AN EXAMINATION OF THE ACHIEVEMENT GAP AND SCHOOL LABELS IN A SOUTHWEST SUBURBAN DISTRICT IN THE UNITED STATES By Matthew D. Strom A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Education in Educational Leadership Northern Arizona University December 2011 Approved: Richard L. Wiggall, Ed.D., Chair Walter J. Delecki, Ph.D. Gary Emanuel, Doctor of Arts George Montopoli, Ph.D.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
AN EXAMINATION OF THE ACHIEVEMENT GAP AND SCHOOL LABELS IN A
SOUTHWEST SUBURBAN DISTRICT IN THE UNITED STATES
By Matthew D. Strom
A Dissertation
Submitted in Partial Fulfillment
of the Requirements for the Degree of
Doctor of Education
in Educational Leadership
Northern Arizona University
December 2011
Approved:
Richard L. Wiggall, Ed.D., Chair
Walter J. Delecki, Ph.D.
Gary Emanuel, Doctor of Arts
George Montopoli, Ph.D.
ii
ABSTRACT
AN EXAMINATION OF THE ACHIEVEMENT GAP AND SCHOOL LABELS IN A
SOUTHWEST SUBURBAN DISTRICT IN THE UNITED STATES
MATTHEW D. STROM
School labeling, or ranking, has become common place in the NCLB era of
school accountability. Most states have implemented a system that enables the public to
compare school to school and district to district. Labeling systems were intended by
NCLB to measure the effectiveness of a school and the ability of a school to ensure equal
educations to subgroups throughout their population. NCLB was a “call to arms” to
address the epidemic of lagging student achievement in minority subgroup populations
throughout the United States. Schools that did not leave any children behind were
intended to be recognized as superior to the rest. Ten years later research is muddled on
the effects of NCLB with respect to the very achievement gap it sought to address.
School ranking systems throughout the United States are being examined on how well
they identify schools that have met the requirements of NCLB. The primary requirement
of NCLB is for a school to close the achievement gap. Within this study you will find an
examination of the achievement gap in a suburban school district within the state of
Arizona and consequently an examination of the labels attached to this district’s schools
by the Arizona Department of Education. The findings for the research can be
summarized under two major themes. One theme was that a wide majority of schools in
this district, with exceptional and non-exceptional labels issued by ADE, still had
significant work to be done in closing the academic achievement gap between ethnicities.
iii
The second theme being that a school label within this district is highly associated with
certain demographic variables. Combining both of these themes results in a better
understanding of the relationship between ADE issued school labels and the ability of a
school to accomplish the mandate set forth in NCLB of closing the achievement gap
between ethnic subgroups. Administrators, teachers and parents throughout the suburban
school district need to be aware of the relationships studied in this research. School-level
and district-level administrators throughout the district must understand that while several
schools in the district, and the district itself, are viewed favorably throughout the state of
Arizona there is still much to accomplish with respect to closing the achievement gap.
Teachers throughout the district must not rest on the accomplishment of their school
being labeled highly by ADE. Teaching, educating and mentoring students of different
ethnicities is not best measured in a school label. Minority parents throughout the
district, as a result of this research, need to continue to become educated about what a
school is doing to best service the need of their individual child. Minority parents must
understand that this is the case whether their child is attending a school with an excelling
label or an underperforming label. All shareholders within this district must be cautious
in consuming the ADE issued school labels. Specifically, the shareholders must be
careful in interpreting what a school label means for an individual child and in particular
an ethnically diverse individual child.
iv
ACKNOWLEDGEMENTS
My grandfather, Herman Strom, fought in World War II to earn the GI Bill so he
could get his college degree. I would like to express my gratitude for my family
members who have sacrificed in their life so that I was in position to accomplish what I
have done in mine. These family members include: Herman Strom, Madeline Strom,
Harold Davis, Letha Davis, Andy Strom, Megan Strom and Betsy Jenkins. Most
importantly, I would like to express my thanks to my parents, Larry and Kathy Strom.
I am very grateful to have had a strong committee for this dissertation. Dr. Ric
Wiggall, my chair, served as a critical voice that kept positive in the constant revision
process. Dr. George Montopolli was a source of knowledge in the statistical analysis
relevant to my ideas. Dr. Walter Delecki and Dr. Gary Emanuel provided feedback and
suggestions to ensure the quality of my dissertation. I also wish to express my gratitude
to Dr. Edie Hartin whose expertise in writing ensured a smooth dissertation process.
I also had a group of colleagues that helped me cope with the daily reality of
being employed full time and in a doctoral program concurrently. Whether it was a
round of golf, a game of cards or a lunch time venting session the list of my colleagues
and friends that I owe thanks to for preserving my personal sanity include: Darin
Lawton, Matthew Barber and Sean Casey. Many thanks to all of those people
aforementioned as this dissertation would not have been started or finished without you.
History of Assessment ................................................................................... 18
History of Achievement Gap ......................................................................... 22
Historical Background of Equity in Education.............................................. 25
No Child Left Behind..................................................................................... 29
vi
CHAPTER PAGE
Studies and Reports Regarding the Trends in the Achievement Gap since NCLB............................................................................................ 34
4 Findings and Results ...................................................................................... 50 Introduction.............................................................................................. 50 Analysis of the Achievement Gap Using AIMS Proficiency Percentage............................................................................. 51 2010 AIMS Summary – Overall ........................................................ 51 2010 AIMS Summary – By Subject .................................................. 58 2011 AIMS Summary – Overall ........................................................ 66 2011 AIMS Summary – By Subject .................................................. 73
Summary of AIMS Proficiency Data from Spring 2010 and Spring 2011.............................................................................................. 80
vii
CHAPTER PAGE
Analysis of the Achievement Gap Using AIMS Scale Score .................. 80
2011 and 2011 Achievement Gap Analyzed through Average Scale Score............................................................................................... 81
Summary of ANOVAs and Average Scale Score.................................. 101 Ethnicity Proportion and Z-Score .................................................... 101 Correlation and Linear Regression between Ethnicity Proportions and Z-Score .................................................................. 102 2010 Data ................................................................................... 103 2011 Data ................................................................................... 106 Summary of Linear Regression Analysis .............................................. 110 A-F Letter Grade and Demographic Data.............................................. 111 Regressing A-F Letter Grade Value onto Ethnicity Proportions, Free and Reduced Lunch Rate and ELL Proportions Using Multiple Linear Regression ............................... 111 Summary of Relationship between School Level Variables and School Letter Grades....................................................................... 120 Summary of Chapter 4 ........................................................................... 121 5 Conclusions, Summary, Implications, and Recommendations.................... 123 Summary of the Study ........................................................................... 123 Overview of the Problem....................................................................... 124 Purpose Statement.................................................................................. 124 Research Methodology .......................................................................... 125 Major Findings Summary ...................................................................... 125 Research Question 1 ........................................................................ 126 Research Question 2 ........................................................................ 126 Research Question 3 ........................................................................ 127 Research Question 4 ........................................................................ 127 Major Findings Discussion .................................................................... 127
viii
CHAPTER PAGE
Findings Related to the Literature.......................................................... 130 Divergent Findings................................................................................. 133 Conclusions............................................................................................ 135 Implications for Action .......................................................................... 136 Recommendations for Further Research................................................ 139 Concluding Remarks.............................................................................. 140 REFERENCES .............................................................................................................. 143
APPENDICIES
A CUSD IRB Approval ......................................................................................... 154
1 ELL Percentages and Free and Reduced Lunch Percentages Comparison............44
2 Ethnic Comparison between Suburban School District and State of Arizona.......45
3 Spring AIMS 2010 Subgroup Performance by Ethnicity and Elementary School .................................................................................................52
4 Spring AIMS 2010 Subgroup Performance by Ethnicity and Junior High School ................................................................................................53
5 Spring AIMS 2010 Subgroup Performance by Ethnicity and High School ...........................................................................................................55
6 Spring AIMS 2010 Subgroup Proficiency Gaps Summary of All Schools ...........57
7 Spring AIMS 2010 Subgroup Proficiency Gaps Summary of Excelling Schools...................................................................................................58
8 Spring AIMS 2010 Elementary School #1 Performance by Subject and Ethnicity .............................................................................................59
9 Spring AIMS 2010 Junior High #4 Performance by Subject and Ethnicity .............................................................................................60
10 Spring AIMS 2010 High School #1 Performance by Subject and Ethnicity .............................................................................................62
11 Percent of All District Schools with Observed Gap in Mathematics, Reading and Writing by Ethnicity for 2010 Spring AIMS Administration...........63
12 Number of All District Excelling Schools with Observed Gap in Mathematics, Reading and Writing by Ethnicity for 2010 Spring AIMS Administration...........65
13 Spring AIMS 2011 Subgroup Performance by Ethnicity and Elementary School .................................................................................................67
14 Spring AIMS 2011 Subgroup Performance by Ethnicity and Junior High School ................................................................................................68
x
TABLE PAGE
15 Spring AIMS 2011 Subgroup Performance by Ethnicity and High School ...........................................................................................................69
16 Spring AIMS 2011 Subgroup Proficiency Gaps Summary of All Schools ...........71
17 Spring AIMS 2011 Subgroup Proficiency Gaps Summary of Excelling Schools...................................................................................................72
18 Spring AIMS 2011 Elementary School #1 Performance by Subject and Ethnicity .............................................................................................74
9 Spring AIMS 2011 Junior High #4 Performance by Subject and Ethnicity .............................................................................................75
20 Spring AIMS 2011 High School #1 Performance by Subject and Ethnicity .............................................................................................76
21 Percent of All District Schools with Observed Gap in Mathematics, Reading and Writing by Ethnicity for 2011 Spring AIMS Administration...........77
22 Number of All District Excelling Schools with Observed Gap in Mathematics, Reading and Writing by Ethnicity for 2011 Spring AIMS Administration...........79
23 Average Scale Score throughout the District on 2010 AIMS Mathematics Administration .......................................................................................................82
24 Levene’s Test for Homogeneity of Variance P-Values for Each School across Ethnicities with Respect to Average Scale Score .......................................85
25 Kolmogorov-Smirnov (KS) P-Values for Normality for 2010 and 2011 AIMS Distributions by Ethnicity ..................................................................88
26 Results from the 2010 ANOVA for 29 District-Wide Schools that did not violate the Assumptions of the ANOVA ...............................................................91
27 Results from the 2011 ANOVA for 34 District-Wide Schools that did not violate the Assumptions of the ANOVA ...............................................................94
28 2010 Results for Tukey HSD – Post Hoc Tests.....................................................97
29 2011 Results for Tukey HSD – Post Hos Tests .....................................................99
xi
TABLE PAGE
30 Linear Correlation Summary for 2010 Z-Score regressed on Percentage of Asian/Caucasian (ACP) Students at a School......................................................104
31 Coefficients and Standard Error of Coefficients for 2010 Z-Score Regressed onto Percentage of Asian/Caucasian Students at a School.................105 32 Linear Correlation Summary for 2011 Z-Score regressed on Percentage of Asian/Caucasian (ACP) Students at a School...............................107 33 Coefficients and Standard Error of Coefficients for 2011 Z-Score Regressed onto Percentage of Asian/Caucasian Students at a School.................108 34 Inter-correlation Matrix for Three Variables being examined in 2011 Multiple Linear Regression..................................................................................116 35 Collinearity Statistics for Three Variables used in 2011 Multiple Linear Regression............................................................................................................116 36 2011 Multiple Linear Regression Model for Letter Grade regressed onto the variables of SUM3 and Percentage of Asian Students at a School................119 37 2011 Single Variable Linear Regression Model for Letter Grade regressed onto the variable of Free and Reduced Lunch Percentage...................120 38 2011 Coefficient of Determination for Letter Grade regressed onto the variable of Free and Reduced Lunch Percentage.................................................120
xii
LIST OF FIGURES
FIGURE PAGE
1 NCLB Student Achievement Expectations for English for All Subgroups...........29
2 NCLB Student Achievement Expectations for Mathematics for All Subgroups ........................................................................................................30
3 Scatterplot of 2010 Z-Score versus Proportion of Asian and Caucasian Students at a School .............................................................................................105
4 Residual Plot for Regression Model regressing 2010 Z-Score onto Percentage of Asian/Caucasian Students at a School ..........................................106
5 Scatterplot of 2011 Z-Score versus Proportion of Asian and Caucasian Students at a School .............................................................................................108
6 Residual Plot for Regression Model regressing 2011 Z-Score onto Percentage of Asian/Caucasian Students at a School ..........................................110
7 Residual Plot for 2011 Regression that Regresses School Letter Grade onto Four Independent Variables.........................................................................112
8 Scatterplot Matrix for All Variables in 2011 Multiple Regression......................113
9 Residual Plot for 2011 Regression that Regresses School Letter Grade onto Three Independent Variables .......................................................................114
10 Scatterplot Matrix for Three Variables in 2011 Multiple Regression .................117
11 Residual Plot for 2011 Regression that Regresses School Letter Grade onto SUM3 and Percent of Students at a School that are Asian........................ 118
xiii
DEDICATION
This dissertation is dedicated to the four people who have shared in the sacrifice,
time commitment, highs and lows throughout the process. I would like to dedicate this
dissertation to my wife, Marcia, and three sons, Zavian, Quentin and Elijah. My passion
for educational equity has been maximized by your involvement in my life. My belief in
my own abilities has been secured through your constant support. And my purpose in life
is solidified in your existence.
