How Culturally Responsive Leaders and Teachers Influence the Mathematics Performance ... · 2020....

How Culturally Responsive Leaders and Teachers Influence the Mathematics Performance of High School and Middle School African American Students in One Urban Virginia School

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Angela Nicole Byrd-Wright

Dissertation submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of

Doctor of Education

In Educational Leadership and Policy Studies

Carol S. Cash, Chair Ted S. Price, Co-Chair

Carol A. Mullen Sharmaine D. Grove

January 30, 2020 Newport News, Virginia

Keywords: African American, building conceptual understanding, culturally responsive

leadership, culturally responsive teaching, mathematics


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ABSTRACT

Analysis of multiple data sources revealed a prevalent gap between high school and

middle school African American students and their White counterparts in mathematics. Based on

these data and a gap in the literature, further research was needed regarding how the mathematics

performance of African American students is influenced by culturally responsive leadership and

culturally responsive teaching. The purpose of this study was to determine if culturally

responsive behaviors of high school and middle school principals influence the behaviors of

mathematics teachers resulting in building conceptual understanding of their students; and, how

teachers’ culturally responsive actions impact the mathematics performance of African American

students.

The research questions guiding this qualitative study were (1) To what extent, if any, do

principals at the high school and middle school levels that exemplify culturally responsive

leadership influence mathematics teachers’ use of culturally responsive teaching that results in

building conceptual understanding in mathematics? and, (2) To what extent, if any, do culturally

responsive teaching practices impact the mathematics performance of African American students

at the high school and middle levels? The results indicated that the purposive sample of high

school and middle school principals (n = 7) exhibited critical consciousness (self-awareness) and

interrelationships amongst teachers and students; communication and being present; and, data-

driven decision-making. The purposive sample of high school and middle school mathematics

teachers (n = 23) exhibited content knowledge that allowed for differentiated instruction

inclusive of building conceptual understanding through multiple mathematical representations;

and, engaged their students in mathematical discourse requiring students to reason and justify

their solutions. Thus, such actions created a familial-like atmosphere inherent in optimal learning

environments for African American students. Students with culturally responsive teachers

performed better on division-wide assessments, with the effect of reducing the achievement gap

between African American and White students compared to teachers not self-identified as having

high levels of cultural responsiveness with results statistically significant at the 0.01 level after

conducting a two-proportions z-test.


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GENERAL AUDIENCE ABSTRACT

The purpose of this study was to determine if culturally responsive behaviors of high

school and middle school principals influence the behaviors of mathematics teachers resulting in

building conceptual understanding of their students; and, how teachers’ culturally responsive

actions impact the mathematics performance of African American students. The synthesis of the

literature review and the results of this study could provide information that would assist school

leaders and teachers in not only understanding their respective roles impacting and influencing

the mathematics performance of African American students at the high school and middle school

levels, but also understanding the pedagogical, conceptual understanding, and leadership

practices and factors that can lead to this improvement.

A qualitative study design was used in one urban Virginia school division encompassing

a preliminary screening of high school and middle school principals and mathematics teachers;

observations of high school and middle school principals and mathematics teachers; and, a

culminating culturally responsive leadership practices survey. The researcher sought to examine

(1) To what extent, if any, do principals at the high school and middle school levels that

exemplify culturally responsive leadership influence mathematics teachers’ use of culturally

responsive teaching that results in building conceptual understanding in mathematics? and, (2)

To what extent, if any, do culturally responsive teaching practices impact the mathematics

performance of African American students at the high school and middle levels? Data from

division-wide assessments demonstrated that the students of culturally responsive teachers

iv performed better and with a reduced achievement gap between African American and White

students compared to teachers not having self-identified with high levels of cultural

responsiveness. Observations from the high school and middle school principals and

mathematics teachers revealed specific behaviors and strategies used consistently across the

sample. From the findings, implications for practices and recommendations for future studies

were rendered.

vi

Dedication

I would like to dedicate this dissertation to my parents, Linwood and Gail Byrd – two

baby-boomers that grew up in a segregated South who did not have the opportunities afforded to

me to pursue their advanced education beyond that of the high school and nursing school levels

respectively. My parents continue to inspire me daily with their hard work ethic, their love for

one another, and their service to their church and community. They are humble people and I am

bound to their love and their prayers.

I would like to dedicate this dissertation to the three loves of my life – my husband, Justin

Wright, and our sons, Westin and Hudson Wright. Justin has spent countless hours shuttling our

boys to school and extracurricular activities while I sat for just as many countless hours nestled

on our living room couch writing. My husband provides me with an unyielding love filled with

encouragement with a wicked gleam in his eye and a joke or two that kept my spirits lifted. I

thank my eldest son Westin for his hugs, notes written on paper towels and post-it notes with

rainbows, hearts, and “you can do it” on so many occasions. For several evenings, Westin kept

me company on that aforementioned couch while he read his books and studied for his own

school assignments. I thank my youngest son Hudson for his wit and the warm cuddles and

nuzzles he gave throughout this process. Hudson would often be found at my feet in the living

room surrounded by stuffed animals. Said stuffed animals would ask me on multiple occasions,

“Mommy are you done yet?” It is through these times that my children could see my tenacity and

perseverance of which I hope to have planted the seeds for their own personal and professional

journeys ahead.

Lastly, I would like to dedicate this dissertation to my grandparents who have gone on

before us: Elda Smith Kearney, Willie Kearney, Jr., Joseph Byrd, and Beulah Hedgepth Byrd.

vii Acknowledgements

I would like to express my deepest gratitude and appreciation to the high school and

middle school principals and teachers from the urban school division and their willingness to be

a part of my dissertation study.

I extend my sincere thanks to my dissertation committee, Dr. Cash, Dr. Price, Dr. Mullen,

and Dr. Grove. Your feedback helped to shape my learning and to make this dissertation a

reality. A special appreciation is extended to Dr. Cash for her keen eye and feedback on the

statistical analyses involved in my study. Dr. Price, has been invaluable to the completion of my

doctoral studies and my dissertation. Dr. Price’s feedback was continually supportive,

thoughtful, and insightful. He is the embodiment of a cheerleader and coach to whom I will be

forever grateful for his time and personal commitment to my success.

viii TABLE OF CONTENTS

Abstract ii

General Audience Abstract iv

Dedication vi

Acknowledgements vii

List of Tables xii

List of Figures xiv

CHAPTER 1 INTRODUCTION 1

Introduction 1

Overview of the Study 2

Historical Perspective 3

Statement of the Problem 10

Rationale and Significance 11

Purpose and Justification of the Study 15

Research Questions 15

Conceptual Framework 16

Limitations 17

Delimitations 18

Definitions of Key Terms 18

Overview of the Dissertation 22

CHAPTER 2 A REVIEW OF LITERATURE 24

Introduction 24

Culturally Responsive Leadership 24

ix Cultural Deficit Theory Counterexamples 28

Culturally Responsive Teaching 32

Building Conceptual Understanding 46

Need for Further Research 51

CHAPTER 3 METHODOLOGY 54

Purpose of the Study 54

Research Design and Justification 54

Research Questions 55

Sample Selection 56

Data Collection Procedures 58

Data Gathering Procedures 64

Instrument Design and Validation 64

Data Treatment and Management 67

Data Analysis Techniques 69

Timeline 70

Methodology Summary 72

CHAPTER 4 DATA ANALYSIS 74

Introduction 74

Preliminary Screening Survey of High School and Middle School Principals (Phase 1a) 75

Preliminary Screening Survey of High School and Middle School Mathematics Teachers (Phase 1b)

96

Observations of High School and Middle School Principals (Phase 2a) 119

Observations of High School and Middle School Teachers (Phase 2b) 137

x Examination of High School and Middle School Mathematics Student Performance Data (Phase 3)

142

Culturally Responsive Leadership Practices Survey (Phase 4) 162

Data Analysis Summary 182

CHAPTER 5 FINDINGS, SUMMARY, AND CONCLUSION 186

Summary of Findings 187

Implications 196

Recommendations for Future Research 201

Conclusion 201

Reflection 203

REFERENCES 204

APPENDICES 220

Appendix A: IRB Certificate of Completion in the Training of Human Subjects 221

Appendix B: Virginia Polytechnic and Institute University Institutional Review Board Approval

222

Appendix C: Western Institutional Review Board Determination Letter 224

Appendix D: Research Authorization Request 226

Appendix E: Research Authorization Committee Approval Letter 230

Appendix F: Participant Letter 231

Appendix G: Participant Response Letter 234

Appendix H: Informed Consent Agreement 235

Appendix I: Self-Assessment for School Administrators 238

Appendix J: Self-Assessment for School Teachers 240

Appendix K: Reformed Teaching Observation Protocol (RTOP) 242

xi Appendix L: Culturally Responsive Leadership Practices Survey 245

Appendix M: Survey Validation Instrument and Responses 247

xii List of Tables

Table 1 2019-20 Urban School Division Fall Membership at the High School and Middle

School Levels

61

Table 2 Subscales as Predictors of the RTOP Total Score 66

Table 3

Preliminary Screening Survey Results of High School and Middle School Principals by Item (Overall, n=12)

77

Table 4 Preliminary Screening Survey Results of High School and Middle School Principals (Individual)

81

Table 5 Preliminary Screening Survey Results of High School and Middle School Principals (Purposive Sample, n=7)

83

Table 6 Preliminary Screening Survey Results of High School and Middle School Principals Rank Ordered by Consensus and Mean (Purposive Sample, n=7)

86

Table 7 Preliminary Screening Survey Results of High School and Middle School Principals (Non-Qualifiers, n=5)

90

Table 8 Preliminary Screening Survey Results of High School and Middle School Principals Rank Ordered by Consensus and Mean (Non-Qualifiers, n=5)

93

Table 9 Preliminary Screening Survey Results of High School and Middle School Mathematics Teachers by Item (Overall, n=37)

98

Table 10 Preliminary Screening Survey Results of High School and Middle School Mathematics Teachers (Individual)

103

Table 11

Preliminary Screening Survey Results of High School and Middle School Mathematics Teachers (Purposive Sample, n=23)

106

Table 12

Preliminary Screening Survey Results of High School and Middle School Mathematics Teachers Rank Ordered by Consensus and Mean (Purposive Sample, n=23)

108

Table 13 Preliminary Screening Survey Results of High School and Middle School Mathematics Teachers (Non-Qualifiers, n=14)

113

Table 14 Preliminary Screening Survey Results of High School and Middle School Mathematics Teachers Rank Ordered by Consensus and Mean (Non-Qualifiers, n=14)

116

Table 15

Demographics of High School and Middle School Principals (Purposive Sample, n=7)

120

xiii Table 16 Demographics of High School and Middle School Mathematics Teachers

(Purposive Sample, n=23)

137

Table 17 Reformed Teaching Observation Protocol (RTOP) (Purposive Sample, n=23)

140

Table 18 4.5 Weeks Assessment Content by Course

144

Table 19 4.5 Weeks Assessment Results of African American Students Compared to White Students (n=37)

148

Table 20

Critical Skills Assessment Content by Course

152

Table 21

Critical Skills Assessment Results of African American Students Compared to White Students (n=37)

156

Table 22

Two-Proportions Z-Test to Determine Statistical Significance of High School and Middle School Mathematics Student Performance Data

160

Table 23

Culturally Responsive Leadership Survey Results of High School and Middle School Mathematics Teachers by Item (Overall, n=37)

164

Table 24 Culturally Responsive Leadership Survey Results of High School and Middle School Mathematics Teachers (Individual)

168

Table 25

Culturally Responsive Leadership Survey Results of High School and Middle School Mathematics Teachers (Purposive Sample, n=23)

171

Table 26

Culturally Responsive Leadership Survey Results of High School and Middle School Mathematics Teachers Rank Ordered by Consensus and Mean (Purposive Sample, n=23)

173

Table 27 Culturally Responsive Leadership Survey Results of High School and Middle School Mathematics Teachers (Non-Qualifiers, n=14)

177

Table 28 Culturally Responsive Leadership Survey Results of High School and Middle School Mathematics Teachers Rank Ordered by Consensus and Mean (Non-Qualifiers, n=14)

179

xiv List of Figures

Figure 1 A model to describe the overarching variable of culturally responsive leadership

influencing the mathematics performance of African American students at the high school and middle school level

16

Figure 2 A model to describe the data collection process 63

1 Chapter 1

Introduction

Introduction

July 4, 1776, 56 male governmental figures signed the Unanimous Declaration of the

thirteen United States of America. For it is written:

We hold these truths to be self-evident, that all men are created equal, that they are

endowed by their Creator with certain unalienable Rights, that among these are Life,

Liberty and the pursuit of Happiness. That to secure these rights, Governments are

instituted among Men, deriving their just powers from the consent of the governed. That

whenever any Form of Government becomes destructive of these ends, it is the Right of

the People to alter or to abolish it, and to institute new Government, laying its foundation

on such principles and organizing its powers in such form, as to them shall seem most

likely to affect their Safety and Happiness. (The Declaration of Independence, U.S.,

1776, para. 2)

It is the right of all people to have opportunity and access to an education that in turn can

lead to an abundant life, the freedom to navigate a democratic society, and the happiness and

safety of learning that education offers (Gonzalez, 2005; Martin, 2012; Tate,1995). Tate (1994)

asserted that “failing to provide African American students with mathematics curriculum,

instruction, and assessment centered on their experiences, culture, and traditions is a major

obstacle to achieving equity in mathematics education” (p. 478).



2 building conceptual understanding of their students; and, how teachers’ culturally responsive

actions impact the mathematics performance of African American students. An overview of the

study follows. To set the context for the study, background national and state data have been

provided to set a historical perspective. As an outgrowth of these background data, the statement

of the problem, rationale, and significance of this work have been given. A conceptual

framework was created based on the review of relevant literature that embodies a theoretical lens

for conducting the study. Research questions that guided the study have been presented along

with limitations and delimitations. Definitions of key terms have been given to assist in the

understanding of the content presented.

Overview of the Study

The researcher engaged in a qualitative study consisting of a preliminary screening

survey measuring culturally responsive leadership and culturally responsive teaching through an

established criterion distributed to high school and middle school principals and mathematics

teachers of an urban school division in Virginia. The researcher performed observations of the

high school and middle school principals and mathematics teachers having met the established

criterion. Student mathematics performance data were collected and disaggregated to compare

the performance of African American students to that of White students on two division-wide

assessments – assessments taken at two distinct portions of the first nine weeks. Further, these

student performance data were compared to teachers within and not within the purposive sample.

A culminating culturally responsive leadership survey of practices, developed by the researcher,

was given to high school and middle school mathematics teachers within the purposive sample

and those that were not. Coding and triangulation were used to extrapolate the connections as

rendered by these data.

3 Historical Perspective

Traversing the achievement gap at the national level. Multiple measures have been

cited to illustrate an existing achievement gap between African American and White students

(Aronson & Laughter, 2016; Bol & Berry, 2005; Bonner, 2014; Jackson & Jackson, 2012; Tate,

1995; Ukpokodu, 2011). Statistics provided reveal “that the farther students progress in school,

the wider these gaps in mathematics become” (Bonner, 2014, p. 377).

The National Assessment of Educational Progress (NAEP), reported by the National

Center for Education Statistics (NCES), is given to grades 4, 8, and 12 in several subject areas.

NAEP is a common assessment instrument used across the United States and selected urban

divisions/districts. NAEP results serve as a common measure in content and stability as minimal

changes are made to the design and mode of delivery. This is done to maintain the reliability of

measurement and consistency (reproducibility, repeatability, and stability of the score), thus

allowing for valid conclusions and interpretation of results (NCES, 2015g). Reporting is by

population performance, content achievement, and gap performance regarding eighth grade and

twelfth grade mathematics performance as these grades are representative of the high school and

middle school levels.

Bol and Berry (2005) specifically defined the achievement gap as:

an indicator of disparities between groups of students usually identified (accurately or

not) by racial, ethnic, linguistic, or socioeconomic class with regard to a variety of

measures (attrition and enrollment rates, drug use, health, alienation for school and

society attitude toward mathematics, as well as test scores). (p. 36)

Per the NAEP National Results Overview Report, the percentage of African American eighth

grade students performing at or above the proficient level in mathematics was at 13% in

4 comparison to White eighth grade students performing at or above the proficient level in

mathematics at 43%, a 30% negative differential (NCES, 2015c). Even starker is that the

performance of African American students at this grade level was the lowest in comparison to all

ethnic groups (Hispanic, 19%; Asian, 61%; Pacific Islander, 29%; American Indian, 20%)

(NCES, 2015c). The percentage of African American twelfth grade students performing at or

above proficient in mathematics was at 7% in comparison to White twelfth grade students

performing at or above proficient in mathematics at 32%, a 25% negative differential (NCES,

2015d). Again, the performance of African American students at this grade level was the lowest

in comparison to all ethnic groups (Hispanic, 12%; Asian, 47%; Pacific Islander [sample size

insufficient]; American Indian, 10%) (NCES, 2015d).

Data are reported by the NAEP National Achievement Level Report to provide

performance bands categorized as below basic, basic, proficient, and advanced. At grade eight:

● the percentage of African American students performing at a below basic level was at

52%, compared to White students at 18%, a negative 34% differential;

● the percentage of African American students performing at a basic level was at 35%,

compared to White students at 39%, a negative 4% differential; and,

● the percentage of African American students performing at an advanced level was at

2% in comparison to White students with an advanced percentage rate of 11%, a

difference of 9%. (NCES, 2015a)

Likewise, at grade 12:

● the percentage of African American students performing at a below basic level was at

64%, compared to White students at 27%;

● at a basic level of 29%, compared to White peers at 41%; and,

5 ● an advanced level could not be reported as the percentage would round to 0% in

comparison to White students with an advanced percentage rate of 3%. (NCES, 2015b)

NCES provides an overview of mathematics performance through the NAEP National

Score Gap Report in relation to scale score on the mathematics assessment to capture the trend

data between racial/ethnic groups. During the 2015 administration of the NAEP mathematics

assessment, eighth grade results yielded a 32-point African American to White point divergence,

with African American students scoring on average 260 on a 500-point scale to that of White

students who scored on average 292 out of 500 possible points (NCES, 2015e). Similarly,

African American students at the twelfth-grade level experienced a 30-point scale score point

gap, scoring on average 130 on a 300- point scale compared to 160 out of 300 possible points of

their White peers (NCES, 2015f). Beginning with eighth grade data collected since 1990 and

twelfth grade data since 2005, these racial/ethnic groups have maintained on average a 35-point

achievement gap and 30-point achievement gap respectively (NCES, 2015e; NCES, 2015f).

As an additional preponderance of the evidence, mathematics data from the Scholastic

Achievement Test (SAT) and Preliminary Scholastic Achievement Test (PSAT) will be

provided. SAT results from the 2015 test administration as well as 2017 SAT, PSAT 10, PSAT

8/9 mathematics results have been given to capture the pervasiveness of African American

versus White students gap in achievement. The SAT assesses students’ understanding and

application of concepts and skills within a subject area, with data to be reported via mean score

and associated standard deviation. Standard deviation represents the average distance from the

mean (Howell, 2011). Therefore, it informs those that are reading and interpreting research on

how each value in a data set on average varies from the mean. Because the standard deviation is

stated in the original units from which it was derived, it gives an outlook of the spread of the data

6 or how close the data are to the mean (data dispersion). The standard deviation is used to

compare data sets as well as facilitate the construction of the normal curve in order to understand

the distribution and variability of the data. Per the 2015 SAT College-Bound Seniors Total Group

Profile Report, there were 1,698,521 students tested with an overall mean score in mathematics

of 511 with a standard deviation of 120 (The College Board, 2015a). The data provided are for

high school graduates in the year 2015 who took the SAT during high school up to June 2015.

Should a student have taken the test past the initial test, then the highest score was reported. The

mean score of African American students was 428 with a standard deviation of 100 in

comparison to White students with a mean score of 534 and a 104 standard deviation, producing

a 106-point difference in performance between these two groups (The College Board, 2015a).

The 2017 SAT Suite of Assessments Annual Report provides data about students who took

the new SAT, PSAT 10, and PSAT 8/9 during high school of the 2016-2017 school year. Due to

the restructuring of the new SAT instrumentation design, score reports could not be compared to

the 2015 test administration; however, similar trends in outcomes have been noted. In addition,

the new SAT reports with a math benchmark score, which means that:

the section score is associated with a 75% chance of earning at least a C in a first-

semester, credit-bearing, college-level course in algebra, statistics, pre-calculus, or

calculus; the PSAT 10 and PSAT 8/9 report grade-level benchmarks that indicate whether

a student is college and career ready. (The College Board, 2017a, p. 2)

In mathematics, African American students earned:

● a mean score on the SAT of 462, meeting the specified benchmark at only 22% compared

to White students earning a mean score of 565, meeting the specified benchmark at 61%,

a 39% negative differential;

7 ● a mean score of 422 on the PSAT 10, (tenth graders) meeting the grade-level benchmark

at only 20% compared to White students who earned a mean score of 507, meeting the

aforementioned PSAT 10 criteria benchmark at a rate of 57%;

● a mean score of 443 on the PSAT 10, (eleventh graders) meeting the benchmark at 21%

while White students fared at a mean score of 545 with 60% of test-takers deemed

college and career ready. (The College Board, 2017a)

African American eighth graders and ninth graders earned mean scores of 381 and 461

respectively on the PSAT 8/9, meeting the grade-level benchmark at only 22% and 58%, while

their White peers earned mean scores of 435 (eighth grade, 58% benchmark met) and 545 (ninth

grade, 60% benchmark met) (The College Board, 2017a).

Analyzing the achievement gap at the state level. NCES also provides an overview of

state mathematics performance through the NAEP 2015 Mathematics State Snapshot Report

(Virginia, Grade 8, Public Schools) about the average scale score on the mathematics assessment

to relay the gap and proficiency results between racial/ethnic groups. Per the NAEP Virginia

Student Groups and Gaps Data Report, only results from grades 4 and 8 data are recorded (grade

12 results were not reported) (NCES, 2015i). Because the focus of the review of related literature

and study are on African American mathematics performance at the high school and middle

school level, only the eighth-grade data have been shared.

During the 2015 administration of the NAEP mathematics assessment, eighth grade

results yielded a 30-point African American to White point differential (NCES, 2015h). The

Virginia Department of Education (VDOE) (2015) noted:

8 38% of Virginia eighth graders achieved proficient or advanced scores in 2015, with 10

percent performing at the advanced level. Forty-six percent of white students achieved

proficient or advanced scores, compared with 12 percent of blacks. (p. 1)

African American students scored on average 265 on a 500-point scale compared to White

students who scored on average 288 out of 500 possible points (NCES, 2015i). Although, the

average score performance of tested eighth-grade students in Virginia increased from the year

2000 to 2015, the distance in achievement of African American to White students at the state

level has remained stagnant with a 30-point gap since the year 2000 (NCES, 2015i; VDOE,

2015). Performance bands results, categorized as basic, proficient, and advanced yielded the

following:

● the percentage of African American students performing at or above basic was at

55%, compared to White students at 84%, a negative 29% differential;

● the percentage of African American students performing at or above a proficient level

was at 12%, compared to White students at 46%, a negative 34% differential; and,

● the percentage of African American students performing at an advanced level was at

2% in comparison to White students with an advanced percentage rate of 12%, a

difference of 10%. (NCES, 2015i)

Virginia mathematics SAT results from the 2015 test administration as well as the 2017

SAT, PSAT 10, PSAT 8/9, are provided to illustrate the results between African American and

White students at the state level in mathematics. As with the national data, both the mean score

and its corresponding standard deviation are provided. Per the 2015 SAT College-Bound Seniors

Total Group Profile Report - Virginia, there were 59,621 students tested with an overall mean

score in mathematics of 518 with a standard deviation of 107 (The College Board, 2015b). The

9 data provided are for high school graduates in the cohort year 2015 who took the SAT during

their high school years to June 2015 with their highest score being reported. The mean score of

African American students in mathematics was 435 with a standard deviation of 91 in

comparison to a mean of 535 and a standard deviation of 99 for White students, producing a 100-

point difference in performance, comparative to the 106-point difference between the two groups

at the national level on the SAT (The College Board, 2015b).

