort over innate ability—a quality observed in
campuses that have narrowed the achievement gap. Schools that sustain high expecta-
tions but provide resources and supports for historically low-performing students provide
access that minority students may not necessarily receive at home. Thus, relationships
with educators and other institutional agents may have great potential for student
academic success.
Classroom practices in some schools that have narrowed the achievement gap
include student discourse, removal of tracking, collaborative environments, and ample
time to think through problems using dialogue or writing (Goldberger & Bayerl, 2008).

71
When teachers utilize student prior knowledge, student learning is incorporated into
lessons as fuel to guide teaching. Learning occurs at the student’s level, rather than
teaching at the student’s expense maneuvered by the teacher-guided lecture. In these
settings, a higher likelihood of social capital exists as student inputs are incorporated into
classroom learning experiences.
Reduction of the achievement gap permeates schools through programs, practices,
and cultural norms that are created to raise student achievement. The UPCS example
showed that institutional support coupled with a rigorous curriculum can enhance student
learning. This cultural norm was a theme found in all math classes that allowed students
to feel successful as evidenced by high student achievement on the Grade 10 state math
examination. The reduction of the achievement gap also includes practices displayed in
Railside, where a mathematical program was generated through the cultural norm of
collaboration (Boaler & Staples, 2008). Teacher collaboration was conducive to con-
struction of a math program that enhanced student learning. Teacher practices of
developing social and sociomathematical norms, which were classroom norms, were also
instrumental in developing understanding of math. Teacher practices conducive to
narrowing the achievement gap included emphasizing effort over ability as well as
development of classroom norms conducive to student learning (Goldberger & Bayerl,
2008).
Schools and organizations that experience sustainability display cultural norms,
practices, and programs that have supported student achievement. Elmore (2003)
described a process of school improvement that starts from problem recognition and ends

72
in self-management of improvement to transform the organization as stakeholders
internalize the values of managing and monitoring their own learning. The TVAAS
system and the hiring practices at Railside depict the results of hiring the most effective
teachers for historically underperforming students. Furthermore, teaching practices at
Railside and UCPS, including staff collaboration and classroom practices of student
cooperative learning, were conducive to elevated student learning. The UCPS provided
an example of the benefits of a rigorous math program coupled with the cultural norm of
teacher support. Thus, the elements of cultural norms, practices, and programs are the
focus areas in this dissertation.
Summary and Conclusions
A history of inequality helped to generate an achievement gap between minority
students and their White counterparts. Educational reforms generated a spark to close the
academic disparity but a history of segregation, racism, and poor teaching practices
placed a cog in attempts to narrow the gap. NCLB focused on the educational achieve-
ment of the historically underperforming subgroups in the United States and created a
goal that all students must meet proficiency by the 2013-2014 school year.
Although the achievement gap persists today, some practices have contributed to
its reduction, including those that may be sustainable and replicable. The TIMSS studies
have highlighted teaching as a cultural practice and the focus on teaching quality to
enhance teaching practices and student learning. Some studies indicate that three-
segmented mathematics lesson are ineffective and that practices should be focused on
student learning processes in which students are asked to reflect about their learning,

73
articulate and explain ideas, and make connections between prior understandings and new
material. The TVAAS has shown that assigning students to highly qualified teachers
raised achievement by students to offset the impact of low socioeconomic status. Also,
as displayed by the Railside study, assigning students to highly effective teachers placed
them with teachers who were more likely to have subject matter knowledge and peda-
gogical understanding to make the curriculum more conducive to learning outcomes.
To continue global competitiveness, today’s students must not only be taught
effectively to meet the growing demands of technological and computer-based fields.
More important, they must be instilled with confidence to learn mathematics by being
taught via a rigorous and cognitively demanding curriculum. The teachers at UPCS
accomplished this task by providing students support and resources that allowed them to
meet high expectations and attain academic achievement.
Addressing the achievement gap is critical because the education of the growing
minority population will impact the status of the United States as an international power.
According to the Committee on Equal Opportunities in Science and Engineering (2000),
the United States relies heavily on foreign-born people to fill science and engineering
jobs. In fact, nearly half of all science and engineering doctorates are awarded to foreign-
born persons.
This literature review highlights the persistent achievement gap and a subplot of a
mathematics achievement gap. It discusses the critical nature of some practices that
researchers have cited as factors to help raise student learning of mathematics and narrow
the achievement gap. A case study of an effective school has great potential to contribute

74
to the literature. Essentially, it would contribute to research centered on urban students’
mathematics achievement and the broader topic of the achievement gap. This case study
examines cultural norms, programs, and practices that have been instrumental in narrow-
ing the achievement gap and sustaining student achievement. The research is focused on
an urban intermediate school that experienced rising API scores for the past 3 years,
coupled with a sustained elevated proficiency level in Algebra 1.

75
CHAPTER 3
RESEARCH METHODOLOGY
This research study focused on cultural norms, practices, and programs employed
by an urban school that are perceived to have contributed to narrowing the achievement
gap and sustaining academic success. The impetus for the study was a desire to identify a
school’s qualities that contribute to student learning, elevated test scores, and greater
student achievement, particularly in math. Mathematics achievement has been a widely
discussed issue due to the algebra-for-all-eighth-graders mandate. Focusing on a school’s
efforts to narrow the achievement gap, there was a desire to shed light on a phenomenon,
which is the primary reason for conducting a case study (Gall, Gall, & Borg, 2003).
A qualitative design was used for this study. The researcher did not manipulate
the phenomena, community, or interactions within the school (Patton, 2002). The follow-
ing research questions were designed to shed light on the narrowed achievement gap in
an urban middle school and gather evidence for increased mathematical success:
1. What cultural norms, practiced within the school, are perceived to have
narrowed the achievement gap and sustained success?
2. What practices employed by the school are perceived to have narrowed the
achievement gap and sustained success?
3. What programs employed by the school are perceived to have narrowed the
achievement gap and sustained success?
The use of case study research required a large amount of data to represent the
phenomenon (Gall et al., 2003). Understanding the phenomenon of enhanced student

76
achievement, as well as high mathematics performance within an urban school, required
instrumentation such as document review, interviews, and surveys. The process involved
a detailed description of the school setting and its stakeholders, particularly the adminis-
trative staff and teachers who have worked toward the goal of increasing student achieve-
ment. The study was designed to reveal reasons and evidence for academic success and
the narrowed achievement gap in this urban school. The results could have major impli-
cations for contributing to research concerning qualities of urban schools that attain high
student outcomes.
Nine doctoral candidates from the University of Southern California (USC),
including this researcher, chose the theme of “urban schools that have narrowed the
achievement gap” as a dissertation focus. Although the theme of “urban schools that
have narrowed the achievement gap” was a commonality, each candidate conducted an
independent case study. The doctoral students created their criteria for selecting a school,
which included demographics and sustainability of achievement. Demographics were
defined as the subgroups within a school’s population and the school’s status as an urban
school. The school’s subgroups were significant if there were at least 100 students within
the subgroup or the subgroup accounted for 15% of the student population. The school
was considered urban if the population caused a school to modify programs to accommo-
date the risk factors that are associated with a population including ELL, low SES, and
Title I.
For the purpose of the study, the achievement gap was measured as student
performance versus similar schools on the API as well as general state rankings.

77
Sustainability for achievement was included as a criterion for studying prospect-
ive schools to ensure that the schools did not experience short-lived success that would
have no validity. The nine doctoral students defined sustainability as a minimum of 2
consecutive years in which API subgroups had narrowed the achievement gap, specific-
ally, schoolwide scores or subgroup scores that were meeting targets or exceeding
averages.
The nine thematic group members met on a monthly basis to discuss elements of
the dissertation process, including the design of the research questions, to share research
articles contributing to the study of the achievement gap and to hold each other account-
able in the dissertation process. Informal meetings were conducted with more frequency
in which students collaborated, shared ideas, and most important, maintained heightened
morale to sustain higher levels of self-efficacy than would otherwise exist.
The thematic group members chose a framework to guide the case study research
(Figure 2). Clark and Estes’s gap analysis was used as a process model for conducting
the research in a systematic, procedural manner. The framework of the study was helpful
in conducting research because it provided a map to guide data collection.
This chapter addresses sample and population, instrumentation, data collection,
and data analysis. The sample and population section reiterates the criteria used for the
case study school selection, describes the samples selected and the population from
which the sample was drawn. The instrumentation sections identifies the various means
by which data were gathered and the role that each researcher/doctoral candidate played
in the creation of instruments.

78

Figure 2. Framework of the study based on Clark and Estes’s gap analysis.

Sample and Population
This section provides relevant information regarding the target school for the
study: Beacon Intermediate School, located in southern California, including information
about the district and about students and staff at Beacon Intermediate School. Data
included information specific to the school’s API, presented in the School Accountability
Report Card (SARC) to build a case for studying Beacon’s culture of math achievement.
All of these items were pertinent to the study as they provided direction in determining
critical elements to narrowing the achievement gap and enhancing student achievement in
math.

79
District Level
Beacon Intermediate School was located in one of southern California’s largest
school district. The district, which was the seventh largest in the state, included a student
population of which 60% of the students were classified as ELL and 80% participated in
the free/reduced-price lunch program. The school district contained 64 schools (9 middle
schools, 9 high schools, 4 alternative schools, 7 charter schools, and 35 elementary
schools).
According to the 2008-2009 CBEDS, the school district’s largest subgroup was
the Latino contingent, accounting for 92.4% of their population. Their demographics
also included 3.1% White non-Hispanic, 2.7% Asian, and 0.6% African American. The
school district’s enrollment was 57,439 students.
Beacon Intermediate School earned a score of 731 on the 2007-2008 API, which
was an increase of 29 points from the previous year. Their largest subgroup, Latino
students, increased their API from 696 to 710 in the same school year. Other subgroups
within the district were not numerically significant, as their populations did not exceed
2% of the student population.
In 2008 Beacon’s school district entered Year 3 of program improvement. It did
not meet the criteria for all ELA and mathematics, as required by the AYP. In fact,
according to the Grade Span Reports that show ranges of scores from Grades 2 through 5,
6 through 8, and 10, none of the aforementioned ranges met ELA or mathematics
requirements.

80
At the beginning of this study, Beacon’s school district had 2,709 teachers, of
whom 2,641 were full-time teachers, 7 were university interns, 1 was a district intern, and
1 was teaching under an emergency credential. The data on experience showed 14.8
years as the average number of years teachers had taught, including an average of 12.5
years within the district. When data were collected for the study, the district had 71 first-
year teachers and 83 second-year teachers.
School Level
Beacon’s staff consisted of 62 teachers, 4 of whom held emergency permits to
teach. The experience of teachers at Beacon was an average of 14.2 years of teaching,
including an average of 12 years in the district. The school had only one first-year
teacher. Although Beacon’s SARC reported these data, the SARC also stated that 100%
of the classes were taught by NCLB-compliant teachers. The administrative staff
consisted of the principal, three assistant principals (one for each of grade level), and two
counselors.
At the beginning of the study Beacon had 1,725 students. Each grade level
enrolled approximately the same number of students: Grade 6 had 596 students, Grade 7
had 552 students, and Grade 8 had 577 students. The school’s ethnic makeup consisted
of a large Latino population (97.6%) and a smattering of African American, Filipino,
Pacific Islander, White (not Hispanic), and Asian students accounting for 2.4% of the
student body. Beacon’s socioeconomically disadvantaged subgroup represented 91% of
the student enrollment. ELL students comprised 54.6% of the student population. These

81
demographics, especially the high Latino population, qualified the school to meet the
criterion for this case study.
Beacon’s students experienced a steady improvement on CSTs from 2006 to
2008. ELA had 23%, 24%, and 32% of their students score proficient or advanced
throughout this time period. Math had 37%, 39%, and 45% of their students score up to
at least proficient in the same time period. Both subjects had percentages exceeding
district averages and the state average. The Latino subgroup, the largest subgroup, scored
31% and 44% on ELA and mathematics, respectively, on the 2008 CSTs.
Beacon’s schoolwide API score in 2008 was 731, having gone up from 692 and
680 the previous 2 years. The school’s success is displayed in their API statewide rank-
ings of 4, 4, and 4 during the past 3 years. The API similar school rankings were 10, 10,
and 10 during the same period, placing Beacon in the spotlight. In this study the achieve-
ment gap was measured as the variance in Beacon’s student performance in their similar
school rankings versus their statewide rankings. Since Beacon displayed significant
elevated student performance compared to similar schools, the school was worthy of
insight regarding its cultural norms, practices, and programs.
Although Beacon has experienced a period of sustained success, their 2008-2009
score was 706, a 25-point decline from the previous year. This statistic was not available
prior to identification of Beacon as a case study subject. Nevertheless, although the
school-wide API score has fallen, Beacon still met the criteria generated by the thematic
group.

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Mathematics
In mathematics, 28% of Beacon’s sixth graders and 53% of its seventh graders
scored proficient or advanced in 2007-2008. More than half (50.1%) of the eighth-grade
students took the Algebra 1 CST, mirroring the goal of algebra for all students. In this
subgroup, 80% of the students scored at least proficient. The students who did not enroll
in Algebra 1 took the general math test containing sixth- and seventh-grade math
standards; 25% of the students earned proficient or advanced on this test.
Beacon experienced sustained elevated test scores in various areas such as ELA
and math, making it a strong candidate for this study. Furthermore, Beacon’s math
department was an ideal candidate for this case study due to their high minority popula-
tion, high concentration of ELL students, and large socioeconomically disadvantaged
subgroup. Although these elements are usually indicators of low achievement and
diminished test scores, Beacon displayed the opposite trends in increasing math test
scores and increasing placement of eighth graders in Algebra 1.
Beacon’s response to California’s pressure to place eighth-grade students in
Algebra 1 has been encouraging. From 2006 to 2008, the percentage of eighth graders
taking Algebra instead of General Math increased steadily: 41.1%, 45%, and 50.1%. In
the same time period Beacon’s eighth graders have been earning consistent proficient and
advanced scores: 82%, 81%, and 80%. Since eighth graders have experienced sustained
success in Algebra 1, the spotlight has slowly shifted to Beacon.

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Instrumentation
The thematic dissertation group of nine doctoral candidates generated a concep-
tual framework and the data collection instruments in spring 2009. Although the group
worked collaboratively to formulate research questions and data instruments, each
researcher conducted research independently at a separate focus school.
This case study included four data collection instruments: surveys, interviews,
observations, and document reviews. Collecting data required nine site visits. The
researcher was mindful of days that would be most conducive to gathering data. One of
these events involved staff meetings in which teachers worked collaboratively; another
observed event was a leadership meeting that included the principal and teacher leaders;
another day focused on department meetings to provide snapshots of conversations and
dialogue specific to instruction; other days were focused on observing actual classroom
teaching. Due to strong interest in math achievement, the researcher made a concerted
effort to visit as many math classrooms as possible to collect observational data.
Document Review
A couple of thematic dissertation members generated a document review master
list (Appendix A). This allowed the researcher to determine the usefulness and import-
ance of specific documents and artifacts for the study. For instance, the SARC for 2007-
2008 provided the impetus to choose Beacon Intermediate School for the case study, as
the SARC indicated a progression in elevating math academic achievement. The
school’s Single Plan for Student Achievement (SPSA) for 2008-2009 and the staff
handbook provided a wealth of school information.

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To study student achievement at Beacon, the researcher gathered artifacts with the
most potential to impact student learning, such as common assessments, teacher lesson
plans, and meeting notes. This provided triangulating of data collected through inter-
views and surveys regarding student learning as a function of classroom practices.
The researcher collected documents reflecting the rising student achievement in
math. To accomplish this task, the researcher asked administrators to share student
achievement scores from the past several years. Since each group of students varied from
one year to the next, the researcher looked only at percentages of students who scored
proficient or advanced as a means to triangulate data acquired through other means.
Surveys
The survey instrument (Appendix B) was designed by a couple of thematic group
dissertation members. The document underwent revisions by other pairs of doctoral
candidates within the group. The final copy allowed respondents to provide open-ended
feedback. Some questions were reframed to acquire substantive responses. Furthermore,
uniform spacing was included in the final copy, in contrast to the cluttered appearance of
the initial draft. The revisionists were mindful of the survey’s length, being mindful of
the fact that excessively long surveys often produce a low number of returns.
The survey addressed elements such as collaboration opportunities, school leader-
ship, program implementation, data analysis, intervention, and classroom instruction.
Inquiries in each section were intended to describe the various facets of the school that
created the most impact on student achievement and the reduced achievement gap. The
instrument was given to administrators and teachers. Since the researcher was interested

85
in math achievement, there was an extra incentive to ensure that math teachers received
the instrument.
The instrument’s section on collaboration opportunities inquired about the
frequency of collaboration, identification of leaders, and topics of discussion. The
section on school leadership identified the capacity in which administration managed and
fulfilled their defined leadership roles at the school. This instrument was designed to
identify the various areas in which school leaders were involved and whether their roles
directly fueled student mathematical learning. Some items were designed to determine
whether programs enhanced student learning, whether data analysis was commonly prac-
ticed and whether it directly impacted student learning, whether interventions were in
place to support student learning, and what effective classroom practices helped students
to learn.
Interviews
The interview questions (Appendix C) were created by a couple of USC thematic
dissertation members and revised by the group. The questions were intended for stake-
holders such as counselors, administrators, and teachers. Although the researcher’s focus
was on math achievement, the researcher interviewed multiple teachers, administrators,
the attendance technician, and a District Outreach coordinator, and the teacher leaders
within the math department.
The questions addressed topics in the survey, such as collaboration, school leader-
ship, program implementation, data analysis, intervention, and classroom instruction.

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Other questions focused on professional development, sustainability of school success,
and practices supporting the reduced achievement gap.
Interviews were audio recorded for 45 minutes. They included 30 questions about
collaboration, school leadership, program implementation, data analysis, and invention.
Interview participants remained anonymous throughout the interview and were all
consented individually. Administrative staff, general teachers, and math teachers were
interviewed to identify cultural norms, practices, and programs that were instrumental in
producing student achievement and reducing the performance gap.
A set of interview questions specific to math instruction were generated and titled
“Interview Follow-Up Questions” (Appendix D). Participants in these regular and
follow-up interviews were math teachers. Influential sixth-, seventh-, and eighth-grade
teachers participated in the process aimed at determining elements in math classes that
impacted student achievement in mathematics. Furthermore, the process allowed the
researcher to gain a closer view of the practices, culture, and programs in math classes
that had resulted in math achievement.
Observations
There are various benefits to conducting an observation in case study research.
Patton (2002) cited acquisition of better understanding of a context and setting as a one
benefit. With this in mind, a couple of doctoral candidates within the thematic disserta-
tion group created a school observation guide. The observation guide (Appendix E) was
not intended as a check-off list but was designed to support awareness of cultural

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elements and practices that could be conducive to student learning and academic
achievement.
According to Patton (2002), firsthand experience within a setting allows the
researcher to be discovery oriented and inductive rather than relying on preexisting con-
ceptualizations about the setting. This was particularly important because the researcher
had collected information regarding Beacon through colleagues at USC who had worked
in the district. Therefore, it was important for the researcher to construct personal, unin-
fluenced knowledge regarding Beacon. An example was completion of classroom
observations that allowed the researcher to verify data gathered through other instru-
ments. Creswell (2003) offered triangulation as one of a host of strategies to check the
accuracy of findings.
Data Collection
Creswell (2003) discussed the various means of collecting data through hand-
written note taking, audiotaping, and videotaping. Note taking and audiotaping were
utilized in data collection for this study. In fact, two or more electronic tools were used
simultaneously in case one malfunctioned or simply lost power, as was the case during
one interview with an ELA /Social Studies teacher.
A framework specific to the research questions was created to support data
collection. A data table (Appendix F) was created to optimize functionality of instru-
ments in gathering data to address research questions. In essence, the table provided a
visual reminder of the usefulness of instruments and the areas in which the researcher
may choose to pursue more data for triangulation purposes.