xiv
“Do we truly will to see each and every child in this nation develop to the peak of his or
her capacities?”
Asa Hilliard, 1991
CHAPTER 1
Overview
Introduction
The average person makes many decisions on a daily basis, both serious and
mundane. In making these decisions, they have to account for various different
competing needs that must be prioritized. So, more often than not the average person
finds themselves looking for a label of sorts to help them make a decision that is both
informed and efficient. For example, one might read food labels to sort out the poor from
the good quality products; or society may judge politicians by the label of their political
party. Specifically, this study focuses on the average person who uses labels to identify
which school may provide the best quality education for their child while understanding
the requirement of No Child Left Behind (NCLB) to close the achievement gap. Prior to
NCLB a parent or guardian used sources such as word of mouth information from
community members to gather more information about a school. Now parents and
guardians alike enjoy the convenience of judging a school based on a label garnered from
student achievement data.
In 2001 President George W. Bush signed into law the No Child Left Behind Act
(NCLB). A reauthorization of the 1965 Elementary and Secondary Education Act,
NCLB was implemented with bipartisan support throughout the legislative branch (Hess
& Petrilli, p. 18). In fact spearheading the implementation of NCLB and school
accountability were democrats Senator Edward Kennedy and Representative George
Miller, and republicans Senator Judd Gregg and Representative John Boehner (Hess &
2
Petrilli, p. 19). These four members of the United States Congress served as critical
leaders in molding the principles implanted in NCLB.
One of the main reasons that Democrats and Republicans favored NCLB was due
to its sweeping reform with respect to the achievement gap (Hess & Petrilli, p. 21). In
essence “the law is premised on the notion that local education politics are fundamentally
broken, and that only strong, external pressure on school systems, focused on student
achievement, will produce a political dynamic that leads to school improvement” (Hess
& Petrilli, p. 23). NCLB required states to set up standards and measure whether students
performed to those standards broken down by subgroup. Consequently, student
achievement broken down by subgroup could address the overriding concern of the
achievement gap. The goal became to close the achievement gap by the school year
ending in the spring of 2014.
In the era of NCLB accountability is a mainstay for students, schools, districts,
and states. NCLB has caused the education system to emphasize a new culture of
accountability. It requires the closing of the achievement gap by 2014 and schools are
currently ranked, or labeled, based on their ability to make adequate yearly progress
(AYP) toward that goal. As a measurement, a school ranking should possess the quality
of correctly identifying those schools that are performing the best across all subgroups
and making progress toward closing the achievement gap by 2014. One might assume,
based on NCLB requirements, the schools ranked highest would be those showing gains
toward closing the achievement gap or schools that have already accomplished closing
the gap. Branding a school with the highest label, although it shows no progress in
3
diminishing the achievement gap, may garner criticism about the validity of the
measurement system used with respect to the goals of NCLB.
Upon the implementation of policies to satisfy NCLB the state of Arizona
determined that in order to be identified as an excelling school a school must be at least
one standard deviation above the average school in the percentage of students that exceed
on the Arizona Instrument to Measure Standards (AIMS) test (ADE, 2008, pg. 21).
Using this method of measurement to determine an excelling school versus a highly
performing school begs the question of whether the achievement gap is being closed at
schools in the state of Arizona. If a school needs to only score one standard deviation
above average in exceeds then are schools with a high proportion of White and Asian
students at an advantage? And if this is the case then does the label attached to schools in
Arizona have meaning beyond identifying the demographics and socioeconomic status of
a school? Essentially, are schools in the state of Arizona labeled as such because they
continue to attack the educational epidemic of low student-achievement within ethnic
minority subgroups?
The achievement gap between Hispanic and Black high school students in
comparison to their White and Asian peers appears to present an unsolved challenge
within the American and Arizona educational system. These gaps have existed at the
national, state, district and school level for decades. Furthermore, research suggests the
gaps are persisting within the twenty-first century educational climate. In a
Center for Education Policy release in October of 2009 it was stated:
Across subgroups and states, there was more progress in closing gaps at the
elementary and middle school levels than at the high school level. Even with this
4
progress, however, the gaps between subgroups often remained large – upwards
of 20 percentage points in many cases (p. 2).
The annually recurring achievement gaps at schools throughout the nation are
alarming. In the national era of school, district and state accountability it has been
deemed mandatory that educators take corrective measures to address this continuing
trend (NAEP, 2009, p.4).
The educational goal of closing the achievement gap is a necessity in ensuring the
civil rights of children in America. According to NCLB, in order for schools and districts
to receive their Title I funds each state shall establish annual measurable objectives for
subgroups within districts and schools. Schools and districts that fail to make adequate
yearly progress (AYP) toward those objectives for each subgroup will be subject to
corrective actions as determined by the state. NCLB mandated, to the applause of
politicians on both sides of the aisle, that the achievement gap be addressed within every
school, and district, nationwide.
Berliner, School Accountability and the Achievement Gap
David C. Berliner of Arizona State University is possibly one of the United
States’ foremost critics of NCLB and the remnants of school accountability. Berliner
views accountability sought by NCLB as placing the blame for low-achievement among
certain minority subgroups on teachers and administrators (Berliner, 2009). Berliner
argues that other factors, primarily out-of-school factors (OSFs), are more to blame for
the achievement gap in certain subgroups than the school, the teachers, or the
administrators.
5
One can ascertain that poverty and socio-economic status (SES) are central
problems for certain ethnic groups within America. Poverty exists at a higher rate in
America among both Hispanic and Black populations, 25.3% and 25.8% respectively,
than it does among White and Asian populations, 12.3% and 12.5% respectively
(DeNavas-Walt, Proctor, & Smith, 2010). Understanding this Berliner says there are
several educational consequences for children that live in poverty that result in a
persistent achievement gap (Berliner, 2009). One out-of-school factor that Berliner
brings to light in his research is Low Birth Weight (LBW) and Very Low Birth Weight
(VLBW). “African Americans, for example, are almost twice as likely as European
Americans to have a LBW child and almost three times as likely to have a VLBW child”
(Berliner, 2009). He goes on to mention that birth weight and IQ are correlated at
approximately 0.70 and that LBW children grow up to have IQs that are on average 11
points lower than those born at or above normal birth weight. Berliner’s argument is
simply that the effects of poverty more readily explain the achievement gap rather than a
failing educational system.
Throughout his research Berliner suggests several other OSFs that could be just as
prevalent in the achievement gap as teacher pedagogy. Berliner cites, with
accompanying statistics, OSFs like food insecurity, pollution, family violence and
neighborhood communities can all have a significant impact on the achievement gap.
The negative aspects of all of these OSFs occur more frequently in lower socio-economic
status (SES) and high poverty areas. All of these OSFs present one more hurdle for a
student in the educational process. The majority of these OSFs occur at a higher rate
among Hispanic and Black students because they, in higher proportions, live in poverty.
6
Berliner is not the only researcher who believes that the impact of poverty on
education might be the biggest factor in the relentless achievement gap. Achievement
gaps among subgroups within a population do not just occur in the United States.
Birenbaum and Nasser (2006) and Zuzovsky (2008) concluded that there is an
achievement gap in Israel between children who speak Hebrew and those who speak
Arabic. The Arab population in Israel is typically from families that have parents with
less education, lower income levels and a higher percentage of families that live below
the poverty line. These studies found that Jewish children, those who speak Hebrew,
perform better than the poorer Arabic children at mathematics. In fact, Birenbaum and
Nasser (2006) found the coefficient of determination to be around 0.6. Thus, about 60
percent of the variation between Jewish and Arabic children in mathematics can be
explained by the variation in their socioeconomic status and their variation in educational
resources.
The link between poverty, ethnic background and student achievement did not
begin with Berliner. The concern over these factors and equality of education started to
become a central focus when Dr. James S. Cooper of Johns Hopkins University published
Equality of Educational Opportunity in 1966. The study, known better as the Coleman
Report, concluded that, “black children started out school trailing behind their white
counterparts and essentially never caught up”(Viadero, p. 1). The study found that the
leading factor in contributing to this perpetual achievement gap in student’s academic
performance was their family backgrounds (Viadero, p. 1). Borman and Dowling (2010)
summarized, in the introduction to their research, that Coleman’s finding still holds a lot
of educational clout. Family background was a variable that inevitably included the
7
socioeconomic status of the family and could be classified within Berliner’s idea of out-
of-school factors.
Although poverty is quickly dismissed by many politicians as an excuse to not
produce a better educational system, Berliner’s idea that failing schools and the
achievement gap may be more the result of poverty should not be ignored. Berliner
simply believes that, “the problems of achievement among America’s poor are much
more likely to be located outside the school than in it” (Berliner, 2009, pg. 4). Poverty
can create a multitude of side effects including poor health, lack of food, minimal
prenatal care and consequently children that, on average, underperform in academics.