The 2017 SAT Suite of Assessments Annual Report – Virginia provides data on students

who took the new SAT as well as the PSAT 10 and PSAT 8/9 during 2016-2017. The same

parameters of college and career readiness articulated during the review of national results are

applicable at the state level. Although African American and White students in Virginia

performed above the mean score nationally, results from the new SAT given during the 2017 test

administration still reflect an achievement gap in mathematics at the high school and middle

school level with the former Virginia Superintendent of Public Instruction, Stephen R. Staples,

having stated:

Virginia students begin this new SAT trend line achieving at levels well above their peers

nationwide. Our challenge moving forward is to narrow — and ultimately close — the

achievement gaps evident in these results and make sure all of our students are college

and career ready when they complete high school. (VDOE, 2017d, p. 1)

In mathematics, African American students in Virginia earned:

● a mean score on the SAT of 469, meeting the specified benchmark at only 23% compared

to White students earning a mean score of 562, meeting the specified benchmark at 65%,

a 42% negative differential;

10 ● a mean score of 416 on the PSAT 10, (tenth graders) meeting the grade-level benchmark

at only 20% compared to White students who earned a mean score of 493, meeting the

aforementioned PSAT 10 criteria benchmark at a rate of 58%;

● a mean score of 440 on the PSAT 10, (eleventh graders) meeting the benchmark at 21%

while White students fared at a mean score of 531 with 61% of test-takers deemed

college and career ready. (The College Board, 2017b)

African American eighth graders and ninth graders earned mean scores in mathematics of 382

and 406 respectively on the PSAT 8/9, meeting the grade-level benchmark at only 20% and 33%,

while their White peers earned mean scores of 424 (eighth grade, 46% benchmark met) and 480

(ninth grade, 67% benchmark met) (The College Board, 2017b).

Statement of the Problem

African American students at the high school and middle school level of mathematics

have and continue to achieve at a lower rate than their White peers; the dissonance between

understanding, applying, and analyzing complex mathematics and African American students’

performance is entrenched in the data sources presented (NCES, 2015a; NCES, 2015b; NCES,

2015c; NCES, 2015d; NCES, 2015e; NCES, 2015f; NCES, 2015h; NCES, 2015i; The College

Board, 2015a; The College Board, 2015b; The College Board, 2017a; The College Board,

2017b; VDOE, 2015; VDOE, 2017d). Therefore, an examination of the leadership practices,

pedagogical methodology, and conceptual understanding development used to solidify a deep

mathematical understanding of African American students at the high school and middle school

level, thus resulting in their increased performance is tantamount to close or minimize the

achievement gap.

11 Rationale and Significance

Cultural deficit theory. Cultural deficit theory fosters the proposition that students will

demonstrate a lack of knowledge and understanding of essential knowledge, skills, and behaviors

needed to be successful in school and beyond based solely on their race and familial

environment. The incongruity between African American students and their achievement and

performance persists as a result of proponents of cultural deficit theory – a theoretical framework

developed by Deutsch. Deutsch (1963) conducted a longitudinal study that attempted to

“manipulate mediating environmental variables and measure behavioral modifications or

facilitation in intellectual growth” (p. 24). Five hundred forty-three students were represented in

the study stratified by race and by grade level. Through their collective research that examined

the students involved in the longitudinal study, Deutsch and Brown (1964) further provided that

a linear relationship exists between “Negro children…and their performance level” asserting that

“clearly the means for white children are significantly higher than are mean IQ scores for their

Negro counterparts” (p. 26).

Cultural deficit theory correlates underachievement of students and their performance to

negative stereotypes often affiliated with the population. This is affirmed by Bol and Berry

(2005) who suggested that lower student achievement levels, especially for African American

students, are exacerbated by teachers’ expectations and perceived notions regarding African

American students’ performance – believing these students cannot achieve at the levels

experienced by their White peers. The basis of this theory is the assumption of poor performance

and ubiquitous underachievement is attributed to students’ socioeconomic status and familial

origin. Lewis (1966) added to the cultural deficit theory base that broken-homes (i.e., fatherless),

gang culture, the cycle of poverty or “slum community,” and the attitudes, values, and character

12 structures of students of color push them toward helplessness, dependence, and inferiority (p.

20). The subsumption of cultural deficit theory is that students of color continually exemplify a

depreciated value of self and fail to capitalize on their cultural capital due to their innate inability

to be motivated and to achieve – further worsened by parents’ indifference or apathy toward

education (Lewis, 1966; Silverman, 2011).

Bourdieu (1986) expanded the idea of “cultural capital,” defining it as centered on the

familiarity of the dominant culture, including such elements as an ability to communicate and to

possess its language. Using this line of theory, the assumption is that students of color and by

extension their families, fail to value education as much as middle-class and upper-middle-class

White peers. Contrariwise, middle- and upper-middle-class students are more often likely to do

well or excel because they inherently have more cultural capital. Not possessing cultural capital

also suggests that failure is an outgrowth of families’ lack of involvement in the academic

process and thereby a byproduct of the educational outcomes of their communities (Bourdieu,

1986; Silverman, 2011).

Martin (2012) warned that any research that focuses on Black children should be

scrutinized for the “way it conceptualizes and frames these children and the way it frames

Blackness, either explicitly or implicitly” (pp. 50-51). Cultural deficit theory conforms “Black

children’s existence to a single, pathological set of material and cultural circumstances: at-risk,

poverty-ridden communities, ghettos, dysfunctional families, and oppositional stances toward

schooling” (Martin, 2012, p. 51). The school itself is not held accountable and is exonerated

from its responsibilities to educate with liberty and justice for all, shifting stigmatic charges of

disengagement, disenfranchisement, and aloofness to students and by extension, their families.

Instead of the pursuit of life through institutional advancement, students of color are

13 systematically depressed through the depravity of subtle and not-so-subtle overtones of

inferiority and non-assimilation of what is deemed ideal through the “eradication of the

linguistic, literature, and cultural practices many students…brought from their homes and

communities and to replace them with what are [sic] viewed as superior practices” (Paris, 2012,

p. 93).

As evidenced by the previously cited national and state performance data, there is a

dichotomy between performance and achievement in high school and middle school mathematics

for African American students and White students. Cultural deficit theory was offered as a

theoretical framework that provides a lens into the reason why this pervasive gap exists.

However, the United States Department of Education (USDOE) (2015) set forth provisions in its

Every Student Succeeds Act (ESSA), to ensure quality schools and success for all students to

include “advancing equity by upholding critical protections for America's disadvantaged and

high-need students” (p. 1). Like its predecessor of 2002, No Child Left Behind (NCLB), ESSA

seeks to:

put in place measures that expose achievement gaps among traditionally underserved

students and their peers in order to spur on an important national dialogue on education

improvement. This focus on accountability has been critical in ensuring a quality

education for all children, yet also revealed challenges in the effective implementation of

this goal. (USDOE, 2015, p. 1)

As a requirement of ESEA Section 1111(c)(2)(B), states must have an accountability plan

to measure the success of all students and specifically cite the “major racial and ethnic groups

that are included as subgroups for the purposes of calculating accountability” (VDOE, 2017d, p.

9). These accountability measures are inclusive of achievement, student growth, early warning,

14 persistence, and college- and career-readiness indicators (USDOE, 2015). In response, Virginia

has implemented accountability measures that include “rigorous state content standards and

assessments for all students” and:

benchmarks in mathematics that were adopted by the state Board of Education as part of

the state accountability system are identified as the long-term goals for all students and

subgroups. Virginia’s accountability benchmarks, adopted as long-term goals, place the

federal accountability focus on subgroups that have historically failed to meet growth

targets. This gap-closing model is rigorous and attainable and emphasizes the importance

of improved achievement for low-performing subgroups. (VDOE, 2017c, p. 12)

VDOE (2017c) has denoted a seven-year timeline to measure intermittent progress

toward long-term goals for academic achievement in order to close acknowledged achievement

gaps, with African American students to attain at least a 60% pass rate on mathematics

assessments administration for the 2018-2019 school year growing steadily to at least a 70% pass

rate by the 2024-2025 school year. In addition, the revised standards of accreditation “evaluate

schools on their success in narrowing achievement gaps in…mathematics. Under the previous

accreditation system, high overall performance could make underperformance of certain student

groups” (VDOE, 2018). Because of the accountability measures mandated at both the federal

(national) and state levels, schools must utilize resources and strategies to ensure that African

American students are successful, meet incremental achievement levels, or face poor school

quality indicators for achievement of students and the failure to narrow achievement gaps

(VDOE 2017c; VDOE, 2018).

Culturally responsive leadership and culturally responsive teaching while building

conceptual understanding have been cited throughout the subsequent review of related literature,

15 that when applied, increase the mathematics performance of African American students. It is

with this lens that the provision of a review of related literature follows in Chapter 2 with a

distinct focus on culturally responsive leadership and culturally responsive teaching while

building conceptual understanding.

Purpose and Justification of the Study




actions impact the mathematics performance of African American students. Specifically, the

synthesis of the review of related literature and the results of this study could provide

information that would assist school leaders and educators in not only understanding their

respective roles impacting and influencing the mathematics performance of African American

students at the high school and middle school levels, but also understanding the pedagogical,

conceptual understanding, and leadership practices and factors that can lead to this improvement.

As an outcome, by embodying and employing these practices, teachers and school administrators

could meet or exceed federal (national) and state accountability mandates to improve learning

outcomes and success for African American students.

Research Questions

The research questions guiding this qualitative study were:

1. To what extent, if any, do principals at the high school and middle school levels that

exemplify culturally responsive leadership influence mathematics teachers’ use of

culturally responsive teaching that results in building conceptual understanding in

mathematics?

16 2. To what extent, if any, do culturally responsive teaching practices impact the

mathematics performance of African American students at the high school and middle

levels?

Conceptual Framework

A conceptual framework was created to illustrate the overarching variable of culturally

responsive leadership, undergirded by culturally responsive teaching practices inclusive of

building conceptual understanding. The conceptual framework captured that when these

variables are applied, an expected outcome of increased mathematics performance of African

American students at the high school and middle school levels may occur. The visual

representation investigated in this study are shown below (see figure 1).

Figure 1 A model to describe the overarching variable of culturally responsive leadership influencing the mathematics performance of African American students at the high school and middle school levels.

African American stadents at the high school and middle school

mathematics performance or

African American students 11 the bigh school and middle school

17 Limitations

The outcomes and results of this qualitative study were limited to the purposive sample

from which the data were drawn. An examination of culturally responsive leadership was limited

to only building principals without including the additional variable of assistant principals. High

school and middle school principals and mathematics teachers observed in this study were only

those that met the minimum standard of at least 40 points on the preliminary screening criteria;

therefore, there was no comparison made to those that did not earn 40 points to advance to the

primary study. The sample and locality (urban school division) limit the generalization to other

demographics and geographical regions (i.e., suburban and rural). Data collection involved

general educators and did not introduce another factor of special educators, although samples

may have been drawn from inclusion settings. Groups of classes reflected varying levels of

mathematical performance historically. While high school teachers may teach more than one

course, only the data from SOL-tested courses have been provided. Demographic comparisons

were limited to only African American versus White students (ethnicity) with factors such as

economically disadvantaged or students with disabilities not being the focus of the study.

Validity and reliability could have been limited due to the accuracy and subjectivity of

the responses gleaned from participants. Because of this, it could not be ensured that bias was

fully devoid from participant responses.

Transferability and generalizability were limited to mathematics performance outcomes

of African American students high school and middle school levels and cannot be implied to

apply to African American students at the elementary level. Transferability and generalizability

cannot be inferred to other ethnic groups or socioeconomic status – neither of which were the

foci or factors of this study.

18 Delimitations

The study involved data collection from principals and mathematics teachers of an urban

school division in Virginia at the middle and high school levels. High school and middle school

principals and mathematics teachers’ observations were limited to those who qualified for the

primary study by meeting the established criterion of 40 points or more on the preliminary

screening survey. High school and middle school mathematics teacher data and student

performance data were limited to teachers who self-identified as being culturally responsive.

Parents and students were not chosen by the researcher to be a part of the study.

Definitions of Key Terms

The following key terms have been provided as a resource to assist with understanding

the content of this study.

Algebra Readiness Formative Assessment Items. Sample formative assessments

created by the Virginia Department of Education (VDOE) aligned to the 2016 Mathematics

Standards of Learning that teachers may utilize to assess students’ understanding of mathematics

content (VDOE, 2019a). These assessments specifically address the Number and Number Sense;

Computation and Estimation; and, Patterns, Functions, and Algebra strands of middle grades

courses (VDOE, 2019a). These assessments also address the Equations and Inequalities,

Expressions and Operations, and Functions strands of Algebra I. There are no Algebra Readiness

Formative Assessment Items that address mathematics courses beyond Algebra I. Sample

Algebra Readiness Formative Assessment Items were utilized and embedded into the urban

school division’s mid-nine weeks assessments and Critical Skills Assessments.

African American. A “person having origins in any of the Black racial groups of Africa”

(United States Census Bureau, 2017, p. 1).

19 Collaborative Learning Team (CLT). Job-embedded interdependent teams of mutually

accountable mathematics teachers designated by content (e.g., Mathematics 8) who meet

frequently to collaboratively plan for instruction and to analyze student performance data with a

shared commitment to continuous and improved learning (DeFour, DuFour, Eaker, Many, &

Mattos, 2016).

Conceptual understanding. Conceptual understanding, “(i.e., the comprehension and

connection of concepts, operations, and relations) establishes the foundation, and is necessary,

for developing procedural fluency (i.e., the meaningful and flexible use of procedures to solve

problems” (Leinwand et al., 2014, p. 7).

Critical Skills Assessments. Deployed by the urban school division, these assessments

are intended to measure the progress of students and their proficiency in understanding the

content learned during every nine weeks of instruction. A student scoring at least 60% on the

assessment is deemed a passing score as per division-wide equating measures designed by the

urban school division’s Research, Planning, and Evaluation. In the context of this study,

mathematics performance was examined and analyzed in the first nine weeks of study of the

2019-2020 school year as a part of the data collection process. The data from SOL-tested courses

has been reported.

Cultural deficit theory. The:

perspective that minority group members are different because their culture is deficient in

important ways from the dominant majority group…The deficit model asserts that

racial/ethnic minority groups do not achieve as well as their White majority peers in

school and life because their family culture is dysfunctional and lacking important

characteristics compared to the White American culture. (Salkind, 2008, p. 1)

20 Culturally responsive leadership. Leadership that “influences the school context and

addresses the cultural needs of the students…improves teachers’ craft in ways that result in

improved student outcomes…and promotes [sic] a climate that makes the whole school

welcoming, inclusive, and accepting of minoritized students” (Khalifa, Gooden, & Davis, 2016,

pp. 1274-1275).

Culturally responsive teaching. Teaching practices that “use the cultural knowledge,

prior experiences, frames of reference, and performance styles of ethnically diverse students to

make learning encounters more relevant, affirming, and validating for them – it teaches to and

through the strengths of these students” (Gay, 2002, p. 106). To be culturally responsive, one

must embody culturally relevant pedagogy – “a pedagogy that empowers students

intellectually, socially, emotionally, and politically by using cultural referents to impart

knowledge, skills, and attitudes” (Ladson-Billings, 1995b, pp. 482-483). The theoretical

framework developed by Ladson-Billings (1995a) “rests on three propositions: (a) students must

experience academic success; (b) students must develop and/or maintain cultural competence;

and, (c) students must develop a critical consciousness through which they challenge the status

quo of the social order” (p. 160).

Curriculum Framework. Content specific assessments were created using the Virginia

2016 Mathematics Standards of Learning Curriculum Framework as a guide as specifically

intended. Each curriculum framework is:

a companion document to the 2016 Mathematics Standards of Learning, amplifies the

Mathematics Standards of Learning and further defines the content knowledge, skills, and

understandings that are measured by the Standards of Learning assessments. School

divisions are encouraged to incorporate the standards and Curriculum Framework into a

21 broader, locally designed curriculum. The Curriculum Framework delineates in greater

specificity the minimum content that all teachers should teach and all students should

learn. The Curriculum Framework also serves as a guide for Standards of Learning

assessment development. (VDOE, 2016, p. 3)

Fundamental middle school. Choice school fostering high behavioral and academic

standards that also requires entry via parent and student application (Urban school division,

2019, p. 2).

Magnet middle school. Comprehensive choice school offering “innovative scheduling

and twice the traditional class time for math and language arts/reading” that requires entry via an

extensive parent and student application and lottery process (Urban school division, 2019, p. 2).

Mid-nine weeks assessments. Division-wide assessments given to ascertain students’

understanding and proficiency of mathematics content provided in the middle of each nine

weeks. Consistent with the Critical Skills Assessment, a student scoring at least 60% on the

assessment is deemed a passing score as per division-wide equating measures designed by the

urban school division’s Department of Research, Planning, and Evaluation. In the context of this

study, the 4.5 weeks assessment of the first nine weeks of the 2019-2020 school year was used.

Mathematics performance data were examined and analyzed as a part of the study. The data from

SOL-tested courses has been reported.

Standards of Accreditation (SOA). The Standards of Accreditation “measure

performance on multiple school-quality indicators…and provide information on overall student

achievement, achievement gaps, and student engagement” (VDOE, 2017b, p. 1).

Student Detail by Question Report (SDBQ). The Student Detail by Question Report is

comprised of an item descriptor by strand for each tested item on the Standards of Learning test.

22 Test item difficulty (high, medium, low) are provided as well as specificity of individualized

correctness. The SDBQ Report is “the most granular piece of data available from the VDOE on

SOL assessments” (VDOE, 2019b, p. 43).

Standards of Learning (SOLs). The established “minimum expectations for what

students should know and be able to do at the end of each grade or course” (VDOE, 2017b, p. 1).

These assessments measure the “success of students that meet the state Board of Education’s

expectations for performance and achievement” (VDOE, 2017b, p. 1). The 2016 Mathematics

Standards of Learning for grades 6 – 8 are delivered through an online computer adaptive test

model; Algebra I, Geometry, and Algebra II are delivered online and are not computer adaptive

(VDOE, 2017a).

Urban school division. The National Center for Education Statistics (2006) designated

an urban school division or locale as one being a “territory inside an urbanized area and inside a

principal city with a population greater than or equal to 100,000” (p. 1). The urban school

division of study is situated within a principal, independent city in Virginia with a population of

134,313 (United States Census Bureau, 2018, p. 1)

White. A person “having origins in any of the original peoples of Europe, the Middle

East, or North Africa” (United States Census Bureau, 2017, p. 1).

Overview of the Dissertation

In this chapter, background national and state data were provided to set the context for

the study. The statement of the problem, rationale, and significance were given to further add to

the scope of the study – leading to the development of the conceptual framework.



23 building conceptual understanding of their students; and, how teachers’ culturally responsive

actions impact the mathematics performance of African American students. The research

questions, addressing the purpose of the study, were presented. The limitations and delimitations

were provided to set parameters of generalizability as well as address validity, reliability, bias,

and transferability. Definitions of key terms were given to assist with contextualization.

Chapter 2 provides a review of related literature that specifically details culturally

responsive leadership and culturally responsive teaching while building conceptual

understanding. A description of the methodology used in the study of the research questions is

presented in Chapter 3. An analysis, description, and explanation of the data as received from the

study is presented in Chapter 4. A discussion of the findings with connections back to the review

of the related literature, to include a reflection on the process of the study, considerations for

areas for further research, and recommendations for practice is presented in Chapter 5.

24 Chapter 2

A Review of Literature

Introduction

The National Council of Supervisors of Mathematics (NCSM) and TODOS: Mathematics

for All (2016) jointly posited that “a social justice priority in mathematics education is to openly

challenge deficit thinking and the institutional tools and practices that perpetuate static views

about children and their mathematics competencies” (p. 2). To sustain culturally responsive

teaching where mathematics teachers seek to build the capacity of students by building up their

conceptual understanding, there must be, based on the literature, leadership that supports and

nurtures that environment (Delpit, 2012a; Khalifa, Gooden, & Davis, 2016; Klotz, 2006).

Therefore, a literature review of the overarching variable of culturally responsive leadership and

its influence in improving the mathematics performance of African American students will be

presented and discussed. The integral characteristics of leaders who promote culturally

responsive leadership and the practices employed to promote the achievement of this population

of students to create a culturally responsive learning environment will be examined.

Culturally Responsive Leadership

During her 15-year qualitative study of the examination of culturally responsive teacher

and leadership practices and perspectives, Delpit (2012a) centered on the cultivation of character,

courage, and creativity and how overtones of inadequacy are minimized when effective

leadership is at the helm of schools. A synthesis of results yielded the following themes in regard

to the characteristics of building-level leadership to include (a) recognition of the importance of a

teacher and good teaching, (b) provision of students with social, emotional, and academic

supports, (c) and, recognition and celebration of the strengths of students.

25 Characteristics of leaders that promote culturally responsive leadership.

Synthesizing relevant literature, Khalifa, Gooden, and Davis (2016) found that culturally

responsive leaders influence the school’s climate to accept often marginalized students by being

inclusive of cultural diversity. These leaders are consistently reflective of their practices,

frequently review and monitor data to ensure that no one falters in their learning, and actively put

in supports and interventions as the data generates. These leaders go out and get out into the

community to establish relationships with families as well as community leaders that can serve

as mentors or support resources for the school (Delpit, 2012a). Khalifa and Atkins (2019)

described in their podcast that culturally responsive leaders “engage with communities on the

community’s terms and do this by honoring students” and affirm them by positive service and

advocacy. Khalifa, Gooden, and Davis (2016) assert that above all else, these leaders “resist

oppressive education and leadership…This oppression most often comes when school leaders

hold deficit-oriented opinions and views about minoritized children and families” (p. 1289).

Any form of cultural deficit theory or practices are unacceptable to the school as they are

“barriers to equitable learning environments” (Khalifa, Gooden, & Davis, 2016, p. 1289).

The assertion of Khalifa, Gooden, and Davis (2016) harkens back to that of Johnson

(2006) who wrote that principals who are culturally responsive work to promote equality and

advocate for the learning environment to reflect the multiculturalism that the students bring to

school – doing this in a warm, yet firm stance of high expectations for all students. These

principals incorporate “students’ cultural knowledge as a vehicle for learning, fostering the

development of sociopolitical consciousness” (Johnson, 2006, p. 20). Further, culturally

responsive leaders “embrace restorative justice, which seeks to minimize the use of

exclusionary…practices” (LaCour, York, Welner, Valladares, & Kelly, 2017, p. 10).

26 Leadership practices that create a culturally responsive learning environment. Klotz

(2006) stated that the goal of culturally competent school leadership is to establish a culture and

climate where all students are nurtured, comfortable, engaged, and connected, captured in the

essence of high expectations. Further, Klotz (2006) defined a “culturally competent school” as

“one that honors, respects, and values diversity in theory and practice and where teaching and

learning are made relevant and meaningful to students” (p. 11). She cited multiple key

components of leadership practices to include:

● acknowledgment of students’ learning styles and capitalizing on them to make

instruction and the culture of the building real and relevant;

● use of a data-driven model to examine and monitor student performance

frequently to make just in time adjustments to set students up for success; and,

● the hiring of qualified personnel having mastered their content, thereby having

instructional staff that can provide experiences for their students that increase the

depth of understanding. (Klotz, 2006)

As an extension of hiring content-rich personnel, culturally responsive leaders match students to

the appropriate teacher and place the most experienced teacher with students in need of

additional supports to master the content (Klotz, 2006). Khalifa, Gooden, and Davis (2016)

agreed that culturally responsive leaders are a “vital part of the process in recruiting and

retaining the best teachers for children who have been marginalized...additionally, the right

leader will hold an understanding of the need to recruit and sustain culturally responsive teachers

who are better prepared to work with children of color” (p. 1273).

Grounded in the previous work of Ladson-Billings and Gay, Madhlangobe and Gordon

(2012) conducted a case study (interpreted and grounded theory in scope and practice) of a

27 building-level high school leader. The study encompassed multiple interviews with teachers,

parents, and students along with extensive immersed job shadowing for several weeks. Themes

arose from their study of the high school leader – that being caring, the building of relationships

through present and positive communication, persistence in the implementation of culturally

responsive teaching, the modeling of these theoretical frameworks consistently through inclusive

practices and professional development, and the fostering of cultural responsiveness.

Madhlangobe and Gordon (2012) stated that culturally responsive leaders understand “how to

reduce biases and undue prejudicial practices by having their teachers to engage in equity

pedagogy” in order to “help teachers become knowledgeable of their students’ cultures, not only

so they avoid bias in their teaching, but also to make the students’ cultures part of their teaching”

(p. 179).

Specific to mathematics, Rigby et al. (2017) found that culturally responsive principals

communicate instructional expectations that are in alignment with high-quality and rigorous

mathematics as a part of their eight-year longitudinal mixed-methods study of middle school

principals. These leaders informally and formally observed mathematics teachers and provided

them with frequent and just in time feedback. Further, principals constructed the master schedule

that allowed for the majority of teachers to meet. During those times, the principal also attended

to hear how teachers were planning and provided suggestions for instructional delivery. When

assessments were given, the principal worked with teachers to monitor and disaggregate the data

to provide supports and interventions. This is reflective of the best practice recommendations for

building-level leadership provided by Leinwand et al. (2014) to ensure that students have the

opportunity and access to become proficient in mathematics. To promote access and equity,

effective building-level leadership ensures that all students are provided with sufficient time for

28 instruction to maximize their learning, promise, and potential while eliminating deficit thinking

practices such as tracking, and implement intervention and supports that help students that

struggle with mathematics (Leinwand, 2014; Walkowiak, Pinter, & Berry, 2017).