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Research question 1 asked, What are the cultural norms that have been employed
by the school that have helped to narrow the achievement gap and sustain success? To
address this question, the researcher utilized surveys that included a section specific to
cultural norms. Secondary steps were to investigate findings through interview ques-
tions. The interview questions included sections with reframed questions to validate or
refute what was explained in surveys. Finally, for triangulation purposes, the researcher
conducted observations with a keen eye for elements that were reported in the survey and
interviews.
Research question 2 asked, What are the practices that have been employed by the
school to narrow the achievement gap and sustain success? To address this question, the
researcher gathered schoolwide meeting notes and math department meeting notes. The
researcher also distributed the survey that included a section with the function of eliciting
a response on practices. To mine for more information on practices in math, the
researcher did not limit interviews to a general group of teachers but also interviewed key
math teachers, hoping to find themes in practices. Finally, to triangulate data and pursue
potential rich information regarding teacher practices, the researcher conducted observa-
tions in sixth-, seventh-, and eighth-grade classrooms. This was particularly critical in
identifying teacher practices that cultivated classroom norms conducive to student learn-
ing, including mathematics learning.
Research question 3 asked, What are the programs that have been employed by
the school to narrow the achievement gap and sustain success? For the purpose of this
study, a program was defined as a tool created by teachers or purchased by the school or

89
district from an outside vendor to address instructional needs of students. Furthermore, a
program has a specific implementation plan, a training component, and a set of materials
for teachers and students. In order for the program to have schoolwide effect, it must be
implemented with fidelity to goals specified by the program’s developers.
To address research question 3, the researcher gathered meeting minutes from
schoolwide meetings and department meetings. The researcher also inquired about
specific independent programs employed within the school. After conducting interviews
with the teaching staff, including teachers in the math department, the researcher con-
ducted observations to examine the benefit of identified programs. The researcher
determined whether programs endorsed classroom norms that promoted student learning.
Institutional Review Board
The researcher was required to attain Institutional Review Board permission to
secure the protection of human participants during the study. Initially, the thematic
dissertation group members created a generic permission letter used for principal
approval for research to occur at the various schools chosen by the doctoral candidates.
This permission letter was submitted to the Board along with other study protocols.
Data Analysis
The process of this case study involved collection of detailed descriptions of the
setting, teachers, and administration. The case study also involved an analysis of themes
focused on cultural norms, practices, and programs that were instituted to reduce the
achievement gap. This process became more focused when analyzing themes specific to
the same criteria impacting achievement in mathematics.

90
To optimize collection of detailed descriptions, this researcher used a framework
for data analysis and interpretation. Creswell (2003) offered a generic process of data
analysis through a step-by-step process.
Organizing and Preparing
Data were collected and organized according to the instrument used for collection.
The study began with document collection, sparking an interest in Beacon Intermediate
School. The SARC, district and school personnel information, and STAR results were
obtained from the CDE website, Beacon Intermediate School’s website, and the district
website.
The researcher used a collection of electronic tools to collect data: a digital audio
recorder and substitute regular digital audio recorder, and a personal laptop in which to
store valuable electronic data. Interviews conducted using these tools were completed in
September through November 2009. The teacher and administrator interviews were
conducted with two digital recorders simultaneously to ensure collection in case one
recorder malfunctioned or failed.
Obtaining a General Sense
The data were read and reviewed multiple times for identification of themes. The
researcher sought to make generalizations and find common elements in the interviews
and surveys. Transcribed interviews, observation notes, and collected documents were
used to categorize data to inform the researcher of the direction to take the case study.
Subsequent interviews, observations, especially those focused on math classes, and
surveys were conducted to triangulate the findings.

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Coding
As data were collected, major topics emerged. The topics were assigned codes
and related topics were grouped together. Creswell (2003) noted the usefulness of color
coding transcripts or taking text segments and storing them on note cards. The researcher
organized the information in folders and binders, which were then color coded. For
instance, interviews were transcribed and highlighted with different colors based on
assigned codes. Electronic copies were created in digital folders stored in a flash drive
and on the researcher’s laptop computer.
Generating Descriptions
The researcher identified themes during the coding process. The usefulness
themes became apparent in searching for connections between general elevated student
achievement and mathematics student achievement. Themes were also instrumental in
attributing success to administration, teachers, and cultural elements within the school.
This process allowed the researcher to discover emergent themes and prevalent areas, as
well as those that pertained specifically to student learning of mathematics.
Qualitative Narrative
A narrative (Chapter 4) conveyed the findings of the analyses. This included a
discussion of the themes and their interconnectedness. The themes were expressed in
order of the research questions that they addressed.
Interpretation
A final step of interpretation and determination of the meaning of the data was
completed. The correlation of data collection instruments to research questions was

92
utilized as a framework to glean the main ideas in the study. Lessons learned through the
study were compared with information from the literature on reduction of the achieve-
ment gap and elevated student mathematics achievement.
Data analysis required organization and constant review of gathered data to pro-
vide accuracy in coding and to obtain a general sense of Beacon Intermediate School’s
successes. The data were reviewed consistently and coding was completed to identify
descriptions pertaining to administration, teachers, and cultural elements that were
instrumental in narrowing the achievement gap.
Summary
Chapter 3 offered an account of the way in which the case study was conducted.
A description of the sample and population were provided to support the selection of
Beacon Intermediate School as the focus of the study. The data instruments and the data
collection and analysis processes were described. The conceptual framework utilized to
measure the usefulness of data instruments was meaningful in providing direction to the
data collection process.

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CHAPTER 4
RESULTS
The purpose of this study was to identify programs, practices, and cultural norms
that have been conducive to raising student achievement and narrowing the achievement
gap in urban schools. As the NCLB target date of 2013-2014 nears, when all students
must reach proficiency on academic content standards, there is a need to determine ways
to increase student achievement, especially for historically poor and underserved
students. Determining factors that brought student achievement for schools serving
minority students is critical because such information would be valuable for similar
schools that wish to improve student achievement.
This chapter provides a description of the results of the qualitative case study
through the use of document review, surveys, observations, and interviews. The research
findings are presented as they are relative to three research questions specific to pro-
grams, practices and cultural norms, followed by a reflection on the findings. Included in
this chapter is a narrative of the primary site visit to Beacon Intermediate School, includ-
ing a general description of the campus: its size, its population, and its location. Study
participants and their participation through surveys, interviews, and observation is
included. The study’s data and findings are arranged by research questions. The con-
cluding section presents a discussion of emergent themes.
Beacon Intermediate: Meet and Greet
I want to help students that are going to grow up and go to college. We are
dealing with students of poverty. 100% of our students are on free and reduced
[price] lunch . . . . But that doesn’t mean we can’t change the lives of all the

94
students we possibly can and open up the doors to a better future for them. (Mr.
Corral, Principal of Beacon Intermediate School)
The quest to learning about Beacon Intermediate School began during the second
week of September 2009. My morning arrival provided ample time to explore the
campus’s exterior. At that point it was well over an hour before the period 1 bell would
ring. The nearly empty staff parking lot containing only 12 vehicles indicated my early
arrival. My stroll toward the main office was shared by students in white shirts and blue
khakis. We converged at the school’s front gate away from the staff parking lot. The
blur of cars and traffic noise along the main boulevard was part of the morning ambiance;
vehicles became noticeable only when they dispensed children at the front curb.
Beacon Intermediate School was inviting to school and community stakeholders,
including members of its heavily Latino community. The campus was well groomed:
trimmed grass surrounded neatly swept walkways leading to the main office door. A
banner on the exterior wall read, “Attendance is important—Get to School every day.”
An electronic marquee on the northwest corner of the campus flashed “16th Annual
Parent Conference Day 9 AM to 3 PM on October 11th” in both English and Spanish.
As plainly dressed children entered the school’s front gates, the few students with
colored tops contrasted with their peers. It was Spirit Friday, a day celebrating clubs and
activities. It was evident that the colored shirts were affiliated with Beacon; they repre-
sented student leadership: the Associated Student Body. Soon, Beacon’s principal, Mr.
Corral (pseudonyms are used to refer to stakeholders), approached with a large grin. “I
saw you in the parking lot,” he remarked without salutation. Mr. Corral appeared from
the staff lot adjacent to the main office. Before a conversation commenced, his view was

95
spontaneously fixed on a boy. He barked, “You need to tuck in your shirt—the front.
The back’s good, you need to tuck in the front.” Soon, it would become apparent that his
abrupt directives to students were commonplace.
The remainder of that morning was spent in shadowing Mr. Corral, who also
represented a Beacon student organization. He wore a “Think Together” shirt, identify-
ing with the after-school program. Informal conversation with Mr. Corral was inter-
mittently interrupted as he admonished students who did not follow the school’s dress
code policy. For instance, a student whose polo shirt was not well tucked into his khakis
was pulled aside for a reminder not merely of proper attire but also the policy’s location
in the student agenda, and for Mr. Corral to sign the page in which the dress code policy
was printed. Mr. Corral made this a daily practice to “correct the behavior of students”
and to bring awareness of the school’s rules. Multiple infractions under Mr. Corral’s
supervision resulted in detention. His pinpoint laser-like vision spotted students whose
attire wavered even slightly from the school’s dress code policy. “Gentlemen, pull your
pants out of your shoes please! Thank you. Keep them that way. Thank you.” Then our
conversation resumed.
Mr. Corral described his daily morning practice of meeting and greeting students
and parents as “elementary-ish.” Nevertheless, he commented, “I think it makes a
difference. I know it makes a difference for my staff.” I stood in the shadow cast by Mr.
Corral that morning, trying to capture every word. Before the period 1 bell had rung, I
was enthusiastic to learn about Beacon Intermediate School, the factors within its

96
organization that contributed to its student achievement, and how much of that was
attributed to its charismatic, energetic, and astute leader.
The morning’s events were critical to the study, including observation of and
interviews with Mr. Corral. Chatting with and watching Mr. Corral interact and speak
with students and staff gave indications of his influence. Although my plan was already
calculated and focused on interviewing the principal, watching Mr. Corral that morning
validated my choice to begin the study with the organization’s leader.
Beacon Intermediate School: Physical Nature
My first day at Beacon was spent in shadowing Mr. Corral and acclimating to the
extensive campus. Beacon Intermediate School consisted of five middle buildings
numbered 300, 400, 500, 800, and 900 from the north side of the school behind the main
office to the rear, where the 900 building was located. The 300, 400, and 500 buildings
housed seventh-grade ELA and Social Studies, seventh- and eighth-grade math, and
eighth-grade ELA and Social studies, respectively. The buildings were parallel and
included classrooms with two doors, one on the exterior that students used to enter and
exit and the other that led to the communal hallway that gave access to student restrooms.
All classrooms were equipped with an ELMO
®
document reader and a projector. More
technology was found in the interior hallways, including three large laser jet printers that
were accessible to all teachers. In fact, each printer was situated about one third of the
distance down the communal space for easy and fair access. Teachers in each building
had the use of a large paper copier that was set in the center of the hallway.

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The school’s auditorium was situated in the northwest corner of the school, with
the Professional Development Center and Library directly behind it. The school’s newest
two-level structure, the 600 building, was completed in August before the start of the
2009-2010 school year. This was located next to the expansive athletic field on the east
side of the school.
Sections of grassy areas surrounded by paved walkways separated the 300 and
400 buildings and the 400 and 500 buildings, where students entered classrooms from the
buildings’ exteriors. The classrooms’ hallway entrances were allowed to students only
during rainy days or student restroom breaks. The staff agenda stated that students must
be supervised when using interior hallways, which were to be kept clean and free from
clutter.
Students walked to and from buildings through breezeways that were located on
the east and west sides of the 300, 400, and 500 buildings. The breezeways emptied into
the lunch area south of the 500 building. The eastern breezeway led to the school’s
multipurpose room, which was adjacent to the student locker rooms. The multipurpose
room, which was next to the athletic field, provided space for students to participate in
physical education activities, to hold parent gatherings, and to use as a gym.
Traversing the campus gave an impression of the massive student body that
attended the school. The breezeways had been painted recently with lines that separated
students walking north toward the main office and those walking south toward the 900
building’s science classrooms. The lines resembled dividers on roads assigned to delin-
eate traffic directions. It was helpful to designate walking space, considering Beacon’s

98
population of 1,700 students. In fact, even the two-story 600 building, which were
assigned to sixth-grade students, had lines to direct opposing traffic up and down the
stairs into the second-floor classrooms. While observing or walking down the breezeway
during passing period, it was customary to hear Mr. Corral shout, “Walk right! Stay
right!” so that students would use their half of the breezeway to prevent congestion. Like
a hawk, Mr. Corral scoured the school for children whose necklaces and crucifixes hung
loose, whose shirts were untucked, and whose arms were locked with those of friends.
“Ladies, hands to yourselves!” was heard fairly often.
Venturing about the campus revealed Beacon’s compulsively clean nature. Even
with its large student body, there was very little trash (wrappers or remnants of food)
throughout the campus, even in the lunch area. According to the one of the school’s two
campus security officers, students who misbehaved during lunch or nutrition periods
picked up trash with supervision by lunch duty supervisors, the security officers, or one
of the administrators.
The Eastern Breezeway included murals depicting character traits valued at
Beacon. Each of the barriers separating the 600 building from the 300, 400, and 500
buildings had a graphic describing Responsibility, Caring, Citizenship, Trustworthiness,
or Friendship. These murals were appropriately situated, as they were very visible to the
many students who passed by daily. If they were vandalized (as occurred during the final
week of data collection), the damage was quickly removed to ensure that the students
observed the messages as they were intended. If there was trash in the breezeways or the
areas designated for foliage, noon duty aides patrolled the halls to ensure cleanliness.

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Participants
Mr. Corral and I met initially in mid-August to discuss the research: the number
of days required for data collection and the dissemination of surveys. Subsequently, 6
full school days were devoted to interviews and classroom observations, not including
three partial-day visits. Overall, nine formal interviews were conducted: two with
administrators and seven with teachers. Other conversations and informal discussions
contributed to the research to triangulate findings. These included less formal interviews
with teachers, campus security officers, the school secretary, the attendance technician,
and a district outreach consultant.
The two formal administrative interviews were conducted with Beacon’s princi-
pal, Mr. Corral, and with Ms. Katie, the returning assistant principal of the school’s two
assistant principals. Both administrators provided a wealth of information because they
had been at Beacon as the school had initiated its heightened student achievement.
Forty-eight of 62 teachers participated in completing the survey, representing
74% of the teaching staff. Mr. Corral suggested that the surveys be administered to these
staff members, rather than to the entire teacher force. Mr. Corral explained that, with
almost 1 of every 4 teachers new to the site, newer staff members would not be able to
provide substantial information because they did not yet know enough about Beacon’s
culture and teacher expectations. This was evident during the initial staff meeting, which
occurred on the Friday before the first day of school. Mr. Corral and Ms. Katie spent 5
hours explaining Beacon’s teacher expectations, which were included in the staff
handbook that was distributed that morning. In fact, during Back to School Night, Mr.

100
Corral was apologetic regarding the long wait that I endured during the staff meeting
before I presented my study to the staff. He explained, “There was just so much to
cover.” Dr. Allen, a seventh-grade ELA and Social Studies teacher, explained that the
seventh-grade ELA team had convened before the school year as a means of getting to
know one another and creating expectations within the department. In fact, Ms. Katie
reported the harsh reality of reduction in teacher force:
We had a turnover of teachers last year, much like this year. This year we have
17 new teachers. Last year, we had 14, I believe. They’re not only learning the
school culture and the expectations of the school, but they’re also learning the
new curriculum because these new teachers were all coming from elementary.
Furthermore, since a handful of these teachers were relocated after receiving pink
slips, knowledge about Beacon Intermediate School may be scant, particularly for the
former elementary teachers arriving from some of the district’s 30 elementary schools.
Previously, during the 2008-2009 school year, Beacon had experienced the loss of many
members of its original staff. The statewide budget cuts and decline in economy had led
to the reduction in force, accounting for more than 10 teaching positions.
Research Questions
There were factors at Beacon Intermediate School that contributed to academic
success. To identify these factors, three research questions provided direction and focus
for the study. Three research questions were aimed at determining the programs, prac-
tices, and cultural norms of Beacon Intermediate School that fueled elevated student
performance and the narrowed achievement gap.
1. What cultural norms, practiced within the school, are perceived to have
narrowed the achievement gap?

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2. What practices employed by the school are perceived to have narrowed the
achievement gap and sustained success?
3. What programs employed by the school are perceived to have narrowed the
achievement gap and sustained success?
Criteria
Mr. Corral once described the challenges that Beacon’s leadership faced in meet-
ing the needs of at-risk students: “Our entire population is at risk. You try to do every-
thing you possibly can. We’re all doing this together.”
Beacon Intermediate School was selected for this study because it met the criteria
set by the thematic dissertation group. The campus was located in a large city in southern
California, overlooking a major avenue. The school served a student population that
contained a significant subgroup of Latinos (92.4% of all students). There was also a
large ELL population (54.6% of all students). Beacon’s socioeconomically disadvant-
aged subgroup, was eligible for free and reduced-price lunches, was also large (91% of
all students).
Beacon had shown growth in overall student achievement from 2006 to 2008,
when API scores were 680, 692, and 731, respectively. Furthermore, perhaps more
uncommon, was that within those years Beacon’s Algebra 1 scores had been consistently
high (82%, 81%, and 80%) as the number of students placed in Algebra 1 slowly
increased (41.1%, 45%, and 50.1%).

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Findings for Research Question 1
The first research question asked, What cultural norms, practiced by the school,
are perceived to have narrowed the achievement gap and sustained success? Several
themes emerged related to this research question, including prevalent publicity of student
work, staff collaboration, and shared leadership.
Publicity of Student Work
I am very, very grateful, you have put on a beautiful face at the entry to Beacon.
When people come in to our school, they look at those things and go, “Wow.
They have student work right here in the office.” It really makes an impact on
new students in particular. This is a school that’s really serious about academics.”
(Mr. Corral)
When I entered the main office during my primary visit, the immediate sight was
the large V-shaped counter where office attendants were welcoming. In the waiting area,
the volume of student work on each wall leading to the counter was evident. The display
boards were designated for various subjects for equitable sharing time. When data
collection began in September, the science department was allotted the space. Therefore,
student descriptions of the Scientific Method covered the walls, along with a large area
with student-generated colored graphs. The celebrated student work was obvious to
visitors. On my last visit to Beacon, expository papers on “The Influence of Islam” and
student-written drafts depicting the writing process were displayed. During Beacon’s
first staff meeting, Mr. Corral explained,
It’s like all summer long when parents come in to register, they read this stuff and
it’s really, really neat. . . . So most people put up their reports that students have
done. And some of them have really good graphics and stuff like that and it’s
really, really neat.

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A few steps down the hall adjacent to the waiting area, a display board assigned to
the Think Together Program showed miniature cutouts of Hawks, the mascot of a local
state university. The paper Hawk designs signified Beacon’s proximity to the university
and the ties that many of the teachers had to the school. Each paper cutout displayed a
student’s name, his or her aspiration for a career, and the university that he or she desired
to attend. This was visible to visitors who approached the main office’s counter and
those with appointments to see administrators.
In the 300, 400, and 500 interior halls there was evidence of a large volume of
student work. A seventh-grade teacher explained that all seventh-grade ELA and Social
Studies teachers made the effort to use display boards that were nearest their classrooms.
She also said that student work display was a departmental decision. Although student
work was not as evident in the 400 building’s hallway, which housed the seventh- and
eighth-grade math department, many projects and posters were displayed in classrooms.
This contrasted to the 300 and 500 buildings, where the halls included eighth-grade
expository writing, student-created maps, flip charts completed in seventh-grade social
studies classes, and other examples of honored student assignments. Specifically, the 300
building contained two display boards full of reports on Martin Luther King and a board
titled the “Fall of Rome,” with its own set of projects. The 500 building, which housed
eighth-grade ELA and Social Studies classes, had a display board “The First Americans”
with maps and pictures, and other boards titled “Weakness in the Articles of
Confederation.”

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In the 400 building, the eighth-grade math department displayed student-
generated projects on classroom walls, mobiles describing mathematical expressions, and
mathematical models with student-generated explanations describing their understanding.
All of these displays showed that Beacon Intermediate School valued student work and
made the strong effort to publicize it. Navigating Beacon gave the sense that educators
projected school pride in their students’ work as it appeared inside and outside of class-
rooms. Furthermore, these locations were communal spaces accessible to students,
teachers, and parents. There was no escaping display of student work.
Staff Collaboration
We all have something to learn, we all have something to contribute. To the
extent that that happens, things get better and better. To the extent that this
doesn’t happen and people become insular, and they close themselves in their
classrooms, instruction will not improve and achievement will not either. (Mr.
Corral)
According to the survey results, the majority of respondents strongly agreed that
teacher collaboration was supported by the administration (Table 1). This was observed
often, either formally in structured staff meetings or informally between periods or during
conference periods. According to Beacon’s staff handbook, teachers had at least 1 day
per week in which they collaborated with their departments or grade levels. In fact,
document review revealed that teacher collaboration was an agenda item in all of
Beacon’s staff meetings. Observations and interviews revealed that teachers convened
more frequently than was required by administration. Structured collaboration was
provided by administration and informal collaboration occurred outside of formal teacher
meetings.