The Contraposition of Berliner
Some rectangles are not squares. In Euclidean geometry this statement is true.
Logically, if the propositional statement is valid then the contraposition of that statement
must also be valid. “Some a are not b,” naturally implies that “Some not b are not a”
(Tidman & Kahane, 2003, p. 319). In this geometry case, the contraposition is some non-
squares are not rectangles and it must be valid in Euclidean geometry. This final
statement must also be true because the argument is valid and the premise in Euclidean
geometry is true (Tidman & Kahane, 2003, p. 8). Berliner argues that some variables
associated with poverty result in poor student achievement. Furthermore, he provides
statistical evidence to suggest that the statement is valid (Berliner, 2009). Therefore, the
contraposition of his argument must be both valid and true. The contraposition is that
some high (non-low) student achievement is the result of variables associated with wealth
(non-poverty).
8
In fact, the contraposition of Berliner’s preposition is something that American
educators and educational leaders continue to ignore. In light of the conflicting evidence
with respect to the achievement gap, one could be hard pressed to argue with Berliner’s
viewpoint that the achievement gap has been the result of something much broader than
the educational system. The failures of schools with respect to student achievement
might be caused by more than poor teachers and poor administrators. The failure of
schools might have more to do with our inability as a country to fix our inept social
policies for those in poverty than fixing our educational system (Berliner, 2009). But, if
we are to conclude this we must not continue to ignore the contraposition. Schools that
we deem to be good or excellent throughout our states and our nation might be this, not
because of their best practices in the classroom and in administration, but due to their
limited exposure to the ill effects of poverty.
Educators and educational leaders have long thrived on the single school in a
district where all children are exceeding the standards. In the state of Arizona, the
excelling schools are those written about in the papers and those recognized by the
public. It must be the curriculum at those schools; it must be the teachers at those
schools; it must be the administrative leadership at those schools that cause them to be
excelling schools. The envy of all other schools in the state of Arizona excelling schools
are viewed as the places where things are done right; best practices are implemented and
leadership has a vision. Might it be that out-of-school factors are just as much to blame
for the excelling status of a school as OSFs are to blame for the failing status of another?
A staunch supporter of public education, Berliner attempts to protect the poor side
of education while glossing over the implications of his argument to the wealthy side.
9
The following research seeks to provide a foundation for framing school labels in the
state of Arizona: Berliner’s home state. Could it be that, even though a school is granted
a dignified label, little progress has been made at that school with respect to the
achievement gap? Might it be that these schools receive accolades merely because of
their demographics?
Statement of Problem
The purpose of this study was to examine the achievement gap in mathematics
and reading at all non-alternative schools within a suburban school district in the state of
Arizona for the 2009-2010 and 2010-2011 school years. The study was specifically
interested in student achievement, as measured by scale score, across ethnic subgroups
with respect to the state standardized AIMS examination. Furthermore, the study sought
to examine demographic reasons on why schools in this district obtained a certain school
label. Other interests of the study included the descriptive analysis of cross-sectional data
in reading and mathematics at these schools from 2009-2010 and 2010-2011 and the
predictive abilities of the percentage of non Black/Hispanic students with respect to the
percentage of students that exceeded on the AIMS examination. Using four main
research questions as a guide, data from two prior years was analyzed at schools
throughout the suburban school district.
Purpose of the Study
The purpose was to examine the achievement gap in mathematics and reading at
all non-alternative schools within a suburban school district within the state of Arizona
for the 2009-2010 and 2010-2011 school years. Furthermore, the study sought to
examine demographic reasons on why the schools within the suburban school district
10
obtained high and low school labels. The study was specifically interested in student
achievement across ethnic subgroups with respect to the state standardized AIMS
examination. Another interest of the study included the descriptive analysis of cross-
sectional data in reading and mathematics at these schools from 2009-2010 and 2010-
2011. Furthermore, the study sought to define the predictive abilities of the percentage of
non Black/Hispanic students with respect to the percentage of students that exceeded on
the AIMS examination. Using four main research questions as a guide, data from two
prior years was analyzed at schools throughout the suburban school district.
Research Questions
This dissertation was guided by the following questions:
1. What is the two year cross-sectional data trends for the achievement gap among
White, Asian, Hispanic and Black students on the 2009-2010 and 2010-2011
AIMS mathematics, reading and writing sections at all schools in the suburban
school district?
2. Is the average student achievement, as measured by average scale score, in ethnic
subgroups different for the 2009-2010 and 2010-2011 AIMS examinations at each
non-alternative school throughout the suburban school district?
3. Is the percentage of Asian and White students correlated with the state-issued z-
score, a standardized score for the percent of students that exceed on the AIMS
examination at a school in a given year, which helps determine school labels
within the state of Arizona?
4. Are free and reduced lunch rates, English Language Learner rates, percentage of
Asian students and percentage of White students correlated with the AZ LEARNS
11
A-F letter grades published by the state of Arizona for schools within the
suburban district?
These questions examine the achievement gap in the suburban district in order to
establish a baseline for the current validity of the school labeling system.
Significance of the Study
Despite the efforts of NCLB nine years ago, the eradication of the achievement
gap continues to elude our nation, our states and our districts (CEP, 2009). In an attempt
to solve why the achievement gap still persists one must identify a group of root causes.
Furthermore, the group of factors must be separated into what is controllable versus
uncontrollable by the education community. Thus, of the factors that contribute to the
persistence of the achievement gap many researchers believe that variance among
subgroup achievement can be most readily explained by out-of-school factors (OSFs).
OSFs can provide a multitude of reasons for the lingering gap (Berliner, 2010). Berliner
argues that schools are “not in the position to eliminate the achievement gap” because the
gap is the result of variables outside the schools control. Other researchers believe that
the unrelenting achievement gap is more related to teacher-level factors (Levine &
Researchers have taken note of the ceiling effect and as a result a focus on growth
rates among subgroups has become equally as important as the gap itself. Essentially, to
close the achievement gap it is necessary to have the growth rates of lower performing
subgroups to be higher than the growth rates of the highest performing subgroups. The
key to NCLB is that this must be achieved while the performance of all subgroups
increases. Unfortunately, research suggests that growth rates remain approximately
36
constant across ethnic groups when initial performance position is taken into account
(Goldschmidt, 2004).
The 2005 NWEA report initially concludes that there is statistically significant
evidence to suggest that the achievement gap since the implementation of NCLB has
been reduced. However, upon further analysis the report recognized that when other
measurements are taken into account less dramatic conclusions can be made about the
achievement gap since the implementation of NCLB. At one point in the report it is
stated, “In sixth grade mathematics, the actual achievement gap between European-
American and Black students in our sample increased from a gap of 7 points to 10 points
between the fall of 2003 and the spring of 2004” (NWEA, 2005, pg. 46). The devices in
which we choose to measure the achievement gap are of critical importance. A complete
picture of the gap will not be captured on simply the difference between the percentages
of students that meet proficiency between subgroups.
In October 2009, the Center on Education Policy (CEP) produced a report on
2007-2008 state test score trends and the test implications about the achievement gap.
The report included five main findings in state testing data:
1. All subgroups showed more gains than declines in grade 4 at all three
achievement levels.
2. As measured by percentages of students scoring proficient, gaps between
subgroups have narrowed in most states at the elementary, middle and high
school levels, although in a notable minority of cases gaps have widened.
37
3. Most often gaps narrowed because the achievement of lower-performing
subgroups went up rather than because the achievement of higher-performing
subgroups went down.
4. Gaps in percentages proficient narrowed more often for the Hispanic and
Black subgroups than for other subgroups.
5. Although mean scores indicate that gaps have narrowed more often than they
have widened, mean scores give a less rosy picture of progress in closing
achievement gaps than percentages proficient.
The overriding conclusion to these findings might be that state test scores suggest that the
achievement gap is being addressed. However, the fifth finding of this report poses
questions that are a necessity when measuring anything. The question that must be asked
when measuring is, “What is the measurement device and how is the measurement
constructed?” In this case the report, itself, addressed the issue.
When examining the achievement gap with the percentage of students that met the
proficient status on the state mandated standards assessment, the Center for Education
Policy found that seventy-one percent of the time the achievement gap had been
narrowed (CEP, 2009). Alternatively, when examining the same exact data with a mean
score as the measurement device the achievement gap was only narrowed fifty-nine
percent of the time. The report provided similar data with respect to areas were the
achievement gap actually widened. “Mean gaps also widened more than percentage
proficient gaps—37% of the time for mean scores versus 24% of the time for percentages
proficient” (CEP, 2009). The Center for Education Policy report does suggest that
overall the achievement gap is being narrowed. But, the important underlying issue that
38
is presented in the report of “how do we measure the achievement gap” must be noted.
Once again, variance in measurement techniques can create very different understandings
of the impact of NCLB.
The enactment of NCLB certainly moved the Elementary and Secondary
Education Act into the age of accountability. In every state the state-wide standards
based testing varies but the main objective remains to hold schools accountable for
student achievement in every subgroup. The argument can be made whether these
accountability systems play a role in increasing student achievement. Costrell (1997) and
Bishop (1997), in separate studies, concluded that exit examinations created awareness
and improvement of student achievement among leadership, faculty, and students. But,
much like differing opinions on the impact of NCLB on the achievement gap, other
researchers have concluded just the opposite. Studies have concluded that high-stakes
exit examinations have little to no effect on student achievement and can actually cause
an increase in dropout rates among low-achieving students (Jacob, 2001). Perhaps one
of the most infamous critics of high-stakes testing includes David Berliner. Amrein and
Berliner (2002) ran a group of studies on the precipice of NCLB that concluded that little
change was found when school based accountability was in place. Other researchers
have concluded that there is improvement in student achievement with school based
accountability systems in place (Carnoy & Loeb, 2002; Hanushek & Raymond, 2004).
Ultimately, as research continues to waffle over the impact of state accountability
systems for schools they also continue to debate over the impact of these systems on the
achievement gap. Hanushek and Raymond (2003a, 2003b, 2004) concluded that while
accountability increased student achievement for the White, Black and Hispanic
39
populations there were varying results with respect to the achievement gap. They found
that the White and Black achievement gap grew while the White and Hispanic
achievement gap got smaller. Differing effects for two different achievement gaps during
the era of school accountability created by NCLB.
Summary
Accountability has long been an issue within education. Oral examinations
served as an accountability technique for students during the thirteenth century. In the
nineteenth century Mann and Howe implemented written examinations in order to hold
students accountable for knowledge. Over the course of the last century accountability
has expanded to now include teacher, school, district and state accountability.
School, district and state accountability over that last five decades have had a
primary focus on equity in education. Brown v. Board of Education, Title IX, IDEA, and
NCLB all have primary purposes that can be generalized under the common theme of
equity in education. Holding schools, districts and states accountable for equal
educational access and equal educational outcomes is the goal of these judicial and
legislative developments.
NCLB was thought to be the first major Civil Rights Act of the twenty-first
century. Closing the achievement gap amongst various subgroup populations in
American education was the central focus in NCLB. The achievement gap had been
documented during the previous three decades and NCLB set out to make education
equitable for all race, gender, and SES subgroups.