Cultural Deficit Theory Counterexamples

There are existing theoretical and conceptual frameworks with diametrically dissimilar

outlooks in direct response to cultural deficit theory, capturing and urging teachers and building-

level leadership to maximize on the “human capital of culture” and resiliency that African

American students bring into the classroom that is specifically idiosyncratic. Culture is involved

in all aspects of learning as it is not a static set of characteristics located within individuals or a

nation’s identity, but is fluid and complex. Culture is “central to the understanding of human

relationships” (Marshall, 2014, p. 47). Cultural factors impact the knowledge work and

investment in human capital (Marshall, 2014; Trilling and Fadel, 2009). At the core of

understanding each framework is the counter-argument to cultural deficit theory – culturally

responsive teaching.

Paris and Alim (2014) declared that culturally responsive teaching is a direct response to

the alternative disposition and view of cultural deficit theory, stating:

deficit approaches to teaching and learning have echoed across decades of education in

the United States. Such approaches view the languages, literacies, and cultural ways of

being of many students and communities of color as deficiencies to be overcome if they

are to learn the dominant language, literacy, and cultural ways of being demanded in

schools. (p. 87)

To understand through the focal point of culturally responsive teaching, a historical linear

progression to and then through it has been provided.

29 Afrocentricity and mathematics pedagogy. As results from national assessments

continued to indicate a discernible achievement gap between African American students and

their White peers, Tate (1995) questioned, “What type of mathematics pedagogy must African

American students negotiate to be successful in school? Is it possible to develop high-level

mathematics competence for African American students within a Eurocentric paradigm?” (pp.

164, 168). Tate engaged in a case study of one teacher and her students in a predominantly

African American middle school. The first phase centered on documenting the pedagogy of the

teacher (collecting observations, first-hand observations, and videotapes of instruction). The

second phase included interviewing the teacher and students (ethnographic in scope) to discuss

the teacher's philosophy of education, background, support from building leadership, and

parental and community involvement.

Several themes emerged from Tate’s (1995) study such as problem-solving through

investigation and formulation of ideas; communication through debate and persuasive proof;

reasoning through representations; connecting mathematics to other disciplines and present state;

developing numerical and computational fluency; and, social action through those problem-

solving strategies. African American students within the teacher's class demonstrated success

with complex mathematics by making connections to text and life, thus creating a context and

relevancy for process and practice. Further, for her students to positively respond to her

instructional delivery, the teacher provided opportunities to learn through storytelling,

cooperative work, and questioning (Tate, 1995).

As an outgrowth of his work, Tate (1995) provided an Afrocentric approach to

mathematics instruction built from the previous posits of Woodson (as cited by Tate, 1995) who

stated that African American students often experience an unfamiliar learning experience that

30 does not adhere to their roots and learning style, leading to insufficient achievement in complex

algorithms and only development of rote computational skills not suitable for transferability and

navigation in an ever-growing society. Tate (1995) continued by stating, “African American

students are not prepared to use mathematics as a tool to negotiate the complex democratic

process of the United States” (p. 166). Further, providing African American students with

curriculum, instruction, and assessment devoid of their experiences and culture is a hindrance to

their success in mathematics (Tate, 1995). Therefore, Afrocentricity looks to “center African

American students within the context of their traditions and experiences so that they are better

able to relate to other cultural perspectives” (p. 168). The Afrocentric approach is focused and

reliant upon a collaborative and communicative dynamic between teacher and student,

investigative and exploratory learning, and “open-ended [sic] problem solving connected to

students’ realities,” perspectives, and experiences tied to social action (Tate, 1995, p. 172). The

contextual transference situated perspective work of Boaler (1993) is aligned to the Afrocentric

approach, where she suggested that learning mathematics in context provides the transference of

motivation, interest, and participation through connections to real-life, thus making mathematics

more attainable to students instead of devoid of approachability through rote problems and

procedures. Boaler (1993) provided that “if the students’ social and cultural values are

encouraged and supported in the mathematics classroom, through the use of contexts or

acknowledgment of personal routes and direction, then their learning will have more meaning”

(p. 17). Culturally relevant pedagogy “attempts to connect the meaningfulness between home

and school experiences to content concepts and students’ social realities” (Gay, 1990, p. 62).

Culturally relevant pedagogy. The theoretical framework developed by Ladson-Billings

(1995a) “rests on three propositions: (a) students must experience academic success; (b) students

31 must develop and/or maintain cultural competence; and, (c) students must develop a critical

consciousness through which they challenge the status quo of the social order” (p. 160). She

specifically cites the work of Irvine (1990) as the underpinnings of the culturally relevant

pedagogical framework (Ladson-Billings, 1995a). Irvine engaged in micro- and macro-analysis

of teacher-student interpersonal contexts and expectations; however, a theoretical or operational

model was not an outcome of the study. Using both Tate and Irvine’s work as subgrade, Ladson-

Billings sought to expand their research. In addition to the constructs of culturally relevant

pedagogy, students must have the autonomy to exhibit cultural competence – meaning that

students must be able “to maintain their cultural integrity while succeeding academically”

(Ladson-Billings, 1995b, p. 476).

Ladson-Billings (1995a, 1995b, 2009a) engaged in a three-year ethnographic study of

eight middle school teachers in urban school districts to examine how their specific styles of

instruction coalesced into what is defined as culturally relevant pedagogy. Each teacher

exemplified specific characteristics, practices, and beliefs about students that transcended beyond

race, gender, or even teaching style. The study included interviews, video-taped instructional

observations, and collaborative analysis. Each selected teacher was interviewed and agreed to

collaboratively participate in a research cohort tasked with analyzing and interpreting the data

and then jointly respond to their exhibited expertise. Students exposed to the three criteria

exhibited demonstrative gains on district and national assessments; further, the teachers created a

community of learners while maintaining an expectation of collaboration, trust, and respect

(Ladson-Billings, 1995b). Results also yielded that the teachers felt it was their responsibility to

be the catalyst through which their students thrived by providing immediate supports and

modifications to instruction (Ladson-Billings, 1995b).

32 Culturally responsive intrinsic motivational framework. Similar in scope to culturally

relevant pedagogy, and designed during the same timeframe as the work of Ladson-Billings,

Wlodkowski and Ginsberg (1995) created the culturally responsive intrinsic motivational

framework that seeks to “engage learners while respecting their cultural integrity” (p. 17). This

four-pronged framework provides motivational conditions that the teacher must create to foster a

culturally responsive classroom – “establish inclusion, develop positive attitude, enhance

meaning, and engender competence” (Wlodkowski & Ginsberg, 1995, p. 18). Wlodkowski and

Ginsberg (1995) maintained that teachers establish subsumption by shared, equitable,

responsibility and accountability to tasks, through collaboration, not isolation. In doing so, a

positive attitude toward learning is developed through reciprocal teacher to student relationships,

leading to connections to the content. This is reflective of the triangular relationship model later

developed by Delpit (2006a) where teachers of communities of color recognize that teaching and

learning first begins with the connection between the teacher and student, thus leading students

to want to learn the content because of the established relationship of mutual respect. This model

of instruction illustrates that the “strongest relationship is between student and teacher, with

content as only one aspect of their relationship” (Delpit, 2006a, p. 140).

Culturally Responsive Teaching

Rhodes (2017) stated “culturally responsive teaching is an umbrella term which

encompasses a variety of approaches, such as culturally relevant. This equity-based approach

places students’ cultures at the core of the learning process” (p. 45). Therefore, competence is

engendered by connecting the assessment process through multiple representations and entry

points to access the curriculum by utilizing students’ experiences and learning styles as

33 foundational referents. Inspired by Ladson-Billings, Gay (2002) actualized the theoretical

framework of culturally responsive teaching, defining it as:

using the cultural characteristics, experiences, and perspectives of ethnically diverse

students as conduits for teaching them more effectively. It is based on the assumption that

when academic knowledge and skills are situated within the lived experiences and frames

of reference students, they are more personally meaningful, having higher interest appeal,

and are learned more easily and thoroughly. (p. 106)

Culturally responsive teaching extends beyond just good teaching – it draws from and capitalizes

on students’ culture, experiences, and acknowledges cultural identity (Zeichner, 2003).

Culturally responsive teaching seeks to encourage teachers to develop culturally diverse

understanding; design culturally relevant curricula; demonstrate caring through the development

of a familial or a communal atmosphere; provide explicit and clear communication; and,

establish reciprocity in classroom instruction through multiculturalization, meaning to match

teaching styles to that of the learning styles of those that are being taught (Gay, 2002). Gay

(2002) refuted cultural deficit theory stating, “because culture strongly influences the attitudes,

values, and behaviors that students and teachers bring to the instructional process, it has to

likewise be a major determinant of how the problems of underachievement are solved” (p. 114).

Intertwining mathematics and culturally relevant and responsive frameworks.

Aronson and Laughter (2016) conducted a synthesis of over 40 studies where authors noted the

difference between the two frameworks with Gay's seeking to impact competency and

methodology while Ladson-Billings’ works to influence attitudes and dispositions regarding

curriculum, instruction, and assessment with a sociopolitical consciousness slant. Leonard,

Brooks, Barnes-Johnson, and Berry (2010) proposed marrying the aforementioned through social

34 justice pedagogy and culturally relevant pedagogy concerning mathematics instruction. The

authors described this framework as follows:

(a) access to high-quality mathematics instruction for all students; (b) curriculum that is

focused on the experiences of marginalized students; (c) use of mathematics as a critical

tool to understand social life, one’s position in society, and issues of power, agency, and

oppression; and, (d) use of mathematics to change society through the means of informed

citizenship. (p. 262)

Therefore, social justice is a component of culturally relevant pedagogy and vice versa. These

two frames support the goals of cultural competency, academic success, and the development of

social and critical consciousness as prescribed primarily by Ladson-Billings (1995a, 1995b,

1997).

Seeking to help teachers to analyze and to critique their lesson planning and delivery of

instruction to align with culturally relevant pedagogical practices, Aguirre and del Rosario

Zavala (2013) created the non-evaluative, Culturally Responsive Mathematics Teaching (CRMT)

Lesson Analysis Tool. Moreover, the CRMT was created to help teachers to reflect on their

instructional practices with a focus on mathematical thinking, equity, and access consisting of six

categories of mathematics instruction: “cognitive demand; depth of knowledge and student

understanding; mathematical discussion; potential; vocabulary; and, cultural- and community-

based knowledge” (Aguirre & del Rosario Zavala, 2013, p. 169). Qualitative in design, the

researchers conducted a three-year study using teacher interviews, student and teacher artifacts,

and professional development sessions. They then transcribed, coded, and examined each for

themes using a constant comparative method. An analysis of the results provided an outcome

that referenced teachers' ability to help students explore, analyze, and reason; deepen

35 mathematical thoughts and processes; give voice and choice with equitable distribution of

students’ values and contributions to the mathematical discourse; create connections and make

mathematics relevant and real; and, create lessons that support social justice and issues of change

within their own lives or the community-at-large (Aguirre & del Rosario Zavala, 2013).

The CRMT Lesson Analysis Tool created opportunities for dialogue between teachers

participating in the study to improve their practice regarding culturally responsive teaching

(Aguirre & del Rosario Zavala, 2013). The review and subsequent critical analysis of math

lesson plans addressed social justice, mathematical reasoning, cultural competency, and

language. In turn, the process fostered deep reflections of practice and discussions about needed

adherence to culturally responsive practice. Aguirre and del Rosario Zavala (2013) asserted that

teachers have to comprehend that:

mathematics is used as a primary academic performance indicator of students to evaluate

state, national, and global competitiveness. In addition, teachers must identify and

challenge how mathematics is a primary gatekeeper to advanced courses and career

trajectories with serious economic and social consequences. (p. 168)

Paris (2012) and Paris and Brown (2014) worked to capture the essence of Ladson-

Billings and Gay's research as they moved farther into the idea of pluralism and multiculturalism

with their conceptual framework of culturally sustaining pedagogy. Culturally sustaining

pedagogy “requires that teachers support young people in sustaining the cultural and linguistic

competence of their communities while simultaneously offering access to dominant cultural

competence…both within-group cultural practices and across-group practices” (Paris, 2012, p.

95).

The stances of each framework described reveal the perpetual fracture between African

36 American students’ performance in high school and middle school mathematics and the

detrimental results if the trend of the achievement gap continues to fossilize and become a

societal norm and expectant performance (Aronson & Laughter, 2016; Bol & Berry, 2005;

Bonner, 2014; Tate, 1994; Tate 1995) and as previously evidenced through NAEP, SAT, PSAT

10, and PSAT 8/9 outcomes. Throughout the literature base, culturally relevant pedagogy or

culturally responsive teaching serves as either the foundation or the bower to which other

conceptual frameworks are derived. As suggested by the literature, culturally relevant pedagogy

is subsumed under culturally responsive teaching (Gay, 2002; Munter, 204; Rhodes, 2017) and

heretofore will be referenced to construct parallelism between it and culturally responsive

leadership. Guided by the literature, it is necessary to drill down farther to understand the role of

culturally responsive teaching on the mathematics performance and achievement of African

American students at the high school and middle school levels. Embedded will be the

examination of African American learning styles and preferences, characteristics and

dispositions of teachers that employ culturally responsive teaching, and, the strategies used by

teachers that create a culturally responsive mathematics classroom.

Farinde-Wu, Glover, and Williams (2017) stated that there is a need to “exchange

antiquated, Europeanized approaches to teaching and learning with culturally responsive

instruction that more accurately reflects the academic audience” (p. 280). Boaler (2000)

provided, through interviews of 76 middle and high school students, her results of a four-year

qualitative study that “social interactions, variety, and meaning were central to positive learning

experiences, yet dominant school practices they [students] experienced were memorization,

reproduction of procedures, and individualized work” (p. 379). Regarding traditional approaches

to learning, Gay (1990) asserted:

37 some of the most devastating educational inequities are perpetuated not through the

formal instructional programs but through the social norms, procedural rules, and cultural

contexts that govern teaching and learning. These hidden curricula transmit to students

powerful subliminal messages about how educational opportunities are allocated and

socialize students into behavioral patterns that conform to the inequalities that exist in the

larger society. If we are to achieve equality, we must broaden our conceptions of

curriculum. (p. 61).

Farinde-Wu, Glover, and Williams (2017) combined the theoretical framework of Ladson-

Billings (culturally relevant) under the work of Gay (culturally responsive) – providing that this

form of instruction is (a) responsive in that it establishes connections between students’ frames

of reference and cultural backgrounds back to the content, (b) rejects the stance of cultural

deficiency, (c) promotes an awareness and places value on the diversity of the student

population. Therefore, the “challenges in achievement African American students face are, at

least, partially informed by a cultural divergence between the institutional practices in public

schools and the learning preferences of this population” (Boykins, Tyler, & Miller, 2005, p. 522).

In particular and relevant to the content and context of this research, Ellis (2018) provided that

culturally responsive mathematics teaching creates an environment such that each student is

involved in mathematical reasoning; each student is valued and respected for their mathematical

approaches; and, each student is responsible for the overall success of the collective. Further,

culturally responsive teaching specifically envelopes a sense of awareness and ability to

understand the “cultural patterns that influence the behavioral and mental ecology of the

classroom” (Hsiao, 2015, p. 241).

38 African American learning styles and preferences. Farr (2010) argued that there are

two stances on the importance of students’ culture and learning styles — one being a traditional

view, the other with a focus on cultural responsiveness:

The more traditional view stresses that ‘good teaching is good teaching’— that the

methods, strategies, and techniques that good teachers learn and master are equally

valuable for students of a variety of cultures. This theory holds that no special knowledge

and skills other than the mainstream, traditional knowledge bases of teacher education are

needed to train teachers for classrooms of students from culturally and linguistically

diverse backgrounds. The key to serving students of diverse backgrounds, according to

this view, is simply vigorous and intense work, using the same techniques as you would

with a non-diverse class. A competing perspective, however, argues that what works for

White, middle-class students (which, some would argue, represents the conventional

canon of teaching methods taught to new teachers) may not necessarily work for less-

affluent, minority students. (p. 85)

Gay (1994) explained that students’ learning styles are at the core of their being, shaping

their approaches to and perceptions of learning; therefore, teachers must understand the learning

styles of diverse cultures to be responsive through appropriately applied instructional strategies

and practices. Embedded within the framework of culturally responsive teaching is the

understanding of the learning styles and preferences of African American students (Garvey,

1987; Gay, 2002; Hale, 2016; Ladson-Billings, 2009a). After conducting multiple qualitative and

mixed-methods studies analyzing research findings, theoretical claims, practical experiences,

teacher observations, and analysis of student performance of African American, Latino, and

Native American students, Gay (2002) provided that when:

39 understanding learning styles of ethnically diverse groups, it is imperative to examine

them within the parameters such as physical and social preferences to learning, oral and

written communication structures, stimulation for processing and perceiving information

(cues both verbal and non-verbal), motivation, incentives and rewards, and

interdependence. (p. 113)

In light of this, the Afrocultural framework of Boykin, Tyler, and Miller (2005)

delineated African American students’ educational experiences as those that incorporate

movement (expression, dance, rhythm); verve (repetitiveness, physical/sensate simulation);

orality (call-and-response); and, communalism (social and cognitive interdependence). Further,

Delpit (2006b) contended that African American students, boys in particular, thrive on

interpersonal interactions with peers in the classroom when performing tasks; however, not

understanding this aspect of their learning can lead teachers that do not exhibit culturally

responsive teaching practices “unduly” label students as disruptive and penalize them for talking

and acting out (p. 169).

Berry and Thunder (2012) further examined how African American students negotiate

their mathematics learning and participation. They conducted a six-step qualitative meta-

synthesis of existing literature and synthesis of themes about the mathematics identity of African

American students and found that students negotiated their learning through the lens of their

values, perceptions of success, access, and efficacy. To reach optimal levels of efficacy and

maintain a secure mathematics identity, Hale (2016) provided that African American students

prefer novelty, music, storytelling, personal distinctiveness, and understand mathematics

concepts by registering in on similarities and differences globally instead of a narrow focus of

right versus the wrong answer. The reasonableness of answer is evident as African American

40 students rely on estimation before arriving at an exact answer and they prefer learning through

inferences instead of inductive and deductive reasoning (Hale, 2016; Ladson-Billings, 1995a).

Characteristics and dispositions of teachers that employ culturally responsive

teaching. Ladson-Billings (2009c, 2009d) compared teacher dispositions to that of an

assimilationist – the assimilationist is static with direct instruction being the key method of

instructional delivery, exemplifies content neutrality, and separates excellence from individual

differences and diversity. Contrariwise, she wrote that teachers that embody culturally relevant

pedagogy (a) view knowledge critically, with fluidity and not stagnation; (b) are excited about

the content; (c) help students to hone the skills necessary to understand increasingly complex

mathematics; and (d) use the diversity that students bring into the classroom to strengthen the

dialogue, discourse, and approaches to solving problems (Ladson-Billings, 2009c; Ladson-

Billings, 2009d).

To further delve into the work of Ladson-Billings while extending into culturally

responsive teaching behaviors, Malloy (2009) examined the temperament of teachers who help

African American middle school students gain conceptual understanding in mathematics and that

mold students’ development of knowers and doers of mathematics over the course of the three-

year Mathematics Identity Development and Learning (MIDDLE) longitudinal study. Three

disposition themes developed from her qualitative, ethnographic research of four teachers –

reflective practitioner, building communities of learners, and giving voice and value to students –

resulting in practices that:

(a) acknowledge and use individual student preferences in the acquisition of knowledge;

(c) value student discourse and verbal knowledge; and,

41 (e) encourage, support, and provide feedback to students as they learn. (Malloy, 2009, p.

91)

Malloy (2009) found that teachers successful with this population of students maintained high

expectations for performance, choosing to focus in on the “capital of culture” that African

American students bring into the classroom, instead of cultural deficit models harkening back to

negative labeling and stereotypes (p. 91). Teachers successful with these students recognize the

capital of culture – understanding that rhythm, music, sound, and movement are commodities to

be invested (Farinde-Wu, Glover, & Williams, 2017; Malloy, 2009).

Ukpokodu (2011) based his qualitative study of culturally responsive teaching practices

on Gay’s culturally responsive teaching. He found that teachers successful with this population

of students work to contextualize understanding by using students’ speech patterns, language,

and experiences to begin mathematical discourse undergirded by scaffolding questions that allow

them to be open to students’ variances in mathematical thinking (Ukpokodu, 2011). Because of

the acceptance of multiple representations or creations to arrive at a solution, students are valued,

and their self-advocacy, mathematics identity, and efficacy increase exponentially (Berry &

Thunder, 2012; Ladson-Billings, 2009b; Martin, 2012; Ukpokodu, 2011). For instance, culturally

responsive teachers know how to leverage mathematical learning to extend thinking through the

cultivation of connections between prior and current knowledge to real-world experiences –

building from places of strength to foster critical thinking (Aguirre & del Rosario Zavala, 2013;

Delpit, 2012b).

The work of Rubel and Chu (2012) is enveloped in the Centering the Teaching of

Mathematics on Urban Youth (CTMUY) project; and, through their work, the CureMap, a

conceptual framework was developed with three key components: “teaching mathematics for

42 understanding, centering instruction on students’ experiences, and developing students’ critical

consciousness about or with mathematics” (p. 44). Teachers participating in the qualitative study,

consisting of classroom immersion observations in four rounds, were found to teach for

understanding using open-ended tasks fostering connectivity within and amongst mathematical

concepts. The emphasis on respecting multiple modalities was key to African American students

feeling connected to the content (Rubel & Chu, 2012).

The work of Rubel and Chu is aligned to that of Hammond (2015) and her Ready for

Rigor Framework in which culturally responsive teaching is its foundation. However, Hammond

(2015) took on the component of neuroscience and how teachers must understand the copious

functions of the brain to meet students of color in the context of their culture to increase student

achievement. The teacher prepares the way for African American students by infusing

affirmation, validation, and instructional discourse, thus “expanding [the brain’s] ability to do

more complex thinking and learning” (Hammond, 2015, p. 49). Teachers of this population find

success when they do not tamp down the cognitive rigor of tasks as this slows down the capacity

of the brain and is counterintuitive as it seeks to absorb new knowledge (Hammond, 2015). This

assertion is linked to the work of Delpit (2012a) who stated:

when we look out at a classroom of black faces, we must understand that we are looking

at children at least as brilliant as those from any well-to-do white community. If we do

not recognize the brilliance before us, we cannot help but carry on the stereotype societal

views that these children are somehow damaged goods and that they cannot be expected

to succeed. What happens when we assume that certain children are less than brilliant?

Our tendency is to teach less, to teach down, to teach for remediation. (p. 5-6)

43 Because the culturally responsive teacher treats students as competent, students exhibit

competency in response to the scaffolding and guidance that the teacher provides to extend the

learning and stretch students’ thinking, and as a byproduct their abilities (Ladson-Billings,

2009a). It is in this vein, that a review of the mathematics classroom strategies that prevail as a

result are examined.

Strategies used by teachers that create a culturally responsive mathematics

classroom. As a part of the Mathematics Identity Development and Learning (MIDDLE)

longitudinal study, Malloy (2009) conducted research and review of the methodology of teachers

who help African Americans in the middle grades enhance their conceptual understanding.

Malloy (2009) found that these teachers observed and responded to students to ascertain their

level of understanding or misconceptions; created a classroom culture of trust, respect, and rigor;

and, acted as a facilitator instead of a lecturer. When facilitating instruction, teacher participants

emphasized the whole (the why behind the learning), recalled connections to multiple

mathematical ideas, engaged in social-emotional content material, and, focused on interests and

extrinsic motivation. Berry and Thunder (2012) agreed that environments, where students are

given multiple opportunities to represent mathematics in their own way and are given various

contexts to explore, make mathematics real to them. Ellis (2018) described this way of teaching

as delving deep to create an environment with “coherent and connected mathematical

understandings” (p. 5). African American students must have visible examples of what it means

to be viable in mathematics through verbal praise, imagery, and clear modeling to experience a

pathway that will lead to success (Berry & Thunder, 2012).

Multiple methods of teaching and presentation of content with reciprocal receipt of

multiple solutions are paramount to mathematical discourse (Delpit, 2012b; Malloy, 2009;

44 Walkowiak, Pinter, & Berry, 2017). Leinwand et al. (2014) provided high leverage mathematics

teaching practices aimed at ensuring success for all students in Principles to Actions produced by

The National Council of Teachers of Mathematics (NCTM) stating, “teachers must understand

the use the social contexts, cultural backgrounds, and identities of students to foster access,

motivate students to learn more mathematics, and engage student interest” (Leinwand et al.,

2014, p. 115). Teachers that facilitate meaningful mathematical discourse create an environment

that promotes problem-solving. Imagine a zigzag conversation model with student-student,

student-teacher, and then teacher-student talk that “builds shared understanding of mathematical

ideas by analyzing and comparing student approaches and arguments” (Leinwand et al., 2014, p.

10).