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Table 1

Responses to Survey Items 1-6

SA/ A/ SoD/ St/D/
Survey item Most Sometimes Rarely Never

1. The school supports collaboration
among teachers. 35 11 0 1
2. The teachers at this school believe
that students can achieve at high levels. 18 28 0 1
3. School administration creates a positive
school culture for teachers and students. 36 7 4 0
4. Leadership is shared among school
personnel. 29 16 3 1
5. Teachers collaborate to discuss student
data to improve student learning. 32 12 1 0
6. The school addresses the needs of
struggling students. 31 16 1 0

Note. SA = Strongly Agree, A = Agree, SoD = Somewhat Disagree, StD = Strongly
Disagree, Most = Most of the Time.

Responses to survey items 1, 4, 5, and 6 reflected collaboration practices at
Beacon. Responses to survey item 1 revealed that a significant number of teachers
agreed that collaboration existed, particularly in structured staff meetings. Survey items
5 and 6 reflected a norm depicting informal collaboration, although teachers also formed
structured, formal meetings to discuss student data to improve teaching. Survey item 4

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specifically alluded to the existence of Beacon’s leadership team, which many times led
structured and informal collaborations.
Structured collaboration. Teachers had multiple opportunities to convene,
which was structurally designed.
They [teachers] have formal meetings by contract. We have early release on
Wednesdays. I control one of those Wednesdays. Two Wednesdays per month
are mine, and I control those. The first Wednesday of every month is a staff
meeting. And the third Wednesday is a grade-level meeting and the sixth-grade
teachers get together with the seventh-grade teachers and eighth-grade teachers.
(Mr. Corral)
Within the school calendar, Beacon’s teachers were afforded opportunities to
meet weekly with grade-level teams, department teams, and the entire staff. Since such a
structure existed, Beacon’s teachers made communicating with one another habitual. Mr.
Stevens, a Teacher on Special Assignment (TOSA) and ELA Department Chair, com-
mented on the ample opportunities for collaboration during his interview: “Collabora-
tion’s fairly strong because we have the course-alike preps, mixed collaboration, or
should I say the opportunity for collaboration is very good.”
Mr. Corral supported Mr. Stevens’s statement during his formal interview:
What we have in our best collaborative relationships are that in the course-alike
meetings, which are held officially every about other week, unofficially on a daily
basis because all of the teachers have common preps. Collaboration looks like an
ongoing conversation about what we teach, how we teach it, how we measure it,
and what we do when they didn’t learn it.
Document review revealed that collaboration was such a critical item at Beacon
that teacher collaboration, along with student engagement, was consistently included in
staff meeting agendas. Also, the SPSA indicated that staff meetings were structured to
provide teachers with specified collaborative time to address the needs of students.

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Informal collaboration. Staff collaboration extended beyond structured time and
occurred often. Mr. Stevens commented on the amount of informal collaboration that
was a daily norm at Beacon. In his interview he mentioned that, although collaboration
existed, quantifying it was difficult. Since his office was situated at the end of the 500
building, Mr. Stevens noticed the consistency in collaboration that was audible in the
interior hall.
The amount of collaboration is hard to assess. I see it sporadically. You know,
it’s an ad hoc thing. It’s not legislated. It’s encouraged obviously. . . . I hear it in
the hallway all the time. In this hallway here I hear it. A minute here, a couple of
minutes there. Sharing information: “What do you use for this? What do you do
for that?” You know, so it’s going on all the time.
Dr. Allen added, “But you can see that we do talk. We’re very open. . . . You’ve
got to be able to trust your colleagues that, if you make mistakes, you’ve got to catch
each other and help each other and make that better.”
In addition to interviews and classroom observations, I observed collaboration
that occurred within interior halls. One instance transpired during a November half-day
visit. Standing in the 400 building’s interior hallway, I tallied the number of times an
Algebra teacher visited his next-door neighbor and curriculum partner. In this instance,
Mr. Oliver and Mr. Williams, Algebra 1 teachers who permitted me to record their con-
versations, discussed the challenges that students had on that day’s activity—organizing
algebraic expressions into seven separate methods for simplification—as well as the
strengths that students exhibited. A portion of the conversation unfolded as follows:
But is it a matter of them just mixing it up? Unfortunately, they want to do it in
procedural–the procedural level, right? So no matter what we do, it all drops back
to procedural level. But the good news is, I think that they understand the pro-

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cedures pretty well. So it’s a matter of when to apply which procedure. That’s
what they’re having trouble with. And that’s OK. (Williams)
Not for the “one.” Maybe for the “four, five,” yes. I think it’s beyond not being
able to recognize. I think it goes back to, “Did I learn how to use the strategy?”
Here it was the wrong strategy, but sometimes it’s the right strategy but they do it
wrong. (Oliver)
Teachers communicated about student performance, which supported responses to
survey item 5, “Teachers collaborate to discuss student data to improve student learning.”
These results suggest that collaboration was a cultural activity at Beacon.
Collaboration at Beacon was important because it provided teachers the opportunity to
discuss student learning and how to improve teaching. Collaboration was not only
structured within the school calendar; it was also a function of daily communication
between some teachers. Partaking in informal collaboration to discuss student learning,
such as that of Mr. Williams and Mr. Oliver, displayed a sincere effort and desire in
teachers to improve their craft and enhance student learning. As impactful as the cultural
norm of collaboration may have been, its existence and influence were hinged on the
leadership that existed at Beacon.
Shared Leadership
I think everyone is encouraged in leadership to take on more leadership and I
think that’s one of the biggest things I love about this place because if you got an
idea, there’s a lot of safety, there’s a lot of trust. (Dr. Allen, seventh-grade
ELA/Social Studies teacher)
Beacon Intermediate School’s cultural norm of shared leadership was consistent
with data from responses to survey item 4, “Leadership is shared among school person-
nel.” In the free response section of the staff survey, some teachers commented, “We
have the opportunity to be leaders of leaders” and the principal’s motto is “He is a leader

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of leaders” and “Choosing and empowering effective leaders has been key.” Since Mr.
Corral exemplified the role of leader of leaders, Beacon’s leadership team and other
specific staff members, who were identified as having a larger influence on student learn-
ing outcomes, were identified as teacher leaders on Beacon’s campus. Mr. Williams, Mr.
Stevens, and Mr. Oliver, whose efforts and influences are discussed in this section, were
specific teachers who had greater impact on student learning and performance.
In her formal interview Ms. Katie emphasized Mr. Corral’s leadership based on
his passion.
I was a little concerned coming from high school into intermediate, because I had
asked some of my friends what it was like at the intermediate level, and when I
saw the leader of this school cry in front of me and say, “These are my goals, this
is my vision, and this is my mission,” it just kind of blew me away. Because
when a grown man cries, that means that there’s passion, that means that there’s
heart there. And, I’ve been here for 4 years, and I’ve had the best mentor.
Ms. Katie was not the only teacher to reference Mr. Corral’s leadership. Mr.
Williams, an Algebra 1 teacher, also discussed his appreciation of Mr. Corral during a
conference period interview.
Mr. Corral gives us a lot of freedom; he sees it [Algebra 1 curriculum] as a
successful program. He supports us. He runs interference with the district for us.
You know, if Mr. Corral died in a motorcycle accident tomorrow, I’d probably
start sending my resume out to the Bay Area.
Mrs. Noelle, the eighth-grade Social Studies Chairperson as well as an eighth-
grade ELA teacher, also mentioned Mr. Corral’s strong leadership.
Mr. Corral [is] an amazing principal and he’s the driving force, but he doesn’t like
to take full credit. He likes the fact that all department chairs work together on
what’s called BALT: the Beacon Academic Leadership Team.

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Throughout my 5 full days of observations and data collection, Mr. Corral’s
passion and zeal for educating his students slowly unfolded. Although he was stern with
students, he also exuded uncommon compassion, thoughtfulness, and love for his
students and their families. According to Beacon’s Onsite Outreach Director and the
school’s attendance technician, Mr. Corral made an effort to visit student homes. Before
Thanksgiving break, Mr. Corral reported that he already completed approximately 20
home visits, on one of which I accompanied him. He made these visits to address
attendance problems and truancy, as well as to distribute turkeys prior to the holiday
season. It was the simple gesture of caring conveyed by Mr. Corral’s presence that struck
parents and students.
Even with Beacon’s recent successes and although symbols of personal recogni-
tion sat on his shelf, such as the 2006-2007 District Administrator of the Year, Mr. Corral
never took credit for the successes at Beacon. A cultural norm that resided in Beacon
was distributed and shared leadership, which was explained by Mr. Corral.
I stress to people here there’s no way on God’s green earth I could possibly lead
this school all by myself. I have to be a leader of leaders. And to a huge extent, I
can see that happening on my campus.
Thus, leadership derived not only derived from Mr. Corral but from various
teachers on campus. Some of them were members of formal teacher teams and others
were simply recognized as influential, key members. An example of a formal teacher
leader group was BALT.
The existence of BALT was consistent with survey data. The most common
response to survey item 1 (“The School supports collaboration amongst teachers”) was

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strongly agree (35 of 46 respondents). Furthermore, 29 of 48 survey participants
expressed agreement with survey item 4, “Leadership is shared amongst school
personnel” most of the time.
The BALT was composed of teacher leaders and department chairs from all grade
levels and subject matter areas. These teachers were often referred to as “Course-Alike
Leaders” because they took the leadership role in subject matter groups within the
various departments. The BALT convened on the first Wednesday of every month after
school in a meeting facilitated by Mr. Corral. These meetings started once staff meetings
concluded. The BALT meetings were located in either the school’s Professional
Development room, located next to the library, or in the conference room in the main
office. The BALT formed a governing body that allowed Mr. Corral to discuss organiza-
tional issues and elements of instruction more deeply than during general staff meetings.
Mr. Corral described the structure of the BALT-led meetings and contrasted them with
staff meetings:
The alternate Wednesdays that are not controlled by admin are controlled by
teachers and that agenda is set by the course-alike leader. Admin will provide
some input occasionally on things we want to make sure they’re covering,
pressing issues. But they control their agenda and then they present an agenda
and take minutes on that agenda. The course-alike leaders really have to be
leaders.
Mr. Corral and the administrative team trusted those in leadership roles, provided
them voices, and calculated their input in decision-making situations. Ms. Katie
described the Course-Alike Meetings run by BALT:
The Course Alike Meeting [is] basically run by collegial leaders. We do not step
in unless we’re present and they ask a question because there may be question on
any future dates they have for common assessments or if they have problem with

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curriculum that the department chairs are unclear with. Then that’s when we’ll
usually step in. But, we have true confidence in our department chairs and they
run the meetings.
BALT supported Mr. Corral’s role as a leader of leaders. Although many
influential teachers were members of this organization, other teachers assumed leadership
roles without formal roles or titles. Like the BALT, these key teachers influenced
discussions during collaborations, but also did so in more impactful ways.
Mr. Corral was consistent in sharing leadership among staff members at Beacon, a
notion supported by the staff survey (Table 1). On Back to School Night Mr. Corral
mentioned one of the teacher leaders, Mr. Williams, and the common belief that they
shared regarding student learning in algebra.
He [Mr. Williams] and I, I think, have a similar belief that we could probably get
to the point where we have as many as 90% of our students in algebra 1 and 90%
of them proficient and advanced and it’s not because the material is difficult, it’s
the way that we teach: it’s instruction.
Mr. Williams was a key teacher because of his extensive influence on the
previous Algebra 1 and eighth-grade science CST scores. He was the former Algebra 1
Course-Alike Leader as well as Science Department Chair when Beacon maintained its
elevated Algebra 1 scores of 82%, 81%, and 80% proficient and advanced for 3 con-
secutive years and the years in which Beacon made significant gains in eighth-grade
science, from 26% to 37% to 54% proficient and advanced. Mr. Williams was also a
teacher leader because he spearheaded the eighth-grade Algebra 1 curriculum that
Beacon used during the years that scores rose from 55% proficient and advanced in
2004-2005 to 82% in 2005-2006. The Algebra 1 curriculum generated by Mr. Williams

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and implemented by Beacon’s teachers was wholly divergent from the district-adopted
text.
Even without a formal title of Course-Alike Leader or Department Chair, Mr.
Williams was a leader of leaders in Beacon’s eighth-grade staff because he not only
served as architect of the Algebra 1 program but supported other teachers in their
implementation of it. For example, Mr. Oliver, another eighth-grade Algebra 1 teacher,
began using the Algebra 1 program 3 years ago and even contributed to its improvement.
Therefore, when the program was published, they were listed as its authors.
Another teacher leader contributed to the success of ELA. Mr. Corral reported
that Beacon Intermediate School had the highest CST scores in ELA for of all
nonfundamental schools in the district. This occurred during the period that Beacon’s
API scores were rising (Table 2). In describing the gains that the school had made since
his arrival, Mr. Corral stated, “When I got to Beacon, it was only 9% proficient and
advanced. Now we’re at 31.”
Beacon Intermediate School’s ELA department has been influenced by its
Department Chair, Mr. Stevens. In describing Mr. Stevens’s adeptness at analyzing
student data, Mr. Cramer, an eighth-grade ELA/Social Studies teacher said, “We have
Mr. Stevens, who’s department chair for Language Arts, who’s a real guru. He likes
doing that stuff, especially in Language Arts. He’s the one who disseminates [student
data].” Mr. Stevens was also the school’s nominal data analysis expert for ELA. He was
quite skilled at creating spreadsheets and distributed data on student performance for each

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Table 2

Percentages of All Students Scoring Proficient or Advanced in English-Language Arts:
Three-Year Comparison

School 2005 2006 2007

Beacon 23 24 32
McKenzie 20 23 31
Spears 15 19 22
Williams 14 16 19
Suerte 13 17 20
Lawrence 16 16 19
District 26 28 32
State 42 43 46

of the ELA levels. Mr. Stevens was an influential leader because of his direct
relationship with all grade levels. According to Mr. Cramer,
He [Mr. Stevens] is the only department chair here who’s not in the classroom.
. . . He was a classroom teacher, [but] because of his computer skills, they decided
to get him out of the classroom so he can do this. . . . Collecting data, disseminat-
ing the data, interpreting the data is just one of the things he does.
Mr. Stevens was effective in supporting a culture of collaboration by promoting
data analysis practices, which was reflected in responses to survey item 10 (Table 3). He
was largely responsible for contributing to the data-driven culture at Beacon when he
created a spreadsheet to collect, analyze, and disaggregate student ELA data based on
student performance as measured on common assessments.

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Table 3

Responses to Survey Items 7-16

Most of Some-
Survey item the time times Rarely Never

7. School administration conducts classroom
observations frequently. 29 19 0 0
8. The school has a systematic process for
identifying and assisting struggling students. 13 32 3 0
9. School administration communicates
vision and goals to the staff. 40 6 0 0
10. School administration ensures the
analysis of student assessment data. 34 8 0 0
11. School administration provides support for
implementation of new instructional practices. 33 14 1 0
12. School administration provides ways
to improve instructional strategies to meet
the needs of students with diverse backgrounds. 27 19 1 0
13. CST scores and District Assessments are
used to plan your instructional program? 40 7 1 0
14. Student data is used to identify the
instructional needs of my students. 41 7 0 0
15. You utilize the California State Standards
to plan and deliver instruction. 46 2 0 0
16.You provide differentiated instructions
to meet the needs of all students. 38 10 0 0

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When asked how data were used to support student learning, Mr. Stevens replied,
“It’s identifying the specific needs of specific students.” Mr. Stevens collected the
student performance results from each ELA teacher and input them into his program. He
then disseminated the results to teachers. The impact of this activity was profound
because all student performance was publicized. Teacher accountability was promoted
because student outcomes were exposed, as well as teachers responsible for those out-
comes. The result was a collaborative norm as teachers sought ways to improve their
teaching by communicating with one another.
Mr. Stevens was a leader among leaders on Beacon’s campus because his spread-
sheets nurtured collaboration among staff. This was supported by survey results specific
to administration ensuring analysis of student assessment data. In fact, both Mr. Cramer
and Dr. Allen, a seventh-grade ELA and Social Studies teacher, displayed data reports
that had been distributed to them by Mr. Stevens. Thus, although he was not a classroom
teacher, Mr. Stevens contributed significantly to all grade levels through his efforts to
create spreadsheets of student data for teachers. With his influence, Beacon nurtured the
practice of analyzing student data to inform teaching. Data analysis, a practice at
Beacon, was supported by responses to survey item number 14 (see Table 3).
Another teacher leader on campus was Mr. Jefferson, a sixth-grade math teacher
and Beacon’s math Department Chair. Aside from these roles, Mr. Jefferson also taught
a Single Subject Mathematics Methods course in a nearby state university’s teacher
preparation program. Thus, according to Mr. Williams, Mr. Jefferson was influential
because, although Beacon did not have access to a formal professional development

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program, they had Mr. Jefferson as a resource. Mr. Williams cracked, “Henry Jefferson
is our professional development.” With sincerity, Mr. Williams described the importance
of Mr. Jefferson in the department:
Henry [Mr. Jefferson] is the magic guy. Henry knows K-12. You can ask him at
any grade level . . . what are they doing, you know, with integers? And he’ll be
able to tell you off the top of his head. He’s amazing, he’s a genius. He knows
K-12 standards really cold. And his thinking is very progressive. So, he’s a real
guiding light.
Aside from his general knowledge of math and instruction, Mr. Jefferson played a
critical role at Beacon as a conduit of ideas. His conference period was strategically
placed in the final period of the day so he could provide colleagues support while they
taught their classes. Furthermore, other teachers could observe his classes during their
conference periods.
On the day of his formal interview Mr. Jefferson allowed me to observe his
meeting with the teachers of general math, referred to as transitional math at Beacon.
Mrs. Cable and Mr. Song inquired about some tips on teaching adding and subtracting
expressions and Mr. Jefferson not only provided resources for them to use but also
explained the thought processes involved in teaching the skills.
Mr. Garcia, a seventh-grade math teacher and seventh-grade math leader at
Beacon, gave an example of Mr. Jefferson’s broad influence. According to Mr. Garcia,
Mr. Jefferson took responsibility for rewording each math standard that teachers posted
in classrooms. Mr. Garcia explained, “He made it student friendly by keeping it to one
sentence or one phrase.”