Research on the impact of NCLB with respect to the achievement gap is
convoluted. Findings from different researchers often paint different pictures to whether
40
NCLB has had a significant impact on closing the achievement gap across the United
States. Some research suggests that the achievement gap has been decreased in years
following the implementation of NCLB. Other research suggests that while the gap may
have been reduced the reduction is minimal at best. Finally, some research implies that
the metric in measuring the achievement gap can play a significant role in ones
conclusion on the impact of NCLB on the achievement gap.
Mann and Howe turned the keys to ignition over fifteen decades ago when they
began administering written examinations as a means for measuring student progress.
Measuring has now become of instrumental importance to American educators. The
achievement gap has been of particular interest to measure as evidenced by the
implementation of NCLB. The impact of NCLB and its school accountability systems on
the achievement gap may take another fifteen decades to unravel.
Chapter 3
Methodology
Introduction
A description of the research design, the research questions that guided the study,
the target population, sample procedures, the sample, research instrumentation, data
collection procedures, and data analysis plans are presented. Before providing the
methodology for the research a brief review of the purpose of the study and the research
questions are provided.
Restatement of the Problem
The purpose of this study was to examine the achievement gap in mathematics
and reading at all non-alternative schools within a suburban school district in the state of
Arizona for the 2009-2010 and 2010-2011 school years. The study was specifically
interested in student achievement, as measured by scale score, across ethnic subgroups
with respect to the state standardized AIMS examination. Furthermore, the study sought
to examine demographic reasons on why schools in this district obtained a certain school
label. Other interests of the study included the descriptive analysis of cross-sectional data
in reading and mathematics at these schools from 2009-2010 and 2010-2011 and the
predictive abilities of the percentage of non African-America/Hispanic students with
respect to the percentage of students that exceeded on the AIMS examination. Using four
main research questions as a guide, data from two prior years was analyzed at schools
throughout the suburban school district.
42
Restatement of Research Questions
This dissertation was guided by the following questions:
1. What is the two year cross-sectional data trends for the achievement gap among
White, Asian, Hispanic and Black students on the 2009-2010 and 2010-2011
AIMS mathematics, reading and writing sections at all schools in the suburban
school district?
2. Is the average student achievement, as measured by average scale score, in ethnic
subgroups different for the 2009-2010 and 2010-2011 AIMS examinations at each
non-alternative school throughout the suburban school district?
3. Is the percentage of Asian and White students correlated with the state-issued z-
score, a standardized score for the percent of students that exceed on the AIMS
examination at a school in a given year, which helps determine school labels
within the state of Arizona?
4. Are free and reduced lunch rates, English Language Learner rates, percentage of
Asian students and percentage of White students correlated with the AZ LEARNS
A-F letter grades published by the state of Arizona for schools within the
suburban district?
These questions examine the achievement gap in the suburban district in order to
establish a baseline for the current validity of the school labeling system.
43
Research Design
Ex-post facto data was analyzed with quantitative methods for this research. The
use of quantitative research methods allowed evaluation of Arizona’s school labeling
system with respect to the suburban school district according to two years of cross-
sectional data.
Target Population
The population of interest includes all schools within the suburban school district
in the state of Arizona. In specific, due to the convenience sample the actual population
is specifically limited to the suburban school district being analyzed.
Sample
From the 2009-2010 and 2010-2011 school years the suburban school district had
41 schools. Within those two years the district schools received diverse labelings from
the Arizona Department of Education. Specifically, the district had schools ranging from
underperforming to excelling. Furthermore, since the district is a unified district these
labels were distributed across the elementary, junior high and high school levels. As a
result, a convenient sample for this study consists of state testing data, student
demographic data and school labels from the 2009-2010 and 2010-2011 school years for
the 41 schools in the suburban school district that existed for both of the testing years.
44
Sampling Procedures
The suburban school district was selected as a convenient sample of schools in the
state of Arizona. The district has a diverse population of students across ethnic groups,
SES status and English-language learners. As reflected in Table 1, the population of
students in the district was 4.77% ELL in comparison to a statewide ELL rate of 6.7%
(ADE, 2011). The district also had 28.47% of their students receiving Free and Reduced
Lunch Program benefits in comparison to the statewide rate of 41.5% (ADE, 2011).
Table 1
ELL Percentages and Free and Reduced Lunch Percentages Comparison
ELL
Free and Reduced Lunch Percentages
District 4.77% 28.47%
Statewide 6.7% 41.5%
According to ethnic demographics (see Table 2) the suburban district is 6.7%
Black, 25.8% Hispanic, 57.1% White and 8.5% Asian while the state is 5.5%, 42.2%,
42.9% and 2.8% in those respective categories (ADE, 2011).
45
Table 2
Ethnic Comparison between Suburban School District and State of Arizona
District
State of Arizona
Black 6.77% 5.5%
Hispanic 25.8% 42.2%
White 57.1% 42.9%
Asian 8.5% 2.8%
The diversity of this district in comparison to the state made it an ideal convenience
sample for the purposes of the study.
Data Collection Procedures
Data were gathered from the results of the statewide AIMS test which is given on
a yearly basis to third through eight grade and tenth grade students. The data was
obtained from the Arizona Department of Education (ADE) website for each of the two
academic school years and three subject areas to be analyzed. The data, as distributed by
ADE, is provided to the general public in a Microsoft Excel spreadsheet. This
spreadsheet was utilized to obtain student achievement data.
46
Data Analysis
The quantitative analysis examined whether a school label is linked to the closing
of the achievement gap at that school within the suburban school district. Cross sectional
data trends were examined by creating bar graphs showing the difference in average scale
score between subgroups over the spring 2010 and 2011 exam administrations.
Furthermore, cross sectional data were analyzed by constructing stacked bar graphs based
on student achievement labels of exceeding, meets, approaching, and fall far below to
examine the first research question.
In order to examine the second research question, priori ANOVA tests, with
family-wise α ≈ 0.06 due to six post-hoc pair-wise comparisons, was performed using
average scale score and standard deviation of scale score for each subgroup in each
testing year at every district school. Post-hoc tests using Tukey-Kramer method were run
to analyze pair-wise comparisons. The Tukey-Kramer post-hoc analysis was conducted
at α=0.01. The post-hoc alpha level accounts for the Bonferroni correction and limits the
overall probability of committing a Type I error to 0.06 because, at most, six pair-wise
comparisons were made.
In order to analyze the third research question, Pearson’s correlation coefficient
and, subsequently, a linear regression was performed on the two bivariate scatterplots
produced using district data from each of the AIMS administrations in 2010 and 2011.
The model uses a percentage of Asian and White students as the independent variable and
the z-score produced by the state as the dependent variable. After performing the
analysis, the coefficient of determination, the slope of the regression model, the standard
error of the slope and the p-value for the slope were recorded in order to show if there is
47
statistical significance in the model. A coefficient of determination greater than 0.30 will
suggest that the percentage of Asian and White students has predictive capability for the
z-score that ADE uses to label and excelling school because the effect size, as measured
by r, will be medium (Cohen, 1992, pg. 157).
A simple multiple linear regression was performed on 2011 letter grade data to
examine the fourth research question. The model used free and reduced lunch rate,
English Language Learner rates, percentage of Asian students and percentage of White
students as the independent variables and the quantitative A-F letter grade as the
dependent variable. The coefficients, standard error of the coefficients, t-score and p-
value for each independent variable was noted along with the coefficient of determination
for the entire model. P-values for each coefficient being less than α = 0.05 will suggest
that the variable significantly contributes to the model. A coefficient of determination
greater than 0.13 will suggest that the simple multiple regression model has predictive
capabilities for the ADE A through F letter grade because the effect size, as measured by
f2, will be medium (Cohen, 1992). Corresponding residual plots for regression models
will also be analyzed to ensure the errors in the regression models constructed are
random.
Validity
Validity is a term within research that has a wide variety of definitions. Kerlinger
(1964) simply stated, “Are we measuring what we think we are?” Black and Champion
(1976) offered the following definition for validity, “the measure that an instrument
measures what it is supposed to.” Hammersley’s (1987) stated that, “an account is valid
if it represents accurately those features of the phenomena, that is intended to describe,
48
explain or theorise.” The purpose of the study was to examine the achievement gap at
schools in the suburban school district and the labels placed on these schools by Arizona
Department of Education system. Validity therefore can be seen in the ability of the
study to accurately reflect the achievement gap at these schools and consequently provide
some explanation for that schools corresponding school label. The theory of the study
being that labels attached to district schools provide little evidence, through descriptive
and inferential statistics, for the closing of the achievement gap.
External Validity
External validity addresses the ability to generalize a study to other populations.
The results from this research study cannot be generalized to other districts in the state of
Arizona. Because the sample consists of a convenience sample of one suburban school
district future research in other districts will need to be completed before any results can
be generalized throughout the state of Arizona. Furthermore, the extent to which the
results can be generalized to other states with different school ranking, or labeling,
systems exist is limited as well.
Internal Validity
Internal validity deals with the truth about inferences made with respect to a
cause-effect relationship (Trochim, 2006). Curren and Werth (2004, p. 220) state that
internal validity is the, “assertion that an observed relation between two variables reflects
a causal process or that the lack of an observed relation reflects the lack of a causal
process.” The research was performed on ex-post facto data from an observational study
49
which is the AIMS test. As a result, no inferences about cause and effect relationships
will be made in this study. Therefore, since there will be no inference about a causal
relationship between variables internal validity is not a concern within this study.
Chapter 4
Findings and Results
Introduction
The study reported in this chapter examined the achievement gap at schools in a
suburban school district in the southwest United States. Furthermore, this study sought to
examine the relationship between variables such as percent of students at a school that
were of Asian and White ethnicities and numeric variables such as z-score that help ADE
in determining school labels. The chapter is organized in terms of the four specific
research questions that were posed in Chapter 1 and restated in Chapter 3.
First, a report of the analysis is provided on the achievement gap at the 40 schools
throughout the district by examining proficiency percentages during 2010 and 2011
AIMS examinations administrations. Second, the chapter moves to the analysis of the
achievement gap at the 40 schools throughout the district by examining average scale
score by running ANOVAs on 2010 and 2011 AIMS data. Third, an examination of the
relationship between z-score, a variable instrumental to determining AZ Learn Legacy
school labels, and percent of Asian and White students at a school by using correlation
and regression. Finally, in continuing with the relationship between variables the chapter
commences with examining the relationship between four different school-level variables
and the school letter grade assigned by ADE for the 2011 school year. A final summary
of all the information found throughout the chapter is the concluding analysis that
presides at the end.
51
Analysis of the Achievement Gap Using AIMS Proficiency Percentage
The analysis of the achievement gap using the proportion of students proficient on
the AIMS examination during the 2010 and 2011 AIMS test administration follows. This
analysis addresses the first research question of:
1. What is the two year cross-sectional data trends for the achievement gap
among White, Asian, Hispanic and Black students on the 2009-2010 and
2010-2011 AIMS mathematics, reading and writing sections at all schools in
the suburban school district?
The analysis of this research question is divided into two sections. One of these sections
addresses the results of the 2010 AIMS administration and the other addresses the results
of the 2011 AIMS administration.