Bonner (2014) examined the “major pedagogical themes that drive mathematics

instruction and discipline” and how those themes interact, finding that mathematical discourse

was a key factor in strengthening the performance of African American students in high school

and middle school mathematics (p. 379). Bonner (2014) engaged in grounded theory from data

collected on three mathematics classrooms which focused on the dynamics of interaction and

discourse using a three-stage process consisting of immersion, data collection, and triangulation

of themes. Bonner (2014) found that “teacher interactions with students, which are social and

therefore culturally significant, have a great impact on student identity development and

perceived ability in mathematics” (p. 380). These interactions are based on trust, with teachers

making sure to first start with establishing relationships and then moving on to content. Again,

this is reflective of the teacher-student-content triangular model prescribed by Delpit (2006b)

who stated that “when instruction allows no opportunities for children to use their minds to

45 create and interpret content, then children will only focus on low-level thinking and their school-

based intellect will atrophy” (p. 174).

Based on the dominant theme of mathematics discourse, Bonner (2014) created a

discourse model of culturally responsive mathematics teaching where power is equally

distributed between students and the teacher built on a trusting relationship. Power is not viewed

in the sense of authoritarianism, but of distributed leadership where the teacher takes the lead in

facilitation, while the student takes the lead in discovery through active discourse. The teacher

leverages power in the classroom by capitalizing on relationships and students' funds of

knowledge, having a keen awareness of the cultural values and modalities of each learner to

foster a mathematics classroom full of life and shared responsibility. Because everyone is

accountable to their learning, attainment, and then application of mathematical knowledge, it is

indiscernible who is “in charge” in the classroom. In essence, the teacher “creates spaces where

students develop and maintain strong racial and cultural identities” (Bonner, 2014, p. 394).

Culturally responsive teachers use the strategy of family (familial-style) to create cultures

of success bolstered by building students up through frequent praise and structured, student-

centered, content-driven accountability measures – indicative of African American learning

preferences (Boykin, Tyler, & Miller, 2005; Ukpokodu, 2011). This sense of family fosters

interdependence, and through interdependence, the confidence to pursue complex mathematical

challenges independently (Hammond, 2015; Ellis, 2018; Ladson-Billings, 2009a; Malloy, 2009).

Mathematics in a culturally responsive classroom is visible and palpable where everyone

is expected to learn from and with each other and where the expectation to build conceptual

understanding is akin to “pulling knowledge out like ‘mining instead of putting knowledge into

like ‘banking’” (Ladson-Billings, 2009d, p. 60). Building conceptual understanding has been

46 cited within the literature base to increase the performance of African American students (Jones,

2016; Leinwand et al, 2014; Malloy & Jones, 1998; Thomas, Santiago, & Malloy, 2002).

Therefore, building conceptual understanding will be examined through the lens of culturally

responsive teaching and how, by its implementation with fidelity as the literature suggests,

deepens mathematical thinking and problem solving as a process for African American students

at the high school and middle school levels.

Building Conceptual Understanding

Ladson-Billings (1997) implored, “How might we construct mathematics learning

situations that improve students' mathematics operating system? What can we discover about

certain aspects of learning that work well in the classroom system?” (p. 706). She provided the

metaphor of likening a paradigm shift of building conceptual understanding to that of a “net”

rather than a “sieve” (Ladson-Billings, 1997, p. 699). Mathematics teachers must move away

from the repetitiveness of “drill and kill” as it does not adhere to the cultural competence nature

of African American students – those that thirst for movement, social interaction,

interdependence, and collaboration (Boykin, Tyler, & Miller, 2005; Ladson-Billings, 1997).

Thomas, Santiago, and Malloy (2002) concurred, stating that building connections in

mathematics foster a love for doing mathematics; at the middle school level, investigations to

build conceptual understanding are “emphasized with the intent of broadening students'

perspectives on mathematics as an integrated whole” while at the high school level, “emphasize

investigations of mathematical connections” going further to “include a focus on the interplay

among mathematical topics and applications” (p. 485). Almarode et al. (2019) provided that

“conceptual understanding and the application of concepts and thinking skills are essential

aspects of learning mathematics” (p. 2).

47 NCTM standards “suggest pedagogical practices that includes the use of inquiry-based

and cooperative learning, which are aspects of culturally responsive teaching” (Ukpokodu, 2011,

p. 48). Conceptual understanding, “(i.e., the comprehension and connection of concepts,

operations, and relations) establishes the foundation, and is necessary, for developing procedural

fluency (i.e., the meaningful and flexible use of procedures to solve problems” (Leinwand et al.,

2014, p. 7). High leverage teaching practices such as implementing activities that require

students to reason and to problem-solve are in alignment with both NCTM standards and

culturally responsive teaching (Bol & Berry, 2005; Gay, 2002; Ladson-Billings, 1995a; Ladson-

Billings, 1997; Leinwand et al., 2014; Malloy, 2009). Building conceptual understanding is the

doing of mathematics that:

● uses procedures to create connections between mathematical concepts and ideas;

● provides multiple representations to develop understanding and connections;

● requires complex, non-algorithmic thinking, and considerable cognitive effort;

● requires exploration and understanding of concepts, processes, or relationships;

and,

● requires accessing and applying prior knowledge and relevant experiences and

tasks to facilitate connections and problem-solving. (Jackson & Wilson, 2012;

Jones, 2016; Leinwand et al., 2014; Munter, 2014)

To extend the practice of integrating rigorous mathematical tasks to build conceptual

understanding, Jones (2015) created the Culturally Relevant Cognitive Demanding (CRCD)

Mathematics Task Framework to assess whether mathematics performance assessments provided

to African American students at the high school and middle school levels exemplified cultural

relevance and cognitive demand. Jones (2015) provided that culturally relevant and cognitively

48 demanding mathematics tasks encompass “(a) procedures with connections to concepts, meaning

and understanding of mathematics, culture and community, and (b) doing mathematics for the

purpose of becoming empowered intellectually, culturally, and politically and socially” (p. 5).

Low-level tasks require rote memorization of facts and formulae, while high-level tasks require

students to be stretched cognitively and creativity (Jones, 2015; Jones, 2016). Ellis (2018)

concurred:

Learning to select and implement tasks that support high levels of cognitive demand and

deep learning and developing a classroom culture that values students’ mathematical

thinking is just as important as the social and cultural elements. (p. 20)

This draws back to the interconnectedness, divergent thinking, and interdependence reflective of

African American learning preferences (Boykin, Tyler, & Miller, 2005). Hammond (2015) added

that creating an environment where building conceptual understanding is the focus is integral for

the physiological and cognitive development of African American students to develop

independent thinking and to build intellective capacity through the transference and the

applicability of knowledge and skills across mathematics content and context. Therefore, it is

important to attend to the mathematical relationships, discourse, and contextual quality that

evolve when conceptual understanding is established (Jackson, Garrison, Wilson, Gibbons, &

Shahan, 2013).

Malloy and Jones (1998) examined the problem-solving characteristics and strategy

selection of 24 eighth-grade African American students. Qualitative in design, students were

interviewed about their problem-solving practices and their attitudes about learning mathematics

to code and determine their level of mathematics efficacy and identity. Students were videotaped

and asked to engage in a think-aloud process of problem-solving with retrospective interviews to

49 occur after problems were completed. Malloy and Jones (1998) found that African American

students utilized oratory and verbal expressionism with a relational approach to mathematics

problem solving, often time conveying their understanding of mathematical concepts

kinesthetically or through field dependence; therefore, they recommended that teachers build

conceptual understanding through holistic and inferential reasoning rather than through

analytical reasoning.

To extend her aforementioned work from 1998, Malloy (2009), as a part of the

Mathematics Identity Development and Learning (MIDDLE) longitudinal study previously cited,

conducted research to examine how the variable of building conceptual understanding deepens

the mathematical thinking and problem solving as a process for African American students at the

high school and middle school levels. Based on her qualitative analysis, building conceptual

understanding was demonstrated by the participant teachers’ respect of students' prior knowledge

and capitalizing on it to bridge connections between previous and current concepts. Observations

and field notes documented the provision of problem-solving opportunities using intentional and

meaningful learning experiences that required students to share, question, debate, and explore

mathematics in a collaborative setting (Malloy, 2009). This leads back to the underpinnings of

culturally responsive teaching – providing an environment that is nurturing and where students’

reasoning and conclusions are deemed important and accepted (Gay, 2002; Farinde-Wu, Glover,

& Williams, 2017).

Parallel to this is understanding is the Reconceptualized Opportunity to Learn (OTL)

Framework developed by Walkowiak, Pinter, and Berry (2017), which focused on the

dimensions of teachers’ mathematical knowledge, time, tasks, and talk. Building conceptual

understanding is manifested through four distinct dimensions:

50 1. Teacher knowledge of mathematics content: ensuring mathematically accurate lesson

content, design, and connections between concepts;

2. Time: maximizing the learning block to ensure that connections are made and for

students to process their learning;

3. Tasks: providing tasks that are student-focused that provide them the opportunity to

demonstrate multiple representations (concrete, pictorial, abstract); and,

4. Talk: justifying and proving the reasonableness of response.

This model is used to increase student engagement by decreasing anxiety – students know where,

when, and how to go about their work in a structured, yet open classroom environment (Jackson

& Wilson, 2012; Jones, 2016; Ladson-Billings, 1997; Ladson-Billings, 2009b; Walkowiak,

Pinter, & Berry, 2017). Hale (2016) provided that “by including real-life applications of

mathematics, teachers help students make more conceptual connections. Making presentations,

writing in journals, building models, and other individual or group assignments can increase

interest and success in mathematics by offering students the freedom to express their

mathematical knowledge in alternative ways” (p. 114).

Delpit (2012b) emphasized that building conceptual understanding extends beyond math

operations:

math is not a discrete skill set, rather an application of interwoven processes that when

used can evolve in multiple entry points; teach to create relevancy. When we teach

appropriate conventions and strategies within the context of critical thinking, we can

produce the educated people we strive for. (pp. 133, 135)

51 Need for Further Research

Multiple data sources reveal an existing and prevalent achievement gap between African

American and White students in high school and middle school mathematics (NCES, 2015a;

NCES, 2015b; NCES, 2015c; NCES, 2015d; NCES, 2015e; NCES, 2015f; NCES, 2015h;

NCES, 2015i; The College Board, 2015a; The College Board, 2015b; The College Board, 2017a;

The College Board, 2017b; VDOE, 2015; VDOE, 2017c). While cultural deficit theory was

provided as a rationale and explanation for performance levels between African American and

White students, the theoretical frameworks, culturally relevant pedagogy and culturally

responsive teaching, were given as counterexamples. Several theoretical and conceptual

frameworks as well as a myriad of qualitative, ethnographic, and case studies, were cited (with

culturally relevant pedagogy being subsumed under culturally responsive teaching) where

culturally responsive teaching served as the overarching framing infrastructure. Building

conceptual understanding and culturally responsive leadership were also reviewed in order to

give a holistic scope of not only the curriculum and instruction needed to support African

American students at the high school and middle school levels of mathematics, but also the

leadership commitment required to be successful with this population of students as evidenced

by the literature base.

However, a gap still exists – in the literature – regarding the collective impact and

influence of culturally responsive leadership and culturally responsive teaching on African

American performance and achievement in mathematics at the high school and middle school

levels. For instance, Berry and Thunder (2012) expressed, “there is insufficient work on how to

integrate or synthesize findings across qualitative studies related to equity and the mathematics

experiences of Black learners” (p. 43) with Jones (2016) having provided that there is a call for a

52 culturally responsive approach to teaching and leadership specific to mathematics. Bonner

(2014) stated, “a gap in the literature exists in terms of how culturally responsive teaching is

practiced explicitly in the context of mathematics” (p. 379). Further, Johnson (2006)

acknowledged:

There is little discussion of leadership that is culturally responsive. There have been few

attempts to apply the culturally responsive framework to the study of leadership practices

in urban schools. Two aspects of ‘culturally relevant leadership’ that have received little

attention in previously published case studies ... how school leaders have incorporated the

history, values, and cultural knowledge of students’ home communities in the school

curriculum and worked to develop critical consciousness among both students and faculty

to challenge inequities in the larger society. (pp. 23, 26-27)

Moreover, to meet the challenges that inequitable and deficit-thinking present, Sarason (1996)

articulated how culture interacts with implementation efforts and is the most foundational feature

of educational systems; and, consequently warns that the failure to contextualize systems through

the lens of culture is akin to synthesizing in a vacuum. Hence, studies of educational leadership

and instructional methodology must be “concern[ed] [sic] with the nature of the relationship

between culture and pedagogy” which is further forged by “concepts of teacher identity and

learners’ experiences of school” (Phillips & Schweisfurth, 2014, p. 175). By extension,

pedagogical approaches and practices are grounded in culture and the pursuit of such approaches

is reliant upon the lens in which the teacher operates and in turn how the receptive processing of

students is absorbed. Rigby et al. (2017) confirmed that “it is unlikely that a single support on its

own will lead toward instructional improvement at scale, rather organizational systems must be

redesigned” (p. 477).

53 Due to the gap as evidenced by the literature, further research is needed regarding how

the mathematics performance of African American students is influenced by culturally

responsive leadership and culturally responsive teaching. Therefore, Chapter 3 – Methodology

represents an outgrowth of a systematic approach examining the constructs of the influence of

culturally responsive leadership and culturally responsive teaching while building conceptual

understanding of African American students at the high school and middle school levels in

mathematics as suggested by the gap in the literature base.

54 Chapter 3

Methodology

Purpose of the Study

Merriam (2009) provided that, “qualitative researchers are interested in understanding

how people interpret their experiences, how they construct their worlds, and what meaning they

attribute to their experiences” (p. 5). Further, qualitative research, foundationally grounded

within phenomenology, intends to search for meaning by understanding natural settings and

behaviors through rich narrative descriptions, direct data collection, and participant perspectives

(McMillan & Wergin, 2010). The purpose of this study was to determine if culturally responsive

behaviors of high school and middle school principals influence the behaviors of mathematics

teachers resulting in building conceptual understanding of their students; and, how teachers’

culturally responsive actions impact the mathematics performance of African American students.

Research Design and Justification

This was a qualitative study as the methodology involves “data collection directly from

people through observation along with interactive data collection” (McMillan & Wergin, 2010,

p. 90). Merriam (2015) provided that qualitative research is undergirded by constructivism –

where the researcher’s interest is attaining understanding through the meaning of the studied

phenomenon. This understanding coincides with the work of Creswell (2007):

Individuals seek an understanding of the world in which they live and work. They

develop subjective meanings of their experiences…These meanings are varied and

multiple, leading the researcher to look for the complexity of views. (pp. 20–21)

55 Specifically, the data collected from this study were organized into themes to bring to the fore

the sociocultural patterns of the participants and phenomena studied and by extension delineating

understanding and deriving meaning.

This qualitative study employed a preliminary screening survey to measure culturally

responsive leadership and culturally responsive teaching through an established criterion. After

which, as a part of the primary study, observations of principals and teachers enhanced by

detailed field notes as a complete observer; an examination of mathematics student performance

data of selected principals and teacher participants at specific checkpoints; and, a parallel

culturally responsive leadership survey of practices developed by the researcher to be

disseminated to participating teachers within and outside of the purposive sample were

conducted. The data collected through the preliminary screening survey, primary observations,

an examination of mathematics performance, and parallel concluding survey were coded and

recognized to “illustrate important patterns or relationships,” thus leading to “generalizations and

conclusions” (McMillan & Wergin, 2010, p. 91).

Research Questions

The research questions for this qualitative study were as follows:




mathematics?

2. To what extent, if any, do culturally responsive teaching practices impact the


levels?

56 Sample Selection

Non-probabilistic purposeful sampling was used for this qualitative study. Merriam

(2009) provided, “purposeful sampling is based on the assumption that the investigator wants to

discover, understand, and gain insight and therefore must select a sample from which the most

can be learned” (p. 77). The purposeful sample was comprised of high school and middle school

principals and mathematics teachers of an urban school division. Therefore, to obtain a purposive

sample to glean information-rich cases, a determination of the selection criterion was made as it

was essential to and reflective of the purpose of the study.

Preliminary screening survey of high school and middle school principals (Phase

1a). This study sought to determine if culturally responsive behaviors of high school and middle

school principals influence the behaviors of mathematics teachers resulting in building

conceptual understanding. Therefore, the preliminary screening survey, Self-Assessment for

School Administrators (Appendix I), created by the Colorado Department of Education (CDOE),

was used as it specifically measures culturally responsive leadership practices (CDOE, 2010).

This preliminary screening survey tool is a part of the Colorado Department of Education’s

larger Equity Toolkit for Administrators created with the intention to “measure and create

personal awareness and an understanding of the complexities and actions related to equity,

cultural competence, cultural proficiency, and cultural responsiveness” (p. 6). The Self-

Assessment for School Administrators is comprised of three distinct headers (e.g., most of the

time, some of the time, and never) in relation to each culturally responsive leadership indicator.

To establish a selection criterion baseline to choose the principals and thus their building sites to

be studied, point values were assigned to each header as follows – most of the time (2 points),

some of the time (1 point), and never (0 points). Because there are 25 indicators, the maximum

57 point total results in 50 points. For a principal to move to the next phase of the study, one had to

have attained at least 40 points (or an 80% response rate). Principals scoring at least 40 points on

the preliminary screening survey made up the purposive sample of the primary study.

Preliminary screening survey of high school and middle school mathematics

teachers (Phase 1b). This study also sought to determine how teachers’ culturally responsive

actions impact the mathematics performance of African American students. Therefore, of the

high school and middle school principals that scored at least 40 points on the Self-Assessment for

School Administrators, each mathematics teacher of the select principals’ sites was provided the

Self-Assessment for School Teachers (Appendix J; CDOE, 2010). The preliminary screening

survey for teachers was selected as it reflected similar indicators and headers as the Self-

Assessment for School Administrators; thus, its inclusion as a selection criterion tool assisted the

researcher in identifying the information-rich culturally responsive teacher cases reflective of the

purpose of the study. In addition, the Self-Assessment for School Teachers draws parallelism to

the principal preliminary screening survey to which themes were ascertained during the data

collection process. Headers were assigned the same point values as the previously described

principal preliminary screening survey. Because there were 25 indicators, the maximum point

total would result in 50 points. For a teacher to move to the next phase of the study, one had to

have attained at least 40 points (or an 80% response rate). The teachers that scored at least 40

points on the preliminary screening survey comprised the purposive sample of the primary study.

Teachers not scoring at least 40 points were not a part of the purposive sample of the primary

study and were not observed as the intention of the study is to observe teachers having a high

level of culturally responsive pedagogical practices.

58 Data Collection Procedures

Data were collected through the observations of high school and middle school principals

(seven total); observations of 23 mathematics teachers; an examination of mathematics student

performance data of principal and teacher participants at specific checkpoints; and, a concluding

culturally responsive leadership practices survey deployed to both the purposive sample of

mathematics teachers and those teachers not involved in the primary study regarding the

leadership practices of their building principal.

Observations of high school and middle school principals (Phase 2a). Observations

were used as a method of data collection instead of interviews due to the element of firsthand

account, rather than a secondhand account obtained via sample participants (Merriam, 2009).

Field notes were used to account for observations such as the purposive high school and middle

school principals’ interactions with mathematics teachers and students (and in particular,

students described as African American). Field notes were descriptive and reflective as

prescribed by Merriam (2009):

Field notes should be highly descriptive. What is described are the participants, the

setting, the activities or behaviors of the participants, and what the observer does. By

highly descriptive…enough detail should be given that readers feel as if they are there,

seeing what the observer sees. There is also an important reflective component to field

notes. This reflective component is captured in observer commentary. (pp. 130-131).

Hence, the field notes were structured such that the researcher captured the setting, activities and

interactions, conversations using direct quotes or synopsis of discussions, and subtle factors (i.e.,

inferred meanings and connotations, nonverbal communication, etc.) while maintaining

reflective comments in the margins and/or narrative using distinguishing font features [italicized

59 bracketing and the initials “OC” to stand for observer comments]. Two 90-minute observations

were conducted – once prior to the 4.5 weeks assessment and once prior to the Critical Skills

Assessment of the first nine weeks of the 2019-20 school year.

Observations of high school and middle school mathematics teachers (Phase 2b).

Developed by Piburn et al. (2000) of the Evaluation Facilitation Group of the Arizona

Collaborative for Excellence in the Preparation of Teachers, the Reformed Teaching Observation

Protocol (RTOP), was specifically developed to measure reformed or culturally responsive

mathematics teaching practices specifically at the high school and middle school levels. The

RTOP (Appendix K), measures three distinct subsets that are reflective of the related review of

the literature and when observed provided the researcher with information-rich data.

The first subset of the observation protocol is entitled, Lesson Design and

Implementation. Consisting of five items, this subset measures:

a lesson that begins with recognition of students’ prior knowledge and perceptions, that

attempts to engage students as members of a learning community, that values a variety of

solutions to problems, and that often takes its direction from ideas generated by students

(Piburn et al., 2000, p. 8)

The second subset, Content, is comprised of ten items that speak to the observed teacher’s

utilization of problem-solving as a process through inquiry as well as quality lesson

implementation (Piburn et al, 2000). The third subset, Classroom Culture, consists of ten

questions addressing the culture of the classroom. The third subset is aligned to the research

within the literature base as Piburn et al. (2000) provided that “[subset 3] is interpreted here as

embodying concern for ‘fairness’ or ‘justice’ or ‘equity’ in the classroom” (p. 17). Using the

RTOP provided the researcher with three distinct subsets in which to glean understanding from

60 the teacher purposive sample. The subsets given also assisted the researcher in creating a

structure in which to code and to categorize data of specified behavior (Merriam, 2009). Two 90-

minute observations were conducted – once prior to the 4.5 weeks assessment and once prior to

the Critical Skills Assessment of the first nine weeks of the 2019-20 school year.

Examination of high school and middle school mathematics student performance

data (Phase 3). To assess students’ understanding, two division-wide assessments were

deployed. As defined in Chapter 1, a mid-nine weeks assessment is given to ascertain students’

understanding and proficiency of mathematics content provided in the middle of each nine

weeks. In the context of this study, the 4.5 weeks assessment of the first nine weeks of the 2019-

20 school year was used; however, it was not used as a baseline assessment. Critical Skills

Assessments intend to measure the progress of students and their proficiency in understanding

the content learned during each nine weeks of instruction. In the context of this study, high

school and middle school mathematics performance data were examined and analyzed in the first

nine weeks of study of the 2019-20 school year. This allowed the researcher to collect student

performance data at two distinct checkpoints consistent with division-wide testing expectations.

While high school teachers may teach more than one course, only data from SOL-tested courses

have been provided.

Directly following the 4.5 weeks assessment and Critical Skills Assessment, student

performance data were collected. African American versus White students’ performance was

compared as is representative of the achievement parameters as specified in Chapter 1. The

student performance data of the purposive sample of mathematics teachers were compared to

that of those that did not advance to the primary study. This was done to see if the variable

application of culturally responsive teaching practices, as visually represented in the researcher’s

61 conceptual framework, had an impact on the performance of African American students in

comparison to their White peers and if there was a significant difference in achievement between

the two groups.

The urban school division of focus is comprised of four high schools (inclusive of

specialized academy structures); five middle schools (inclusive of one fundamental and one

magnet school); two combined PreK-8 schools; and, one gifted center housing grades three

through eight. Table 1 below represents the 2019-20 Fall Membership enrollment and ethnic

make-up of the school division at the high school and middle school levels (inclusive of students

with disabilities and English Language Learners) (VDOE, 2019c):

Table 1

2019-20 Urban School Division Fall Membership at the High School and Middle School Levels

Race Grade 6

Grade 7

Grade 8

Grade 9

Grade 10

Grade 11

Grade 12

Total Count

American Indian or Alaska Native 7 6 6 9 2 6 8 44

Asian 21 31 26 34 32 29 31 204

Black, not of Hispanic origin 845 945 846 1,169 979 849 719 6,352

Hispanic 86 104 85 76 83 69 64 567

Native Hawaiian or Pacific Islander 4 2 1 4 8 5 2 26

Non-Hispanic, two or more races 135 109 125 113 102 83 75 742

White, not of Hispanic origin 365 330 304 386 317 312 267 2,281

Note. Adapted from “Urban School Division: Fall Membership,” by the Virginia Department of Education, 2019. Retrieved from https://p1pe.doe.virginia.gov/apex/f?p=180:1:11347911110859:SHOW_REPORT:NO:::. Copyright 2019 by the Virginia Department of Education.

Culturally responsive leadership practices survey (Phase 4). A researcher-developed

survey was used to gather concluding responses from the mathematics teachers of the culturally

62 responsive leadership practices of their principal. The survey was deployed to mathematics

teachers in the purposive sample and mathematics teachers not in the purposive sample to

analyze similarities and differences in perceptions of the leadership practices of their principal.