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Mr. Jefferson reported that colleagues commonly sought resources from him. A
good example was reflection sheets that students used during post assessments or at the
end of a unit to think about what they had learned or to continue to think about what had
been challenging. Mr. Jefferson explained that he usually tacked these documents above
his desk in the rear of the room. The reflection sheets would normally be removed, many
times without asking, which became a common accepted practice.
In general, Beacon’s teacher leaders collaborated with and influenced other staff
members. They were leaders among leaders because they created a network for a flow of
information and ideas. For instance, the BALT epitomized the collaborative culture at
Beacon because they met regularly with Mr. Corral and fellow teachers in department
meetings. Mr. Williams not only created Beacon’s Algebra 1 program; he also shared
ideas with other teachers, such as Mr. Oliver, who helped to improve the curriculum.
The result of their effort was a published workbook that students used. Mr. Stevens was
influential at Beacon because his astute knowledge of spreadsheet software produced a
program to disaggregate ELA common assessment data. Mr. Stevens distributed student
performance data to his colleagues, which became the focal points of conversation. His
effort reinforced normative collaboration among the ELA staff. Mr. Jefferson was also a
large influence on Beacon’s campus because his role as department chair provided him a
position to collaborate with all levels of the math staff. Furthermore, since he had a
wealth of ideas and resources, he supplied support to others.
Beacon Intermediate School’s students experienced academic success due to the
influences on instruction generated by teacher collaborations and communication about

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improving teaching. Teacher leaders such as Mr. Williams, Mr. Stevens, and Mr.
Jefferson had broad influences on student learning. Mr. Williams and Mr. Jefferson
impacted student learning through their methodology in math teaching and ideas that
even resulted in creation of an Algebra 1 curriculum. Mr. Stevens had a broad influence
on teachers and students because of his role as a TOSA and his contribution of the data
spreadsheets. These teachers at Beacon exerted influence that was easily identifiable.
Findings for Research Question 2
Research question 2 asked, What practices employed by the school are perceived
to have narrowed the achievement gap and sustained success? Several themes regarding
specific school practices emerged in relation to this research question: (a) the teacher
practice of data analysis and prevalent utilization of common assessments; (b) school-
wide expectations to use a classroom management tool called CHAMPs; (c) a common
emphasis on student engagement; (d) “writing across the curriculum,” an expectation that
students in all subjects would complete an expository paper throughout the school year;
and (e) a lack of set daily routine or protocol in math classes, particularly Algebra 1. In
addition to these findings, discrepant information is discussed to build credibility to the
accounts (Creswell, 2009).
Data Analysis
At this school, we work together as best we can . . . we have course-alike planning
where we get together with other teachers that are teaching the same subject area.
That time we have to work together to look at student work or else talk about
what engaging lesson plans we’re creating. (Mrs. Noelle, eighth-grade
ELA/Social Studies teacher)

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Data was a common topic of conversation at Beacon. From the moment that CST
results were reported in August, teachers and administrators used CST data to create
classes. In fact, the subject of data was such a critical topic that student CST scores and
performance results were publicized. Mr. Corral did this by sharing his username and
password to the district’s data analysis program, Data Director. Since teachers had Mr.
Corral’s administrative access, data was made public. Also, since collaboration existed
as a cultural norm, teacher discussions focused on the topic of student performance.
Ms. Katie, who designed the master schedule, described the process:
In the past, we usually did it by teacher recommendation. We no longer do that.
The way I was taught is, yes, I’ll consider teacher recommendation, but I’m
looking at data. I’m looking at multiple measures. I’m looking at writing
samples. I’m looking at CST scores.
The data were such an important aspect of scheduling that even became involved
in structuring classes. Ms. Katie reported that Algebra 1 teachers were helpful in the
process of creating the master schedule as they determined the ratio of advanced,
proficient, basic, and below basic students that would be divided among the classes.
According to Mr. Williams, students placed in Algebra 1 met a specific requirement. He
explained, “Coming into Algebra 1 are all the proficient students in seventh-grade plus
another third or whatever percentage who are basic.” The Algebra 1 teachers tried to
adhere to a 70:30 ratio: approximately 70% proficient and advanced, coupled with
approximately 30% basic and below basic as the makeup of their classes.
Data-driven decisions also affected ELA. Mr. Stevens described the process by
which students were assigned classes based on California English Language

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Development Test (CELDT) scores as well as CST percentages. The classes became
homogenized as students were grouped based on test scores and CST performance.
At the school level, we’ve got the homogenization of classes with students with
specific issues ending up in the same kind of class. So you’re not trying to teach
to the high, to the middle, to the low in one class. It’s kind of crazy when the
pressure’s on, as it is now, to get students more proficient. (Mr. Stevens)
As much as CST scores were emphasized for scheduling purposes, they were not
the only measures of importance to teachers. Beacon’s teachers also looked at formative
assessments in the form of common assessments used to inform teaching. Data analysis
occurred frequently in the form of common assessments. According to Mr. Williams,
Schoolwide, we created the common assessments, which was a way to force
teachers to teach in sync and to collaborate. And I think it was a solution because
it forced some teachers to look at what they do and how they do it.
The practice of utilizing common assessments was piloted by Beacon and two
other intermediate schools in the district a couple of years ago. Now, student perform-
ance on such measures was a consistent topic of conversation among Beacon staff
members. According to Mr. Cramer, the common assessments shared by Beacon
teachers offered valuable data. He explained, “We use the data off of that to decide
what’s working, what’s not working.”
The teachers used common assessments to hold themselves accountable for
covering material critically relevant to the CST. In Algebra 1, both standards tests and
common assessments included standards tested on the CST. According to Mr. Corral,
information gathered from common assessments was meant for corrective teaching. Mr.
Stevens also described common assessments as identifying the needs of students. In

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general, such assessments were used formatively to inform teaching and to provide
direction in the teaching process.
Data analysis was a result of using common assessments that contributed to
collaboration. Mr. Stevens explained this process:
Everyone sees what everyone did. And they share information. “How did you
teach this? How come your students did better on this question than mine? Did I
miss something? What do you do? How do you teach that?” And they share
information. That’s the underlying principle.
Using and sharing common assessments were parts of Beacon’s normative
practices. In fact, the cultural norm of collaboration and the practice of using common
assessments made Beacon a data-driven school.
CHAMPing
CHAMPs is the title of a “proactive and positive approach to classroom manage-
ment. It is a subset of the Safe and Civil Schools program. The term was well known at
Beacon because CHAMPing students was a schoolwide expectation, printed in the staff
handbook. CHAMPs provided teachers a classroom management plan that gave structure
for establishing routine procedures and high expectations from the first day of school.
Each Beacon teacher was provided a CHAMPs transition worksheet in the staff
handbook. This document allowed them to discuss a particular routine that they estab-
lished as a classroom norm. At the primary staff meeting, Mr. Corral discussed CHAMP-
ing sixth graders to teach them how to walk up and down the stairs properly and where to
wait for teachers before classes started. It was a critical routine for the school’s youngest
students because they were new to the school; even teachers needed to become acclim-
ated to using the two-story sixth-grade building.

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Ms. Katie referred to CHAMPs as a schoolwide practice during her formal
interview.
We CHAMP our students and at the beginning of the school year that is an
expectation of the teachers to do throughout the school year. . . . You will con-
tinue to see that not only with the teachers, but administrators will CHAMP the
students in discipline assemblies and out there during nutrition.
CHAMPing students was routine practice throughout Beacon. From the norma-
tive ways that sixth graders retrieved and shelved their social studies books, to the ways
that seventh-grade students filed in line outside their classrooms before class, to the ways
that eighth-grade students wrote Cornell notes quietly, CHAMPs was an influential
practice at Beacon because it helped teachers to define their classroom norms and
expectations.
Student Engagement
“We’ve recognized the importance of instructing our students in engaging
fashions so that learning is not boring” (Mr. Corral).
Each of Beacon’s staff meeting agendas contained student engagement as an item.
Mr. Corral and Ms. Katie described it as an expectation for classroom teaching. Thus, it
was no surprise that student engagement was also the first item under schoolwide
expectations in the staff handbook.
According to Mr. Corral, student engagement was a critical aspect of teaching
Beacon’s students. Mr. Corral explained the critical nature of engagement:
The majority of our students—even our best students—are not like we were. Our
students tend to be visual students, we were good with audio. So we need to give
them a lot more visual, they need more movement, a lot more engagement with
each other, they need more oral language.

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To find engaging practices, a common practice at Beacon was videotaping
classroom activities or teacher practices that exemplified student engagement. This
supported the importance that Beacon placed on engagement. Each month, Beacon’s
technology technician visited a classroom or teacher to obtain video exemplifying
engagement practices to show during the subsequent staff meeting. A staff meeting in
November showed an eighth-grade teacher’s maximal use of her whiteboard to provide
her students (Social Studies, ELA, and Associated Student Body [ASB]) the assignments,
standards, and activities for the week. The video provided a medium for this teacher to
describe how she utilized the whiteboard to enhance engagement for student learning.
Engagement was observed in classes at Beacon. There were instances in which
sixth- grade and seventh-grade Social Studies teachers discussed Egyptian history and
African geography, respectively, and students reflected about their reading and created
folding charts where information was drawn and written. In a sixth-grade math class, Mr.
Jefferson took his students near the multipurpose room where enlarged versions of
number lines were written on the pavement. There, he and students played games of
“Simon Says” to review fractions and number sense. In general math, Mrs. Cable used
miniature, individual Etch-a-Sketch
©
-type writing devices to review with her students.
Each student wrote using the tool and raised it in the air when answers were completed.
In eighth-grade Social Studies, a teacher allowed her students to create a board game that
described the process of Senate bills becoming laws.

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Discrepancy Related to Student Engagement
Creswell (2009) described presentation of discrepant or negative information as a
way of assessing accuracy of findings and to convince readers of that accuracy. This
process was necessary for certain findings, including Beacon Intermediate School’s
emphasis on student engagement. Although documentation, namely the staff handbook
and staff meeting agendas, administrative interviews, and classroom observations,
validated the emphasis on student engagement, a handful of observations caught practices
that were inconsistent.
In an eighth-grade class I observed a post common assessment activity. While
discussing an “easy” question, the teacher commented, “You see that, you only got one
right. It tells me you’re lazy and you want attention.” I was surprised by this teacher’s
disparaging comment. In a math class a teacher reviewed the previous night’s homework
with students. One problem at a time, the teacher demonstrated how the problems were
solved. While students sat in rows, they followed by copying the teacher’s procedures.
In near rapid-fire fashion, the teacher checked for student understanding. “How was
homework guys? Easy? You guys OK?” She received confirmation from one student in
the front center, “Hmm hmm.” I could not locate this student because the class lacked
interaction and life that existed in engaging classes. In a science class, to draw me near
to show me the day’s lesson, the teacher actually prompted me in an impolite manner:
“You, come here.” Standing by the rear door to observe the class, I was taken aback by
the condescending tone. The teacher proceeded to explain the day’s lesson. This was
after the students had started watching a video on chemical reactions from a website,

126
United Streaming. Before the video was played, the teacher prompted a student to
remove his backpack. When asked “Why?” The teacher screamed, “Because I told you
to!”
Although student engagement was an expectation at Beacon, there was already an
understanding that students had “plateaued.” The word plateau was used repeatedly by
teachers to describe student performance. One ELA teacher explained the phenomenon
during a meeting:
What were frustrated with is we’re not making growth to the extent we need for
them to pass these tests on any level. They’re just not getting it within their own
classroom either . . . even with their own performance in their room.
Multiple staff members echoed the sentiment “Our students are intermediate for
life” when describing students’ language proficiency levels. One math teacher did not
even discuss engagement as the derivative of students’ struggles. He explained,
But most of the time, really, with these students, the reason why they don’t get it
sometimes, because sometimes they’re not really focused. They’re not getting
enough practice.
In his formal interview Mr. Corral explained the nature of teaching to engage
students. “If it’s by the book, then many of the students will be bored to tears and many
of them can’t even access the book because the text is at a level they can’t read at.”
This was supported by Mr. Jefferson who explained, “I’d say the biggest thing that’s
happened, and I’ll say it’s happened somewhat in language arts, but it’s happened more
and more in math, is to set aside what any published text was saying.” Although this was
the expectation, ELA teachers relied on textbooks and student engagement was missing
in some instances.

127
Student engagement was an expectation at Beacon, but there were at least three
situations in which teacher practice did not reflect the ideal. Furthermore, teachers
described performance as having already “plateaued.” Two situations conveyed frustra-
tion with students in which teacher behavior did not draw students to the learning experi-
ence. One was a situation in which a teacher worked to model procedures for students
but was unaware that only one student displayed meager attentiveness. Also, since
student performance had “plateaued,” engagement was consistently a topic of discussion.
Writing Across the Curriculum
Paul C. Corral
Principal
Beacon Intermediate School
where the instructional focus is on . . .
Writing expository text across the curriculum!

All of Mr. Corral’s emails included the above information. It was widely under-
stood at Beacon that writing expository text was the school’s focus. Ms. Philips, the
Science Chairperson, explained, “We try to, at least the principal really tries to, reinforce
the notion that everyone’s an English teacher. So that’s the cultural norm. We know
there’s a real emphasis on the reading and writing.” In fact, the information on writing
expository texts was included in the staff handbook, written in the statement of instruc-
tional focus and in the student planner, where the program was not only delineated but its
complementary writing method was provided to students with a model.
When asked what was the school’s mission and vision, Mrs. Noelle said, “Just
promoting literacy—writing across the curriculum. Every single department has to do a
research paper, so the students are writing five papers a year.” Students were required to

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generate a research paper in each subject matter, including Physical Education. In fact,
the previous year’s Physical Education expository papers on Summer Olympic hero
Michael Phelps were still on display in Beacon’s multipurpose room during the first full
day observation in September. Furthermore, according to Mr. Corral during the primary
staff meeting, most of the student work displayed in the main office was student-
generated expository writing in the various subjects. Expository writing was also found
in the 300 and 500 buildings’ internal hallways, as well as in many ELA/Social Studies
classrooms.
Conveying the emphasis placed on expository writing was its accessibility to
students. The writing assignments were spread throughout the year, ensuring no overlaps
of submission dates between subjects. Thus, a school calendar listing months that the
writing assignment was assigned to different subjects was printed on the back of student
planners. Furthermore, since the research project was complemented with the Jane
Schaeffer writing model, which provided a color-coded, formulaic writing strategy, the
writing model was included in the “Writer’s Handbook,” a section also inserted in the
student planner.
Mr. Corral explained the value of writing expository texts across all subjects:
“Beacon’s schoolwide focus on writing expository text and doing research papers has
made a big difference in language arts growth, which hasn’t been as spectacular as our
math growth, but it has been strong.” Mr. Corral strongly supported Beacon’s writing
program, which is why it was implemented across the board, including math classes and
physical education. classes.

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Discrepancy in Writing Across the Curriculum
Observable data supported the practice of having students write expository
papers. Examples were found in classrooms, posted in the main office, and displayed in
the 400 and 500 buildings. Mr. Corral was a proponent of the writing practice; it was
announced in his district emails. Furthermore, reminding students was intensely
emphasized through descriptions and samples printed in the student planner.
However, influential teacher leaders at Beacon expressed doubts about the
influence of the writing program on student CST performance. One teacher commented
on his perceptions of writing expository texts across the curriculum:
If you talk to Paul [Mr. Corral], he’ll tell you it has a direct impact; it has to have
because expository writing’s important. But having said that, I think it could also
be argued that yes, expository writing is important, but are they getting it just
because they do five reports a year?
In his formal interview the teacher reemphasized his doubt and provided an
alternative to the practice:
In report writing, I’m not so sure that it’s having the desired impact in terms of
the students’ ability to write. They know how to do a report, but I would argue
that doing one report for 3 weeks or doing two essays per week for 3 weeks, I
think that the two essays per week for 3 weeks would be a better practice. That’s
my opinion.
Another ELA teacher expressed doubts that, although the writing program came
with a rubric, it was determined that some teachers were not using the rubric.
Does it make sense for the English department to do the writing project when the
other teachers aren’t following along? Seventh grade did it, sixth grade did not,
and eighth grade did not. Some didn’t do the colored writing; the Jane Schaeffer
method wasn’t followed.

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When asked about the influence of the writing program, an influential math
teacher commented, “I don’t think it has that much influence. For me, it’s the doing
something every other week that goes intensely just to clarify the topic.” This teacher
described using graphic organizers to help students to write paragraphs about concepts
that they learned every other week.
The practice of writing expository papers was clearly emphasized at Beacon.
Although teachers were not interviewed specifically regarding the practice, I obtained the
perceptions held by key, influential staff members. Generally, there was disagreement
with respect to its implementation or its intended effect.
Having a Routine Where There Is No Routine
I have lesson plans, but I have to write them and submit them to my evaluator
every Monday. At the end of the week, what I’ve done and what I’ve planned are
two different things. (Mr. Oliver, eighth-grade Algebra 1 teacher)
Beacon Intermediate School’s Algebra 1 department boasted 3 consecutive years
of at least 80% proficient and advanced, with growing numbers of students enrolled in
Algebra 1 (Table 4). The eighth-grade teachers assigned to teach the subject attributed
part of their success to the curriculum that they had created. In fact, Mr. Corral spoke
highly of the document when he showed it to me on my initial visit to Beacon.
According to Mr. Williams, originator of the program, the Algebra 1 curriculum
was “designed to grow.” Mr. Oliver, his eighth-grade curricular partner who worked on
the program during Mr. Williams’s hiatus, also described the program’s organic nature:
“We’re always ready to adapt to a new situation like in a matter of minutes.” Although
the document was prearranged, bounded, and distributed to students like a workbook, the

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Table 4

Percentages of Algebra 1 Students Ranked Proficient and Advanced (P&A) on the
California Standards Test

2005-2006 2006-2007 2007-2008
School % Grade 8 % P&A % Grade 8 % P&A % Grade 8 % P&A

Beacon 41.1 82.0 45.0 81.0 50.1 80.0
McKenzie 57.8 18.0 57.6 27.0 37.4 43.0
Spears 12.9 53.0 16.8 42.0 23.5 62.0
Williams 13.3 17.0 14.6 29.0 24.3 43.0
Suerte 97.0 3.0 17.6 47.0 31.3 40.0
Lawrence 27.6 43.0 44.2 34.0 44.3 38.0

actual assignments and lessons were subject to constant change. According to Mr.
Williams,
We’ll change our thinking on something that day sometimes or we’ll say, “Oh,
OK, this is what we need right now, this is what I need to do right now” and we
go to the computer and get something we can pull up and modify fast and we print
it. So, as opposed to the rigidity that goes on with using a textbook, you know
we’re all on Microsoft, everything we’ve got is on Microsoft Word. So, that
means it’s built to change as fast as we see the need.
Mr. Williams and Mr. Oliver made curricular modifications based on student
needs. In fact, Mr. Oliver explained, “We adapt it [the curriculum] every year with the
new population of students that we have.” Furthermore, based on classroom visits and
document review, Mr. Oliver provided students as many as 10 variations of correction

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sheets for the most commonly missed problems on common assessments. Thus, if a
student needed more practice on particular skills, the resources were readily available.
Mr. Williams and Mr. Oliver consistently made instructional decisions based on
assessments and data that they collected on a daily basis. In his formal interview Mr.
Oliver explained,
There is no daily routine. Every day is completely different. Sometimes, 10
minutes before class, we have an idea and we say we’re done. I mean, it’s all the
data we gather and every day, every minute, to see how the students are doing.
In fact, this quote supported an observation made in both Algebra 1 teachers’
classes. After Mr. Oliver performed an activity in which students reviewed the most
challenging problems in the most recent common assessment, he and Mr. Williams
discussed their observations regarding student strengths and skills that were lacking.
Thus, rather than cycling the same activity, the teachers talked about how they had taught
the skills to identify modifications for corrective teaching.
Beacon placed more students in Algebra 1 year after year (Table 4). Mr. Oliver
explained that, to maximize proficiency coupled with greater numbers of students, “We
have to modify the assignments, we have to modify the order in which we teach it to
some extent.” Mr. Oliver also explained that modifications were made in the actual
teaching of concepts.
We are using lots of visuals, hands on, because the students remember better this
way. Right now, we are using the generic rectangle to be able to multiply poly-
nomials. We are going back to tiles to show students we can factor using tiles.
We can build the rectangle using tiles and be able to tell the size. The problems
vary a lot depending on the day and depending what we expect students to learn.

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Mr. Oliver explained that instructional decisions were made based on whether
students understood material with manipulatives, situations in which the material was
confusing, and the various ways of making the topics easier. Mr. Williams and Mr.
Oliver thought hard about how to modify their curriculum to make it comprehensible to
more eighth graders.
The Algebra classes also practiced collaborative activities. Sometimes, collabora-
tions even spilled into the hallways, where students worked together and peer teaching
occurred. When prompted for classroom practices that support student learning, Mr.
Williams replied, “I think we tried a lot of peer tutoring.” Mr. Oliver provided an exten-
sion to the response:
Within the classroom and between classrooms also we share students. We
exchange to do activities. For example, a high kid from his class who got it, a
high kid from his class who got it, we make one big class of students we can play
a game; the other we set we do remediation.
During observations there were also times that students created posters and made
generalizations about algebraic expressions. On other days they retook assessments
while other students walked around and gave help. Thus, having variability in classroom
activities was evident. Mr. Oliver explained,
The problems vary a lot depending on the day and depending what we expect
students to learn. Sometimes, it will just be doing 10 problems, one at a time, 20
minutes like this, working around, doing a worksheet. Sometimes it will be a
group, and hands on making a poster of all the things we have to learn and how
they are different from each other. It can be many things. Sometimes we play
games.

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Since classroom routines were variable, Mr. Williams and Mr. Oliver were
prompted to explain what algebra students were expected to do on a daily basis—an
inquiry derived from the “Follow-Up Questions” (Appendix D). Mr. Oliver explained,
The day is for learning something new. The day is for practicing something they
know. Try to do lots of review. Try to go back and remember what we’ve done
and why. How does it correlate with what we’re doing now? Or can we set
things apart? Can we categorize different topics? Why are they different? What
did we do with each of them?
Mr. Williams gave a narrowed response: “Compare and contrast. This is what
we’re getting wiser at all the time, I think is cyclical review.” Thus, although there was
no classroom routine, teachers made it a point to relate new skills and concepts to those
previously learned. This was evident in the classroom as posters and mobiles described
skills that were routinely being discussed and found in the common assessments.
Mr. Williams and Mr. Oliver implemented practices that resembled practices of
Mr. Jefferson. Mr. Jefferson remarked, “I would say at least in my classroom, the routine
is there is no routine. We do different things on different days.” Each time I observed
Mr. Jefferson’s class or attempted to speak with him, his students were doing something
distinctly different. For instance, on the day of his formal interview Mr. Jefferson’s class
was performing an activity to review understanding of rational numbers. The class
convened outside the 600 building near the field and physical education area, where
enlarged axes depicted number lines. The class played a game of “Simon Says” in which
the students moved to particular numbers when “Simon called them” or simply moved up
and down the number line.