2010 AIMS Summary - Overall
An achievement gap during the 2010 Spring AIMS administration was noted at
the majority of the schools in the suburban school district with respect to proficiency.
Proficiency is determined by the proportion of students that meet or exceed the standards
on the AIMS examination. As revealed in Table 3, at Elementary #1, 98.33% of the
Asian students were proficient on the AIMS examination while only 67.15% and 77.53%
of the Black and Hispanic students were proficient, respectively. The gap in proficiency
between Asian and Black students was 31.18% and the proficiency gap between Asian
and Hispanic students was 20.8%. Similar performance gaps at Elementary School #1
exist between White and Black students and White and Hispanic students. In fact, the
gap between both of these groups was 21.21% and 10.83%, respectively.
52
Further examination of the other two elementary schools on Table 3 shows similar
results with respect to the achievement gap amongst students of different ethnicities
during the 2010 Spring AIMS administration. At Elementary #2 Asian and White
students were proficient on the exam at 92.23% and 92.3%, respectively. In contrast,
Black and Hispanic students were proficient on the exam at a rate of 76.67% and 81.3%,
respectively. At Elementary #3 Asian and White students were proficient on the exam at
95.52% and 89.71%, respectively. This compares to Black and Hispanic students being
proficient on the exam at 81.6% and 80.75%, respectively. Once again the gaps in
performance amongst different ethnic subgroups are observed.
Table 3
Spring AIMS 2010 Subgroup Performance by Ethnicity and Elementary School
School
Ethnicity % FFB % Approach % Meets % Exceeds
Elementary School #1
Asian 0% 1.67% 38.89% 51.44%
Black 5.71% 27.14 52.86 14.29
Hispanic 7.34% 15.14 58.26 19.27
White 2.08% 9.56 51.23 37.13
Elementary School #2
Asian 0.49% 7.28 44.66 47.57
Black 4.44% 18.89 58.89 17.78
Hispanic 4.88% 13.82 67.48 13.82
White 1.37% 6.33 59.81 32.49
(table continues)
53
Table 3 (continued)
School
Ethnicity % FFB % Approach % Meets % Exceeds
Elementary School #3
Asian 1.63% 2.86 47.76 47.76
Black 0% 18.39 70.11 11.49
Hispanic 7.49% 11.46 60.96 19.97
White 3.60% 6.69 56.75 32.96
Achievement gap trends are also seen at the junior high level during the 2010
Spring AIMS administration. As reported in Table 4, at junior high #4 89.43% and
87.59% of Asian and White students were proficient on examinations taken. Noticeably
below this performance, at junior high #4 Black and Hispanic students were 70.79% and
73.77% proficient, respectively. The smallest gap in proficiency existed between White
and Hispanic students at junior high #4 where White students were13.82% more likely to
be proficient than Hispanic students.
Table 4
Spring AIMS 2010 Subgroup Performance by Ethnicity and Junior High School
School
Ethnicity % FFB % Approach % Meets % Exceeds
Junior High #4 Asian 3.40% 7.17% 55.85% 33.58%
Black 10.11% 19.10 56.18 14.61
Hispanic 8.83% 17.40 60.52 13.25
White 4.14% 8.27 62.77 24.82
(table continues)
54
Table 4 (continued)
School
Ethnicity % FFB % Approach % Meets % Exceeds
Junior High #5 Asian 3.59% 5.99 53.89 36.53
Black 6.17% 14.81 66.67 12.35
Hispanic 9.47% 11.89 58.15 20.48
White 2.87% 6.65 61.21 29.27
Junior High #6 Asian 7.32% 18.29 50.00 24.39
Black 18.86% 21.14 48.57 11.43
Hispanic 20.41% 24.55 47.75 7.28
White 7.53% 11.88 59.53 21.06 At the high school level a similar trend is noticed for the Spring 2010 AIMS
administration. As stated in Table 5, all four high schools in this suburban school district
displayed more than a 10% difference in proficiency for every comparison of
White/Asian and Black/Hispanic performance. The smallest achievement gap between
these subgroups existed at High School #4 where Asian students were only 11.95% more
likely to be proficient than Hispanic students. The largest achievement gap between
these subgroups existed at High School #2 where the White-Hispanic gap was at 30.62%
with respect to proficiency.
55
Table 5
Spring AIMS 2010 Subgroup Performance by Ethnicity and High Schools
School
Ethnicity % FFB % Approach % Meets % Exceeds
High School #1 Asian 1.08% 4.30% 58.06% 36.56%
Black 7.81% 20.31 57.03 14.84
Hispanic 12.84% 13.76 55.96 17.43
White 4.34% 9.37 59.20 27.09
High School #2 Asian 4.17% 9.52 41.07 45.24
Black 11.36% 17.73 55.91 15.00
Hispanic 14.81% 27.53 48.17 9.49
White 4.39% 7.32 57.91 30.37
High School #3 Asian 1.59% 5.82 40.74 51.85
Black 9.74% 13.96 55.19 21.10
Hispanic 9.93% 16.06 53.79 20.22
White 3.56% 5.84 50.36 40.24
High School #4 Asian 3.03% 9.09 55.30 32.58
Black 16.33% 22.45 52.04 9.18
Hispanic 8.15% 15.93 57.04 18.89
White 2.52% 7.65 62.74 27.09
A summary table of all achievement gaps as measured by proficiency percentage
on the 2010 Spring AIMS examination can be found in Table 6. The data shows that of
the 40 schools within the suburban school district the majority of them still exhibit large
56
differences in proficiency between Black/Hispanic students and Asian/White students.
For example, 29 out of the 40 schools, or 72.5%, exhibited a gap in proficiency that was
at least 10% lower for Black students as compared to White students. Similarly, 62.5%
of the schools within the district showed at least a 10% proficiency gap between Hispanic
and White students.
As found in the Spring 2010 AIMS administration, schools within this district
continued to struggle with closing the achievement gap with respect to proficiency
percentage. Also detailed in Table 6, only 3 out of 40 schools within the district showed
a successful closing of the achievement gap between Black and Asian students. Of
further note is that two of these three schools had special circumstances in closing this
gap. One of the schools was a preparatory school set up by the district in order to capture
high achieving students and maximize their academic achievement. Another of these
schools had a significantly small portion of Asian students and the closing of the gap was
most likely the result of increased variance amongst such a small Asian student sample.
The data in Table 6 shows that achievement within the district still continues to be
different between ethnic subgroups.
57
Table 6
Spring AIMS 2010 Subgroup Proficiency Gaps Summary of All Schools
Number of Schools with Observed Gap
Ethnicity
X* < -10%
-10% < X < 0% 0% < X < 10% X > 10%
Black-Asian 32 5 2 1
Hispanic-Asian 27 11 1 1
Black-White 29 9 2 0
Hispanic-White 25 14 1 0
Note. *X represents the difference between percentages of students proficient in each ethnic subgroup given in the gap column.
The data from the 2010 Spring AIMS administration as compared to school labels
is more prevalent when examining the achievement gaps at each school by label. Table 7
summarizes the achievement gaps observed for all excelling schools in the district. The
data in Table 7 shows that of the 22 excelling schools during the 2010 school year
anywhere from 63.6% to 72.7% of them showed a sizeable achievement gap between
Hispanic/Black students and White/Asian students. Once again, one of the only schools
to have realized a closing of the achievement gap between these subgroups was a
specialty school designed for high academic achieving students. This school can be
observed in the gap column represented by 0% < X < 10%. Besides this school only two
other schools that were labeled excelling demonstrated a closing of the achievement gap.
One of these schools exhibited this closing between Black and Asian students and the
58
other between Hispanic and Asian students. Overall the majority of excelling schools
demonstrated persistent achievement gaps during the 2010 AIMS administration.
Table 7
Spring AIMS 2010 Subgroup Proficiency Gaps Summary of Excelling Schools
Number of Excelling Schools with Observed Gap
Ethnicity
X* < -10%
-10% < X < 0% 0% < X < 10% X > 10%
Black-Asian 15 5 1 1
Black-White 16 5 1 0
Hispanic-Asian 14 6 1 1
Hispanic-White 14 7 1 0
Note. *X represents the difference between percentages of students proficient in each ethnic subgroup given in the gap column 2010 AIMS Summary – By Subject
Examining the results of the 2010 Spring AIMS administration on the school level
by subject matter gives a similar picture as the overall summary presented above. At the
vast majority of schools large achievement gaps are observed between White/Asian and
Hispanic/Black subgroups in each of the three subjects: mathematics, reading and
writing. These gaps exist across all levels of schooling within the district from the
elementary level to the high school level.
Elementary #1 exhibits disparate performance amongst ethnic subgroups when
broken down by subject. As demonstrated in Table 8, the largest achievement gap exists
between the Asian and Black students at Elementary #1 where it was 36.47% more likely
59
for an Asian student to show proficiency on the mathematics examination than a Black
student. One should also observe that the smallest achievement gap is observed between
White and Hispanic students in writing. A White student during the 2010 Spring AIMS
administration was only 4.34% more likely to show proficiency in writing in comparison
to a Hispanic student. Overall, Table 8 reveals that Elementary School #1 still exhibits
large performance gaps between ethnic subgroups at this school when disaggregated by
subject.
Table 8
Spring AIMS 2010 Elementary School #1 Performance by Subject and Ethnicity
Subject
Ethnicity % FFB % Approach % Meets % Exceeds
Mathematics Asian 0% 2.82% 19.72% 77.46%
Black 10.71% 28.57 35.71 25.00
Hispanic 11.63% 13.95 50.00 24.42
White 3.98% 9.48 36.39 50.15
Reading Asian 0% 1.41 53.52 45.07
Black 3.57% 28.57 64.29 3.57
Hispanic 4.65% 17.44 63.95 13.95
White 0.91% 8.23 60.37 30.49
Writing Asian 0% 0 47.37 52.63
Black 0% 21.43 64.29 14.29
Hispanic 4.35% 13.04 63.04 19.57
White 0.62% 12.42 62.73 24.22
60
Information provided in Table 9, shows similar patterns exist at the junior high
level with respect to the achievement gap across subgroups. Junior high #4 displayed
issues that were seen across most of the junior highs within the district. As one can
observe in Table 9, Black/Hispanic proficiency rates were lower than White/Asian
proficiency rates across all three subjects. The most significant proficiency gap is the
Asian-Black gap in mathematics where Asian students were 34.98% more likely to be
proficient at mathematics than their student peers that were Black. The smallest
achievement gap was in writing where Black students lagged behind their Asian peers by
5.38% in proficiency. Table 9 clearly demonstrates the existing gaps in proficiency
between ethnicities at junior high #4.