Collie and Rine (2009) provided that surveys are an expedient and structured process to

measure perceptions, attitudes, and knowledge about a particular phenomenon of study. Further,

the survey questions should be concise and reflect the content of the survey with close

monitoring of indicator wording (Collie & Rine, 2009). In light of this, the researcher-developed

survey was comprised of 18 indicators of culturally responsive leaders and a rating scale of 0 to

3 with 0 being none (no evidence), 1 being the lowest (low), 2 (moderate), and 3 (high) to

capture the principals’ level of culturally responsive leadership. This information was mapped

back to the data gleaned from having observed the principal to determine parallelism between the

observed and the articulated responses, how culturally responsive leadership was performed, and

its impact on instructional behaviors. The Culturally Responsive Leadership Practices Survey

(Appendix L) was created from the culturally responsive leadership references cited within

Chapter 2 – A Review of Literature. As the literature base dictated, three specific headings

emerged in which to assess – school culture, communicative interactions, and relationships;

equity; and, influence on instructional behaviors and processes. The survey validation process is

described in the Instrument Design and Validation section of this chapter.

A visual representation of the study has been provided to illustrate the data collection

process (see figure 2).

63

Figure 2 A model to describe the data collection process.

.. I I -,1a1 I I

l ( \

Prtlimllll')' s<rtoillg ""'tr oflligll s<bool ud middlo s<bool Prf'liawry sc:retlliag san-ty of mp sc•oo1 aad middle sc•oo1 principals (Pllas• la ). Use tbe SIJlf-.b:•:smentft,r School mathematics tncbtrS(Pllase l b). Oftbe priDcip3ls that scored at least MntlmstrotM cruted by die Colond:> Oep""""" ol Educlllon 40 poinb Oil dlt 5,/f-,w,:,...,,t p S<hoo/ ,ldm/n/s...,,,,, , tad> (CDOB). For • priDcipal 10 IIIO\'t 10 the..., plwe of dlt srudy, mathe:m:atia teacher of the select priDdpals • site enppd iD die StJIJ, ooe must hn--e attsiDed at )east 40 points (or an 80% r5poose A.5s(l;ID1tfflljbr School TeocMl"S created by tbe Colorado Department of Dtt). Emcuioo (COOB). For I,._ 10IIIO\'t10111,-plwe oldlt , rudy,

one must ba\'e attained at Je3st 40 points ( or an so,• response rate). Principals who scored at least 40 poirltsou tbe prelimii:my l0'ffllUII IIIMJ' IDW ,.i the p;,xipal pwposi\~ l lllq)it o( the Tucbln wbo K0IM II lmt 40 poiDn oa. tbt prtliaii:wy ICl'IIIWll primary study. Stll\Y)' comprise the pwposi\.--e sample of the pmwy srud)t.

- 1 PIL..,-.., 1-Obsen-.tioD.s of priDcipals (Pllase la) . The primaJy study ObsKn.tioas of tncltn (Ph.as• 2b). De\u,ped by Pibln el al.

m\'Oh'OI IWO ®""~°""' of Ibo pwpowfbl ~ It ol prindpal• (2000) of Iba E,..iu,..., FldliU°"" ~ of d>t Arizoaa Two 9<Hninme obsen·ations- ODCe prior to the 4.5 weeks Collaborative for Excelleoce in tbe Prepc.u:ation ofTeacbm , the

assessment and ooce prior to the Critical st ills Assessment of tbe ~ T«J</lfot 06, ,n ~tfon l'>'otoeol {RIOP), wu ,p<d4cally lint DiDo wetb of Ibo 201P-20 ldlool yur "'"' coaduclld. Fitld de'l..'fflll)ed to measw-e rt!ormed or culturally respcm.i\'e mathematics

notes were used to account for ob5en--atioos such as interactioos 1eac.hiDg practices specifically at tbe middle and high school levels. 1\\-o with_, -1>m a.od, rudeott (a.od inpamcwar, PO•milallt obwn-lllom u,mi lbt RroP - ooco prior 10 lbt 4.S Wftks matbematia 5tudeDls dtscn"bed IS AkiclD AmericlD). assessment and once prior to the Critical Skills Assessmem of tbe fim

ome weeks of tbe 2019-20 sc.booJ ~ wen cooduCled.

·• i Ex.amimtio. of sKGD.dary matkt11111tin stuut ~ormuc• d.at• (l'lt.,. 3). Ditoetly rou...mc the 4.S Wftks ..,""""" , 111<1 Crilicel Skills As.sessme.tll, stooe.Dt petformm:e cbta was collected. African AmeriCG 1tudtm ptr{ormmct \\'U compared 10 Whi1t nudton cl. rhost in dle pmposi\.•e sample to that of those that did DOt ad\'aDCe to tbe prim.,ry study. This was dooe to see iftbe variable applicatfooof culnnlly mpomi\'t 1ffChiD& pl'ICtictt bad m influtaC.t an tbt perfonnaoce of African American mtdems iD compari.soo to their \\'bite cowueq,om 111<1 ;{Ibero b a ,Jgmlkam dllffflllC t In acb!,,·..,.., becweeo me rwo poup1.

! cuttanll)' nspomin lt ..strs:llip pnc:fin s swny (Pllase 4) [p,upomw StlJflJW iaclten tu14 kac.htn IUli im'Ob-ff in the pMrp<nb-.. S01ffp/~J. Tbe resean:btr-de\•e)oped Cu/tMm/b' RISJX)Nhw Llodmh;p Pmaius Sa.n'4)'was used to gatbercooductingrespomes frcm the """'°''" 10Kbor ,aq,1' 111<1111o,o not in\"Ol\'td in the po1po1l\• sample regrin; dle culturally respoosi\'e le:uterwp practices of dleir priDdpal. This inlom,a~oo Wti mapped bock 10 lbe data gl....d from u,;q oboffl'td !bl prmdp<l ill order co dlwmillt pmll,liun-., the obsen:ed and tbe aniculated r5pooses , bow culturally respoosi\--e ~ .,., ptrlonued, a.od h, !nllueoco oo ln<l!\ICll<xw bebavkn . lbe w:n.y was dtplO)'td iD order to aml)'zt mu.ilmtin md dif&.rtocts in perceptions ofdle leadership practices of the prlDdpals of the prpo1r.-. umpLt.

64 Data Gathering Procedures

Because the nature of this qualitative study required research involving interactions with

individuals as well as obtaining information about living individuals, Virginia Polytechnic and

Institute University Institutional Review Board (IRB) approval with the Western Institutional

Review Board determination was attained before the study was conducted. Before the

submission of the IRB Online Protocol application, the researcher completed required IRB

training and received a Certificate of Completion in the Training of Human Subjects Protection

(Appendix A). Upon Virginia Tech Institutional Review Board approval (Appendix B) and

receipt of the Western Institutional Review Board Determination Letter (Appendix C), the

researcher sought approval from the urban school division’s Department of Research, Planning,

and Evaluation by completing the Research Authorization Request (Appendix D) of which is

reviewed by the Research Authorization Committee. The decision of the committee was

rendered to the researcher and provided via the Research Authorization Committee Approval

Letter (Appendix E). The Participant Letter (Appendix F), Participant Response Letter

(Appendix C), and Informed Consent Agreement (Appendix H) were provided via email to all

participants for the study with a description of the researcher’s topic, approved research study

procedures for both the preliminary and primary study, and directions about how to return all

documents associated with the study.

Instrument Design and Validation

Preliminary screening survey tools. The preliminary screening survey tools, the Self-

Assessment for School Administrators and the Self-Assessment for School Teachers, were used to

assess and to measure culturally responsive leadership and teaching practices. These tools are a

component of the Equity Toolkit for Administrators developed by the Colorado Department of

65 Education (2010). The preliminary screening survey tools were adapted from the work of the

Minneapolis Public Schools, Positive School Climate Tool Kit, First Edition in association with

the Georgetown University’s National Center for Cultural Competence (NCCC) and the

Georgetown University Center for Child and Human Development (CCHD) (CDOE, 2010;

Papke & Davidson, 2004). The preliminary screening survey tools were validated through

commissioned task forces representative of policy, administration, support delivery, and

community stakeholders designated by the Georgetown University’s National Center for Cultural

Competence and the Georgetown University Center for Child and Human Development through

extensive interrater reliability workgroup sessions:

The active involvement of individuals, groups, and communities is a highly valued and

integral aspect of the self-assessment process. The data collection, analysis,

interpretation, presentation, and dissemination approach…is commensurate with

culturally competent and participatory action designs in research and evaluation. (NCCC,

2004, p. 3)

Reformed Teaching Observation Protocol (RTOP). The Reformed Teaching

Observation Protocol (Piburn et al., 1999), developed by the Evaluation Facilitation Group of

the Arizona Collaborative for Excellence in the Preparation of Teachers, was used as the

observation tool for the purposive sample of high school and middle school mathematics

teachers. The construct validity of the RTOP is captured in the theoretical relationships of

inquiry-based, standard-based instruction, and standard-based orientation – validated using a

“correlational analysis performed on the five subscales” representative of the range of standards

within the breadth of the 25-items divided into three subsets (Piburn et al., 2000, p. 12). To test

the construct validity, the inquiry-based orientation that permeates each of the subscales of the

66 subsets with, “high R-squares support[ing] the hypothesis and low R-squares serv[ing] to reject

it” were tested (Piburn et al., 2000, p. 12). Table 2 below provides the subscales as predictors of

the RTOP total score:

Table 2

Subscales as Predictors of the RTOP Total Score

Predictor R-squared as Predictor of Total

Subscale 1 0.956

Subscale 2 0.769

Subscale 3 0.971 Subscale 4 0.967

Subscale 5 0.941 Note. From “Reformed Teaching Observation Tool (RTOP) (Technical Report No. IN00-3)” by M. Piburn, D. Sawanda, K. Falconer, J. Turley, R. Benford, and I. Bloom, 2000, Arizona State University. Retrieved from http://www.public.asu.edu/~anton1/AssessArticles/Assessments/Biology%20Assessments RTOP%20Reference%20Manual.pdf. Copyright 2000 by the Arizona Collaborative for Excellence in the Preparation of Teachers. Reprinted with permission. The analysis produced a strong interrelationship and cohesiveness across each subscale;

therefore, the construct validity of the RTOP supported its inclusion as a tool in this study

(Piburn et al., 2000).

Piburn et al. (2000) provided that the predictive validity of the instrument was obtained

from a minimum of two observations conducted by six instructors in 38 mathematics classrooms

across one semester of instruction. The normalized gain scores, defined as a “proportion of the

potential gain” had a correlation of “0.94 for conceptual understanding and 0.92 for number

sense, thus significant at the 0.01 level” (Piburn et al., p. 14).

Researcher-developed culturally responsive leadership practices survey. The

Culturally Responsive Leadership Practices Survey was created from the culturally responsive

leadership references cited within Chapter 2 – A Review of Literature. The survey tool was

comprised of 18 indicators of culturally responsive leaders and a rating scale of 0 to 3 with 0

67 being none (no evidence), 1 (low), 2 (moderate), and 3 (high) to capture the principals’ level of

culturally responsive leadership.

Merriam (2009) stated that how items are “worded is a crucial consideration in extracting

the type of information desired” (p. 95). Therefore, to address the validity of the survey

questions, the researcher asked administrators of the Virginia Polytechnic and Institute

University Doctoral Program Hampton Roads Cohort familiar with the target population and

constructs of culturally responsive leadership practices to review and to provide feedback.

Feedback was obtained through a survey validation instrument (Appendix M) – measuring the

relevance of the survey indicators to the research questions and for clarity (readability) through a

five-point ordinal Likert scale [strongly agree (5), agree (4), neither agree nor disagree (3),

disagree (2), and strongly disagree (1)]. The researcher’s goal for instrument validity was to

obtain a greater than or equal to 80% (a rating greater than or equal to 4 points), indicating an

“improved conclusion validity and good statistical power” and an ability to “reach credible

conclusions about relationships in [the] data” (Trochim, 2006, p. 1). Based on the feedback on

the survey, all indicators reached the 80% threshold. The survey validation instrument and the

responses from the group are maintained in Appendix M.

Data Treatment and Management

Consent and confidentiality. The provision of the Informed Consent Agreement

(Appendix H) was given to all participants that outlined the topic and the nature of their

participation. The consent form provided assurances of confidentiality of identity and the data

collected for the sole purpose of parameters outlined. All participants were informed of their

rights, the option to participate, or the ability to opt-out of the study.

68 Survey management. All preliminary and primary surveys were distributed

electronically as prescribed in the aforementioned Appendices via Qualtrics. Once survey

responses were obtained, all data were immediately saved and stored being accessible only to the

researcher by log-in and password. Hard copies of responses were printed and stored in a locked

file cabinet. The researcher was the sole owner and the only individual with a key.

Observation field notes and RTOP management. All field notes obtained from

observations of the purposive sample of principals were typed soon after each observation and

placed in a folder entitled, “Principal Observation Field Notes.” Each principal was assigned a

number beginning with ‘1’ (e.g., Principal 1), in which they were subsequently referred to in

Chapter 4 – Data Analysis.

Observations of the mathematics teachers of the purposive sample were housed within a

folder entitled, “Teacher RTOP Observations.” All identifying information was removed to

preserve confidentiality. Teachers were identified with a numeral aligned with the building site

of the corresponding principal and a lower-case letter beginning with ‘a’ (i.e., Teacher 1a,

Teacher 1b, etc.).

All data were immediately saved and stored being accessible only to the researcher by

log-in and password. Hard copies of responses were printed and stored in a locked file cabinet.

The researcher was the sole owner and the only individual with a key.

Student performance data. Student performance data from the 4.5 weeks assessment

and the Critical Skills Assessment were reported as a pass rate percentage and not by individual

students; therefore, no identifying information was obtained on students. The pass rate

performance was assigned to the principals and mathematics teachers comprising the purposive

sample. Student performance data was obtained from a division-wide online assessment database

69 in which the researcher has a unique log-in and password. Student performance of the purposive

sample was housed within a folder entitled, “Student Performance Data [4.5, Critical Skills

Assessment].” All identifying information was removed to preserve confidentiality. Teachers

were identified with a numeral aligned with the building site of the corresponding principal and a

lower-case letter beginning with ‘a’ (i.e., Teacher 1a, Teacher 1b, etc.). Teachers not involved in

the purposive sample, but to which student performance data were compared, were notated as

Teacher 1a, Teacher 1b, and so on.

Study completion actions. Once the study was completed and after a successful defense

of the dissertation, all electronic documents and hard copies will be maintained for one full year

with accessibility only to the researcher. After one full year, all electronic documents and hard

copies associated with the study will be purged and shredded.

Data Analysis Techniques

The observations of the seven high school and middle school principals; observations of

23 mathematics teachers; an examination of mathematics student performance data of selected

principal and teacher participants at specific checkpoints; and, a concluding culturally responsive

leadership practices survey deployed to the purposive sample of teachers and teachers not a part

of the purposive sample regarding the leadership practices of their building principal were

categorized, coded, and triangulated into themes that emerged during the data collection process.

Merriam (2009) stated that triangulation is the “most well-known strategy to shore up the

internal validity of a study” (p. 215). Further, McMillan and Wergin (2010) contended that the

triangulation of multiple resources results in the discovery of similar findings. The triangulation

strategy was used to check the observed with the articulated bounded by what was practiced.

70 Timeline

The initial study was developed as of January 2019 and submitted to the dissertation chair

for review and feedback. Permission was granted to move forward with the study and submission

of an IRB for approval to the Virginia Polytechnic Institute and University Institutional Review

Board after a successful prospectus examination was conducted in February 2019. The study was

submitted for IRB approval in April 2019. The study was referred to the Western Institutional

Review Board with a decision rendered as of May 2019. The researcher completed the Research

Authorization Request per the directives of the urban school division in May 2019. Upon receipt

of the Research Authorization Committee Approval Letter, the researcher moved forward with

the implementation of the study.

The preliminary screening of high school and middle school principals, Phase 1a,

commenced July 2019. Of the 12 principals surveyed, seven attained a score of at least 40 points.

As an outgrowth of the data analysis, the seven principals scoring at least 40 points (or an 80%

response rate) were identified as the purposive sample. These principals moved on to Phase 2a of

the primary study.

Of the identified high school and middle school principals, the preliminary screening of

high school and middle school mathematics teachers, Phase 1b, began August 2019. Seventy

mathematics teachers were provided the preliminary screening survey. Of the 70 provided the

survey, 37 gave consent to participate. Of the 37 mathematics teachers surveyed, 23 attained a

score of at least 40 points. As with the principals, mathematics teachers scoring at least 40 points

(or an 80% response rate) were identified as the purposive sample. These mathematics teachers

moved on to Phase 2b of the primary study.

71 Observations of the purposive sample of high school and middle school principals (Phase

2a) and high school and middle school mathematics teachers (Phase 2b) took place during

September and October 2019 – once proceeding the 4.5 weeks assessment testing window and

again proceeding the Critical Skills Assessment testing window.

The student performance data were collected and analyzed immediately following the

close of the 4.5 weeks assessment window and the Critical Skills Assessment window – early

October 2019 and November 2019 respectively (Phase 3).

The concluding Culturally Responsive Leadership Practices Survey (Phase 4) was given

to the mathematics teachers that participated in the primary study (n = 23) and those not within

the purposive sample (n = 14) directly following the conclusion of the Critical Skills Assessment

window in early November 2019.

The completion of the study occurred in November 2019. The researcher analyzed and

triangulated emergent themes gleaned from the data collection process – inclusive of field notes,

principal observations, observations of mathematics teachers, student performance data, and the

concluding culturally responsive leadership survey. The process of coding was used as the

researcher looked for data that was “potentially relevant” for answering the research questions to

construct categories that “captured [a] recurring pattern that cut across [the] data” (Merriam,

2009, pp. 178-179). The researcher derived the categories from the data – checking whether the

categories were substantive, steady, and maintained as subsequent data were analyzed.

Categories were responsive to the purpose of the research and driven by the “meanings made

explicit” by the triangulation of the data (Merriam, 2009, p. 184). The researcher moved from an

inductive process of analysis to that of deductive as the categories manifested and took shape –

creating a sense of saturation yielding no further new information.

72 Methodology Summary

The purpose of this qualitative study was to determine if culturally responsive behaviors

of high school and middle school principals influence the behaviors of mathematics teachers

resulting in building conceptual understanding of their students; and, how teachers’ culturally

responsive actions impact the mathematics performance of African American students.

The primary study was conducted within an urban school division comprised of high

school and middle school principals and mathematics teachers that at first met the researcher-

established criterion delineated in the preliminary screening survey process.

High school and middle school principals and mathematics teachers of the purposive

sample were observed at specified checkpoints – once prior to the 4.5 weeks assessment testing

window and again proceeding the Critical Skills Assessment testing window. Observations of the

principals of the purposive sample were recorded using extensive field notes. Observations of the

mathematics teachers of the purposive sample were recorded using the Reformed Teaching

Observation Protocol (RTOP).

An examination of student performance data comparing the 4.5 weeks assessment results

and the Critical Skills Assessment results of the mathematics teachers of the purposive sample to

those not within the sample was conducted. This was done to see if the variable application of

culturally responsive teaching practices had an impact on the performance of African American

students in comparison to their White counterparts and if there was a difference in achievement

between the two groups.

A researcher-developed concluding Culturally Responsive Leadership Practices Survey

was disseminated to the mathematics teachers of the purposive sample and those not included in

the purposive sample to denote their responses to the indicators of culturally responsive

73 leadership practices exemplified by their principal. The concluding survey was given to draw

parallelism between the observed and the articulated.

Triangulation was conducted as the strategy of data analysis. McMillan and Wergin

(2010) asserted that qualitative research intends to understand phenomenon and key issues in

order to provide insight:

The heart of the matter for a qualitative study is what the study can teach us – about our

students, our organizations, or our lives. The best studies, therefore, are complete enough

and rich enough that readers are able to judge which findings and insights might be most

applicable to their own settings. (p. 92).

Categories were coded to reflect and to be sensitive to the purpose of the study, exhaustive

(encapsulating all data of relevance), mutually exclusive, and conceptually congruent to answer

the given research questions at the heart of culturally responsive leadership (Merriam, 2009).

The review of data yielded from the study will be provided in Chapter 4 – Data Analysis. The

overview, perceptions, and discussion of the findings will be articulated in Chapter 5 – Findings,

Summary, and Conclusion – inclusive of implications for practice and future studies.

74 Chapter 4

Data Analysis

Introduction




actions impact the mathematics performance of African American students. The research

questions driving this study were:




mathematics?



levels?

The researcher engaged in a qualitative study consisting of a preliminary screening

survey measuring culturally responsive leadership and culturally responsive teaching through an

established criterion deployed to high school and middle school principals and mathematics

teachers of an urban school division. Of those that met the established criterion, the researcher as

a complete observer, engaged in observations of the principals using detailed field notes and

observations of the mathematics teachers using the Reformed Teaching Observation Protocol

(RTOP). The gathering of student mathematics performance data of the purposive sample of high

school and middle school principals and mathematics teachers took place after the 4.5 mid-nine

75 weeks assessment and after the Critical Skills Assessment with a comparison between the

performance of African American students and their White counterparts. Lastly, a parallel

culminating culturally responsive leadership survey of practices developed by the researcher was

given to the mathematics teachers within the purposive sample and those that were not. Each of

the aforementioned was coded and triangulated to capture and to illustrate relationships brought

forth as yielded by these data points.

Preliminary Screening Survey of High School and Middle School Principals (Phase 1a)

Because this study sought to determine if culturally responsive behaviors of high school

and middle school principals influence the behaviors of mathematics teachers resulting in

building conceptual understanding of their students, the preliminary screening survey, Self-

Assessment for School Administrators (Appendix I), was distributed via Qualtrics to the 12 high

school and middle school principals of an urban school division. The researcher obtained a 100%

response rate from the principals. As previously noted in Chapter 3, Methodology, for a principal

to move forward to the primary study, one must have attained a score of 40 points or more (or an

80% response rate) from 25 indicators given the point values assigned to each header as follows

– most of the time (2 points), some of the time (1 point), and never (0 points). Because there

were 25 indicators, the maximum point total would have resulted in 50 points.

Description and explanation of data. The data from the preliminary screening survey

are presented by the overall response rate of the 12 high school and middle school principals of

the urban school division of study; the seven principals advancing to the primary study

(purposive sample); and, then the data of the five principals not advancing to the primary study

(non-qualifiers).

76 Preliminary screening survey results of high school and middle school principals

(overall). The data from the preliminary screening survey are provided in Table 3, Preliminary

Screening Survey Results of High School and Middle School by Item (Overall, n=12), to

illustrate the overall item response rate inclusive of the 12 high school and middle school

principals. Further, the mean and standard deviation of the data were reported to provide

additional granularity with respect to the mean score for each item representing the central

measure of responses; and, the standard deviation to represent the average amount of variability

in the responses (Howell, 2011). The percent response rate, mean, and standard deviation have

been rounded to the nearest hundredth.

77

Table 3

Preliminary Screening Survey Results of High School and Middle School Principals by Item (Overall, n=12)

Item

Number Item Indicator

Never

[0]

Some of

the time

[1]

Most of

the time

[2]

Mean

["#] Standard

Deviation

[SD]

1. I am aware of my own racial, ethnic, and cultural background and understand how

it affects my perceptions and values. 0.00% 8.33% 91.67% 1.92 0.29

2. I seek opportunities to learn about the cultural practices in my school community,

including staff, families, and students. 0.00% 33.33% 66.67% 1.67 0.49

3. I regularly reflect on my own bias and how I view and treat people with cultural

practices that are different than my own. 8.33% 25.00% 66.67% 1.58 0.67

4. Our school regularly examines academic and behavioral data, and examines

achievement gaps by race, native language, socio‐economic status, and gender. 0.00% 16.67% 83.33% 1.83 0.39

5. Strategic plans are put in place to address all achievement gaps. 0.00% 16.67% 83.33% 1.83 0.39

6. Data is disseminated to families with procedures for them to offer support in

improving our school for all students. 16.67% 58.33% 25.00% 1.08 0.67

7.

I support professional development for administrators and faculty to examine our

own cultural awareness and develop culturally responsive school-wide and

classroom practices.

0.00% 25.00% 75.00% 1.75 0.45

8. I actively reach out to families from various backgrounds to give feedback and

assist in the creation of school policies. 16.67% 50.00% 33.33% 1.17 0.72

9. I actively recruit families to volunteer in the school and on committees so that

volunteer pools reflect the student body. 0.00% 41.67% 58.33% 1.42 0.51

10. Our school has clear procedures to report and respond to allegations of inequity.

These issues are dealt with in a sensitive and timely manner. 0.00% 58.33% 41.67% 1.58 0.51

11. I actively recruit applicants of diverse cultural backgrounds and ethnicities to

work in our school. 0.00% 16.67% 83.33% 1.83 0.39

12. Our school has support systems in order to meet the needs of our staff from

diverse backgrounds. 16.67% 16.67% 66.67% 1.00 0.60

78

13.

School communication with families is available in multiple languages and is

sensitive to varying family structures as well as diverse cultural and

socioeconomic backgrounds.