135
In another instance Mr. Jefferson’s class performed an activity in which they
discussed the difference between evaluating expressions and solving equations. A
student chose a name card from a stack and the student whose name was chosen went to
the whiteboard and attempted to complete the task. If the student was unsuccessful, Mr.
Jefferson invited both students to remain in the front to work out the problem together.
In teaching concepts, Mr. Jefferson explained that he made the attempt to perform
certain tasks repeatedly. When asked how math concepts are taught, Mr. Jefferson
replied,
I try to, in each major section, have the mathematics be taught in the course of
some time, taught repeatedly, using something visual, like whether we are draw-
ing pictures of a fraction or as well as something physical that you can touch.
And hopefully at times, something that they can actually do, whether it’s evaluat-
ing a numeric expression by taking a box and putting something in it.
When asked what students were expected to do in math classes, Mr. Jefferson
responded,
I try to make sure they’re expected to think and do. So, they will be doing stuff.
It might be physically doing stuff; it might be drawing pictures; it might be doing
a problem; but they will think and talk and do.
While these math teachers reported a lack of a routine, they clearly established
expectations of how math is learned. The teachers expected students to think and to
generate solutions that sometimes involved a physical activity, drawing and creating
models, and discussing mathematical thinking. A routine was nonexistent because the
way math was learned varied from one to another of the aforementioned pathways.

136
Discrepancy in Routine
The “routine of not having a routine” was apparent in Algebra 1 and mirrored by
the department chairperson. Mr. Corral accepted not having an established routine in
teaching math so long as it resulted in student engagement. This practice was not con-
sistent in the department.
Other Beacon math teachers emphasized homework and practice problems. In
one observation a teacher listed 39 problems that students were expected to complete
during the block periods. As I replicated the teacher’s agenda, students were checking
the answers to the previous night’s assignment listed on a sheet projected by the ELMO.
Students quietly took copious notes of the answers without discussion about the pro-
cedures required to solve the problems. During an informal conversation, another math
teacher described perceptions of the Algebra 1 workbook as a “cookie cutter” program.
Furthermore, this teacher emphasized giving students 30 to 40 problems of homework
per night—a direct contrast to the department chair and Algebra 1 teachers who did not
emphasize homework. With respect to teaching, this teacher consistently assigned
problems from the textbook. Thus, when students were practicing, the classroom was
almost entirely quiet. A teacher who did not teach sixth grade described the class routine
as providing a daily quota, having students practice problems out of the textbook, and
teaching sixth-grade standards. This response was inconsistent with the stated values
because, when the teacher was asked what kinds of problems students completed in class,
the response was, “Anything that deals with the standards.”

137
Not having a routine was observed consistently in classes taught by Mr. Jefferson,
Mr. Williams, and Mr. Oliver. They emphasized the ways that their students learned best
and the variability of practices. Although Mr. Corral lauded the process, other teachers
developed routines and emphasized practice problems. It was also evident that their
teaching was based on assigning textbook problems.
Summary
The findings related to research question 2 related to existing practices at Beacon
that influenced instruction. The prevalent practices included the important finding of
data analysis, which had the widest impact due to the support of the cultural norm of
collaboration. Also, the use of common assessments resulting in data analysis improved
teaching, which further supported the expansive influence of data analysis. CHAMPs
was a prevalent useful tool because teachers set student expectations relative to their
individual classrooms. Aside from emergent themes, there was also discrepant informa-
tion that challenged reported school practices, including engaging practices that were
observed in many classes and not in others. Writing across the curriculum emerged as a
prevalent practice but some teachers doubted its impact on student learning and others
reported variations in the means by which the expository paper was assigned. Some
influential teacher leaders reported an absence of a daily classroom protocol that students
were expected to follow, which allowed math teachers to be flexible and adjust their
teaching to student responses; other math teachers relied heavily on routines such as
bookwork and homework checking. This was an important finding because teachers who

138
relied less on routinized practices were responsible for the elevated Algebra 1 CST
scores.
Findings for Research Question 3
Research question 3 asked, What programs, employed within the school, are
perceived to have narrowed the achievement gap? Research findings emerged related to
the research question relative to programs: (a) use of Data Director, a tool that teachers
used to view and monitor student progress; (b) the schoolwide grading program; (c) ELA
and Math programs consisting of two-period blocks; (d) a spreadsheet program to collect
and disaggregate student data in ELA; (e) the effect of the Algebra 1 program on raising
student math achievement at Beacon; and (f) the Algebra 1 program’s standards sheet to
track student progress.
Data Director
Paul [Mr. Corral] has made it very clear to staff that the information on Data
Director is open to everyone. And he will publish it and I will publish the
benchmarks for all the teachers to see it. So you can’t hide. (Mr. Stevens, ELA
Department Chair)
Beacon’s collaborative culture and use of common assessment made it a data-
driven school. Data Director reinforced this status. Data Director is a web-based
program that collects student performance on the CST and CELDT. Among other things,
it provides staff with a pivot table that allows teachers to view sliders, stickers, and
gainers. Sliders were students who dropped at least one level of proficiency from one
year to the next year. Stickers were students who “stuck” to their level of performance
from one year to the next. Gainers were students who earned higher proficiency levels
from one year to the next.

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According to Mr. Corral, his Data Director username and password were given to
all teachers and staff members. During his formal interview Mr. Corral explained, “On
Data Director, I share my sign in with everyone because I want them to know that they
can look at everyone’s data.” Mr. Corral had made it clear to Beacon’s staff that student
performance data was thus accessible not only for administrators but also for fellow
teachers. Thus, there was no hiding from poor student achievement, since data were
publicized. Furthermore, the practice reinforced teacher collaboration because there was
awareness of teacher effectiveness.
The SPSA conveyed Data Director’s dynamic nature. Through it, teachers were
able to view not only past student performance but current students’ CST, CELDT, and
common assessment performance also. Thus, teachers charted student performance and
identified strengths and weaknesses. Mr. Stevens explained,
You know right from the get go, from the beginning of the year, teachers are told
to download their data and create their seating charts or create their class analyses
based on those [student information on Data Director].
Grading Program
We like the grading system. And you know about the grading system, right?
How hard are you trying and what do you know?” (Mr. Williams, eighth-grade
Algebra 1 teacher)
Beacon Intermediate School’s grading program gave teachers the tool to track
students’ standards-based grades. According to the SPSA, the standards-based grade was
based on the CST grading system. It was instituted with the intent of having predicta-
bility of student performance on the standardized tests. According to Mr. Corral,
Beacon’s common assessments have a 71% correlation to the CSTs.

140
The program (Table 5) was printed in the staff handbook for accessibility to
teachers. It was piloted a couple of years ago, along with two other intermediate schools
in the district. It components were the following: a performance grade, a standards-
based grade, and a citizenship grade.

Table 5

Grading Program

Standards-based grades Student performance grades Citizenship grades

AD Advanced 85%+ 5 Student’s work/
effort is
advanced
90%+ 5 Outstanding
PR Proficient 65%-
84%
4 Student’s work/
effort is
proficient
78% -
89%
4 Above Average
BA Basic 54%-
64%
3 Student’s work/
effort is basic
64% -
77%
3 Satisfactory
BB Below
Basic
27%-
53%
2 Student’s work/
effort is below
basic
50% -
63%
2 Needs
Improvement
FBB Far Below
Basic
0%-
26%
1 Student’s work/
effort is far
below basic
0% -
49%
1 Unsatisfactory

Beacon’s inclusion of the standards-based grade was supported by cultural norms
of collaboration that included the practice of discussing student performance and data.
Student data were used to inform teaching and CST scores were used to plan instruction.

141
The inclusion of standards-based grades provided conversation focus as teachers dis-
cussed overall performance as well as performance specific to the state test.
The grading program was important because it gave the teachers a unique dis-
course to describe student achievement. Mrs. Noelle explained this phenomenon:
Strategic, intensive, and benchmark. And benchmark: Those are our students who
are proficient or advanced. And then strategic, as far as older terms, they’re
below basic and basic. And then intensive is far below.
Two-Period Blocks of ELA/Math
We’ve got a lot of extra time in class. The school structured it that way about 7
years ago. And I think it has been a slow process of finding ways to use the extra
time effectively rather than just doing more of the same. (Mr. Jefferson, sixth-
grade teacher and Math Department Chair)
According to Beacon’s SPSA, the math programs and ELA were given emphasis
by being allotted two periods. Due to the emphasis on these subject matter areas,
electives are virtually nonexistent at Beacon. The “block” was intended to enhance
instruction rather than just giving teachers more time to work. Mr. Williams expressed
the challenge of having two periods: “With the two periods we have every day, how do
we make a variety of activities, you know, review, new stuff, assessment, keep it
dynamic?” In responding to the interview question specific to programs that have
narrowed the achievement gap, Mr. Jefferson said,
People are getting more used to, as I said, using our time by having a variety. It’s
easy to do a small number of things only when you’ve got 42 minutes. You say,
“I’m sorry, that’s all I’ve got time for.” When you suddenly have 90, you’ve got
time to do all that. The more of that variety you use, the more of that 90 minutes
you use effectively.
Having an ELA block supported flexibility in use of instructional methods and
use of student data. Mr. Stevens supported this in discussing practices to help struggling

142
learners in ELA. “You’re going to have to have some standby methods for these
students. Either extra time or a different approach, different explanations, reviews, have
them prepared, all that kind of stuff.” A block of ELA was helpful in this regard.
Mrs. Noelle described the value of having a block of ELA in addition to teaching
Social Studies. First, she mentioned that some students who were not yet proficient at
Language Arts received a lighter version of Social Studies instruction to improve skills in
reading and writing. Since almost all, with only one exception, of Beacon’s ELA
teachers also taught Social Studies, the opportunity to provide one subject extra time over
another was feasible. Furthermore, Mrs. Noelle described the opportunity to provide
students a varied learning experience that depended on student needs. During her formal
interview Mrs. Noelle said,
My main thing is I try to do a variety of activities. As a teacher, I need variety
just to keep me excited about teaching. . . . So the neat thing is what was taught to
me in the credential program, which is changing gears. Doing at least three
different things in a period. So just variety . . . . So, it cannot just be about the
textbook, let’s read it and answer questions. Students are not into learning like
that. So, you have to have some engagement activities.
Mr. Jefferson also talked about the value of extra time and its benefits for flexible
instruction. In math, he described it as time not used for repeated activity. Rather, time
was used effectively in providing students opportunities to think.
I think it has been a slow process of finding ways to use the extra time effectively,
rather than just doing more of the same. Because if you just do more problems,
writing down more problems, the teacher does, or someone else does, and they
write it down, it doesn’t really help that many more people. It’s doing more
variety of getting them to think, rather than just write. So to the extent that we
have, over time, more people involved in thinking and doing in class, it’s getting
better.

143
According to Mr. Corral, the block of math and ELA provided teachers flexibility
in their practices. For instance, there was more time to be creative in engaging students.
Also, having two periods of math or ELA was a benefit because it provided teachers the
opportunity for corrective teaching. Having time for corrective teaching was important
because of the opportunity to regroup students and teach them according to their level of
understanding, as opposed to trudging ahead to new concepts and skills. Mr. Corral also
explained that he felt that this was better practice than providing students support before
school, after school, or in Saturday school.
Use of Spreadsheets to Collect and Disaggregate Student Data
In response to the researcher’s observation, “Oh, so this isn’t a special program,
it’s just a spreadsheet?” Mr. Stevens explained, “It’s just Excel. But I’m damn good.”
To support teachers in their collaboration surrounding common assessments, Mr.
Stevens used the Microsoft
®
Excel
®
program to create a data analysis sheet for all ELA
grade levels. According to Mr. Stevens, ELA teachers provided him with item analysis
cards that they used as answer sheets for student common assessments. He entered the
data into the program to provide teachers a visual representation of student performance.
These spreadsheets were important because they contained data that supported Beacon’s
data analysis practice and reinforced the collaborative cultural norm.
Mr. Stevens was creative in the way he programmed the spreadsheet to provide
the type of data that would be user friendly to teachers. He described color coding that
helped teachers to identify students who were meeting proficiency based on common
assessments. For instance, he explained, “These color codes are telling these particular

144
teachers these classes on these standards are bombing. Black is below basic and far
below basic, red is basic, yellow is proficient, and green is advanced.”
In discussions with ELA teachers, common assessments were identified as a
common practice at Beacon. Therefore, the spreadsheets were useful. According to Mr.
Stevens, “We analyze it [data] every time we take a common assessment. We take the
common assessment, we take the data, we analyze it, we look at it.” Mr. Steven’s
spreadsheets had a great impact at Beacon because their data became a focus of
collaboration, which informed teaching, which directly influenced student learning.
Effect of Algebra 1 on Raising Student Achievement
Almost all of those textbooks and programs are trying to be teacher proof. The
more they try to be teacher proof, they’re unresponsive to the actual students in
the classroom. Because they’re trying to be designed that they can be run without
thinking. But you have to think about who you’re talking to and, when you’re
getting a blank stare, do something else. (Mr. Jefferson, Math Department Chair)
In contrast to the other middle schools in the district, Beacon Intermediate School
scored consistently higher in math than ELA, according to the SARC (Table 6).
When asked what had allowed the school to narrow the achievement gap, Mr.
Corral said, “I would say our Algebra 1 program, which has been Beacon designed and
built, has been the single most influential thing.” The math department chair, Mr.
Jefferson, explained the divergent challenges between ELA and math at Beacon and
offered his belief as to why math generally performed better:
Math is a modeling of physical reality. So it’s easier to take advantage of that
physical reality than language usually is. So it’s been harder for them, but I think
to some extent, they have thought about this is what we want people to know. But
that has happened even more so in math. I think it’s really why, compared to
other schools in our district, most other schools, English and math are close or

145
Table 6

English-Language Arts (ELA) and Math Results for All Students: Three-Year
Comparison

2005 2006 2007
School ELA Math ELA Math ELA Math

Beacon 23 37 24 39 32 45
McKenzie 20 21 23 18 31 26
Spears 15 15 19 19 22 28
Williams 14 13 16 11 19 22
Suerte 13 12 17 17 20 20
Lawrence 16 21 16 18 19 22
District 26 27 28 29 32 33
State 42 40 43 40 46 43

math is behind. At ours, math is dramatically above and I don’t know that
English could do the same thing.
Each year, Beacon Intermediate School bound the published Algebra 1 program at
the district office. Mr. Williams created the program 4 years earlier before he left
McKenzie Intermediate School, one of Beacon’s neighboring middle schools and began
his teaching career at Beacon. The current program is organic because of the hours of
effort that Mr. Williams and Mr. Oliver have put to its continual improvement and
reformatting for student needs.
All I think we’ve really accomplished in math—well, we’ve accomplished a lot,
because we put a lot of work into it. Our algebra has 10,000 hours in it—10,000

146
hours of thinking and producing at this point. I think we’ve just accomplished
what should have always been there: an organized curriculum designed at the
level that teaches things clearly. (Mr. Williams)
The Algebra 1 program impacted student learning at Beacon because, rather than
recycling the same lessons on a yearly basis, activities and instruction were modified for
the current students. According to Mr. Oliver, he and Mr. Williams made modifications
based on their discussions in the morning and afternoon. Mr. Oliver explained their
thought processes and why they changed activities:
What could we do with those kinds of students? With this topic? And then things
change all the time. This year, I’ve been changing lots of what’s in the work-
book; it didn’t match what the students were expecting. But we set the students
what we have. They need something different from what I used last year in a
number of classes, so I had to change things.
In his formal interview Mr. Jefferson shared his view about the elements that have
led to the Beacon’s overall rising test scores. “I’d say the biggest thing that’s happened,
and I’ll say it’s happened somewhat in language arts, but it’s happened more and more in
math, is to set aside what any published text was saying.” The Algebra 1 curriculum was
exactly described by Mr. Jefferson because it was created and continually improved by
Beacon’s teachers, as opposed to originating from a published textbook.
Green Light
The Algebra 1 curriculum had a complementary algebra standards sheet that
impacted student performance. The document was colored red, green, or yellow by
students, depending on their performance on a standards test. Mr. Williams and Mr.
Oliver listed all Algebra 1 standards on the document, allowing students to track their

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progress. According to Mr. Oliver, “It’s been able to target the students who are learning
slowly or not learning at all.”
The standards sheet included printed concepts and skills directly related to
Algebra 1 standards. Furthermore, there were nine columns next to each standard to
provide space for students to indicate their performance on that specific standard. When
a student answered a question on a standard correctly, that student colored that space
green. If the student answered incorrectly, the space was colored red. If a student
answered some samples of the standard correctly and others incorrectly, then the space
next to it was colored yellow. Each standard contained nine spaces that allowed students
opportunities to color a space green in the situation in which multiple attempts were
needed. Coloring the space next to a standard green indicated “green light”: mastery of
the skill. “Green light” was also figurative, symbolizing the right to proceed to the next
standard. Furthermore, “green light” indicated the opportunity to focus effort; for some
students, multiple attempts were required to master the skill.
[The standards sheet] also works for the students who have lots of green on their
chart. I mean, they like to show us that they are all green. They like to see that
they are all green, that they are learning. The ones who are not learning cannot
hide it. I mean it’s red, it’s in front of their faces. (Mr. Oliver)
For the students who were not performing well, the “red light” was a clear, visual
reminder to ask for help, to remain in the classroom during lunch, nutrition, or after
school, to earn a green color with extra attempts.
Since Algebra 1 classes were in blocks, students had multiple opportunities to
retake different versions of assessments in hopes of learning that standard and coloring
the space next to it green on the standards sheet.

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[Students] know, they understand and this is the most visual way to tell them,
“Look here, it’s taking some time, but we’ll get there. You’ll have many more
colors, many more tests, and what we want is by the month of May, we are ready
to take the CST.” (Mr. Oliver)
This section reviewed programs that were perceived to have helped to narrow the
achievement gap: Data Director, the grading program, a block of ELA and Math per day
for students, the use of spreadsheets, and the creation of an Algebra 1 curriculum. Of
these findings, two created the most impact on student learning. One of Beacon’s most
influential programs was the creation of the spreadsheets that contained student perform-
ance on common assessments. This was a critical finding because they contributed to
Beacon’s collaborative norm as well as data analysis practices, which as a system worked
to reinforce each other. The most important finding was the influence of the Algebra 1
program in contributing to Beacon’s overall academic success. While all of the other
schools in the district demonstrated higher ELA scores on the CST, Beacon displayed
higher percentages in mathematics, where Algebra 1 scores were at least 80% proficient
and advanced for 3 consecutive years.
Sustainability
I think we were picking the low-hanging fruit, as Patrick would say. It’s easy to
go up fast, if you do all the easy things, all the no-brainer, easy things. It’s going
to get tougher and tougher if we reach into all the lower students we have. (Mr.
Williams)
Spending more time at Beacon revealed that student academic achievement had
stagnated. This was reflected on the 2008-2009 API scores, reflecting that Beacon
Intermediate had experienced a decline of 25 points (Table 7). Mr. Corral explained the
phenomenon:

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Table 7

Academic Performance Index (API) Scores and Rankings for Beacon Intermediate
School, 2005-2009

2005-2006 2006-2007 2007-2008 2008-2009

API 680 692 731 706
Statewide rank 4 4 5 n/a
Similar Schools rank 10 10 10 n/a

I want to tell you that our drop in API was highly attributable [to] Algebra 1
scores; it went from 80% proficient and advanced to 55% proficient and
advanced. . . . That drop was almost responsible for our drop in API.
The most striking difference between Beacon’s score during the previous aca-
demic year and the prior scores was the disparity in algebra proficiency percentages and
the 1-year absence of Mr. Williams. Mr. Williams left Beacon during the 2008-2009
academic year. This was the school year that Beacon Intermediate School broke its string
of 3 consecutive years with at least 80% proficient and advanced on the Algebra 1 CST.
This significantly impacted the API, as Beacon’s API decreased due to the major decline
in Algebra 1 percentages during Mr. Williams’s absence (Table 8).
Complementing Mr. Williams’s departure was the challenge for Mr. Oliver to
mentor a first-year teacher and Mrs. Cable, who had experience in teaching in an affluent
part of the county. Although Mr. Williams was not at Beacon, he was kept abreast of the
situation.