Table 9
Spring AIMS 2010 Junior High #4 Performance by Subject and Ethnicity
Subject
Ethnicity % FFB % Approach % Meets % Exceeds
Mathematics Asian 6.42% 3.67% 32.11% 57.80%
Black 19.72% 25.35 32.39 22.54
Hispanic 17.11% 23.03 38.82 21.05
White 9.11% 10.01 41.08 39.79
Reading Asian 0.92% 11.01 68.81 19.27
Black 4.23% 16.90 66.20 12.68
Hispanic 3.95% 14.47 73.68 7.89
White 1.02% 8.19 75.03 15.75
(table continues)
61
Table 9 (continued)
Subject
Ethnicity % FFB % Approach % Meets % Exceeds
Writing Asian 2.13% 6.38 80.85 10.64
Black 2.78% 11.11 83.33 2.78
Hispanic 2.47% 12.35 76.54 8.64
White 0.50% 5.03 81.16 13.32
Imparted in Table 10, High School #1 shows that the observed pattern of schools
demonstrating significant achievement gaps in subject areas continues at the high school
level. In mathematics the smallest achievement gap was between White and Hispanic
students where White students were 19.17% more likely to achieve proficiency. In
reading, the gap between White and Black students was the smallest with White students
demonstrating a rate of proficiency that was 7.67% greater. Writing exhibited the
smallest achievement gaps. The smallest of the gaps in writing existed between Hispanic
and White students with Hispanic students being 3% less likely to pass the AIMS writing
examination.
62
Table 10
Spring AIMS 2010 High School #1 Performance by Subject and Ethnicity
Subject
Ethnicity % FFB % Approach % Meets % Exceeds
Mathematics Asian 3.33% 3.33% 36.67% 56.67%
Black 22.73% 25.00 38.64 13.64
Hispanic 30.77% 10.26 39.74 19.23
White 12.06% 9.80 45.98 32.16
Reading Asian 0% 3.33 76.67 20.00
Black 0% 16.67 73.81 9.52
Hispanic 2.82% 21.13 66.20 9.86
White 0.53% 8.47 73.54 17.46
Writing Asian 0% 6.06 60.61 33.33
Black 0% 19.05 59.52 21.43
Hispanic 2.90% 10.14 63.77 23.19
White 0.25% 9.80 58.79 31.16
The patterns illustrated in the examination of the three schools in Table 10, Table
9 and Table 8 across the subjects of reading, writing and mathematics were consistently
observed throughout the schools in this suburban district. The summary of subject level
achievement gaps for all analyzed schools is provided in Table 11. In examining Table
11, it should be noted that at least 87.5% of all the schools within the district exhibited
lower proficiency performance amongst Hispanic/Black students than Asian/White
students in mathematics and reading. The subject where the achievement gap appears to
63
elude educators the most is mathematics where at least 92.5% of the district schools
showed an achievement gap amongst the ethnicities examined. Furthermore, at least
77.5% of the schools had mathematics achievement gaps that were at least a 10-
percentage point difference during the 2010 school year.
Table 11
Percent of All District Schools with Observed Gap in Mathematics, Reading and Writing
by Ethnicity for 2010 Spring AIMS Administration
Mathematics
X* < -10%
-10% < X < 0% 0% < X < 10% X > 10%
Black-Asian 90.00% 2.50 2.50 5.00
Hispanic-Asian 87.50% 5.00 2.50 5.00
Black-White 90.00% 7.50 2.50 0.00
Hispanic-White 77.50% 20.00 2.50 0.00
Reading
X* < -10%
-10% < X < 0% 0% < X < 10% X > 10%
Black-Asian 57.50% 32.50 7.50 2.50
Hispanic-Asian 60.00% 27.50 10.00 2.50
Black-White 62.50% 25.00 10.00 2.50
Hispanic-White 62.50% 30.00 7.50 0.00
(table continues)
64
Table 11 (continued)
Writing
X* < -10%
-10% < X < 0% 0% < X < 10% X > 10%
Black-Asian 52.63% 26.32 21.05 0.00
Hispanic-Asian 47.37% 26.32 21.05 5.26
Black-White 33.33% 28.21 30.77 7.69
Hispanic-White 35.00% 35.00 22.50 7.50
Note. *X represents the difference between percentages of students proficient in each ethnic subgroup given in the gap column.
When analyzing achievement gaps by subject for excelling schools (see Table 12)
the picture during the 2009-2010 school year is not much different. The vast majority of
excelling schools within the school district showed significant achievement gaps in
mathematics, reading and writing. Discovered in Table 12, in mathematics at least 20 of
the 22 excelling schools, or 90.9%, showed an achievement gap with respect to
proficiency. Reading and writing did not fare much better with at least 81.8% and
59.1%, respectively, of the excelling schools showing a gap. Overall, the tables show
that excelling schools within this suburban school district exhibited a distinct
achievement gap during the 2009-2010 school year.
65
Table 12
Number of All District Excelling Schools With Observed Gap in Mathematics, Reading
and Writing by Ethnicity for 2010 Spring AIMS Administration
Mathematics
X* < -10%
-10% < X < 0% 0% < X < 10% X > 10%
Black-Asian 19 1 1 1
Black-White 19 2 1 0
Hispanic-Asian 18 2 1 1
Hispanic-White 17 4 1 0
Reading
X* < -10%
-10% < X < 0% 0% < X < 10% X > 10%
Black-Asian 10 9 2 1
Black-White 12 7 3 0
Hispanic-Asian 11 7 3 1
Hispanic-White 12 8 2 0
Writing
X* < -10%
-10% < X < 0% 0% < X < 10% X > 10%
Black-Asian 8 7 6 1
Black-White 6 7 8 1
Hispanic-Asian 11 6 4 1
Hispanic-White 8 8 6 0
Note. *X represents the difference between percentages of students proficient in each ethnic subgroup given in the gap column
66
2011 AIMS Summary - Overall
As with the 2009-2010 AIMS data, an achievement gap during the 2011 Spring
AIMS administration was noticed at the majority of the schools in the suburban school
district with respect to proficiency. Table 13, as compared to Table 3 in the 2010 AIMS
summary, demonstrated the same pattern in achievement gaps during the 2010-2011
school year. At Elementary #1 96.46% of the Asian students were proficient on the
AIMS examination while only 82.76% and 80.20% of the Black and Hispanic students
were proficient, respectively. Similar performance gaps can be seen at Elementary
School #1 between Black and Hispanic students in comparison to White students where
88.70% of White students were proficient. Further examination of the other two
elementary schools in Table 13 shows similar results with respect to the achievement gap
amongst students of different ethnicities during the 2011 Spring AIMS administration.
At Elementary #2 Asian and White students were proficient on the exam at 95.05% and
91.60%, respectively. This compares to Black and Hispanic students being proficient on
the exam at 76.67% and 81.3%, respectively. At Elementary #3 Asian and White
students were proficient on the exam at 95.52% and 89.71%, respectively. This
compares to Black and Hispanic students being proficient on the exam at 85.71% and
78.22%, respectively. Once again, gaps in performance amongst different ethnic
subgroups are observed.
67
Table 13
Spring AIMS 2011 Subgroup Performance by Ethnicity and Elementary School
School
Ethnicity % FFB % Approach % Meets % Exceeds
Elementary School #1
Asian 1.97% 1.97% 34.48% 61.58%
Black 3.45% 13.79 70.69 12.07
Hispanic 2.54% 17.26 58.88 21.32
White 2.50% 8.80 49.82 38.88
Elementary School #2
Asian 0.50% 4.46 55.45 39.60
Black 3.57% 10.71 61.90 23.81
Hispanic 4.03% 17.74 60.48 17.74
White 1.40% 7.00 57.80 33.80
Elementary School #3
Asian 0.47% 5.16 44.13 50.23
Black 1.64% 16.39 67.21 14.75
Hispanic 4.57% 20.57 62.29 12.57
White 3.95% 11.07 55.25 29.72
Achievement gap trends are also seen at the junior high level during the 2011
Spring AIMS administration (see Table 14). At junior high #4 85.20% and 84.08% of
Asian and White students were proficient on examinations taken. Noticeably below this
performance at junior high #4 Black and Hispanic students were 68.57% and 70.72%
proficient, respectively. The smallest gap in proficiency existed between White and
Hispanic students at junior high #4 where White students were13.36% more likely to be
proficient than Hispanic students.
68
Table 14
Spring AIMS 2011 Subgroup Performance by Ethnicity and Junior High School
School
Ethnicity % FFB % Approach % Meets % Exceeds
Junior High #4
Asian 5.10% 9.69% 50.51% 34.69%
Black 8.57% 22.86 57.14 11.43
Hispanic 10.72% 18.55 55.94 14.78
White 5.52% 10.39 60.84 23.24
Junior High #5
Asian 2.74% 6.16 52.74 38.36
Black 9.35% 17.27 62.59 10.79
Hispanic 6.60% 16.75 57.11 19.54
White 4.37% 8.83 58.05 28.75
Junior High #6
Asian 3.85% 6.41 64.10 25.64
Black 27.87% 25.68 36.61 9.84
Hispanic 23.11% 26.32 45.49 5.08
White 10.53% 15.30 54.83 19.34
At the high school level a similar trend is noticed for the Spring 2011 AIMS
administration. As shown in Table 15, all four high schools in this suburban school
district displayed more than a 10% difference in proficiency for nearly every comparison
of White/Asian and Black/Hispanic performance. The only achievement gap that did not
show a 10% difference was at high school #1 where the gap in proficiency between
White and Hispanic students was 9.17%. The largest achievement gap between these
subgroups once again existed at High School #2 where the White-Hispanic gap was at
69
25.72% with respect to proficiency. All four of the high schools within this suburban
school district were labeled as excelling schools during the 2010-2011 school year.
Table 15
Spring AIMS 2011 Subgroup Performance by Ethnicity and High School
School
Ethnicity % FFB % Approach % Meets % Exceeds
High School #1
Asian 1.00% 3.00% 56.00% 40.00%
Black 13.29% 12.03 67.09 7.59
Hispanic 9.12% 14.04 63.16 13.68
White 5.01% 8.98 65.82 20.19
High School #2
Asian 2.16% 5.95 49.19 42.70
Black 12.15% 16.02 64.64 7.18
Hispanic 12.05% 24.32 55.87 7.76
White 4.05% 6.60 61.73 27.62
High School #3
Asian 1.31% 2.09 49.35 47.26
Black 8.54% 14.95 61.92 14.59
Hispanic 9.78% 17.53 61.25 11.44
White 3.48% 4.84 57.37 34.32
(table continues)
70
Table 15 (continued)
School
Ethnicity % FFB % Approach % Meets % Exceeds
High School #4
Asian 1.72% 5.17 63.79 29.31
Black 12.90% 18.55 55.65 12.90
Hispanic 9.41% 15.68 63.07 11.85
White 4.85% 6.21 64.11 24.83
A summary of all achievement gaps as measured by proficiency percentage on the
2011 Spring AIMS examination can be found in Table 16. The table shows that of the 40
schools examined within the suburban school district the majority of them still exhibit
large differences in proficiency between Black/Hispanic students and Asian/White
students. For example, 25 out of the 40 schools, or 62.5%, exhibited a gap in proficiency
that was at least 10% lower for Black students as compared to White students. Similarly,
60.0% of the schools within the district showed at least a 10% proficiency gap between
Hispanic and White students.