16.67% 25.00% 58.33% 1.08 0.67

14. I make sure that translators are available to improve school and family

communication. 41.67% 33.33% 25.00% 0.83 0.83

15. Artwork and photographs embedded in school communication and school décor

reflect the demographics of our student body and are age appropriate. 0.00% 41.67% 58.33% 1.58 0.51

16. The books in our school library reflect our student body and depict varying

cultural practices in a positive and anti-biased way. 8.33% 33.33% 58.33% 1.50 0.67

17. I openly confront inequitable practices and have policies in place to hold staff

accountable for their actions. I encourage staff to do the same. 0.00% 33.33% 58.33% 1.67 0.49

18.

School policies are created while consciously working towards equity for all

students and families. Historical policies are reviewed for cultural sensitivity.

Members representing the demographics of the community assist in this process.

8.33% 33.33% 58.33% 1.25 0.62

19. Curricula and assessments used in our school are reviewed to make sure that

materials are historically accurate, culturally responsive, and anti-bias. 25.00% 16.67% 58.33% 0.92 0.67

20. Behavior expectations and policies have taken into account the varying cultural

expectations and norms among students and families. 8.33% 41.67% 50.00% 1.33 0.65

21. Curriculum guidelines reflect that culturally responsive lessons are embedded in

day to day teaching, rather than isolated units. 8.33% 25.00% 66.67% 1.17 0.58

22. Our school incorporates differentiation tools to meet the needs of students from

varying backgrounds. 8.33% 41.67% 50.00% 1.25 0.87

23. School policies include how to respect holidays in a manner that is sensitive to

varying religions and cultural practices of the student population. 25.00% 25.00% 50.00% 1.25 0.87

24. Teacher expectations and evaluations include culturally responsive teaching, with

a focus on equity and positive relationships. 8.33% 33.33% 58.33% 1.50 0.67

25. I am comfortable in leading discussions about race, culture, religion, ethnicity,

class, gender, and sexual orientation with staff and students. 0.00% 25.00% 75.00% 1.75 0.45

Note. Adapted from “School Level Assessments and Evaluations,” by the Colorado Department of Education, 2010, Equity Toolkit for Administrators. Retrieved

from https://www.cde.state.co.us/postsecondary/equitytoolkit.

79

Table 3, Preliminary Screening Survey Results of High School and Middle School

Principals by Item (Overall, n=12), indicated a level of consensus – when disaggregating the

data using the Most of the Time header ordered from greatest to least – between 83.33% to

91.67%, a mean ranging from 1.83 to 1.92, and a standard deviation ranging from 0.39 to 0.29

respectively for items (I) 1, 4, 5, and 11. The data revealed a coalescence around an

understanding of personal racial, ethnic, and cultural backgrounds and how these three in tandem

impact personal cognizance, beliefs, and values (I1). In addition, responses indicated that regular

examination of student performance and behavioral data takes place frequently to create strategic

plans to support and to attend to achievement gaps (I4, I5). In so doing, principals indicated that

recruitment of teachers of diverse ethnic and cultural backgrounds was a key practice guiding

their work (I11).

Items 2, 3, 7, 12, 21, and 25 yielded a level of consensus between 66.67% to 75%, a

mean ranging from 1.00 to 1.75, and a standard deviation between 0.60 to 0.45 respectively. The

data indicated a larger spread in responses in regard to the provision of professional

development, discourse, and support to respond to cultural awareness and culturally responsive

practices (I7, I12, I25); self-reflection and regulation of personal bias impact on relationships

with others (i.e., the community, faculty, students, and families) (I2, I3); and, the reflection of

curricula guidelines that integrate culturally responsive lessons throughout instruction instead of

isolative in scope via units (I21).

The remaining items on the preliminary screening survey indicated a level of consensus

between 25% to 58.33%, a mean ranging from 0.83 to 1.67, and a standard deviation between

0.83 to 0.49. Items 6, 8, 10, and 14 yielded the lowest agreement in response rate, as

demonstrated by the lower mean and higher standard deviation, demonstrating a wider spread in

80

the data instead of a quantity tighter to the mean. The content of these items specifically

addressed the principals’ relationships with families either through initiation of feedback on the

systems approaches and policies at the school (I8); data distribution to families regarding school

improvement (I6); or, availability of translators (I14). The principals responded either most of

the time (41.67%) or some of the time (58.33%) that clear steps are designed to report and to

respond to inequitable practices and behaviors in a responsive and thoughtful manner (I10).


Principals (Individual) is the individual response rate for the 12 high school and middle school

principals by item rendered by response selected in numeral form and total points accumulated

on the preliminary screening survey. The principals were assigned a number and have hereafter

been referenced as such because identifiers have been removed to preserve confidentiality as

specified within the Informed Consent Agreement (Appendix H). The principals that earned

greater than or equal to 40 points have been highlighted in bold. A gray bar delineates the

principals that earned greater than or equal to 40 points from those that did not.

81 Table 4

Preliminary Screening Survey Results of High School and Middle School Principals (Individual)

Principal I 1

I 2

I 3

I 4

I 5

I 6

I 7

I 8

I 9

I 10

I 11

I 12

I 13

I 14

I 15

I 16

I 17

I 18

I 19

I 20

I 21

I 22

I 23

I 24

I 25 Total

Principal 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 47

Principal 2 2 2 2 2 2 1 2 2 2 2 2 1 1 0 2 1 1 2 2 2 2 1 2 2 1 40

Principal 3 2 1 2 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2 1 2 1 2 42

Principal 4 2 2 2 2 2 1 2 1 1 2 2 1 1 1 2 2 2 1 1 1 2 2 2 2 2 40

Principal 5 2 2 2 2 2 2 2 2 2 1 2 1 2 0 2 1 2 2 1 2 1 2 2 2 2 43

Principal 6 2 2 2 2 2 1 2 1 1 2 2 2 1 1 2 2 1 1 1 1 1 2 2 2 2 40

Principal 7 2 2 2 2 2 2 1 2 2 1 2 1 1 1 2 2 2 1 1 2 1 2 2 2 1 41

Principal 8 2 2 1 1 2 1 1 1 1 2 2 1 0 1 1 2 2 2 1 1 1 2 1 1 2 34

Principal 9 2 2 1 2 2 0 0 1 2 2 2 1 1 0 2 2 2 1 0 1 1 1 0 2 2 31

Principal 10 2 1 2 2 1 0 2 1 2 1 2 0 1 2 1 1 2 0 0 1 1 1 0 0 2 28

Principal 11 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 23

Principal 12 2 1 0 2 2 1 2 1 1 2 1 0 0 0 1 0 1 1 0 0 0 0 1 1 2 22

82 Table 4, Preliminary Screening Survey Results of High School and Middle School

Principals (Individual), reflected the individual scores of the 12 high school and middle school

principals. Seven of the principals (58%) scored 40 points or greater while five of the principals

(42%) scored fewer than 40 points on the preliminary screening survey.

Preliminary screening survey results of high school and middle school principals

(purposive sample). Table 5, Preliminary Screening Survey Results of High School and Middle

School Principals (Purposive Sample, n=7), is designed similarly to that of Table 3 with specific

emphasis on the seven principals continuing to the primary study – with the provision of their

response rate by percentage, their mean score by item, and the variability of their responses all

rounded to the nearest hundredth. The urban school division of focus has four high schools

(inclusive of specialized academy structures); five middle schools (inclusive of one fundamental

and one magnet school); two combined PreK-8 schools; and, one gifted school housing grades

three through eight. Of the seven principals which comprised the primary study, two are high

school principals; two are combined PreK-8 principals; and, three are middle school principals of

which one is the principal of a fundamental school.

83

Table 5

Preliminary Screening Survey Results of High School and Middle School Principals (Purposive Sample, n=7)

Item


Never

[0]

Some of

the time

[1]

Most of

the time

[2]

Mean

["#] Standard

Deviation

[SD]












7.




0.00% 14.29% 85.71% 1.86 0.38











84

13.




0.00% 42.86% 57.14% 1.43 0.53


communication. 28.57% 42.86% 28.57% 1.00 0.82







18.




0.00% 42.86% 57.14% 1.43 0.53


















Principals Rank Ordered by Consensus and Mean (Purposive Sample, n=7), has been provided

to illustrate the preliminary culturally responsive leadership practices to which the seven high

school and middle school principals self-identified. Consensus was determined by at least an

80% percent rating in the single category of Most of the Time on the 2 point scale (i.e., 0, 1, 2),

and at least a mean of 1.86. Because the standard deviation shows how the measurements for the

purposive sample are spread from the mean, selecting a mean of 1.86 or higher yields a low

standard deviation; therefore, as an outgrowth, the principal responses are close to the mean. A

high standard deviation indicates that the responses have a greater spread or variability (Howell,

2011). The indicators meeting or exceeding these parameters are notated as such above the gray

bar and have been highlighted in bold.

86 Table 6

Preliminary Screening Survey Results of High School and Middle School Principals Rank Ordered by Consensus and Mean (Purposive Sample, n=7)

Item Number Item Indicator Never

[0]

Some of the time

[1]

Most of the time

[2]

Mean ["#]

Standard Deviation

[SD]

1. I am aware of my own racial, ethnic, and cultural background and understand how it affects my perceptions and values. 0.00% 0.00% 100.00% 2 0

3. I regularly reflect on my own bias and how I view and treat people with cultural practices that are different than my own. 0.00% 0.00% 100.00% 2 0

4. Our school regularly examines academic and behavioral data, and examines achievement gaps by race, native language, socio‐economic status, and gender. 0.00% 0.00% 100.00% 2 0

5. Strategic plans are put in place to address all achievement gaps. 0.00% 0.00% 100.00% 2 0

11. I actively recruit applicants of diverse cultural backgrounds and ethnicities to work in our school. 0.00% 0.00% 100.00% 2 0

2. I seek opportunities to learn about the cultural practices in my school community, including staff, families, and students. 0.00% 14.29% 85.71% 1.86 0.38

15. Artwork and photographs embedded in school communication and school décor reflect the demographics of our student body and are age appropriate. 0.00% 14.29% 85.71% 1.86 0.38

24. Teacher expectations and evaluations include culturally responsive teaching, with a focus on equity and positive relationships. 0.00% 14.29% 85.71% 1.86 0.38

7. I support professional development for administrators and faculty to examine our own cultural awareness and develop culturally responsive school-wide and classroom practices.

0.00% 14.29% 85.71% 1.86 0.38

23. School policies include how to respect holidays in a manner that is sensitive to varying religions and cultural practices of the student population. 14.29% 0.00% 85.71% 1.71 0.76

10. Our school has clear procedures to report and respond to allegations of inequity. These issues are dealt with in a sensitive and timely manner. 0.00% 28.57% 71.43% 1.71 0.49

87 16. The books in our school library reflect our student body and depict varying cultural

practices in a positive and anti-biased way. 0.00% 28.57% 71.43% 1.71 0.49

17. I openly confront inequitable practices and have policies in place to hold staff accountable for their actions. I encourage staff to do the same. 0.00% 28.57% 71.43% 1.71 0.49

20. Behavior expectations and policies have taken into account the varying cultural expectations and norms among students and families. 0.00% 28.57% 71.43% 1.71 0.49

22. Our school incorporates differentiation tools to meet the needs of students from varying backgrounds. 0.00% 28.57% 71.43% 1.71 0.49

25. I am comfortable in leading discussions about race, culture, religion, ethnicity, class, gender, and sexual orientation with staff and students. 0.00% 28.57% 71.43% 1.71 0.49

8. I actively reach out to families from various backgrounds to give feedback and assist in the creation of school policies. 0.00% 42.86% 57.14% 1.57 0.53

9. I actively recruit families to volunteer in the school and on committees so that volunteer pools reflect the student body. 0.00% 42.86% 57.14% 1.57 0.53

13. School communication with families is available in multiple languages and is sensitive to varying family structures as well as diverse cultural and socioeconomic backgrounds.

0.00% 42.86% 57.14% 1.43 0.53

18. School policies are created while consciously working towards equity for all students and families. Historical policies are reviewed for cultural sensitivity. Members representing the demographics of the community assist in this process.

0.00% 42.86% 57.14% 1.43 0.53

6. Data is disseminated to families with procedures for them to offer support in improving our school for all students. 0.00% 57.14% 42.86% 1.43 0.67

21. Curriculum guidelines reflect that culturally responsive lessons are embedded in day to day teaching, rather than isolated units. 0.00% 57.14% 42.86% 1.43 0.53

19. Curricula and assessments used in our school are reviewed to make sure that materials are historically accurate, culturally responsive, and anti-bias. 0.00% 42.86% 57.14% 1.43 0.53

12. Our school has support systems in order to meet the needs of our staff from diverse backgrounds. 0.00% 71.43% 28.57% 1.29 0.49

14. I make sure that translators are available to improve school and family communication. 28.57% 42.86% 28.57% 1 0.82

Note. Adapted from “School Level Assessments and Evaluations,” by the Colorado Department of Education, 2010, Equity Toolkit for Administrators. Retrieved from https://www.cde.state.co.us/postsecondary/equitytoolkit.

88 Tables 5 and 6, Preliminary Screening Survey Results of High School and Middle School

Principals (Purposive Sample, n=7) and the Preliminary Screening Survey Results of High

School and Middle School Principals Rank Ordered by Consensus and Mean (Purposive Sample,

n=7) specifically illustrated the responses of the seven high school and middle school principals

that moved forward to the primary study. As the data were sorted in Table 6 using the Most of

the Time header from greatest to least, there was a 100% consensus on items 1, 3, 4, 5, and 11,

with a mean of 2, and a standard deviation of 0 (indicating no variance in the data). The data

revealed unanimity around personal racial, ethnic, and cultural awareness and the impact of each

on one’s thoughts and principles (I1); frequent evaluation of academic and behavioral data that

focuses on subgroup achievement gaps and the strategic planning and recruitment practices to

address such gaps (I4, I5, I11); and, the personal reflection of biases intrinsic to self in order to

understand interactions with others differing in cultural practices (I3).

Items 2, 7, 15, and 24 had a response rate of 85.71%, a mean of 1.86, and a standard

deviation of 0.38. The data for items 2, 7, 15 and 24 yielded an 85.71% response rate

encapsulating a personal initiative to seek out opportunities as well as to provide support of

professional development to staff about culturally responsive practices (I2, I7); and, an

agreement that artwork, teacher evaluations, and teacher expectations are reflective of culturally

responsive and equitable foci (I15, I24). Although item 23 had a response rate of 85.71%, two

principals rated this item at Never, thus the mean was 1.71, and the standard deviation was 0.76.

Items 16, 17, 20, 22, and 25 had a response rate of 71.43%, a mean of 1.71, and a

standard deviation of 0.49. Agreement for these items reflected the principals response to

inequitable practices by confronting them head-on as well as procedures put into place to report

and to address such practices swiftly (I17, I10); implementing behavior expectations and

89 differentiation strategies to meet students where they are while taking into account their cultural

backgrounds (I16, I20, I22); and, demonstrating a comfort level in leading discussions about

cultural differences (I25).

Compared to the first portion of data described having a 100% to 71.43% response rate,

items 6, 8, 9, 12, 13, 14, 18, 19, and 21, indicated a larger spread in responses as evidenced by

the standard deviation ranging from 0.82 to 0.53, mean values between 1.00 and 1.57, and a level

of consensus between 28.57% to 58.33%. Similar to the data discussed in Table 3, items 6

(42.85% response rate, !" of 1.43, and SD of 0.67) and 14 (28.57% response rate, !" of 1.43, and

SD of 0.67) had a lower consensus response rate.

Preliminary screening survey results of high school and middle school principals (non-

qualifiers). Table 7, Preliminary Screening Survey Results of High School and Middle School

Principals (Non-Qualifiers, n=5), has been constructed to provide the responses by percentage

rate for each header along with the mean and standard deviation all rounded to the nearest

hundredth. Of the respondents, two are high school principals; two are middle school principals

of which one is the principal of a magnet school; and, one is the principal of a gifted center

composed of grades three through eight.

90

Table 7

Preliminary Screening Survey Results of High School and Middle School Principals (Non-Qualifiers, n=5)

Item


Never

[0]

Some of

the time

[1]

Most of

the time

[2]

Mean

["#] Standard

Deviation

[SD]












7.




0.00% 40.00% 60.00% 1.60 0.54











91

13.




40.00% 60.00% 0.00% 0.50 0.55


communication. 60.00% 20.00% 20.00% 0.60 0.89







18.




20.00% 60.00% 20.00% 1.00 0.71


















Principals Rank Ordered by Consensus and Mean (Non-Qualifiers, n=5), has been provided to

illustrate the preliminary culturally responsive leadership practices to which the five high school

and middle school principals not advancing to the primary study self-identified. Consensus was

determined by at least an 80% percent rating in the single category of Most of the Time on the 2

point scale (i.e., 0, 1, 2), and at least a mean of 1.80. The indicators meeting or exceeding these

parameters are notated as such above the gray bar and have been highlighted in bold.

93 Table 8

Preliminary Screening Survey Results of High School and Middle School Principals Rank Ordered by Consensus and Mean (Non-Qualifiers, n=5)

Item Number Item Indicator Never

[0]

Some of the time

[1]

Most of the time

[2]

Mean ["#]

Standard Deviation

[SD]

1. I am aware of my own racial, ethnic, and cultural background and understand how it affects my perceptions and values. 0.00% 20.00% 80.00% 1.80 0.45

25. I am comfortable in leading discussions about race, culture, religion, ethnicity, class, gender, and sexual orientation with staff and students. 0.00% 20.00% 80.00% 1.80 0.45

4. Our school regularly examines academic and behavioral data, and examines achievement gaps by race, native language, socio‐economic status, and gender. 0.00% 40.00% 60.00% 1.60 0.54


7. I support professional development for administrators and faculty to examine our own cultural awareness and develop culturally responsive school-wide and classroom practices.

0.00% 40.00% 60.00% 1.60 0.54

11. I actively recruit applicants of diverse cultural backgrounds and ethnicities to work in our school. 0.00% 40.00% 60.00% 1.60 0.54

17. I openly confront inequitable practices and have policies in place to hold staff accountable for their actions. I encourage staff to do the same. 0.00% 40.00% 60.00% 1.60 0.54

2. I seek opportunities to learn about the cultural practices in my school community, including staff, families, and students. 0.00% 60.00% 40.00% 1.40 0.49

10. Our school has clear procedures to report and respond to allegations of inequity. These issues are dealt with in a sensitive and timely manner. 0.00% 60.00% 40.00% 1.40 0.49

16. The books in our school library reflect our student body and depict varying cultural practices in a positive and anti-biased way. 20.00% 40.00% 40.00% 1.40 0.84

9. I actively recruit families to volunteer in the school and on committees so that volunteer pools reflect the student body. 0.00% 80.00% 20.00% 1.20 0.45

94 15. Artwork and photographs embedded in school communication and school décor


3. I regularly reflect on my own bias and how I view and treat people with cultural practices that are different than my own. 20.00% 60.00% 20.00% 1.00 0.71

18. School policies are created while consciously working towards equity for all students and families. Historical policies are reviewed for cultural sensitivity. Members representing the demographics of the community assist in this process.

20.00% 60.00% 20.00% 1.00 0.71

22. Our school incorporates differentiation tools to meet the needs of students from varying backgrounds. 20.00% 60.00% 20.00% 1.00 0.71

24. Teacher expectations and evaluations include culturally responsive teaching, with a focus on equity and positive relationships. 20.00% 60.00% 20.00% 1.00 0.71

14. I make sure that translators are available to improve school and family communication. 60.00% 20.00% 20.00% 0.60 0.89

20. Behavior expectations and policies have taken into account the varying cultural expectations and norms among students and families. 20.00% 80.00% 0.00% 0.80 0.45

21. Curriculum guidelines reflect that culturally responsive lessons are embedded in day to day teaching, rather than isolated units. 20.00% 80.00% 0.00% 0.80 0.45

6. Data is disseminated to families with procedures for them to offer support in improving our school for all students. 40.00% 60.00% 0.00% 0.60 0.55

8. I actively reach out to families from various backgrounds to give feedback and assist in the creation of school policies. 40.00% 60.00% 0.00% 0.50 0.55

12. Our school has support systems in order to meet the needs of our staff from diverse backgrounds. 40.00% 60.00% 0.00% 0.50 0.55

13. School communication with families is available in multiple languages and is sensitive to varying family structures as well as diverse cultural and socioeconomic backgrounds.

40.00% 60.00% 0.00% 0.50 0.55

23. School policies include how to respect holidays in a manner that is sensitive to varying religions and cultural practices of the student population. 40.00% 60.00% 0.00% 0.50 0.55

19. Curricula and assessments used in our school are reviewed to make sure that materials are historically accurate, culturally responsive, and anti-bias. 60.00% 40.00% 0.00% 0.40 0.55


95 Tables 7 and 8, Preliminary Screening Survey Results of High School and Middle School

Principals (Non-Qualifiers, n=5) and the Preliminary Screening Survey Results of High School

and Middle School Principals Rank Ordered by Consensus and Mean (Non-Qualifiers, n=5)

revealed the responses of the five high school and middle school principals not moving forward

to the primary study. As the data were sorted in Table 8 using the Most of the Time header from

greatest to least, there was an 80% consensus on items 1 and 25, a mean of 1.80, and a standard

deviation of 0.45. The data suggested a strong response capturing one’s ideals regarding racial,

ethnic, and cultural awareness as well as a comfort level in leading discussions about these topics

with faculty and students. (I1, I25).

Items 4, 5, 7, 11, and 17 had a consensus response rate of 60%, a mean of 1.60, and a

standard deviation of 0.54. The data for these items yielded a 60% Most of the Time consensus

for regularly reviewing academic and behavioral performance data of students and

disaggregation of such data by performance groups (e.g., race, gender) while putting together

action plans to address skill gaps (I4, I5). Further, professional development is supported to

address issues surrounding race and diversity to review equitable practices and policies (I7, I17).

An effort is made to attract and to recruit a diverse faculty (I11).

Items 2 and 10 had a response rate of 40%, a mean of 1.40, and a standard deviation of

0.49 – illustrating less of a consensus than the aforementioned items and wider spread of data as

evidenced by the standard deviation. The data showed that respondents sought out opportunities

to learn about cultural practices of stakeholders (i.e., students, parents, and families) and clear

procedures to call out inequitable practices (I2, I10). Although item 16 had a response rate of

40% and a mean of 1.40, the standard deviation of this item was 0.84 due to one response of

96 Never (0 points) impacting the coalescence of the data spread regarding literature and media

reflecting multicultural demographics.

Compared to the first portion of data described having an 80% to 40% response rate,

items 3, 6, 8, 9, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23 and 24 indicated a larger spread in

responses as evidenced by the standard deviation ranging from 0.71 to 0.45, mean values

between 0.40 and 1.20, and a level of consensus between 0.00% to 20.00%. In particular, items

6, 8, 12, 13, 20, 21, and 23 each yielded a 0.00% Most of the Time response rate with the data

centered at either the Some of the Time or Never headers – fluctuating between 60% (I6, I8, I12,

I13, I23) to 80% consensus (I20, I21). The data here indicated that this group of principals self-

identified at a lower rate than those that advanced to the primary study of communicating

expectations, data, and policies as well as receptivity to practices and holidays that are reflective

of varying cultural norms of students, staff, and families (I6, I8, I13, I12, I20, I23). Further, the

data revealed an isolative nature of lesson plans and units disassociated from cultural

responsivity (I21).

Preliminary Screening Survey of High School and Middle School Mathematics Teachers

(Phase 1b)

Because this study also sought to determine how teachers’ culturally responsive actions

impact the mathematics performance of African American students, the preliminary screening

survey, Self-Assessment for School Teachers (Appendix J), was distributed via Qualtrics to high

school and middle school mathematics teachers of the purposive sample of principals (70 total).

Thirty-seven mathematics teachers provided consent to participate in the study – a 53% response

rate. Of the 37 mathematics teachers that responded to the preliminary screening survey, 23

(62% of those surveyed) attained a score of 40 points or more (or an 80% response rate) from the

97 25 indicators given the point values assigned to each header as follows – most of the time (2

points), some of the time (1 point), and never (0 points). The maximum point total would have

resulted in 50 points because there were 25 indicators.

Description and explanation of data. The data from the preliminary screening survey

are presented by the overall response rate of the 37 mathematics teachers of the urban school

division of study; the 23 mathematics teachers who advanced to the primary study (purposive

sample); and, then the data of the 14 mathematics who did not advance to the primary study

(non-qualifiers). Data analysis will follow the same format as that of the high school and middle

school principals detailed in the previous section.

Preliminary screening survey results of high school and middle school mathematics

teachers (overall). The data from the preliminary screening survey are provided in Table 9,

Preliminary Screening Survey Results of High School and Middle School Mathematics Teachers

by Item (Overall, n=37), demonstrating the overall item response rate of each mathematics

teacher that participated in the preliminary screening survey process. As with the preliminary

screening survey of the high school and middle school principals, the mean and standard

deviation of the data were reported to illustrate the centrality and variability of responses. The

percent response rate, mean, and standard deviation have been rounded to the nearest hundredth.