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Table 8

Beacon Intermediate School’s Percentages of Proficient and Advanced Scores for
Algebra 1 on the California Standards Test, 2004-2009

2004-2005 2005-2006 2006-2007 2007-2008 2008-2009

55 82 81 80 54

Mr. Oliver had his hands full, just keeping those guys going. Essentially, [Mr.
Oliver] was just the fountain from which resources flowed and they executed
what he was giving them. But that was in terms of collaboration, that was all
there was really time for.
The rookie teacher was not retained and (as shown by document review)
specifically Data Director’s disaggregation of student performance in Algebra 1, Mr.
Oliver’s 66% proficient and advanced percentage contribution to Beacon’s overall
Algebra 1 CST percentage was already insufficient to match the previous year’s 80%.
When Mr. Williams returned after undergoing an interview process and retaining
his former position and classroom, Mr. Corral felt positive that Beacon would retain high
percentages of proficiency in Algebra 1. In fact, it was made explicit that Mr. Corral’s
expectation for 2009-2010 was 85% proficient and advanced with more students enrolled
in algebra.
To explain their success, Mr. Williams described having a critical mass of
teachers with a desire to participate collaboratively in building improvement in teaching.
I think that you have to get yourself to a place where there’s a critical mass of
teachers who want to collaborate and want to work hard. . . . Because most math
departments don’t have that critical mass of teachers who are really on the same

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page, thinking progressive thoughts about how to make things better. Plus there’s
all the limitations districts are imposing now. Where the innovation that people
might be more willing to explore in the past, have been slammed by “We shall do
this on this day and this way,” which makes it really comfortable for the tradi-
tional teachers. . . . It’s like working on a textbook, right? I’m told I gotta do this
this way on this day, which is essentially what the teacher’s edition used to be.
Since Mr. Williams and Mr. Oliver resumed collaboration and shared their prac-
tices with Mrs. Cable, Algebra 1 has displayed potential for recovery and sustainability of
high student outcomes. Furthermore, the Algebra 1 teachers accepted Mr. Song, a
general math teacher hired after the academic year had begun. Mr. Corral explained that
Mr. Song “fit right in” with the eighth-grade teachers. In fact, although Mr. Song was not
formally interviewed by this researcher, he was observed consistently collaborating with
Mrs. Cable, Mr. Oliver, and Mr. Williams, and even Mr. Jefferson.
Although collaboration contributed to success in Beacon’s data-driven culture,
some teachers described a plateau phenomenon.
Based on what I’ve observed, the school still has a lot of room for improvement
. . . . I know the message the past 2 years from Mr. Corral was, “Let’s try to
squeeze as much out of the students as we can.” . . . We’ve gotten the students
who were easy to pick. You know, it’s those hard-to-reach students now. . . . It’s
gotten harder now because we plateaued. (Mr. Garcia)
In his formal interview Mr. Cramer cited something similar: leveling of student
performance as a phenomenon in ELA.
Language arts, we’re kind of like this—you know, we have a good year and we
plateau, then maybe that plateau will stay, and then we have a dip, and then we’ll
have another good year.
When I discussed ELA with an influential teacher leader, the response alluded to
stagnation:

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The problem is we’re doing the best we can. . . . There’s a term that they use in
certain circles referring to these students who are intermediate level CELDT. . . .
These students are called intermediate for life because they’ve hit intermediate,
and nothing else happens.
Mr. Corral viewed the “plateauing effect” as a concern. He shared that Beacon
had finally been outperformed by one of its sister schools in ELA in the past academic
year (Table 9). Thus, before Thanksgiving break, Mr. Corral, Ms. Philips, and Dr. Allen
considered a consultant’s proposal to buffet Beacon teachers with data analysis training.

Table 9

Percentages of Students in English-Language Arts Who Scored Proficient or Advanced
on the California Standards Test at District Schools, 2006-2009, by Grades 6, 7, and 8

2006-2007 2007-2008 2008-2009
School 6 7 8 6 7 8 6 7 8

Beacon 24 27 21 32 31 31 29 35 29
McKenzie 22 24 23 31 37 25 31 41 36
Spears 15 18 17 19 19 20 26 21 21
Williams 18 16 15 22 20 16 22 20 16
Suerte 12 19 20 16 25 25 29 29 20
Lawrence 14 16 18 14 21 20 17 22 20

Ms. Philips, the proponent for seeking external resources to raise student
achievement, explained, “We need a culture where we can diagnose the problem and
apply a treatment. Otherwise, it’s hit and miss.” Although the university professor

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offered to provide training to the entire staff, Mr. Corral agreed to invite the consultant to
work only with the sixth-grade ELA/Social Studies department.
Although Beacon experienced higher ELA proficiency levels than its sister
schools, its most recent API displayed stagnating scores, which prompted the staff to seek
outside consultation. Algebra 1 was led by a critical mass of teachers who fit together,
work hard, and collaborate. Improvement, not sustainability of test scores, was beyond
the reach of Beacon’s ELA staff. Simply collaborating was no longer enough; ideas from
external sources were required to stimulate the ELA department. Algebra 1 was in a
better position for both improvement and sustainability, given its leadership and staffing.
Discussion
The goal in each visit to Beacon Intermediate School was to blend in, to be a “fly
on the wall,” and to gain insights regarding the cultural norms, practices, and programs
that the school employed to narrow the achievement gap. Over time, this occurred as
staff accepted casual conversations, expeditious morning greetings, and invited observa-
tions and chats. Between the second week of September to the day before Thanksgiving
break, I accumulated approximately 9 full and partial-day visits to the school site.
Overall, this provided ample opportunities to identify elements conducive to Beacon
Intermediate School’s academic success.
Discussion of Emergent Themes
I think I know the other cultural norm, too is, I know amongst ourselves, we have
a goal. And our goal is we are going to be better than we were last year. We are
going to be stronger than we were. We are going to build on what we know.
We’re not a hang on and let’s just do the same thing over and over again kind of
place. (Dr. Allen, seventh-grade ELA/Social Studies teacher)

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Beacon Intermediate School has experienced academic success because of
specific factors on its campus. The major themes that emerged from data analysis were
as follows:
1. Leadership was distributed among staff and key individuals who contributed to
make a difference.
2. Teacher collaboration was a cultural norm that supported the practice of data
analysis.
3. Data analysis was a common practice, with specific program supports in ELA
and Algebra 1.
4. The teacher-created Algebra 1 curriculum was instrumental in Beacon
Intermediate School’s API.
Leader of Leaders
Mr. Corral was heralded as a leader of leaders. Numerous staff members referred
to him as such through interviews, and survey data indicated that leadership was shared
by school personnel. Specific staff members who played critical roles in Beacon’s
success were identified.
Elmore (2005) discussed accountable leadership as distributable leadership.
Specifically, he described leadership as being distributed according to expertise as
improvement practices develop within an organization. This description can be framed
within the phenomenon occurring at Beacon Intermediate School.
First, the Algebra 1 program, which produced scores consistently above Beacon’s
ELA program, as well as scores at other schools within the district, was placed in the

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hands of Mr. Williams, who created an organic program. Mr. Williams, a key leader at
Beacon, described the Algebra 1 program as a curriculum that “builds on itself”; it was
shared with Mr. Oliver, who continued its improvement throughout the years, including
during Mr. Williams’ single-year absence. Mr. Corral has provided these math teachers
undeniable support to improve their program continuously.
In ELA, Mr. Stevens, another key leader, was the ELA Department Chair and was
granted a TOSA role that allowed him time to create data analysis tables for ELA
teachers. These data analysis tables became the focal points of discussions, according to
interviews, and were supported by Beacon’s data-driven culture per survey data. The
culture of collaboration was supported by data analysis sparked by Mr. Stevens’ efforts in
creating a spreadsheet containing student performance on common assessments.
When a consultant from a nearby California State University campus gave a
presentation on data analysis and the means by which she would train teachers to utilize it
to produce higher student outcomes, Mr. Corral called on two of his teachers to sit in the
meeting to provide input. One was Dr. Allen, a seventh-grade ELA/Social Studies
teacher who had recently earned a doctoral degree from University of California, Los
Angeles, and Ms. Philips, a seventh-grade science teacher working on a doctorate in
education. Ms. Philips was also the influence behind using the services of the consultant
to create a more data-driven culture within the organization.
Mr. Corral allowed teachers to contribute within their expertise. In fact, he
encouraged it. Mr. Jefferson, another key leader, demonstrated this consistently as he
provided resources and support to math teachers and reinforced certain practices in math.

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In general, teachers contributing within their expertise gave other teachers the oppor-
tunity to employ their skills to improve conditions at the school with respect to student
learning.
Teacher Collaboration
Teacher collaboration was easily observable at Beacon. As Mr. Stevens
explained, collaboration was something that “happened all the time” and “could be heard
in the halls.” Teacher collaboration sometimes occurred as frequently as every class
period and passing period in Algebra 1. It was also something as informal as Dr. Allen
traversing the campus to visit various ELA teachers to assist with grading as her co-
teacher substituted for her. Collaboration was also as informal as eighth-grade Transi-
tional Math teachers meeting after school in Mr. Jefferson’s classroom to get ideas as to
the best way to teach particular skills.
Data-Driven Culture
Beacon’s cultural norm of teacher collaboration had a reciprocal relationship to
the practice of data analysis. Their combination fueled Beacon’s data-driven culture.
The genesis of Beacon’s data-driven culture could be attributed to Mr. Corral’s decision
to provide the entire staff his password and username to Data Director, the school’s web-
based data disaggregating system.
Data analysis was a common practice reinforcing collaboration because the
teachers consistently had discussions focusing on student performance data to improve
practices. These practices were both informal as well as structured. Informal practice of
data analysis occurred between classes or during the nutrition period, when Algebra 1

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teachers talked about student understanding to fuel lessons, activities, and math experi-
ences. Structured practice of data analysis occurred during Course-Alike Meetings in
which discourse focused on ELA common assessment scores and how to improve
teaching.
Algebra Curriculum
As more eighth-graders enrolled in Algebra 1, Beacon’s Algebra 1 CST scores
were consistent. According to Mr. Corral, the goal was to get “at least 90% of the
students in Algebra 1 with 90% of them earning proficient or advanced” on the state test.
For 3 consecutive years, Beacon had scores of at least 80% proficient and advanced as
the number of enrolled students increasingly exceeded 50%.
The Algebra teachers had curricular autonomy. In essence, they were not
restricted to the existing district pacing guide. The Algebra teachers created their own
curriculum, complementary standards assessments, and common assessments, and
managed their own pace throughout the year. With a daily block of math in which to
work, there was flexibility in the activities and experiences that students had with the
content. Mr. Corral had placed laser printers in their classrooms, so the Algebra teachers
could modify instructions to meet the needs of the students instantaneously. During his
formal interview Mr. Williams described the variability and growth of the Algebra 1
curriculum as hinged on student responses. Thus, preplanned lessons were not always
linearly followed because teaching was modified based on what the students were able to
do. Mr. Williams explained, “It’s designed to grow. That’s why we insisted on having
printers in our room.” By having printers, Mr. Williams and Mr. Oliver could modify

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assignments, specific problems, and preplanned activities with the ease of printing them
almost instantaneously.
The Algebra 1 curriculum would not be enough to raise student achievement in
Algebra, especially at the rate it had produced in the past, without the culture of
collaboration. Mr. Williams, Mr. Oliver, and second-year teacher Mrs. Cable con-
sistently monitored and discussed student progress and understanding. Since Mrs. Cable
did not teach the same number of Algebra 1 sections as her colleagues, she checked in
with Mr. Oliver, the BALT leader for Algebra 1, in the morning and after school.
I talk to Mr. Oliver every day . . . I tell him where we are, what went right, what
went wrong, sometimes I share those ideas with Mr. Oliver. And he would tell
me, “By the way, did you try this or this, I know my students did the same thing.
Maybe you want to try this way.” So we share those ideas. (Mrs. Cable)
Because the Algebra 1 teachers had curricular autonomy, they were able to
modify their instruction practices to meet the needs of their students. Mr. Jefferson, the
Department Chair, agreed with this practice.
Just the sheer amount of energy it takes to say, “Look at me and say something.
You know, you have to talk. You can’t just sit there and write what I write.” And
not talk to me; I’m not going to accept the, “I’ll be a good boy and just write stuff
down.” It’s just not enough. There’s this dragging people sometimes in.
Since Mr. Oliver and Mr. Williams designed their own curriculum, they were not
restricted to manufactured published curricula. Thus, the activities were more engaging
and required hands-on activities, as observed in the Algebra 1 classes. These problems
were not the procedural problems that Stigler and Hiebert (2004) discussed, in which
most student effort is expended in solving rote problems. Furthermore, these classes

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were sometimes “chaotic” because students were up and about, some working in the
hallway but doing math.
Algebra 1 at Beacon was successful because Mr. Williams and Mr. Oliver
expected students to construct mathematical knowledge in various modalities such as
manipulatives, posters, and the creative projects. They also expected students to show
comprehension in multiple ways, such as verbal discourse, written explanations, and
execution of procedures. During collaborations Mr. Williams and Mr. Oliver discussed
means of improving instruction to produce student learning and the most effective teach-
ing that results in student learning. They also discussed ways that students can best
represent mathematical knowledge of the standards being taught, as well as the means by
which students explain their mathematical thinking. If students did not grasp concepts,
Mr. Williams and Mr. Oliver discussed ways of modifying their practices to execute
corrective teaching that provided students another representation of the concept rather
than teaching the standard in the same unsuccessful manner.
Carpenter and Lehrer (1999) explained that classrooms conducive to learning for
mathematical understanding provide students opportunities to develop mathematical
relationships, extend and apply mathematical knowledge, reflect about mathematical
experiences, articulate understanding, and take ownership of mathematical knowledge.
These classroom elements are consistent with those practiced by Mr. Williams and Mr.
Oliver, who expected students to construct knowledge, explain thinking in various ways,
display understanding in multiple ways, and perform on standards-based tests. In

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essence, the Algebra 1 teachers at Beacon created a classroom environment conducive to
learning for mathematical understanding.
According to Carpenter and Lehrer (1999), classrooms where learning with
understanding occurs invite students to construct relationships between new ideas and
processes already understood; extend and apply mathematical knowledge less susceptible
to forgetfulness; reflect about learning experiences in order to reorganize knowledge in
coherent ways; articulate understanding verbally, through writing, and through pictures
and diagrams; and making knowledge one’s own in order to develop a personal invest-
ment in learning. Mr. Williams and Mr. Oliver created a curriculum designed for
students to articulate mathematical thinking constantly, invite students to construct
relationships and organize thinking in ways that are comprehensible. Algebra 1 was
successful in raising student CST scores because of instruction, the administrative
support, and the sustained curricular that autonomy granted to teachers.

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CHAPTER 5
SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS
The purpose of the study was to identify cultural norms, practices, and programs
perceived that contributed to narrowing the achievement gap at an urban school. This
was an independent study, one of nine coordinated case studies, that had a theme of urban
schools that have narrowed the achievement gap. The emphasis of the study was on
middle school achievement, particularly in the area of math and algebra.
There is a persistent academic disparity between White and Asian students and
ethnic minority, ELL, and low-income students. Since this issue exists, it is critical to
identify elements within a high achieving urban school that have contributed to academic
success for benchmarking, to identify models of effective practices, and to provide
evidence to generate or sustain hope that historically underserved students can experience
academic success. With regard to math education, the study can contribute to analyses
and comparison of curriculum, instruction, and assessment; studies of relationships
between teaching, instructional materials, and learning; and study of the impact of policy
on equity and student learning, which are elements of algebra research agenda offered by
Ball (2003).
Three research questions guided this study:
1. What cultural norms, practiced within the school, are perceived to have
narrowed the achievement gap and sustained success?
2. What practices employed by the school are perceived to have narrowed the
achievement gap and sustained success?

162
3. What programs employed by the school are perceived to have narrowed the
achievement gap and sustained success?
Beacon Intermediate School’s cultural norms, practices, and programs had much
to offer toward narrowing the achievement gap in urban schools. Haycock (1998a,
1998b) contended that effective teachers are critical for student learning and student
performance. This was a finding at Beacon, where key teacher leaders contributed to
growth in ELA and Algebra 1 achievement. Furthermore, it was Beacon’s collaborative
culture that allowed these teachers to influence and promote practices that impacted
student learning to drive student performance.
Ball (2003) stated that American schools must improve the teaching and learning
of math because historical gaps in proficiency across societal groups have not yet been
eliminated. The elevated Algebra 1 percentages that Beacon achieved on the CST
provided evidence of effective teaching and learning of math. This is valuable to
literature on the achievement gap because Algebra 1 is considered to be a gateway to
higher education and successful participation in a democratic world (Ball, 2003;
Edsource, 2009b; Kriegler, 2001). Furthermore, middle school mathematics is critical for
students whose motivations toward math crystallize into adulthood during the middle
grades (Middleton & Spanias, 1999).
Summary of Findings
The study identified factors that contributed to student achievement at Beacon
Intermediate School. Clearly designated themes fueled the narrowed achievement gap
and high student performance in Algebra 1: (a) leadership and key individuals making a

163
difference, (b) teacher collaboration, (c) data analysis of student assessments, and (d) the
impact of the Algebra 1 curriculum. All of these factors were intertwined and supported
student achievement, with some having more impact than others.
Leadership was a critical factor that contributed to Beacon’s academic success.
Mr. Corral, the principal, was a proclaimed leader of leaders and provided teachers
opportunities to assume leadership. For instance, he positioned key individuals in
particular roles where those teachers not only reinforced collaboration but also influenced
practices and development of programs that impacted student learning and performance.
Leadership was a research finding that was consistent with literature. According to
Marzano et al. (2005), the role of educational leadership is critical, as a highly effective
school leader can create a dramatic impact on the overall academic achievement of
students. Furthermore, input is a responsibility of a school leader related to principal
leadership, in which the principal involves teachers in the design policies and imple-
mentation of critical decisions (Waters et al., 2004).
The impact of teacher effectiveness is more pronounced than other influences of
achievement such as race, poverty, or parent involvement (Carey, 2004; Lee, 2002). This
was a major research finding at Beacon Intermediate School. At Beacon, three influential
teachers were Mr. Williams, Mr. Stevens, and Mr. Jefferson. These teachers’ efforts
fueled Beacon’s academic achievement positively. Mr. Williams was the architect of the
Algebra 1 program that produced 3 consecutive years of elevated proficiency—82%,
81%, and 80%--with increasing numbers of enrollees in Algebra 1. Mr. Williams made a
large impact at Beacon because the Algebra 1 program that he had created was organic

164
and was consistently modified to meet the needs of current students. Students sometimes
made posters, worked collaboratively, made generalizations about their learning and
wrote their thinking in words, or even took quizzes multiple times to earn a perfect score.
Mr. Williams’s classroom practice and Algebra program were consistent with the litera-
ture. According to Carpenter and Lehrer (1999) classrooms where learning with under-
standing occurs invite students to construct relationships between new ideas and pro-
cesses already understood; extend and apply mathematical knowledge less susceptible to
forgetfulness; reflect about learning experiences in order to reorganize knowledge in
coherent ways; articulate understanding verbally, through writing, and through pictures
and diagrams; and make knowledge one’s own in order to develop a personal investment
in learning.
Reducing the achievement gap requires, in part, determining which teachers are
most effective (Peske & Haycock, 2006) to identify practices that are conducive to
student learning. Mr. Stevens supported Beacon Intermediate School in this process as
he generated a program that allowed teachers to identify colleagues who were practicing
instructional methods that resulted in student learning. Mr. Stevens created a spreadsheet
and program that disaggregated student ELA scores on common assessments and distri-
buted results to ELA teachers. This data analysis program reinforced collaborative prac-
tices at Beacon. Since ELA teachers were provided student data results from common
assessments, teachers’ discourse during collaboration became focused on data analysis
and improvement of instruction. This is important because Clark and Estes (2002) cited
insufficient knowledge and skills as one of the three major causes of performance gaps.