71
Table 16
Spring AIMS 2011 Subgroup Proficiency Gaps Summary of All Schools
Number of Schools with Observed Gap
Ethnicity
X* < -10%
-10% < X < 0% 0% < X < 10% X > 10%
Black-Asian 30 8 2 0
Hispanic-Asian 31 6 3 0
Black-White 25 11 2 2
Hispanic-White 24 12 3 1
Note. *X represents the difference between percentages of students proficient in each ethnic subgroup given in the gap column.
During the spring 2011 AIMS administration, schools within the suburban district
continued to struggle with closing the achievement gap with respect to proficiency
percentage. Results from analyzing descriptive statistics suggest that 2011 achievement
gap data remained very similar to 2010 achievement gap data. In the 2009-2010 school
year 3 out of 40 schools within the district showed a successful closing the achievement
gap between Black and Asian students. During the 2010-2011 school year this number
reduced to 2 out of 40. The 2009-2010 school year showed two schools had closed the
Hispanic-White achievement gap but during the 2010-2011 school year this number
increased to 4. Ultimately, it must be noted that for the vast majority of schools within
this school district large achievement gaps remained during the 2010-2011 school year.
The data from the 2011 Spring AIMS administration is more prevalent when
conditionally examining the achievement gaps at each school by label. Table 17 shows a
72
summary of the achievement gaps observed for all excelling schools. Of the 22 excelling
schools during the 2011 school year anywhere from 54.5% to 68.1% of them showed a
sizeable achievement gap between Hispanic/Black students and White/Asian students
(see Table 17). Once again, as detailed in Table 17, one of the only schools to have
realized a closing of the achievement gap between these subgroups was a specialty school
designed for high academic achieving students. This school can be observed in the gap
column represented by 0% < X < 10%. At a minimum 20 of the 22 excelling schools in
the district showed an achievement gap between the ethnic groups being examined.
Table 17
Spring AIMS 2011 Subgroup Proficiency Gaps Summary of Excelling Schools
Number of Excelling Schools with Observed Gap
Ethnicity
X* < -10%
-10% < X < 0% 0% < X < 10% X > 10%
Black-Asian 15 6 1 0
Black-White 13 8 1 0
Hispanic-Asian 14 6 2 0
Hispanic-White 12 8 2 0
Note. *X represents the difference between percentages of students proficient in each ethnic subgroup given in the gap column
73
2011 AIMS Summary – By Subject
Examining the results of the 2011 Spring AIMS administration on the school level
by subject matter gives a similar picture as the overall summary not disaggregated by
subject. At the vast majority of schools large achievement gaps are observed between
White/Asian and Hispanic/Black subgroups in each of the three subjects: mathematics,
reading and writing. These gaps exist across all levels of schooling within the district
from the elementary level to the high school level.
Elementary #1 exhibits disparate performance amongst ethnic subgroups when
broken down by subject. As conveyed in Table 18, the largest achievement gap exists
between the Asian and Black students at Elementary #1 where it was 15.49% more likely
for an Asian student to show proficiency on the mathematics examination than a Black
student. While this is a drastic improvement over the 2009-2010 gap it is still far from
having closed the achievement gap between these two ethnicities. Table 18 shows this
proficiency disparity and several others. One should also observe that the White and
Hispanic achievement gap, which was smallest achievement gap during the 2009-2010
school year, increased from 4.34% to 12.49%. A White student during the 2011 Spring
AIMS administration was 12.49% more likely to show proficiency in writing in
comparison to a Hispanic student. Overall, Table 18 reflects that the trend of large
performance gaps between ethnic subgroups at this school during the 2010-2011 school
year continued.
74
Table 18
Spring AIMS 2011 Elementary School #1 Performance by Subject and Ethnicity
Subject
Ethnicity % FFB % Approach % Meets % Exceeds
Mathematics Asian 2.67% 2.67% 17.33% 77.33%
Black 8.33% 12.50 62.50 16.67
Hispanic 5.33% 16.00 44.00 34.67
White 4.50% 8.41 32.13 54.95
Reading Asian 1.33% 0 48.00 50.67
Black 0% 8.33 79.17 12.50
Hispanic 1.33% 9.33 73.33 16.00
White 1.20% 4.20 61.26 33.33
Writing Asian 1.89% 3.77 39.62 54.72
Black 0% 30.00 70.00 0
Hispanic 0% 31.91 59.57 8.51
White 1.14% 18.29 61.71 18.86
As imparted in Table 19, at the junior high level similar patterns exist with respect
to the achievement gap across subgroups. Junior high #4 displayed issues that were seen
across most of the junior highs within the district. As uncovered in Table 19, one can
observe Black/Hispanic proficiency rates were lower than White/Asian proficiency rates
across all three subjects at junior high #4. The most significant proficiency gap is the
Asian-Black gap in mathematics where Asian student were 18.80% more likely to be
proficient at mathematics than their student peers that were Black. Once again, while this
75
gap between Asian-Black students is significantly lower the 2009-2010 school year it is
still far from demonstrating the requirement in NCLB of closing the achievement gap.
Table 19
Spring AIMS 2011 Junior High #4 Performance by Subject and Ethnicity
Subject
Ethnicity % FFB % Approach % Meets % Exceeds
Mathematics Asian 11.11% 7.41% 30.86% 50.62%
Black 17.91% 19.40 43.28 19.40
Hispanic 24.09% 12.41 40.15 23.36
White 10.61% 9.60 43.69 36.11
Reading Asian 1.23% 7.41 61.73 29.63
Black 0% 20.90 71.64 7.46
Hispanic 2.19% 18.25 67.15 12.41
White 1.89% 7.83 73.23 17.05
Writing Asian 0% 20.59 70.59 8.82
Black 7.32% 31.71 56.10 4.88
Hispanic 1.41% 30.99 64.79 2.82
White 2.70% 16.91 70.10 10.29
As shown in Table 20, High School #1 shows that the observed pattern of
achievement gaps at the subject level continue in the district for high schools. In
mathematics the smallest achievement gap was between White and Hispanic students
where White students were 12.44% more likely to achieve proficiency. As detailed in
Table 20, the gap between White and Black students in reading was the smallest with
76
White students demonstrating a rate of proficiency that was 6.15% greater. Writing
exhibited the smallest achievement gaps. The smallest of the gaps in writing existed
between Hispanic and White students with Hispanic students being 7.52% less likely to
pass the AIMS writing examination. However, this gap in writing proficiency between
Hispanic and White students was more than double the 2009-2010 gap. The achievement
gap rates demonstrated by high school #1 help confirm the trends observed in the subject
level analysis of school data.
Table 20
Spring AIMS 2011 High School #1 Performance by Subject and Ethnicity
Subject
Ethnicity % FFB % Approach % Meets % Exceeds
Mathematics Asian 0% 0% 43.75% 56.25%
Black 28.57% 7.14 51.79 12.50
Hispanic 23.23% 12.12 46.46 18.18
White 11.35% 11.57 47.60 29.48
Reading Asian 0% 0 54.55 45.45
Black 3.92% 9.80 80.39 5.88
Hispanic 2.11% 12.63 70.53 14.74
White 1.78% 5.79 72.38 20.04
Writing Asian 2.86% 8.57 68.57 20.00
Black 5.88% 19.61 70.59 3.92
Hispanic 1.10% 17.58 73.63 7.69
White 1.63% 9.53 78.37 10.47
77
The patterns illustrated in the examination of the three schools across the subjects
of reading, writing and mathematics were consistently observed throughout the schools in
this suburban district. The summary of all analyzed schools for the 2011 AIMS
administration are provided in Table 21. In examining Table 21, it should be noted that
at least 67.5% of all the schools within the district exhibited lower proficiency
performance amongst Hispanic/Black students than Asian/White students in
mathematics, reading and writing. The subject where the achievement gap appears to
elude educators the most is mathematics where at least 90.0% of the district schools
showed an achievement gap. Furthermore, at least 67.5% of the schools had mathematics
achievement gaps that were at least a 10-percentage point difference during the 2011
school year.
Table 21
Percent of All District Schools with Observed Gap in Mathematics, Reading and Writing
by Ethnicity for 2011 Spring AIMS Administration.
Mathematics
X* < -10%
-10% < X < 0% 0% < X < 10% X > 10%
Black-Asian 87.50% 10.00 2.50 0.00
Hispanic-Asian 80.00% 12.50 7.50 0.00
Black-White 70.00% 22.50 5.00 2.50
Hispanic-White 67.50% 22.50 7.50 2.50
(table continues)
78
Table 21 (continued)
Reading
X* < -10%
-10% < X < 0% 0% < X < 10% X > 10%
Black-Asian 60.00% 30.00 7.50 2.50
Hispanic-Asian 57.50% 32.50 7.50 2.50
Black-White 50.00% 30.00 15.00 5.00
Hispanic-White 40.00% 47.50 10.00 2.50
Writing
X* < -10%
-10% < X < 0% 0% < X < 10% X > 10%
Black-Asian 71.79% 10.26 7.69 10.26
Hispanic-Asian 71.79% 17.95 7.69 2.56
Black-White 45.00% 22.50 22.50 10.00
Hispanic-White 57.50% 27.50 12.50 2.50
Note. *X represents the difference between percentages of students proficient in each ethnic subgroup given in the gap column.
When analyzing achievement gaps by subject for excelling schools the picture
during the 2010-2011 school year is not much different than the prior year (see Table 22).
The vast majority of excelling schools within the school district showed achievement
gaps in mathematics, reading and writing. Table 22 also demonstrates that in
mathematics at least 19 of the 22 excelling schools, or 86.3%, showed an achievement
gap with respect to proficiency. Reading and writing had comparable results with at least
86.3% and 72.7%, respectively, of the excelling schools showing a gap.
79
Table 22
Number of All District Excelling Schools With Observed Gap in Mathematics, Reading
and Writing by Ethnicity for 2011 Spring AIMS Administration.
Mathematics
X* < -10%
-10% < X < 0% 0% < X < 10% X > 10%
Black-Asian 17 4 1 0
Black-White 15 6 1 0
Hispanic-Asian 14 5 3 0
Hispanic-White 12 8 2 0
Reading
X* < -10%
-10% < X < 0% 0% < X < 10% X > 10%
Black-Asian 11 9 2 0
Black-White 9 10 3 0
Hispanic-Asian 9 11 2 0
Hispanic-White 6 14 2 0
Writing
X* < -10%
-10% < X < 0% 0% < X < 10% X > 10%
Black-Asian 16 3 3 0
Black-White 9 7 5 1
Hispanic-Asian 14 5 3 0
Hispanic-White 12 6 4 0
Note. *X represents the difference between percentages of students proficient in each ethnic subgroup given in the gap column
80
Summary of AIMS Proficiency Data from Spring 2010 and Spring 2011
After examining proficiency percentages amongst the four ethnic subgroups for
the 40 schools within the suburban school district it is evident that despite school labels
the closing of the achievement gap continues to elude a wide majority of the schools
Each school exhibited minor differences in the achievement gap but upon compilation the
data suggest that whether a school is excelling, or highly performing, there appears to be
distinct proficiency performance differences between ethnic subgroups at these schools.