98

Table 9

Preliminary Screening Survey Results of High School and Middle School Mathematics Teachers by Item (Overall, n=37)

Item


Never

[0]

Some of

the time

[1]

Most of

the time

[2]

Mean

["#] Standard

Deviation

[SD]



2. I seek opportunities to learn about the cultural practices in

my school community, including staff, families, and students. 2.70% 24.32% 72.98% 1.68 0.53

3. I regularly reflect on my own bias and how I view and treat

people with cultural practices that are different than my own. 2.70% 13.50% 83.80% 1.81 0.46

4. As a faculty member, I feel supported and valued for my own identity and

perspectives. 2.70% 35.13% 62.17% 1.57 0.55

5. I value the diverse perspectives and cultural practices of my colleagues. 2.70% 13.50% 83.80% 1.81 0.46

6. I regularly examine academic and behavioral data for achievement gaps by race,

native language, socio-economic status, and gender. 8.10% 56.76% 35.14% 1.27 0.61

7. I review data to inform instruction in ways that best meet the needs of individual

learners, and collaborate with colleagues in data-based decision-making. 2.70% 16.20% 81.10% 1.78 0.48

8. I create positive relationships with families so that we can work as a team to best

meet their child’s needs. 0.00% 16.20% 83.80% 1.84 0.37

9. I engage in professional development to examine my own cultural awareness and

develop culturally responsive teaching practices. 10.81% 32.43% 56.76% 1.46 0.69

10. I encourage all families to give me feedback and volunteer in the classroom. 8.10% 37.84% 54.06% 1.46 0.65

11.

I participate in action research focused on equity to better meet my students’

needs and improve my instructional strategies. I monitor student engagement

within this research.

27.02% 43.24% 29.74% 0.97 0.78

12. Students and families feel comfortable when reporting inequitable practices are

incidents, whether parties involved include me, students, or fellow colleagues. 0.00% 45.94% 54.06% 1.54 0.51

99

13. Communication is available to families in multiple languages. 18.92% 13.51% 67.57% 0.89 0.61


communication. 27.02% 45.94% 27.04% 0.95 0.74



16. I act as a student and family advocate. I openly confront my colleagues if I see

practices that I feel are inequitable. 10.81% 40.54% 48.65% 1.38 0.68

17. I preview visual media to make sure that it is culturally responsive and anti-bias. 13.51% 18.92% 67.57% 1.54 0.73

18. My behavioral expectations and policies have taken into account the varying

cultural expectations and norms in my student demographics. 2.70% 18.92% 78.38% 1.76 0.49

19. I review curriculum and assessments for historical accuracy, cultural

responsiveness, multiple perspectives, and anti-bias. 16.20% 32.45% 51.35% 1.35 0.75

20. Culturally responsive lessons are embedded in my day to day teaching, rather than

taught in isolated units. 21.62% 43.24% 35.14% 1.14 0.75

21. I differentiate to meet the needs of students from varying backgrounds and have

high expectations for all. I provide the support needed to reach expectations. 0.00% 16.20% 83.80% 1.83 0.37

22. Holidays are equally represented and celebrations are sensitive to the varying

religions and cultural practices of my student population. 8.10% 29.74% 62.16% 1.54 0.65

23. I actively dispel racial and cultural stereotypes in my curriculum, assessments,

materials, and classroom décor. 10.81% 10.81% 78.38% 1.67 0.67

24. I am comfortable in leading discussions about race, ethnicity, class, gender, sexual

orientation, and religion with students. 8.10% 29.74% 62.16% 1.54 0.65

25.

I avoid imposing my personal values and opinions and assist students in learning

the difference between fact and opinion. I encourage the sharing of opinions that

are different than my own and looking at multiple perspectives.

0.00% 16.20% 83.80% 1.83 0.37




Mathematics Teachers by Item (Overall, n=37), indicated a level of consensus – when

disaggregating the data using the Most of the Time header ordered from greatest to least –

between 81.10% to 94.60%, a mean ranging from 1.78 to 1.91, and a standard deviation ranging

from 0.48 to 0.36 respectively for items (I) 1, 3, 5, 7, 8, 21, and 25. As evidenced by the data,

respondents had an awareness of how one’s own racial, ethnic, and cultural backgrounds impact

perceptions, values, and interpersonal relationships (I1, I3). Because of this awareness, responses

showed that the diversity of other cultures and their practices were of high personal value and a

source of reflection regarding formulating relationships with colleagues and families (I3, I5, I8).

Data are used to guide instructional practices and supports to meet the needs of diverse learners

coupled with high expectations for performance for all students (I7, I21).

Items 2, 4, 13, 15, 17, 18, 22, 23 and 24 yielded a level of consensus between 62.16% to

78.38%, a mean ranging from 1.54 to 1.76, and a standard deviation between 0.65 to 0.49

respectively. Data indicated a slightly larger spread in responses than the aforementioned.

Respondents indicated that racial and cultural stereotypes are eliminated from curricular

resources and media; and, that established norms in one’s classroom encapsulate student

demographics (I17, I18, I23). Artwork, literature, and holidays are equally represented along

with efforts to make available communication in multiple languages as a standard of practice

(I13, I15, I22). Respondents specified that opportunities to engage in individualized professional

development to understand cultural differences and systems are actively sought after (I2).

However, the lowest consensus of this range was of having less comfortability in leading

discussions about race and ethnicity with students (62.16% response rate, !" of 1.54, SD of 0.65)

101 and the feeling of having an undervalued identity and marginalized perspectives by building

leadership (62.17% response rate, !" of 1.57, SD of 0.55)

The remaining items on the preliminary screening survey indicated a level of consensus

between 27.04% to 56.76%, a mean ranging from 0.95 to 1.46, and a standard deviation between

0.74 to 0.51. Items 6, 11, 14, and 20 yielded the lowest agreement in response rate, as

demonstrated by the lower mean and higher standard deviation, demonstrating a wider overall

variation in the data set in regard to the infrequency of examination of achievement gap data (I6);

participation in equity research (I11); the infusion of culturally responsive lesson plans in daily

instruction (I20); and, the practice of making translators available for better communication

between students and their families (I14). Items 9, 10, 12, 16, and 20 ranged in concurrence of

48.65% to 56.76% with each of these indicators referencing family outreach and soliciting of

feedback from families to inform instructional practices.


Mathematics Teachers (Individual), reflects the individual response rate of the 37 high school

and middle school mathematics teachers by item given by response selected in numeral form.

The total points earned on the preliminary screening survey have been included in the last

column with data presented from the highest total point value to lowest total points accumulated.

Teachers were identified with a numeral coded to the building site of the corresponding principal

and a lower-case letter beginning with ‘a’ (i.e., Teacher 1a, Teacher 1b, etc.) to maintain

confidentiality per the Informed Consent Agreement parameters (Appendix H). The mathematics

teachers that earned greater than or equal to 40 points have been highlighted in bold. A gray bar

serves as a partition between teachers that earned greater than or equal to 40 points to those that

did not. Teachers that did not earn 40 points have been notated as Teacher 1a, Teacher 1b, and so

102 on to provide coding still associated with the building site of the principal while preserving

anonymity.

103 Table 10

Preliminary Screening Survey Results of High School and Middle School Mathematics Teachers (Individual)

Teacher I 1

I 2

I 3

I 4

I 5

I 6

I 7

I 8

I 9

I 10

I 11

I 12

I 13

I 14

I 15

I 16

I 17

I 18

I 19

I 20

I 21

I 22

I 23

I 24

I 25 Total

Teacher 2a 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 50 Teacher 6a 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 48 Teacher 4a 2 2 2 2 2 2 2 2 2 2 1 2 1 1 2 2 2 2 2 2 2 2 2 2 2 47 Teacher 5a 2 2 2 2 2 2 2 2 2 2 1 2 1 2 2 2 2 2 2 2 2 2 2 1 2 47 Teacher 6b 2 2 2 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 0 2 46 Teacher 5b 1 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1 2 46 Teacher 6c 2 2 1 1 2 2 2 2 2 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 45 Teacher 2b 2 2 2 1 1 2 2 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 2 1 2 45 Teacher 6d 2 2 2 1 2 2 2 2 2 2 2 1 1 0 2 2 2 2 2 1 2 2 2 2 2 44 Teacher 7a 2 2 2 2 2 1 2 2 2 2 0 2 1 1 2 2 2 2 2 2 2 2 2 1 2 44 Teacher 7b 2 2 2 2 2 1 2 2 2 2 2 1 1 0 2 1 2 2 2 1 2 2 2 2 2 43 Teacher 1a 2 2 1 2 2 1 2 2 2 2 1 2 1 1 2 2 2 2 2 2 1 2 2 1 1 42 Teacher 1b 2 2 2 2 2 1 2 2 2 1 1 1 2 2 2 2 1 2 0 1 2 2 2 2 1 41 Teacher 7c 0 2 2 2 2 2 2 2 2 1 1 2 0 0 2 2 1 2 2 2 2 2 2 2 2 41 Teacher 5c 2 2 2 0 2 1 1 2 2 1 2 1 1 0 2 2 2 2 2 2 2 2 2 2 2 41 Teacher 1c 2 2 2 2 2 1 2 2 2 1 1 2 0 0 2 2 2 2 1 1 2 1 2 2 2 40 Teacher 6e 2 2 2 2 2 2 2 2 1 2 1 2 1 1 1 2 2 1 1 0 2 1 2 2 2 40 Teacher 6f 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 2 2 2 40 Teacher 4b 2 1 2 2 2 1 2 2 2 1 0 2 0 1 2 2 2 2 2 2 2 0 2 2 2 40 Teacher 3a 2 1 2 2 1 2 1 2 1 1 2 2 1 0 1 2 2 2 2 1 2 2 2 2 2 40

104 Teacher 3b 2 2 2 2 2 1 2 2 1 1 1 2 1 1 2 1 2 2 1 1 2 1 2 2 2 40 Teacher 2c 2 2 2 1 2 1 2 2 1 2 1 2 1 2 1 1 1 2 1 2 2 1 2 2 2 40 Teacher 5d 2 2 2 1 2 1 2 2 2 1 1 1 1 1 2 1 2 2 2 1 2 2 2 1 2 40

Teacher 6a 2 2 2 2 2 1 1 2 1 2 1 1 1 1 1 1 2 2 1 1 2 2 2 1 1 37 Teacher 5a 2 2 2 1 1 1 2 2 2 1 0 2 1 1 1 1 1 2 2 1 2 1 2 2 2 37 Teacher 7a 2 2 1 2 2 1 2 2 2 1 0 1 2 1 2 1 1 2 1 1 2 2 1 1 2 36 Teacher 1a 2 1 2 2 2 1 2 2 1 2 0 2 1 1 0 1 0 2 0 1 2 2 0 2 2 33 Teacher 3a 2 1 1 2 2 1 2 2 1 0 2 2 1 1 2 1 1 1 0 0 1 2 0 2 2 32 Teacher 7b 2 2 2 1 2 1 1 1 1 2 1 1 0 0 0 0 2 2 1 1 2 0 2 2 2 31 Teacher 3b 2 1 2 1 1 0 1 2 1 2 0 2 0 0 0 0 2 2 2 1 2 2 2 1 2 31 Teacher 6b 2 2 2 2 2 1 2 1 1 0 0 1 1 1 2 0 0 2 0 0 2 2 0 1 2 29 Teacher 6c 2 1 2 2 2 0 1 2 0 1 1 1 1 0 1 1 2 1 0 0 2 1 1 2 1 28 Teacher 2a 2 1 2 1 1 1 2 2 0 2 0 2 0 0 2 1 2 0 1 0 2 0 2 1 1 28 Teacher 4a 2 1 1 1 2 2 2 1 0 1 1 1 0 1 1 1 2 2 1 0 2 1 0 0 2 28 Teacher 7c 2 1 2 1 2 1 2 1 1 1 0 1 0 0 1 0 0 1 1 0 1 1 2 2 2 26 Teacher 5b 2 1 2 1 2 1 2 1 1 0 0 1 0 1 1 1 0 1 0 1 1 1 1 2 2 26 Teacher 4b 2 0 0 1 0 0 0 1 0 1 0 1 1 1 2 1 0 1 1 0 1 1 1 0 1 17


Mathematics Teachers (Individual), reflects the individual scores of the 37 high school and

middle school mathematics teachers. Twenty-three out of 37 of the mathematics teachers (62%)

scored 40 points or greater while 14 of the mathematics teachers (38%) scored fewer than 40

points on the preliminary screening survey.


teachers (purposive sample). The data of the mathematics teachers not moving forward to the

primary study were extracted from the 23 mathematics teachers scoring 40 points or higher on

the preliminary screening survey to construct Table 11, Preliminary Screening Survey Results of

High School and Middle School Mathematics Teachers (Purposive Sample, n=23). Each

response rate, mean, and standard deviation have been rounded to the nearest hundredth.


Mathematics Teachers Rank Ordered by Consensus and Mean (Purposive Sample, n=23), has

been provided to illustrate the preliminary culturally responsive teaching practices to which the

23 mathematics teachers self-identified. Consensus was determined by at least an 80% percent

rating in the single category of Most of the Time on the 2 point scale (i.e., 0, 1, 2), and at least a

mean of 1.83. As with the preliminary screening survey of principals, the selection of a mean

greater than or equal to 1.83 renders a low standard deviation specifying that the responses are

closely aligned the mean. The indicators meeting or exceeding these parameters have been

denoted as such above the gray bar and have been highlighted in bold.

106

Table 11

Preliminary Screening Survey Results of High School and Middle School Mathematics Teachers (Purposive Sample, n=23)

Item


Never

[0]

Some of

the time

[1]

Most of

the time

[2]

Mean

["#] Standard

Deviation

[SD]








perspectives. 4.35% 26.09% 69.56% 1.65 0.57











11.




8.70% 56.52% 34.78% 1.30 0.63




107


communication. 26.09% 34.78% 39.13% 1.13 0.81




















25.




0.00% 8.70% 91.30% 1.91 0.29



108

Table 12

Preliminary Screening Survey Results of High School and Middle School Mathematics Teachers Rank Ordered by Consensus and Mean (Purposive Sample, n=23)

Item


Never

[0]

Some of

the time

[1]

Most of

the time

[2]

Mean

["#] Standard

Deviation

[SD]

8. I create positive relationships with families so that we can work as a team to best meet their

child’s needs. 0.00% 0.00% 100.00% 2 0

23. I actively dispel racial and cultural stereotypes in my curriculum, assessments, materials, and

classroom décor. 0.00% 0.00% 100.00% 2 0

2. I seek opportunities to learn about the cultural practices in my school community, including

staff, families, and students. 0.00% 8.70% 91.30% 1.91 0.29

3. I regularly reflect on my own bias and how I view and treat people with cultural practices that

are different than my own. 0.00% 8.70% 91.30% 1.91 0.29


7. I review data to inform instruction in ways that best meet the needs of individual learners, and

collaborate with colleagues in data-based decision-making. 0.00% 8.70% 91.30% 1.91 0.29

18. My behavioral expectations and policies have taken into account the varying cultural

expectations and norms in my student demographics. 0.00% 8.70% 91.30% 1.91 0.29

21. I differentiate to meet the needs of students from varying backgrounds and have high

expectations for all. I provide the support needed to reach expectations. 0.00% 8.70% 91.30% 1.91 0.29

25. I avoid imposing my personal values and opinions and assist students in learning the difference

between fact and opinion. I encourage the sharing of opinions that are different than my own

and looking at multiple perspectives.

0.00% 8.70% 91.30% 1.91 0.29

1. I am aware of my own racial, ethnic, and cultural background and understand how it affects

my perceptions and values. 4.35% 4.35% 91.30% 1.89 0.46

109

9. I engage in professional development to examine my own cultural awareness and develop

culturally responsive teaching practices. 0.00% 17.39% 82.61% 1.83 0.39

15. Artwork and photographs embedded in school communication and school décor reflect the

demographics of our student body and are age appropriate. 0.00% 17.39% 82.61% 1.83 0.39


16. I act as a student and family advocate. I openly confront my colleagues if I see practices that I

feel are inequitable. 0.00% 21.74% 78.26% 1.78 0.42

19. I review curriculum and assessments for historical accuracy, cultural responsiveness, multiple

perspectives, and anti-bias. 4.35% 21.74% 73.91% 1.70 0.56

22. Holidays are equally represented and celebrations are sensitive to the varying religions and

cultural practices of my student population. 4.35% 21.74% 73.91% 1.70 0.56


4. As a faculty member, I feel supported and valued for my own identity and perspectives. 4.35% 26.09% 69.56% 1.65 0.57

24. I am comfortable in leading discussions about race, ethnicity, class, gender, sexual orientation,

and religion with students. 4.35% 26.09% 69.56% 1.65 0.57


12. Students and families feel comfortable when reporting inequitable practices are incidents,

whether parties involved include me, students, or fellow colleagues. 0.00% 34.78% 65.22% 1.65 0.49

6. I regularly examine academic and behavioral data for achievement gaps by race, native

language, socio-economic status, and gender. 0.00% 47.83% 52.17% 1.52 0.51

20. Culturally responsive lessons are embedded in my day to day teaching, rather than taught in

isolated units. 4.35% 39.13% 43.48% 1.52 0.59

14. I make sure that translators are available to improve school and family communication. 26.09% 34.78% 39.13% 1.13 0.81

11. I participate in action research focused on equity to better meet my students’ needs and

improve my instructional strategies. I monitor student engagement within this research. 8.70% 56.52% 34.78% 1.30 0.63



110

Tables 11 and 12, Preliminary Screening Survey Results of High School and Middle

School Mathematics Teachers (Purposive Sample, n=23) and the Preliminary Screening Survey

Results of High School and Middle School Mathematics Teachers Rank Ordered by Consensus

and Mean (Purposive Sample, n=23) responds to the 23 high school and middle school

mathematics teachers that advanced to the primary study. As the data were sorted using the Most

of the Time header from greatest to least, there was a 100% consensus on items 8 and 23, thus

establishing a mean of 2, and a standard deviation of 0. The data revealed a connection to

families by establishing a partnership between home and school while also allaying any racial or

ethnic tropes in curriculum, instruction, assessments, or resources (I8, I23).

Items 1, 2, 3, 5, 7, 18, 21, and 25 each had a consensus response rate of 91.30%, a mean

of 1.91, and a standard deviation of 0.29. The data of the purposive sample demonstrated a

synergism between the components of frequent reflection on personal biases and the impact on

others (I1, I2, I3, I5); taking into account and valuing the diverse beliefs and practices of other

cultures (I18, I25); and, due to such awareness, having the ability to differentiate instruction to

best meet the needs of students while using data and feedback to drive and catalyze instructional

practices (I7, I21).

Items 9, 15, and 17 yielded a response rate of 82.81%, a mean of 1.83, and a standard

deviation of 0.39. The item indicators specifically revealed that respondents embed artwork,

media, and literature reflective of the school demographics (I15, I17) while seeking out

professional development that stimulates an examination of personal cultural awareness and

equitable practices (I9).

Items 4, 10, 12, 13, 16, 19, 22, and 24 represented the next tier of response rates. These

items ranged in a consensus response rate of 65.22% to 78.26%, mean values of 1.65 to 1.78, and

111

standard deviation values of 0.49 to 0.42, thus indicating more of a spread in responses than the

previously cited items. The items within this bracket underscore the respondents’ actions as a

student and family advocate as well as the ability to oppose inequitable practices of colleagues

when witnessed (I16, I10, I12). Communication through multiple means are made available to

families; curriculum and assessments are reviewed for consistency in capturing multiple

perspectives and cultures; and, celebrations conducted in the classroom are sensitive to varying

cultural differences (I13, I19, I22). The lowest response rate in this section from the purposive

sample (65.22% response rate, !" of 1.65, SD of 0.57) were items 4 and 24 – both referencing the

value that they add through their identity and perspectives (I4) and a comfort level in discussing

matters of race and ethnicity with students (I24).

Compared to the first portion of data described having an 82.61% to 100% response rate,

items 6, 11, 14, and 20 indicated an even larger spread in responses as evidenced by the standard

deviation ranging from 0.63 to 0.51, mean values between 1.13 and 1.52, and a level of

consensus between 34.78% to 52.17%. The regular examination of the dissonance in

performance between student groups provided the highest response rate in this tier with 52.17%

responding Most of the Time. In particular, respondents indicated that culturally responsive

lessons were embedded in daily instruction instead of isolative in scope at a response rate of

43.48%, a mean of 1.52, and a standard deviation of 0.59; however, when combined with the

response rate of Some of the Time, consensus agreement yielded an 82.81% response rate (I20).


teachers (non-qualifiers). Table 13, Preliminary Screening Survey Results of High School and

Middle School Mathematics Teachers (Non-Qualifiers, n=14), has been constructed to provide

the responses by percentage rate for each header along with the mean and standard deviation all

112

rounded to the nearest hundredth for those mathematics teachers not moving forward to the

primary study.

113

Table 13

Preliminary Screening Survey Results of High School and Middle School Mathematics Teachers (Non-Qualifiers, n=14)

Item


Never

[0]

Some of

the time

[1]

Most of

the time

[2]

Mean

["#] Standard

Deviation

[SD]








perspectives. 0.00% 54.14% 42.86% 1.43 0.51











11.




64.23% 28.63% 7.14% 0.43 0.65




114


communication. 35.71% 64.29% 0.00% 0.64 0.49




















25.




14.28% 28.57% 71.43% 1.71 0.47




Mathematics Teachers Rank Ordered by Consensus and Mean (Non-Qualifiers, n=14), has been

given to illustrate the preliminary culturally responsive teaching practices to which the 14 high

school and middle school mathematics teachers not moving forward to the primary study self-

identified rank ordered from greatest to least consensus response rate and mean. Item 1, denoted

in bold, is the only item having attained a 100% consensus rate in the single category of Most of

the Time on the 2 point scale (i.e., 0, 1, 2). All other indicators have been listed below the

demarcation gray bar.

116

Table 14

Preliminary Screening Survey Results of High School and Middle School Mathematics Rank Ordered by Consensus and Mean (Non-Qualifiers, n=14)

Item


Never

[0]

Some of

the time

[1]

Most of

the time

[2]

Mean

["#] Standard Deviation

[SD]

1. I am aware of my own racial, ethnic, and cultural background and understand how it affects my perceptions and values.

0.00% 0.00% 100.00% 2.00 0.00

3. I regularly reflect on my own bias and how I view and treat people with cultural practices that are different than my own.

7.14% 21.42% 71.44% 1.64 0.63


21. I differentiate to meet the needs of students from varying backgrounds and have high expectations for all. I provide the support needed to reach expectations.

0.00% 28.57% 71.43% 1.71 0.47

25. I avoid imposing my personal values and opinions and assist students in learning the difference between fact and opinion. I encourage the sharing of opinions that are different than my own and looking at multiple perspectives.

14.28% 28.57% 71.43% 1.71 0.47

7. I review data to inform instruction in ways that best meet the needs of individual learners, and collaborate with colleagues in data-based decision-making.

7.14% 28.57% 64.29% 1.57 0.65

18. My behavioral expectations and policies have taken into account the varying cultural expectations and norms in my student demographics.

7.14% 35.71% 57.15% 1.50 0.65

8. I create positive relationships with families so that we can work as a team to best meet their child’s needs.

0.00% 42.86% 57.14% 1.57 0.51

9. I engage in professional development to examine my own cultural awareness and develop culturally responsive teaching practices.

28.57% 14.28% 57.14% 0.86 0.66

24. I am comfortable in leading discussions about race, ethnicity, class, gender, sexual orientation, and religion with students.

14.28% 35.71% 50.00% 1.36 0.74

19. I review curriculum and assessments for historical accuracy, cultural responsiveness, multiple perspectives, and anti-bias.

35.71% 14.28% 50.00% 0.79 0.70

117 17. I preview visual media to make sure that it is culturally responsive and anti-bias. 35.71% 21.42% 42.87% 1.07 0.92

4. As a faculty member, I feel supported and valued for my own identity and perspectives.

0.00% 54.14% 42.86% 1.43 0.51

22. Holidays are equally represented and celebrations are sensitive to the varying religions and cultural practices of my student population.

14.28% 42.86% 42.86% 1.29 0.73

23. I actively dispel racial and cultural stereotypes in my curriculum, assessments, materials, and classroom décor.

28.57% 28.57% 42.86% 1.14 0.86

12. Students and families feel comfortable when reporting inequitable practices are incidents, whether parties involved include me, students, or fellow colleagues.

0.00% 64.23% 35.77% 1.36 0.49

2. I seek opportunities to learn about the cultural practices in my school community, including staff, families, and students.

7.14% 57.14% 35.72% 1.29 0.61

15. Artwork and photographs embedded in school communication and school décor reflect the demographics of our student body and are age appropriate.

21.42% 42.87% 35.71% 1.14 0.77



11. I participate in action research focused on equity to better meet my students’ needs and improve my instructional strategies. I monitor student engagement within this research.

64.23% 28.63% 7.14% 0.43 0.65

6. I regularly examine academic and behavioral data for achievement gaps by race, native language, socio-economic status, and gender.