165
Teacher quality is a critical influence on student achievement (Hollins & Torres
Guzman, 2005; Rivkin et al., 2005), which is why Mr. Jefferson was influential at
Beacon. Mr. Jefferson was Beacon’s Math Department Chair and a Mathematics
Methods teacher at a nearby state university. He was a key leader in that he provided
resources and support to his colleagues, namely ideas and concrete activities to employ in
classrooms. Although Mr. Jefferson did not teach Algebra 1, he was a wealth of knowl-
edge in the area of math pedagogy and was referred to as Beacon’s “professional
development.” Wenglinsky (2002) and Ladson-Billings (2006) described the importance
of a rigorous curriculum and teachers containing sufficient understanding of their subject
to teach the curriculum. At Beacon, when teachers needed support for adding rigor to the
curriculum and needed ideas regarding enhancing math teaching, they turned to Mr.
Jefferson. In essence, Mr. Jefferson’s main contribution was enhancing teaching quality
by mentoring his colleagues.
One of the major research findings included normative collaboration that inspired
improvement in teacher practices through practice of data analysis. Collaboration was so
common at Beacon that Mr. Stevens reported hearing it all the time in the hall from his
office. In fact, some teachers habitually visited each other during passing periods and
nutrition periods. Collaboration was influenced by Mr. Corral’s decision to disseminate
his Data Director password to staff members, encouraging everyone to focus on teaching
that resulted in higher student achievement. This was consistent with communication, a
leadership responsibility related to principal leaders. Marzano et al. (2005) described
effective communication as the extent to which a school leader is able to establish lines

166
of communication between teachers and their fellow colleagues, between teachers and the
principal, and maintain accessible dialogue with staff. Through communication, empha-
sis was placed on common assessments, which also influenced teacher collaboration, and
teachers developed a culture wherein they convened frequently to discuss teaching and
student learning. In ELA, Mr. Stevens supported the culture of collaboration by dis-
aggregating student common assessment results through his spreadsheets.
Although Beacon experienced elevating CST scores, what largely fueled the
school’s elevated API scores between 2006 and 2008 were Beacon’s outstanding Algebra
1 proficiency percentages. The impact of the algebra program on the school’s API scores
was one of the major research findings. Mr. Corral reported the drop in API and attri-
buted it to the decline of Beacon’s Algebra 1 percentages from 80% in 2008 to 54% in
2009, the year when Mr. Williams left the district and was replaced by two new teachers,
one of whom was a novice teacher. Although Beacon’s Algebra 1 proficient and
advanced percentages declined dramatically in the past academic year, the school
maintained over 50% proficiency rating during the past 5 years, specifically 55%, 82%,
81%, 80%, and 54%, with rising numbers of students enrolled in Algebra 1 each year.
The most critical factor to Beacon’s success was the Algebra 1 program that Mr.
Williams created, reflected by instructional practices that were evident in the math
classes. Mr. Jefferson, the Department Chair, was also influential as he promoted think-
ing and doing of mathematics that involved kinesthetic learning, drawing and modeling
diagrams, as well as verbal expression and writing of math in words. Although he did not
work on the Algebra 1 curriculum, Mr. Jefferson was valuable to Beacon because he was

167
the conduit for math ideas in Beacon’s math department, which boasted the highest math
CST scores in the district.
The existence of the Algebra 1 curriculum and its influence on student perform-
ance was consistent with an aspect of institutional support. Stanton-Salazar (1997)
identified six forms of institutional support, including the provision of various funds of
knowledge associated with academic success. One of these funds of knowledge is
academic task-specific knowledge, which includes subject area knowledge. Beacon’s
success in Algebra 1 was consistent with the provision of this type of institutional sup-
port. Beacon students experienced sustained success in algebra, a result of the program
and Mr. Williams’s influence. This was critical for Beacon students because researchers
such as Ball (2003) explained that algebra is critical to educational advancement and
career opportunities.
Although the API scores dropped during the past academic year, Mr. Corral was
confident that Beacon would recover in overall student performance of math, especially
Algebra 1, since Mr. Williams’s return. The presence of Mr. Williams at Beacon was
consistent with an aspect of institutional support because he assumed the role of a very
influential institutional agent. Stanton-Salazar (1997) explained that institutional agents
have the capacity to transmit institutional resources. Mr. Williams was a conduit of
institutional resources: the algebra curriculum. His absence emphasized his impact on
Beacon’s Algebra 1 program and overall academic achievement.
Aside from the major findings, there were other important themes that were
confirmed via triangulation. One was student engagement, which was consistently part

168
of teacher discourse at Beacon but was missing at times in the classroom. In fact, some
teachers even described student performance as having already “plateaued.” A specific
subgroup of the student population was described as “intermediate for life” in describing
student language proficiency.
Salorzano (1998) explained that critical race theory in education challenges the
dominant view on race and racism as related to education by reviewing the way in which
educational theory, policy, and practices are used to oppress certain racial and ethnic
groups. Staff discourse depicting student performance that has already met its threshold
is consistent with CRT as a practice that subordinates a racial group. According to
Salorzano and Yosso (2000), a theme within CRT is the challenge to dominant ideology.
This theme challenges the traditional claims of the educational system to objectivity,
meritocracy, and equal opportunity (Salorzano & Yosso, 2000). The challenge to domin-
ant ideology is consistent with the phenomenon at Beacon, displaying the expectation
that students have already reached a plateau. The common ideology that students have
already “plateaued” does not reflect a belief in students’ learning potential. Teachers
who did not engage student learning displayed the notion that students had either
plateaued or were responsible for their own limited performance. Furthermore, the
deficit perspective that teachers developed was far from consistent with the theme of
engagement as it promoted a sense of helplessness.
Implications for Practice
The research questions specific to cultural norms, practices, and programs that
were perceived to raise student achievement and narrow the achievement gap at Beacon

169
resulted in researching findings pertaining to leadership, collaboration, data-driven
culture, and the impact of Algebra 1. These research findings assisted in considering
recommendations for practice that could be valuable to other school organizations. The
recommendations are specified for teaching staff, administrators, school districts, policy
makers, and researchers.
Recommendations for Teaching Staff
The first recommendation is for teaching staff to create a culture of collaboration
that is focused on improvement of instructional practices. The staff at Beacon made
instruction their focus, which manifested itself in multiple ways. Teachers used Data
Director to view student CST scores and student performance results on common assess-
ments. ELA teachers also utilized a spreadsheet that reported student assessment results,
which promoted discussion about effective practices. In Algebra 1, teachers used the
green light/red light standards sheet, which was a visual representation of student
standards mastery and areas for improvement. According to Clark and Estes (2002),
critical factors that contribute to performance gaps are the knowledge and skills of
members. If teachers create a culture of collaboration centered on improvement of
instruction, then knowledge and skills of teachers have the potential to be enhanced,
which should support student learning. This is consistent with the notion of identifying
most effective teachers to reduce the achievement gap (Peske & Haycock, 2006) because
identifying effective instructors will be critical in sharing effective practices.
The second recommendation is specific to math teachers. Math teachers should
cease using traditional practices (Stigler & Hiebert, 1999). They should create classroom

170
environments that invite students to construct relationships between new ideas and pro-
cesses already understood; extend and apply mathematical knowledge less susceptible to
forgetfulness; reflect about learning experiences in order to reorganize knowledge in
coherent ways; articulate understanding verbally, through writing, and through pictures
and diagrams; and make knowledge one’s own in order to develop a personal investment
in learning (Carpenter & Lehrer, 1999). This finding was observed at Beacon, consistent
with interviews in which teachers described student tasks such as making generalizations,
writing mathematical thinking, explaining understanding verbally, and “doing” mathe-
matics rather than being guided by a published book.
Recommendations for Administrators
To support a collaborative culture, administrators should implement structures to
cultivate normative collaboration. At Beacon, Mr. Corral, the principal, provided staff
members his username and password to Data Director to convey to the staff that student
data were public and that teachers could not remain anonymous with respect to their
direct impact on student achievement. In order to promote collaboration, structured
collaboration was embedded into the schedule. Teachers had staff meetings, teacher
leaders were chosen to become members of the leadership team, and other informal
teacher leaders were given opportunities to influence their colleagues by promoting
practices and programs that resulted in enhanced student achievement. According to
Waters et al. (2004), culture is a leadership responsibility related to principal leadership
that fosters shared beliefs, generates a sense of collaboration and builds the community.
Mr. Corral, Beacon’s principal, created a culture that shared a belief that student work

171
must be analyzed to identify effective teaching practices to improve instruction. Waters
et al. also described the leadership responsibility of input, which leaders utilize to involve
teachers in the design and implementation of processes. This was consistent at Beacon in
Algebra 1, where Mr. Corral permitted Mr. Williams to implement the Algebra 1 pro-
gram that resulted in sustained elevated student performance on the CST.
Aside from taking input from teachers and creating a culture of collaboration,
school administrators should support innovative teaching and programs that are con-
ducive to student learning and enhanced performance. At Beacon, the absence of Mr.
Williams displayed his impact on the Algebra 1 CST, as proficiency scores plummeted
from 80% to 54% during his hiatus. This also depicts the impact of the Algebra 1
program, as its faithful implementation during Mr. Williams’ presence showed sustained
elevated student proficiency, coupled with increasing numbers of students placed in
Algebra 1. Clark and Estes (2002) cited organizational barriers as one of the main causes
of performance gaps. They described organizational barriers as missing equipment,
inadequate facilities, or faulty processes that can inhibit or stifle work. To enhance
student performance, administrators should support teaching and programs that have been
proven effective because restrictions on such elements could be perceived as organiza-
tional barriers.
Recommendations for the School District
To spread knowledge and skills necessary to raise student achievement, the
district should identify effective teachers to support practices that can be shared within
district boundaries. Thus, rather than add to economic expenditures to acquire external

172
professional development resources, the district can utilize its own resources by elevating
the status of teachers who have learned their craft well. Part of the issue in the topic of
the achievement gap is teacher effectiveness: Teachers do not have the knowledge and
skills to teach their subject. Another issue is quality of teaching: Students are relegated to
learn rote, procedural skills absent of conceptual understanding or a coherent structure of
knowledge to be learned (Carpenter et al., 2004). Clark and Estes (2002) cited lack of
knowledge and skills and low motivation as elements that cause performance gaps, which
are equivalent to student achievement gaps. If specific teachers have tools to provide
students knowledge, skills, and understanding, as well as to instill motivation to perform
well on the CST, these teachers should share their practices within their school and
disseminate them throughout neighboring district schools.
Identification of the most effective teachers can be done through the use of data
analysis systems. These same data analysis systems also allow teachers to recognize
effective practices and areas of improvement. Another recommendation for districts is
to continue to provide teachers these data analysis programs and assign personnel to
disseminate and disaggregate data for teachers. Mr. Stevens, the ELA Department
Chairperson at Beacon, held this position and analyzed the data for teachers. In essence,
he was a source of knowledge that teachers needed to identify more effective practices
when teaching the subject matter.
Recommendations for Policy Makers
Policy makers should seek the best models of urban schools that have met or are
in the process of fulfilling the “algebra for all” eighth graders requirement. Beacon

173
Intermediate School has a block schedule in mathematics and ELA, which has limited
opportunities for electives such as art and choir. Policy makers should decide whether
the practice of doubling time for math and ELA has long-term academic benefits for
students if it shortchanges opportunities to engage in the arts, music, and other worthy
electives.
Policy makers should also review the “algebra for all” eighth graders requirement
to determine its impact on the science, engineering, and technology work force. The
Committee on Equal Opportunities in Science and Engineering (2000) reported unequal
proportions of African Americans and Latinos in these areas of the U.S. work force.
Math education has a function of cultivating citizens with reasoning skills, providing a
broader choice of educational and career opportunities, and analytical thinking required
for the sciences (Ball, 2003). Thus, the impact of the “algebra for all” eighth graders
mandate on the science, engineering, and technology work force should be investigated to
determine benefits for U.S. citizens in general and for its African American and Latino
subgroups.
Recommendations for Research
The literature indicates that effective teaching is required for student learning.
The success at Beacon Intermediate School was highlighted by data analysis of student
performance that reinforced collaboration and identified practices to improve student
learning. In math, this was evident because Algebra 1 teachers assessed learning daily
and modified teaching at a moment’s notice. The following recommendations are based
on the findings, observations, and conclusions gathered from this study.

174
In the day and age of NCLB compliance and teacher accountability, research
should seek up-and-coming urban schools to determine the prevalence of teaching for
mathematical understanding in the United States versus teaching students to prepare them
for standardized tests. Many teachers are pressured to prepare students for standardized
tests. Since U.S. math classrooms are characterized as procedurally oriented and sup-
ported by the assumption that learning occurs as more exercises are practiced (Stigler &
Hiebert, 2004), future research should identify urban schools such as Beacon that garner
high student outcomes in algebra while focusing on instruction that results in learning
and making sense of algebra’s underlying concepts. In general, U.S. math classrooms
lack quality of teaching because teachers maintain ineffective practices of instructing
students to follow rules and practice procedures (Stigler & Hiebert, 1999), as opposed to
teaching for understanding, which includes constructing a coherent structure for the
knowledge to be learned rather than disconnected skills, engaging students in inquiry
and problem solving, and taking responsibility for ideas that students offer and their
procedures (Carpenter et al., 2004).
A recommendation for research is to review the practice of extending mathe-
matics and ELA classes. To face the challenge of teaching subjects most critical to
standardized tests, many schools, including Beacon Intermediate School, have practiced
extension of math and ELA periods. Research on enhancing student performance
describes the critical nature of having a rigorous curriculum and teachers having suffi-
cient understanding of their subject to teach the curriculum (Ladson-Billings, 2006;
Wenglinsky, 2002). Allotting blocks to math and ELA classes must be reviewed because

175
a far too common byproduct of this decision is the excision of art and music programs,
which was reflective of practice at Beacon Intermediate School. Research should investi-
gate the long-term effects of this practice on American society.
Research should investigate the effectiveness of schools that have practiced
curricular autonomy. This research created a segue into this topic as Algebra 1 teachers
at Beacon Intermediate School practiced curricular autonomy by utilizing their own
algebra program, setting aside the district-adopted text and setting aside the district
pacing guide. In the age of NCLB and standards-based testing, many districts have
mandated implementation of standards-based common assessments, coupled with
synonymous pacing guides. However, Stigler and Hiebert (1999) explained that the main
ingredient in promoting student learning is quality of teaching, which requires that
teachers cease utilization of traditional instructional methods. Therefore, schools such as
Beacon should be investigated, where a core group of teachers have created their own
curriculum and employed it to produce high student learning outcomes by focusing on
instruction rather than the district-created benchmark, despite existence of district
pressures to follow a district pacing guide and to teach material included in district
benchmarks.
Conclusion
The achievement gap persists, signifying the wedge between poor and minority
students and their more affluent, historically high-performing counterparts. The goal of
this study was to learn from a successful high-performing urban school in order to con-
tribute to literature regarding cultural norms, practices, and programs that have supported

176
a school in generating high student achievement. This study showed that leadership
distributed among key individuals can make a large difference in student achievement.
Another emergent theme indicated that a data-driven culture, cultivated by a culture of
collaboration and data analysis, can support student learning. The study validated the
potential impact of a single school program in improving student understanding and
performance of Algebra 1.

177
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185
APPENDIX A
DOCUMENT REVIEW MASTER LIST, CATEGORIZED
District
1. Textbook adoption list
2. Modified or year-round school
3. Board policy
4. Vision statement
5. Mission statement
6. Staff development plan to meet the needs of diverse learners
7. LEA Plan
8. District policy for ELM placement
9. District policy for SEI placement
10. LEA code of conduct policy
11. LEA discipline policy
12. LEA drug/alcohol use prohibition policy
13. LEA firearms/weapons policy
14. LEA Gun-Free Schools Act policy
15. LEA plan describing availability of Tobacco Use Prevention Education services
16. LEA policy regarding tobacco use
17. Full desegregation
18. District-established criteria/procedures for reclassification
19. LEA catch-up plan for monitoring and overcoming any academic deficits
20. District policy on qualifications for instructional aides

School level artifacts
1. Meeting schedules
2. Staff Development plan/School site plan
3. Instructional minutes/Master Schedule
4. Assessment tools
5. Preschool availability or pre-kinder offerings
6. Literacy programs
7. Character education
8. SST
9. RTI
10. Tutorial programs
11. Saturday school
12. Interventions during the school day
13. Summer school
14. Student-parent handbook
15. Discipline assembly
16. Vision statement
17. Mission statement
18. Staff development plan to meet the needs of diverse learners
19. Equitable groupings of minority students in classrooms
20. Parent Involvement Policy

186
21. School Accountability Report Card
22. Teacher and paraprofessional assignments
23. Student profile data
24. Counseling availability and function
25. Entitlement funding (i.e., Title I funding)
26. School-parent compact for NCLB/Title I
27. Public reports of suspension, expulsion, and truancy rates from Uniform Management
Information and Reporting System
28. Safe school plan (including disaster procedures, crisis management, or emergency plan)
29. Attendance reports

Instructional
1. Department meeting notes
2. Common planning/Common Assessments
3. Classroom Objectives or standards posted in rooms
4. SMART goals or action plan documents
5. Teacher lesson plans

Differentiated or special services
1. Re-classification of LEP
2. Descriptions of English-language mainstream program
3. Descriptions of structured English immersion program design
4. English learner program evaluation report
5. GATE student identification criteria
6. GATE teacher specifications
7. Analysis of California Healthy kids survey (CHKS) core module data
8. Analysis of CHKS resiliency and youth development module
9. California Healthy kids survey
10. Physical education instructional minutes report

California Department of Education website
1. School data to analyze student proficiency (CST and CELDT)
2. School demographic data
3. School data on Program Improvement status (i.e., AYP and API information)

Pertains to High Schools only
1. College prep/AP/IB offerings
2. School data to analyze % of students in CP/AP/IB/Honors courses
3. Freshman advisory
4. AVID
5. Freshman assembly/freshman first day
6. Student placement criteria into CP/Honors/AP/IB
7. CST data, CAHSEE, AP, and college-bound statistics
8. District career technical education plan and course offerings
9. Work Experience Education District plan
10. Process for adding new courses
11. Description of alternative programs

187
APPENDIX B
The Staff Input Survey
Your school was chosen for this study based on the success and sustainability in
student achievement. The purpose of this study is to identify your school’s cultural
norms, practices and programs that contributed to the closing or narrowing of the
achievement gap. The results of this study could be useful to schools with a similar
student population. Your input on this survey is anonymous. This research project is
being conducted by a doctoral student from the University of Southern California. The
survey will take about 10-15 minutes to complete. Thank you for your cooperation.
Please circle the appropriate response:
1. The school supports collaboration among teachers.
a) Strongly Agree b) Agree c) Somewhat Disagree e) Strongly Disagree
2. The teachers at this school believe that students can achieve at high levels.
a) Strongly Agree b) Agree c) Somewhat Disagree e) Strongly Disagree
3. School administration creates a positive school culture for teachers and students.
a) Most of the time b) Sometimes c) Rarely d) Never
4. Leadership is shared among school personnel.
a) Most of the time b) Sometimes c) Rarely d) Never
5. Teachers collaborate to discuss student data to improve student learning.
a) Most of the time b) Sometimes c) Rarely d) Never
6. The school addresses the needs of struggling students.
a) Most of the time b) Sometimes c) Rarely d) Never
7. School administration conducts classroom observations frequently.
a) Strongly Agree b) Agree c) Somewhat Disagree e) Strongly Disagree

188
8. The school has a systematic process for identifying and assisting struggling
students.
a) Strongly Agree b) Agree c) Somewhat Disagree e) Strongly Disagree
9. School administration communicates vision and goals to the staff.
a) Most of the time b) Sometimes c) Rarely d) Never
10. School administration ensures the analysis of student assessment data.
a) Most of the time b) Sometimes c) Rarely d) Never
11. School administration provides support for implementation of new instructional
practices.
a) Most of the time b) Sometimes c) Rarely d) Never
12. School administration provides ways to improve instructional strategies to meet
the needs of students with diverse backgrounds.
a) Most of the time b) Sometimes c) Rarely d) Never
13. CST scores and District Assessments are used to plan your instructional program.
a) Most of the time b) Sometimes c) Rarely d) Never
14. Student data is used to identify the instructional needs of my students.
a) Most of the time b) Sometimes c) Rarely d) Never
15. You utilize the California State Standards to plan and deliver instruction.
a) Most of the time b) Sometimes c) Rarely d) Never
16. You provide differentiated instructions to meet the needs of all students.
a) Most of the time b) Sometimes c) Rarely d) Never
17. School administration initiates programs that promote student achievement.
a) Strongly Agree b) Agree c) Somewhat Disagree e) Strongly Disagree
18. The school utilizes a specific program to analyze student data.
a) Most of the time b) Sometimes c) Rarely d) Never

189
Please circle all that apply:
19. Who leads the collaboration sessions?
a) Teachers b) Administrators c) Counselors d) Coaches e) Other:_____________
20. What topics are discussed in the collaboration sessions?
a) Curriculum b) Instruction c) Intervention d) Data Analysis e) Operation
f) Standards g) Other: _____________________________________________
21. How does the school make collaboration possible?
a) Substitute release time b) Minimum Days c) Partial Day Release
d) After School Time e) Bank Time Activity f) Staff Meetings g) Preparation
Periods h) Other: ___________________________________________________
22. What type of intervention practices are used for struggling students?
a) Peer Tutoring b) After School Tutoring c) In-class intervention
d) Pull-Out Intervention e) Homework Assistance f) Summer School
g) Off-Track Classes h) Other: _______________________________
23. Who organizes professional development sessions related to intervention programs?
a) Teachers b) Administrators c) Department/Grade Level Chairs
d) Coaches e) Other: ___________________________________________
24. Rate the following instructional strategies you used to enhance student learning.
Extremely Important 1 2 3 4 5 6 Not Important
___ Direct instruction ___ Guided practice
___ Pre-teaching ___ Re-teaching
___ Visual aids/graphic organizers ___ Note-taking
___ Summarizing ___ SDAIE Strategies
___ Cooperative grouping ___ Peer tutoring
___ Individual instruction ___ Higher Order Thinking Questions
___ Scaffolding ___ Using Prior Knowledge
___ Metacognitive Skills ___ Other (please list) ________________

190
25. What specific program does the school use to promote collaboration?
___________________________________________________________________
26. What intervention program(s) at your school have contributed to closing the
achievement gap?
___________________________________________________________________
___________________________________________________________________
27. What instructional programs do you use in your classroom that has helped close the
achievement gap?
____________________________________________________________________
____________________________________________________________________
28. Comments about the role of intervention in closing the achievement gap at your
school:
____________________________________________________________________
____________________________________________________________________
29. Comments about the role of data analysis which helped close achievement gap at
your school:
___________________________________________________________________
____________________________________________________________________
30. Comments about the role of school leadership which helped close the achievement
gap at your school:
____________________________________________________________________
____________________________________________________________________
31. Comments about the role of collaboration which helped close the achievement gap at
your school:
___________________________________________________________________
___________________________________________________________________

191
32. Comments about the role of your classroom instruction which helped close the
achievement gap at your school:
____________________________________________________________________
____________________________________________________________________

Even though this survey is anonymous, please provide the following information:
Your position at the school:
For Elementary Schools -- Administrative Team Teacher Grade level Chair
For Secondary Schools -- Administrative Team Teacher Department Chair
Number of years as an educator: ________________________________
How long have you worked at this school?: ________________________________
Thank you for completing this survey. Your responses are appreciated.