In fact, at a minimum 59.1% of the excelling schools during each of the 2010 and 2011
school years had lower proficiency performance amongst Black or Hispanic students in
comparison to White or Asian students in mathematics, reading or writing. Furthermore,
in this suburban school district, where approximately 75% of the schools receive one of
the two highest labels from ADE, at least 60% of the schools still exhibit achievement
gaps of 10% percentage points amongst academically low-performing ethnic subgroups.
Analysis of the Achievement Gap Using AIMS Scale Score
The analysis of the achievement gap using the average scale score on the AIMS
examination during the 2010 and 2011 AIMS test administration follows. This analysis
addresses the second research question of:
2. Is the average student achievement, as measured by average scale score, in
ethnic subgroups different for the 2009-2010 and 2010-2011 AIMS
examinations at each non-alternative school throughout the suburban school
district?
81
The analysis of this research question is divided into two sections. The first section
provides an analysis of ANOVA results for the 2010 and 2011 school years. The second
section provides a summary of this analysis.
2010 and 2011 Achievement Gap Analyzed through Average Scale Score
After examining the achievement gap relative to the percentage of students that
met proficiency at a given school the next question in the study was to examine the
achievement gap with respect to the average scale score at a given school. The AIMS
examination results in students receiving two types of scores: a raw score and a scale
score. A raw score is simply how many questions did the student get correct on the
exam. The scale score is a transformation of the raw score such that comparisons across
different versions of the test can be made. Essentially, by horizontally scaling an
examination a 6th grade student that took version H of the mathematics exam can be
compared to a 6th grade student that took version G of the mathematics exam. Using the
scaled scores for different ethnic subgroups within each school to analyze the
achievement gap examines the validity of the results drawn in the first part of Chapter 4.
Originally it was believed that average scale score for students of one ethnic
subgroup at a school could be compared to the average scale score of all other ethnic
subgroups at a school using an ANOVA. Unfortunately, upon initially examining
average scale scores it was evident that the process would not be this simple. As noted in
Table 23, average scale scores in mathematics appeared to increase with each grade level
throughout the district. The table shows that across the 7 years in which the AIMS
mathematics examination is administered the average scale score increases from 384.37
to 518.30.
82
Table 23
Average Scale Score throughout the District on 2010 AIMS Mathematics Administration
Grade
Average
3rd 384.37
4th 401.23
5th 410.85
6th 428.72
7th 442.92
8th 453.59
10th 518.30
This suggested that while the AIMS examination was horizontally scaled the
scaling across grade levels was not equivalent. As a result, if a school had a
disproportionate population that included a higher percentage of sixth grade Black
students than third grade Black students the average scale score for Black students would
be skewed by the lack of vertical scaling. Consequently, results of the ANOVA could
possibly reflect the grade location of ethnic students rather than their performance.
One way to account for the lack of vertical scaling across grade-levels was to
transform the data so that every student’s score is on the same scale. Using a simple
linear transformation, xi = zσ + µ, all of the scale scores for each student in the district
were transformed into a z-score based on the average scale score and the standard
deviation of scale score for every grade level. The advantage of using this linear
transformation process is that the original distribution is preserved and the distribution of
83
scores amongst ethnic subgroups is also preserved. After performing the linear
transformation on both the 2010 and 2011 AIMS mathematics and reading scores the
ANOVAs were performed on the z-scores transformed from the average scale score.
In total there were eighty ANOVAs performed on the AIMS data for the 2010 and
2011 school years. Each of the 40 schools had one ANOVA for the 2010 school year and
one ANOVA for the 2011 school year. Transforming mathematics and reading scores
into a z-score allowed for the comparison of mathematics and reading z-scores in
conjunction with each other. A z-score of 1 in mathematics represents the same thing as
a z-score of 1 in reading, which is a student scoring one standard deviation above the
mean on each respective subject test. As a result the ANOVA was analyzed using the
mathematics and reading z-scores as the dependent variable and ethnicity (Black,
Hispanic, White, Asian) as the factors.
When performing an ANOVA it is important to analyze the data to see if any of
the conditions have been violated. The three main conditions for ANOVAs include:
normality of observations within each factor, homogeneity of variances across each factor
and independence of observations across each factor. The most important of the
assumptions when running an ANOVA is independence. Stevens (2007, p. 59) states that
independence is “by far the most important assumption, for even a small violation of it
produces a substantial effect on both the level of significance and the power of the F
statistic.” Fortunately, in the case of this research independency has not been violated.
When evaluating independency Glass and Hopkins (1984, p. 353) issued the statement
that, “whenever the treatment is individually administered, observations are independent.
But where treatments involve interaction among persons…the observations may
84
influence each other.” In the case of the AIMS examination the treatment, or test, is
individually administered. Consequently, according to Glass and Hopkins the
observations on the AIMS examination must be independent of one another for each
individual student.
The second most important of the assumptions in an ANOVA is the assumption
of homogeneity of the population variance across ethnicities. Levene’s test on
homogeneity of variance provided analysis with respect to this assumption. During the
2010 school year 11 of the 40 schools exhibited heterogeneity of variances according to
Levene’s (α = 0.05). During the 2011 school year 6 of the 40 schools exhibited
heterogeneity of variances according to Levene’s (α = 0.05). Although Levene’s test for
these schools showed cause for concern with heterogeneity, the violation of the
assumption is not as problematic unless group sizes are sharply unequal (Stevens, p.58).
Unfortunately, as listed in Table 24, in the case of the 11 schools from 2010 and the 6
schools from 2011 the ratios of the largest group size to the smallest group size all were
in excess of 1.5. As a result, the corresponding ANOVAs for these schools were not
analyzed for the purposes of this research.
85
Table 24
Levene’s Test for Homogeneity of Variance P-Values for Each School across Ethnicities
with Respect to Average Scale Score
School Number
2010 Levene’s
P-Value
Largest/Smallest Group Ratio
2011 Levene’s P-Value
Largest/Smallest Group Ratio
Elementary #1 0.428 0.496
Elementary #2 0.070 0.771
Elementary #3 0.235 0.790
High School #1 0.359 0.710
Junior High #1 0.205 0.129
High School #2 0.037 6.147 0.001 5.565
Elementary #4 0.767 0.086
Elementary #5 0.020 17.632 0.680
Elementary #6 0.538 0.619
Elementary #7 0.178 0.025 8.222
Junior High #2 0.136 0.691
Elementary #8 0.067 0.760
Elementary #9 0.025 4.940 0.029 4.149
Elementary #10 0.120 0.228
Elementary #11 0.472 0.784
Elementary #12 0.055 0.332
(table continues)
86
Table 24 (continued)
School Number
2010 Levene’s
P-Value
Largest/Smallest Group Ratio
2011 Levene’s P-Value
Largest/Smallest Group Ratio
Elementary #13 0.333 0.100
High School #3 0.951 0.001 4.423
Special #1 0.072 0.055
Elementary #14 0.896 0.693
Elementary #15 0.205 0.346
Elementary #16 0.270 0.124
Elementary #17 0.308 0.888
Junior High #3 0.677 0.462
Elementary #18 0.964 0.435
Elementary #19 0.004 11.154 0.549
Elementary #20 0.923 0.171
High School #4 0.443 0.130
Elementary #21 0.134 0.409
Elementary #22 0.239 0.587
Elementary #23 0.213 0.182
Elementary #24 0.113 0.961
Elementary #25 0.589 0.417
Elementary #26 0.042 13.726 0.192
Junior High #4 0.005 10.986 0.023 10.934
(table continues)
87
Table 24 (continued)
School Number
2010 Levene’s
P-Value
Largest/Smallest Group Ratio
2011 Levene’s P-Value
Largest/Smallest Group Ratio
Elementary #27 0.046 10.294 0.066
Elementary #28 0.016 8.881 0.250
Elementary #29 0.033 11.520 0.361
Junior High #5 0.000 11.293 0.287
Junior High #6 0.008 13.875 0.001 12.424
The final assumption for an ANOVA is the assumption of normality within each
group. Kolmogorov-Smirnov tests (α = 0.05) were run on each subgroup within each
school for the 2010 and 2011 school years to determine whether the distribution of scale
scores were approximately normal. As shown in Table 25, during the 2010 AIMS
administration, 106 of the 160 tests failed to reject normality as a reasonable assumption
for each group distribution. In 2011, 105 of the 160 tests failed to reject normality as a
reasonable assumption for each groups distribution. One might become concerned about
the 54 groups in 2010 and the 55 groups in 2011 which violated the assumption of
normality. However, a summary by Glass, Peckham and Sanders (1972) on research
conducted studying the effects of non-normality on an ANOVA shows that non-
normality only has a slight effect on Type I errors. Stevens (1972, p. 57) states, “the F
statistic is robust with respect to the normality assumption.” As a result, even though the
normality assumption was violated in approximately 34%, as shown in Table 25, of the
88
group distributions it should have a negligible effect on the Type I error rate and power of
the ANOVAs due the robust nature of the F statistic when encountering non-normality.
Table 25
Kolmogorov-Smirnov (KS) P-Values for Normality for 2010 and 2011 AIMS
Distributions by Ethnicity
School Number
2010 KS
White
2010 KS
Hispanic
2010 KS
Black
2010 KS
Asian
2011 KS
White
2011 KS
Hispanic
2011 KS
Black
2011 KS
Asian
E #1 0.000 0.200 0.200 0.200 0.038 0.200 0.000 0.085
E #2 0.002 0.031 0.200 0.200 0.000 0.004 0.073 0.088
E #3 0.000 0.001 0.200 0.057 0.001 0.200 0.200 0.039
Matt Strom was born on May 9, 1977 in Boone, Iowa. With a family that always stressed education Matt graduated from Mountain Pointe High School, 1995, Arizona State University, 1998, and received his graduate degree from Northern Arizona University, 2002. During the process of receiving his graduate degree he became married to Marcia Jones. After marrying Marcia, the good Lord blessed the Strom family with three children named Zavian, Quentin and Elijah. Matt has worked in a variety of different roles during his 14 year educational career. As a 21-year old teacher Matt first started teaching mathematics at Mesquite High School. As he was about to turn 25, Matt was hired as the varsity boys basketball coach at a 5A school making him the youngest active large school varsity boys coach in the state of Arizona. Matt has served in several other roles throughout his educational career that include: mathematics department chair, AVID teacher and head varsity golf coach. Currently, Matt’s role includes being the research analyst to the superintendent of his current district. The constant desire that Matt has to learn has enabled him to participate in many learning experiences since his graduate degree. He was a PLC leader for the Project Pathways STEM project out of ASU. He has attended numerous educational workshops including AVID training and NCTM conferences. Furthermore, in an effort to reconnect with his mathematics classes from his undergraduate degree Matt studied for and passed Exam P, Probability for Risk Management, the first exam in the Society of Actuaries exam process. Matt, like the majority of his fellow educators, has a thirst for knowledge and as a result he started the doctoral process in the summer of 2008 through Northern Arizona University. Upon completion of his degree Matt hopes to continue to grow in the educational field. He strongly desires to gain his superintendent’s certificate in an effort to gain employment in district-level educational administration at the K-12 level. In accord with the themes of this dissertation Matt hopes to bear witness to the day when ethnicity is not a determining factor in the quality of education that a child receives.