192
APPENDIX C
INTERVIEW QUESTIONS

1. Collaboration:
a. What does collaboration look like at this school?
b. Who leads the collaboration sessions?
c. With whom do you collaborate? How often?
d. What are the outcomes for student learning?
e. What programs, practices, and cultural norms does the school have in place to
ensure that students achieve?

2. School Leadership:
a. What is the school mission and vision?
b. What is the primary goal for this school?
c. How is the mission/vision/goal communicated?
d. Who is the school leader? Why?
e. How does the leadership foster or help student learning?
f. Is the leadership shared among the various school personnel? How?
g. How does the leadership meet the needs of at-risk populations?
h. Are school decisions based upon student needs? Give an example

3. Program Implementation
a. What programs have been employed that have allowed the school to close
the achievement gap?
b. Are there programs that have improved attendance? And how is this
affecting achievement?
c. What programs have improved the school climate?
d. What programs have improved content learning for all students but
specifically for students with diverse needs?
e. What programs have improved student achievement in literacy skills?
f. What programs have improved student achievement in mathematics?

4. Data Analysis
a. How is data used to support student learning?
b. Who is responsible for dissagregation, dissemination, and review of data?
c. How is this information shared among the various school stakeholders?
d. Does your school utilize a specific data analysis program? If so, which
program?
e. How often is data analyzed at your school site?

193
5. Intervention:
a. What are the supports that are in place for students and their families?
b. Who determines which students get support?
c. How are supports implemented and monitored?
d. What is intervention is offered to students who are underperforming
academically?
e. How are these implemented? Who is involved?
f. How do you make sure that every student has his or her academic needs met?
g. What is the way things are done that supports learning in student groups that are
traditional underperforming?

6. Practices that Support Closing the Achievement Gap:
a. What are the school-wide practices that support student learning?
b. Who determined that this practice happens?
c. How is effectiveness measured? Or what data is collected?
d. How do you know that it is successful?
e. Has this practice been modified since the beginning?
• How do you know that all (EL, low SES, Special Ed, African American,
Hispanic) students have access to these practices?
• How do you know students are appropriately placed in classrooms or
courses?
f. What are the departmental or grade level practices that support student learning?

7. Classroom Instruction
a. What are the classroom practices that support student learning?
b. What are teachers supposed to know and be able to do?
c. How do you know that they have done it?
d. How is classroom instruction differentiated to meet the needs of all students? List
some classroom examples.

8. Professional Development Practices that support closing the achievement gap:
a. What are the professional development opportunities available to teachers?
b. What is the role of the teacher in professional development?
c. What is the role of the administrator in professional development?
d. How do you know that teachers are utilizing skills learned?
e. In the classroom? In specific content areas?

9. Sustainability
a. Have you sustained success?
b. How have you sustained success?
c. What advice would you give to other schools that want to emulate your cultural
norms, programs and practices to close the achievement gap?

Do you have anything you would like to add to this interview in terms of closing the
achievement gap and sustaining success?

194
APPENDIX D
INTERVIEW FOLLOW-UP QUESTIONS
(Based on Data needs in Math Instruction)
1. Describe the daily routine of your class.
2. Describe the types of problems students complete in math class or are expected to learn.
3. How are math concepts taught?
4. How do teachers assess student learning in math classes?
5. Describe the process of lesson planning in math. What do teachers ensure to include?
6. In a regular day, what are students expected to do in math classes?

195
APPENDIX E
SCHOOL OBSERVATION FORM/GUIDE

University of Southern California
Rossier School of Education

Focus: Factors Narrowing the Achievement Gap with Sustained Success in Urban
Schools

Date:_______________________ Page ____of_____
Time: ___________

Type of Observation(Circle One): School Class Leadership Meeting

Observation Log
First Impression
Condition of Surrounding
Neighborhood

Approach to School

!""#$%&'()'"*)+,(%()+")-"
.%'/*%/'&."

!""012+%."2+,"-)1(23&"

!""4/."%/'+52')/+,.6"
72'8(+3""1)%9"%&2*:&'."2+,"
.%/,&+%.

!"";/7&'<(.()+"2')/+,"2+,"
(+"-')+%")-"%:&".*:))1

The Office
!""#+%'2+*&=.&*/'(%>"

!""?)+,(%()+")-")--(*&"
*)@72%(A1&"B(%:"
&$%&'()'C

!"";%2--"(+%&'2*%()+6"B(%:"
3/&.%6"72'&+%.6"
*)@@/+(%>6"2+,"7&&'.

Initial Meeting
!""D(%:"B:)@C"0'(+*(7216"
E..%F"0'(+*(721G

!""H&.%'(*%()+.")+"2**&..C"

196
!"";%2--"%'2--(*"%)"
2,@(+(.%'2%()+6")7&+"
,))'")'"277)(+%@&+%.

Staff
!""I&.(3+2%&,"
'&7'&.&+%2%(<&.6"
'&.%'(*%&,"*:)(*&6")'"-'&&"
2**&.."%)".%2--

""!J&2*:&'"1&2,&'."

""!#@7)B&'&,=K(3/'&"
:&2,.C"

""!#@&'3&+%"1&2,&'.")-"
-)'@21".%'/*%/'&.")-"
1&2,&'.:(7

!""?)112A)'2%()+C"

!Structured, non-
structured?

""!?)@@)+"2..&..@&+%.6"
-)'@2%(<&6"./@@2%(<&

! "#$%&"'
!"";%/,&+%5*&+%&'&,"
*/1%/'&C"

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211"1&<&1.C"E+>"1&<&1.C

197
University of Southern California
Rossier School of Education

Focus: Factors Narrowing the Achievement Gap with Sustained Success in Urban
Schools

Date: ________________ Page: ______ of _______
Time: _______________

Levels of Curriculum Curriculum
!""#;L"

!"";IEM#"
"

!"";0#I"

""!H%M"

!SDC

!ED/SED

!SH
Standard Levels

College Prep

Advanced Placement

International Baccalaureate

Open Access or restricted
entrance

Support Programs

! AVID

!""?'&,(%"H&*)<&'>"

!""?)+*/''&+%"#+')11@&+%"
B(%:"N/+()'"*)11&3&

!""I(.%2+*&"L&2'+(+3"?'&,(%

198
University of Southern California
Rossier School of Education

Focus: Factors Narrowing the Achievement Gap with Sustained Success in Urban
Schools

Date: ________________ Page: ______ of _______
Time: _______________

Classroom Observation
Physical condition of room

Desks or tables
Student work displayed

Learning Goal

Related to Content
Standard

Demonstration of Learning

Asset Development

! Caring

!""O(3:"#$7&*%2%()+."
(

!""P&2+(+3-/1"02'%(*(72%()+"
"

! ")*"%+,%'(
!""I('&*%"(+.%'/*%()+"
(

!"Q/(,&,"7'2*%(*&"
"

!"";*2--)1,(+3"
"

!""R(./21.=Q'27:(*"
S'32+(T&'."

!""?)@72'&"2+,"?)+%'2.%"
"

!"";/@@2'(T(+3")'"+)%&"
%28(+3"

!""JE00L#"UJ&2*:6"E.86"0(*86"
02/.&6"L(.%&+6"#$712(+6"
#$72+,6"#@7:2.(T&"

199
!""J0H"UJ)%21"0:>.(*21"
H&.7)+.&V"

!""?:&*8"-)'"W+,&'.%2+,(+3"
"

-%./&010+2(
!""#$%&+%"2<2(12A1&"
(

!""#$%&+%"/.&,"
"

!""J&2*:&'"/.&"
"

!"";%/,&+%"/.&"
"

!"";%/,&+%=%&2*:&'"-&&,A2*8"
)+"(%."/.&"

200
APPENDIX F
ALIGNMENT OF DATA NEEDS, SOURCES, AND INSTRUMENTATION

RQ 1: What are the cultural norms that have been employed by the school that have
allowed them to close the achievement gap and sustain success?

Data Needs Data Sources Instrumentation
Teacher Collaboration—
common planning, common
assessment, data review

• Dept. meeting notes
• Meeting schedules
• Staff development
plan/school site plan
Document Review
Challenging, rigorous
curriculum
• Textbook adoption list
• College prep/AP/IB
offerings
• Instructional minutes
• Assessment tools
• School data to analyze
% of students in
CP/AP/IB/honors
courses
Document Review, survey
Preventions for at-risk
populations
• Preschool availability
• Literacy Programs
• Pre-kinder offerings
• Character education
• Freshman advisory
• AVID
Interviews, document review,
observations
Interventions for at risk
population and whole school
• SST
• RTI
• Tutorial Programs
• Saturday School
• Intervention during
the school day
• Summer school
• Modified year-round
school
Document review
Behavioral Expectations • Character education
• Student-parent
handbook
• Board policy
• Discipline assembly
• Freshman assembly/
freshman day
Document review,
observations,

201

Leadership--Vision for
success with high
expectations
• Vision
• Mission statement
• Teacher evaluations
• Assessment tools
Document Review
Professional
development/Staff
development focusing on at-
risk and ethnic minority
students
• Staff development
plan to meet the needs
of diverse learners
Document review, surveys,
interviews
Data-driven decision making • SMART goals
• Assessment tools
• School demographic
data
• Student profile data
• Student placement
into CP/AP/IB/ honors
classes
• CST data, CAHSEE,
AP, and college bound
Document review, surveys,
interviews
Recognition of diverse
student population
• Re-classification
• Equitable groupings
of minority students in
classrooms
• Full desegregation
• Counseling
• Entitlement funding
Document review, surveys,
interviews
Standards are key to
curriculum and instruction
• Textbook adoption
• Standards posted in
every room
• Teacher lessons
• Assessment tools
Document review,
observations, surveys

202
RQ 2: What are the practices that have been employed by the school that have allowed
them to close the achievement gap and sustain success?

Administrative leadership on
instructional practices of
teachers
Teacher’s observation
student performance data
Teacher interview, teacher
survey
Instructional practices of
teachers
Classroom observation
Teachers practice in
Professional development
PD records, PLCs Teacher interviews,
observations during PD
meetings
Response to Intervention School data Documents; Interviews
Classroom organization on
SLC, class size, block
schedule
Schoolwide record Master schedule, observation
ELD CELDT scores, course
placement
Course placement,
benchmarks
Documents; interview,
observations
School safety, student
behavior Emergency
Suspension records Interventions

RQ3: What are the programs that have been employed by the school that have allowed
them to close the achievement gap and sustain success?

Information on the program:
How program
works/description of the
program
Who is involved in the
program
Length of program
Goal of program
Level of implementation
Key players/Stakeholders:
Start up sources/
Implementation

Questions on
Interviews/Survey

Assessments: Test scores;
CST Benchmarks District
Wide Assessments (DWA)
Test scores/assessments

CDE / Benchmark
data system

School Artifacts:
Attendance,
Agendas/minutes:
Agendas/minutes/student
and teacher attendance
List of documents
that are being
reviewed
Professional Development
Who
Material
What type: trainer of
trainer/facilitator
Program Environment
Observations

Classroom
observation forms

203
APPENDIX G
RESEARCH QUESTIONS/SURVEY PROTOCOL CORRELATION GRID
Research Question 1
What are the cultural norms that have been employed by the school that have allowed them to
close the achievement gap and sustain success?
1. The school supports collaboration among teachers.
2. The teachers at this school believe that students can achieve at high levels.
3. School administration creates a positive school culture for teachers and students.
4. Leadership is shared among school personnel.
5. Teachers collaborate to discuss student data to improve student learning.
6. The school addresses the needs of struggling students.

Research Question 2
What are the practices that have been employed by the school that have allowed them to close
the achievement gap and sustain success?
7. School administration conducts classroom observations frequently.
8. The school has a systematic process for identifying and assisting struggling students.
9. School administration communicates vision and goals to the staff.
10. School administration ensures the analysis of student assessment data.
11. School administration provides support for implementation of new instructional practices.
12. School administration provides ways to improve instructional strategies to meet the needs of
students with diverse backgrounds.
13. CST scores and District Assessments are used to plan your instructional program?
14. Student data is used to identify the instructional needs of my students.
15. You utilize the California State Standards to plan and deliver instruction.
16. You provide differentiated instructions to meet the needs of all students.
17. School administration initiates programs that promote student achievement.
18. The school utilizes a specific program to analyze student data.
19. Who leads the collaboration sessions?
20. What topics are discussed in the collaboration sessions?
21. How does the school make collaboration possible?
22. What type of intervention practices are used for struggling students?
23. Who organizes professional development sessions related to intervention programs?
24. Rate the following instructional strategies you used to enhance student learning.

204
Research Question 3
What are the programs that have been employed by the school that have allowed them to close
the achievement gap and sustain success?
25. What specific program does the school use to promote collaboration?
26. What intervention program(s) at your school have contributed to closing the achievement
gap?
27. What instructional programs do you use in your classroom that has helped close the
achievement gap?
28. Comments about the role of intervention in closing the achievement gap at your school:
29. Comments about the role of data analysis which helped close achievement gap at your
school:
30. Comments about the role of school leadership which helped close the achievement gap at
your school:
31. Comments about the role of collaboration which helped close the achievement gap at your
school:
32. Comments about the role of your classroom instruction which helped close the achievement
gap at your school:

205
APPENDIX H
MATH DATA NEEDS DATA SOURCES
RQ 1: What cultural norms, practiced within classrooms, are perceived to have raised
math achievement? (What cultural norms, practiced within the ! school, are perceived to have
narrowed the achievement gap?)
Data Needs Data Sources Instrumentation
Students Make Connections to
prior knowledge
Carpenter, Blanton, Cobb,
Franke, Kaput, & McClain
(2004);
Carpenter & Lehrer (1999)
Teacher lesson plan
Student work/reflections
Student discourse
Document review
Observation
Interviews
Math is coherent structure rather
than isolated facts and skills;
students extend and apply
knowledge; variety of solutions
are encouraged
Carpenter, Blanton, Cobb,
Franke, Kaput, & McClain,
(2004);
Carpenter & Lehrer, (1999);
Secada & Berman, (1999)
Teacher Lesson Plan
Curriculum Pacing
Lesson Activities
Document Review
Observation
Interviews
Teachers engage students in
inquiry and problem solving;
students articulate what they
know
Franke, Kaput, & McClain
(2004)
Carpenter & Lehrer (1999)
Romberg, T.A., Kaput, J.J.
(1999).
Secada, W.G, Berman, P.W.
(1999)
Teacher Lesson Plan
Student work/reflections
Lesson activities
Student discourse
Document Review
Observation
Interviews

206
RQ 2: What practices employed by the school are perceived to have raised math
achievement? (What practices employed by the school are perceived to have narrowed the
achievement gap and sustained success?)
Data Needs Data Sources Instrumentation
Teachers provide students
tasks that engage them in
higher level demand and
focus on conceptual
knowledge
Kersaint, Thompson &
Petkova (2009)
Textbook
Teacher lesson plan
Document review
Observation
Interview
Teachers set expectations
that students articulate math
thinking.
Fennema, Sowder &
Carpenter (1999); Ball
(2003)
Teacher Lesson plan
Student discourse
Student work
Observation
Interview
Document review
Use of ongoing assessments
that can include student
mathematical thinking about
their progress.
Fuson, Kalchman, &
Bransford (2005)
Teacher lesson plan
Student work/assessments
Interview
Document review
Observation
Implementation of rigorous
problems/application
problems rather than greater
focus on skills based
problems and routine
exercises
Stigler & Hiebert (2004)
Teacher lesson plan
Student text/workbook
Student work/writing
Document review
Observations
Interview
Implementation of “making
connections” problems taught
as “making connections”
problems rather than “using
procedures” problems
Stigler & Hiebert (2004)
Teacher lesson plan
Student text/workbook
Student work/reflections
Document review
Observations
Interview
Math is taught in an
interrelated manner

Stigler & Hiebert, (2004)
Teacher lesson plan
Student work/writing
Pacing guide
Document review
Observations
Interview

207

RQ3: What characteristics of programs employed by the school are perceived to have
raised math achievement? (What programs employed by the school are perceived to have
narrowed the achievement gap and sustained success?)
Data Needs Data Sources Instrumentation
Deeper study of fewer, more
critical concepts; focus on
conceptual depth rather than
procedural finesse; critical
thinking is part of daily routine
America’s Choice (2006)

Teacher lesson plan
Student work/reflections
Student discourse
Document review
Observation
Interviews
A focus on elementary aspects
of algebra to prepare students
for more advanced math.
America’s Choice (2006)
Teacher Lesson Plan
Curriculum Pacing
Lesson Activities
Document Review
Observation
Interviews
There is an emphasis on prior
knowledge and revising
misconceptions; tasks are
designed to uncover
misconceptions and illuminate
faulty reasoning.
America’s Choice (2006)
Teacher Lesson Plan
Student work/reflections
Lesson activities
Student discourse
Document Review
Observation
Interviews
Encourages language rich
environment where students
articulate their understanding of
mathematical situations;
academic language is used over
and over again in the context of
math.
America’s Choice (2006)
Teacher Lesson Plan
Lesson Activities
Student Discourse
Document review
Observation
Interviews
Encourages rituals and routines
conducive to purposeful
interaction with math and
activities promoting sharing and
discussion of thinking and
strategies
America’s Choice (2006)
Lesson Activities
Teacher Lesson Plan

Document Review
Observation
Interviews
Provides comprehensive
support by offering detailed
instructional guidance, ELL
support, and a host of informal
and formal assessments
America’s Choice (2006)
Lesson Activities
Teacher Lesson Plan
Student work/reflections

Document Review
Observation
Interviews

Abstract (if available)

Abstract The achievement gap is a persistent academic disparity between White and Asian students and ethnic minorities, English Language Learners, and low-income students. The academic disparity exists within the realm of mathematics. Although many factors are cited for contributing to the achievement gap, this study reviews institutional racism, meager institutional support, and poor mathematics instruction as contributors to poor academic achievement by historically poor or underperforming minority students. This case study is one of nine doctoral dissertations focused on the theme of urban schools that have narrowed the achievement gap with a focus on middle school algebra achievement. This study focused on an urban school that experienced sustained academic achievement in garnering at least 2 years of rising scores on the Academic Performance Index and the California Standardized Test (CST) as well as 3 consecutive years of at least 80% proficiency on the Algebra 1 CST. The author cites leadership, a collaborative community, data-driven culture, and instruction focused on conceptual understanding of standards to enhance student learning, especially in Algebra 1. This research raises questions regarding the value of curricular autonomy as opposed to a strong attachment to published curricula related to teaching subjects such as algebra.

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Asset Metadata

Creator Sagun, Theodore (author)

Core Title Urban schools that have narrowed the achievement gap: middle school math achievement in an urban setting

School Rossier School of Education

Degree Doctor of Education

Degree Program Education (Leadership)

Publication Date 04/06/2010

Defense Date 02/26/2010

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

Tag achievement gap,algebra,math,middle school,OAI-PMH Harvest

Place Name California (states)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Gothold, Stuart E. (committee chair), Hocevar, Dennis J. (committee member), Marsh, David D. (committee member)

Creator Email theodor1114@yahoo.com,trsagun@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m2896

Unique identifier UC1152362

Identifier etd-Sagun-3505 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-306276 (legacy record id),usctheses-m2896 (legacy record id)

Legacy Identifier etd-Sagun-3505.pdf

Dmrecord 306276

Document Type Dissertation

Rights Sagun, Theodore

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