21.42% 78.58% 0.00% 0.86 0.53

16. I act as a student and family advocate. I openly confront my colleagues if I see practices that I feel are inequitable.

28.57% 71.43% 0.00% 0.71 0.47

14. I make sure that translators are available to improve school and family communication.

35.71% 64.29% 0.00% 0.64 0.49

20. Culturally responsive lessons are embedded in my day to day teaching, rather than taught in isolated units.

50.00% 50.00% 0.00% 0.50 0.52


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Tables 13 and 14, Preliminary Screening Survey Results of High School and Middle

School Mathematics Teachers (Non-Qualifiers, n=14) and the Preliminary Screening Survey

Results of High School and Middle School Mathematics Teachers Rank Ordered by Consensus

and Mean (Non-Qualifiers, n=14) illustrate the responses of the 14 high school and middle

school mathematics teachers not advancing to the primary study. As the data were sorted using

the Most of the Time header from greatest to least, consensus ranged from 64.29% to 71.44%,

the mean ranged from 1.57 to 1.64, and a standard deviation extended from 0.65 to 0.47 for items

3, 5, 7, 21, and 25. The data from this tier of items indicated respondents’ frequent reflection of

personal biases while valuing the diversity of others without the imposition of one’s own

personal values and judgments (I3, I5, I7). Also, data is reviewed to inform instructional

decisions to differentiate for the varying needs of students (I21, I25).

Items 4, 8, 9, 17, 18, 19, 22, 23, and 24 had a consensus response rate that ranged from

42.86% to 57.15%, mean values between 0.79 to 1.57, and standard deviation values between

0.92 to 0.51. The data of this bracket of items reflected a lower rate of consensus than the

previous tier of items with 57.15% agreement about creating positive relationships with families;

establishment of behavioral expectations consistent with the cultural expectations of diverse

groups; proactive engagement in professional development about equity and cultural awareness;

and, comfort in leading discussions about race and ethnicity with students (I8, I9, I18, I24). Fifty

percent of the respondents indicated that curriculum and assessments have been reviewed for

historical accuracy, biases, and cultural sensitivity (I19); and, 42.86% responded that holidays

and media are reviewed through the same lens (I17, I22). Respondents at a consensus rate of

42.86% felt supported and valued at their school and for their work (I4). A stark deviation in the

data was the response to item 23 centered on the dispelling of racial and stereotypical imagery or

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context in curriculum, assessments, and resources with 28.57% having provided the response of

Never or Some of the Time and 42.86% at Most of the Time.

Items 2, 6, 10, 11, 12, 13, 14, 15, 16, and 20 indicated a greater spread in responses as

evidenced by the standard deviation ranging from 0.77 to 0.47, mean values between 0.43 and

1.36, and a level of consensus between 0.00% to 35.77%. In particular, items 6, 14, 16, and 20

each yielded a 0.00% Most of the Time response rate with the data concentrated at either the

Some of the Time or Never headers. The data here indicated that this group of mathematics

teachers self-identified at a lower rate than those that advanced to the primary study of regularly

examining academic and behavioral data to close skill and achievement gaps (I6); providing

translators to strengthen communication with families (I14); advocating for students and families

when inequitable practices are seen (I16); and, ensuring that culturally responsive lesson plans

are integrated within curriculum units (I20).

Observations of High School and Middle School Principals (Phase 2a)

To answer Research Question 1 (RQ1), “To what extent, if any, do principals at the high

school and middle school levels that exemplify culturally responsive leadership influence

mathematics teachers’ use of culturally responsive teaching that results in building conceptual

understanding in mathematics?” two 90-minute observations of the seven high school and middle

school principals that advanced to the primary study were conducted (14 total observations). An

observation was completed by the researcher once prior to the 4.5 weeks assessment and once

prior to the Critical Skills Assessment deployed by the urban school division. Conducting

observations provided the researcher with an immersive experience of the variation and

congruency of forms of culturally responsive leadership that these principals exhibited, thus

allowing for the initial development of three comprehensive categories from the data – (1) what

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culturally responsive leaders did with people; (2) what culturally responsive leaders did in

reference to curriculum, instruction, and assessment; and, (3) what culturally responsive leaders

did to affect the school environment. The demographics of the principals of the primary study are

detailed below in Table 15.

Table 15

Demographics of High School and Middle School Principals (Purposive Sample, n=7)

Principal School Type Sex Number of Years

Having Served as a Principal

Number of Years Having Served as the

Principal of Study Site

Principal 1 Combined PreK-8 M 1 1

Principal 2 Middle School [Fundamental] M 18 2

Principal 3 High School M 10 2

Principal 4 Combined PreK-8 F 4 4

Principal 5 Middle School F 4 1

Principal 6 High School F 2 2

Principal 7 Middle School F 5 5

Themes were to be supported by the text as lifted from the descriptions from the field

notes and illuminating if rendered integral to the answer posed by the research question. Meeting

these two conditions were three resonating themes of critical consciousness (self-awareness) and

interpersonal relationships amongst teachers and students; communication and being present;

and, data-driven decision-making. Each of these themes cut across the abovementioned broad

categories. Excerpts from each observation have been denoted by the principal code (e.g.,

Principal 1), observation number (O), and line of directly quoted text from the field notes (l).

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Critical consciousness (self-awareness) and interpersonal relationships amongst

teachers and students. All seven principals demonstrated an understanding of the students and

the context in which they lead teachers. The following examples of culturally responsive

leadership were observed where the principals provided teachers and students with social,

emotional, and academic supports while acknowledging the strengths of the school community

bolstered by leadership that influenced the school’s climate through inclusivity.

Social, emotional, and academic supports. Principal 2 was observed holding town hall

meetings with each grade level. The principal began each meeting sharing with staff and students

that they were held to high expectations for academics, attendance, and behavior.

It is expected that everyone here is to have pride in our school because our school is our

community. It is critical that all of us SOAR – meaning that we are safe, optimistic,

demonstrate academic excellence, and develop positive relationships. I believe that all of

us are capable of meeting these expectations. Anything less than your best effort is not

acceptable. (Principal 2, O1, l7-10)

As students responded to questions that Principal 2 posed during the town hall meetings, the

principal would provide the students with “Eagle Wings” – a school-wide commerce incentive

that students could use at the school bookstore to purchase school supplies, homework passes,

gift cards, lunch with the principal, or collectively earn toward class or grade level pizza parties.

Academic supports were emphasized during each town hall meeting with Principal 2 stating:

We will be holding Saturday School beginning next week. This will be held every nine

weeks and you will be required to attend if you have any zeros on assignments or if a

teacher recommends you due to poor academic performance. In addition, your teachers

will be providing tutoring at least twice per week and you may ride the activity bus home.

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It is expected that your teachers support you in your efforts to excel. Likewise, it is

important that you also make arrangements when you know that you need help – it is

critical to not only your success, but also to our school’s overall success. (Principal 2, O1,

l23 – 29).

Similarly, Principal 3 discussed with the Algebra I collaborative learning team (CLT) the

need to incorporate additional time outside of traditional school hours to support students’ needs

to include after school tutoring and Saturday School. Principal 3 articulated:

We must identify those students who are struggling early in mathematics. If we are to

move to the next level in our work in regard to maximizing the potential of our young

people, we must also acknowledge that it will take extended time to help each of them

find success. (Principal 3, O2, l23-24)

An observation with Principal 5 began with a personalized approach. Principal 5 was

observed upon arrival to the study site by the researcher, meeting with an African American male

student struggling in his mathematics class in her office. The principal allowed the student to eat

lunch with her and to discuss his concerns and fears about not understanding mathematics

concepts. The student lamented that he was not “good in math” in which Principal 5 replied,

“You are only as good as your mindset. You need to first make sure that you show all of your

work. Let’s try the next problem step-by-step. I want to see you try” (Principal 5, O1, l4-7). The

student began to simplify the expression with Principal 5 providing on-going encouragement

such as, “What’s the next step? And the next step?” (Principal 5, O1, l10-12). The student then

began to smile as he was able to simplify the expression that he was working on. The principal

encouraged the student by stating, “You can do this. I know that you can. Let me walk you back

to class and speak with your teacher about your progress.” (Principal 5, O1, l16-17). Principal 5

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walked the student back to his classroom and then shared with his mathematics teacher how well

he did in her office. Principal 5 shared with the teacher that she would return later during the

teacher’s planning period to debrief about the student and to suggest behavior interventions that

could be put into place to help with his frustration threshold.

Principal 6 was involved in a freshmen academy meeting with a group of ten high school

teachers (four mathematics teachers, two engineering teachers, two science teachers, and two

English teachers) with the purpose of creating a performance-based learning experience that

integrated mathematics, engineering, science, and English with mathematics serving as the

driving discipline. One of the components of the meeting was to identify a list of students that

would be able to attend an upcoming field trip that supported the learning intentions of the next

mathematics unit. One of the male African American students was suggested to attend the field

trip from two of the academy teachers; however, two other teachers objected to his attendance

remarking that his grades were not yet high enough to attend although some improvements had

been made regarding his work ethic. Khalifa, Gooden, and Davis (2016) provided that “if low

expectations occur because teachers do not eel students are smart enough based on their

behaviors, then the marginalization of students’ social and cultural capital occurs and perpetuates

a cycle” (p. 1280). In response to breaking such an observed cycle, Principal 6 stated:

I want the student to attend the field trip because based on what you all are saying, even

though he may not have the highest grades, he has shown some improvement in his

behavior and academic performance. I think what’s necessary is to give him a chance and

an opportunity. This week, I want each of you to commend the student on working hard

to build himself back up. I am also going to personally follow up with the student and his

parent. (Principal 6, O1, l37-41).

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As a step to further solidify the teachers’ ability to reconnect and to build rapport with the

student, Principal 6 then stated:

I know that he [the student] likes to draw. Allow him time to complete his work in class

and then the last few minutes of class (no more than five minutes), allow him to draw –

but with a purpose. Why not have him to create some imagery depicting the ‘big ideas’ of

the lesson as an exit ticket? That way, we are tapping into a skill set that we know that he

is interested in.” (Principal 6, O1, l47-52).

Recognizes and celebrates the strengths of students and teachers. Principals 4 and 7

were observed recognizing and celebrating the strengths of students and teachers as each

conducted instructional observations of mathematics classes. For example, during each class

visit, Principal 4 would stop and ask students how they were doing and how they were

progressing on their work. The students were eager to share their work – even at times while the

principal was speaking to one student, others would get up from their seats to show her their

papers. Principal 4 exclaimed, “I am so very proud of you”; “You are doing great”; and, “Keep it

up…I knew that you could do it!” (Principal 4, O1, l56-59). The students seemed to beam with

pride and were seen smiling and high-fiving each other after Principal 4 complimented them on

their efforts. Likewise, as Principal 7 entered each mathematics class (three total), students were

excited to share with her their scores on assessments or class assignments. As Principal 7

maneuvered up and down each row or small group seating arrangement, students without any

prompting, began to open their laptops to review their grades with her. As they did this, Principal

7 would high-five or hug each student while stating, “I’m so very proud of you”; “You’re so

awesome”; and, “Wow – you are really making it happen.” (Principal 7, O1, l33-35, 47-49). It

was to be noted that Principals 4 and 7 knew every student by name, gave each student their full

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attention as they spoke, and provided each teacher with a positive note on the way out of each

instructional observation about their classes with a reference to debriefing about the observation

at a later moment at the conclusion of the day.

Likewise, Principal 2 provided an index card of what he called “glows and grows” on the

desk of each mathematics teacher after conducting an instructional observation. Principal 2 listed

the date and time that he wanted to debrief with the teachers later in the day during their planning

block to give just-in-time feedback (Principal 2, O2, l29).

As an example of enhancing teacher efficacy, Principal 4 during a collaborative learning

team meeting, commended the mathematics teachers (three total) for creating a culturally

responsive environment as evidenced by her multiple classroom visits:

I want to tell each of you that your classrooms have exhibited such kindness and respect

toward the children and vice versa. It seems like the students are really enjoying your

classes and you are making our students love math. That is so great to see and to see it

across the board. You all are well on your way to having a great school year. Give each

other a high-five and a fist bump! (Principal 4, O2, l5-9)

The teachers erupted into laughter and gave each other high fives and fist bumps.

Influences school climate by being inclusive of cultural diversity. Examples of

influencing the school’s climate by modeling and demanding inclusivity were demonstrated by

Principal 1 and Principal 6. Principal 1 described the vision of the school as “One Band, One

Sound.” Throughout the building, this mantra was exhibited – be it worn on staff and student T-

shirts, posters in the classroom, and paintings on the walls of the building. Principal 1 described

the “One Band, One Sound” mindset as:

putting people in the right place to do the right work; having sound systems and routines

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for staff and students; being visible in classrooms and hallways; and, out and about in the

community where our families feel comfortable in the leadership and direction of our

school. This is what we stand for here in this building. (Principal 1, O1, l12-16)

In this same vein, Principal 1 stated, while walking to a scheduled mathematics collaborative

learning team meeting:

My goal for this year is to ensure that all of our kids feel safe, know that they are a part of

the same team, and that we move together as one band, one sound. The same goes for the

teachers and families because I need them on the same team in order for our kids to

succeed...it is important to the work that we do here around culture and climate.

(Principal 1, O1, l18-22)

Along the route, Principal 1 stopped to highlight the vision boards and mirrors aligning the walls.

Principal 1 shared that the first week of school was used for students to create a vision board of

where they saw themselves by the end of the year. The staff were also asked to do the same. In

between the vision boards at various places on the walls were mirrors of different sizes and

colors. Several sayings were above the mirrors such as, “Our success depends on…”; “The

reason why we get up…”; and, “Because of…, our band has one sound.” These areas in the

building were meant to serve as interactive spaces where students could stop and see themselves

in the mirrors along the wall as well as fill in the blank of the particular saying. Principal 1

stated:

I want kids to see themselves in every aspect of our building. Our staff needs them to

know that we can’t be successful without them, that we’re up early in the morning to

make sure that they get the education that they need, and that we are playing in the same

band with one sound. (Principal 1, O1, l24-28)

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Principal 6 had the entire freshman class read The Playbook: 52 Rules to Aim, Shoot, and

Score in this Game Called Life (Alexander, 2017). The book was suggested by Principal 6 to the

administrative team and freshmen academy teachers because it was culturally resonant and

responsive to the students served in the building. The book contains quotes and graphics about

goal setting; establishing one’s purpose; and, developing plans for the future using sports as a

metaphor threaded throughout the text. The quotes within the text were to be provided each week

of school and each first block class was to use 15 minutes to discuss the quotes. Principal 6 had

led training before the start of the school year about the development of performance-based

assessments that not only incorporated academics, but also experiences that enhanced

collaboration, citizenship, and mutual respect while understanding the cultural diversity of the

student body. Because of the demographics of the school, Principal 6 took a self-described, “bold

stance” to “establish a culture where students feel safe, nurtured, and enveloped in a school

environment where they see themselves” (Principal 6, O1, l67-68). The book is structured to

resemble four quarters (similar to a basketball or football game); therefore, the students would be

tasked with studying the quotes from each quarter in the text during each of the four nine weeks

of the school year. Principal 6 shared that the freshman class was selected for this school-wide

book study because it is a transition year from middle school to high school:

My goal is to truly make our freshmen feel like a part of this community. By extension, I

want to welcome students into the fold that is the culture of this building while

interweaving the content from the text throughout all core areas. (Principal 6, O1, l76-77)

Communication and being present. The seven principals were specific in their

communication of high-level, cognitively rigorous, and engaging mathematical instructional

practices. Communication of such expectations was observed by the researcher to take place at

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either at CLT meetings that the principals attended routinely or by each principals’ monitoring of

the implementation of culturally responsive teaching practices during instructional observations.

Each principal used varied phraseology that centered on sound mathematics teaching involving

building conceptual understanding.

For example, during a mathematics collaborative learning team meeting with the

mathematics department, Principal 1 reiterated that all mathematics teachers were to ensure that

they were on pace with instructional delivery and that instructional strategies were differentiated;

maintain tight alignment to the Curriculum Framework where instruction matches the cognitive

level of rigor while building conceptual understanding; exercise classroom management that

builds community; and provide timely feedback to students after frequent checks for

understanding (Principal 1, O1, l45-61).

Principal 2 shared with the researcher, en route to conducting mathematics instructional

observations scheduled, that during the first collaborative team meeting held three weeks prior,

he shared the four instructional “look fors” having met shared consensus between himself and

the mathematics department:

During the pre-service session with the mathematics department, it was critical that we

established norms that everyone could get behind. I call them the ‘top four.’ First, we

determined that not only are we teaching mathematics, but we also need to make it

relevant to the students. Second, we need to enhance the building of conceptual

understanding through the use of manipulatives. Next, we need to have high levels of

student engagement. Then finally, we need to maximize the 90-minute bock with a clear

agenda on the board. If it [referring to the agenda] is not on the board, then it should be

projected on the SMART board before diving into the lesson. (Principal 2, O2, l5-12)

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Principal 2 told the researcher that the purpose of the instructional observations was to monitor

and to follow-up on the implementation of each agreed-upon look for.

Principal 3 communicated to Algebra I teachers while facilitating a collaborative team

meeting that they each needed to engage in the process of frequent intentional review of student

performance data to move students forward:

We have to be purposeful in identifying where our students struggle early so that they can

be prepared. Our team cannot expect anything less than that. In order to help our students

where they are, we have to start by building up their conceptual understanding. (Principal

3, O2, l25-27).

As the researcher and Principal 4 were en route to conduct instructional observations of

mathematics teachers, Principal 4 articulated that each was expected to identify and state the

learning intention, success criteria, and real-world applications through enhanced conceptual

understanding for each mathematics class. Also, she shared that student engagement, follow-up

“why?” questioning, and cultivating the learning climate were the school-wide foci for

mathematics:

Building community while learning at high-levels is crucial to the continual success of

the students. As we conduct instructional walkthroughs today, I will be looking for these

components. By the way, our lesson plans have been uploaded onto a shared Google

Drive so that I can check for these components weekly. Teachers must specify in their

lesson plans how students will be engaged from bell to bell in the 90-minute block as

well as how they plan to embed community-building activities into their lessons (i.e.,

student-student talk, math discourse via partners or collaborative groups). (Principal 4,

O1, l14-20)

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To elaborate further, Principal 4 stated:

Why? is a powerful question in mathematics. Such a simple question can then elicit a

response from students where they have to justify their answers. It is super important to

me that our kids can tell how they arrived at their answers. As a team, we can no longer

accept five or 12 as the answer…tell me how you got there. That’s how the learning

begins and how I want to stretch our math teachers. You can find out a whole lot when

you ask that simple, simple question.” (Principal 4, O1, l22-24)

While Principal 5 conducted mathematics instructional observations, she had an

electronic checklist on her laptop with the following items: clear learning intentions; clear

success criteria; student engagement to include building conceptual understanding; and, frequent

checks for understanding. When entering each class, Principal 5 would first look at the board to

see if the learning intentions and success criteria were posted. She then circulated throughout the

classroom greeting students and asking them what they were learning for the day. Principal 5

would then calculate how many students were able to identify or articulate the learning intention

along with how they were going to demonstrate success.

Next, Principal 5 looked for students’ engagement. In one of the classes, students were

using a hands-on equations kit to model how to solve single- and two-step equations in pairs.

Students were finding success in using the concrete representation of the equations before

moving to the pictorial representation that was modeled by Teacher 5b. Teacher 5b then told the

students that she would show them how to solve an equation using the algorithm the next day.

Principal 5 commended the teacher on her way out of the classroom for using hands-on modeling

and for frequently going from each pairing to check for understanding:

I like how engaged the kids are with the manipulatives – what a way to build conceptual

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understanding! They seemed to really like this activity. I will come back during planning

today to debrief with you. (Principal 5, O2, l29-30)

After leaving the class, Principal 5 shared with the researcher that she was specifically looking

for the items identified on her checklist as these were the expectations communicated to all

mathematics teachers during the last joint collaborative learning team meeting:

I have conducted frequent instructional observations with my administrative team and we

have seen some differences in classes. In particular, I want to see more references

back to the learning intention and frequent checks for understanding across all

mathematics classes. Although I’ve seen an improvement across the board with placing

the learning intentions and success criteria on the board and higher levels of student

engagement, I would like to see even more checks for understanding with turn and talks

and math discourse. I’m also interested in seeing frequent checks for understanding either

using a checklist or system in place that teachers can use to ensure that all students really

do know and understand the content. (Principal 5, O2, l33-39).

Principals 6 and 7 communicated instructional expectations by employing probing

questions with the mathematics teachers during collaborative learning team meetings. Principal 6

used this tactic when she inquired of the freshmen academy teachers, “How do you plan to

integrate each of your disciplines to create a performance-based assessment that also

incorporates building conceptual understanding in mathematics?” (Principal 6, O1, l12-13).

Principal 7 asked, “How do you plan to use conceptual understanding to drill down to the

specific skills that students do not know and are not able to do yet? How can we work together to

set a plan in motion?” (Principal 7, O1, l69-71).

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Data-driven decision making. Each principal constructed the master schedule to allow

teachers to meet frequently (e.g., weekly, twice-weekly) to plan for instruction while also giving

way for them to provide recommendations for instructional practices. Because of this

organizational structure, each of the principals was able to maintain a steady and sustained

presence in team planning sessions that emphasized the review of mathematics student

performance data with specific references to student performance groups (i.e., African American,

White, etc.) while using data to guide curriculum implementation and instructional delivery.

Prior to the start of the collaborative learning team meeting with all of the mathematics

teachers, Principal 1 asked all of them to bring in data from their first common assessment.

Using a tracking spreadsheet system, developed at the school site by Principal 1 and his

administrative team, teachers identified the students by student performance group (e.g., African

American, White) for those that had reached mastery level (at least 8 out of 10 questions

correct); near mastery level (6 to 7 questions correct); and those that needed remediation (5 or

fewer questions correct). Principal 1 projected the tracking spreadsheet on the SMART board.

He reminded the teachers to analyze the data after each common assessment so that, “we can

keep our eye out for how each group is doing all year long.” (Principal 1, O1, l75)

As a follow-up after the data was shared, Principal 1 asked, “How are you planning to

address the skill gaps that students have?” (Principal 1, O1, l88). Teachers discussed plans for

students under the near mastery and remediation headings, to conduct small groups over the next

two weeks. The small group rotations would be designed such that students would rotate to each

station with differentiated problems to address the concerns missed on the first common

assessment with at least one of those stations requiring the students to use manipulatives or

pictorial representations to demonstrate mastery, conceptual understanding, and connections to

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more abstract problems. Near mastery students would rotate to the teacher at least twice and

remediation students would rotate to the teacher at least three times next week. Principal 1 stated:

That is a good idea and I like how the team wants to do this across the board. Okay…so

for instructional walks next week, I’ll be looking for small groups, the students that are

identified to be in the small groups, and differentiated assignments during those rotations.

After the 4.5 weeks assessment, let’s check back in on how this strategy is working and

who has or has not shown improvement. (Principal 1, O1, l101-103)

Principal 2 used Student Detail by Question Reports (SDBQ) to help his teachers to

develop their growth goals for the school year. During a collaborative learning team meeting

with the eighth grade teachers, Principal 2 provided each teacher with a personalized SDBQ

spreadsheet that showed them each area that they performed well (any indicator above 50% of

students responding correctly) and those areas needing additional emphasis (any indicator at or

below 50% of students responding correctly).

Principal 3 conducted a data review during a Geometry collaborative learning team

meeting. Geometry is an area of focus for this school per the principal, “Although we had a 12

percent gain in Geometry last year on the SOLs, we are still third in the division for overall

performance out of four schools – that cannot continue” (Principal 3, O1, l3-4). During the

meeting, the principal reviewed the previous year’s SOL data – taking time to point out each

teachers’ overall performance and gains from the 2017-18 school year to the 2018-19 school

year. Principal 3 transitioned into a discussion about drilling down further to unpack the strands

using the SDBQ Report for each teacher. Teachers used highlighters to identify any item

descriptor at or below 50%. These were deemed by Principal 3 as areas of concern. Next,

Principal 3 asked the teachers to open their pacing guides and curriculum units so that the

134

content of concern could be mapped back to where these areas fit into the planning of

instruction. He then asked the teachers to highlight those skills on the Geometry pacing guide,

sharing with teachers:

Now you have a roadmap to the areas that we performed at low levels. This is how we

will begin to grow. The next step is to look into the curriculum resources and extract out

the materials that will help us see better results. (Principal 3, O1, l21-23)

The teachers spent the remainder of the planning block identifying different resources in the

given curriculum that they could implement moving forward for the first nine weeks of

instruction.

Principal 4 worked with teacher leaders and her administrative team to create a

spreadsheet to track student performance data by each teacher and by student performance group.

Because this school has attained a Level One in all student performance categories under the

Standards of Accreditation (SOA) in mathematics, the focus is to continue to close achievement

gaps between African American students and White students. Principal 4 had the eighth grade

mathematics teachers report on how their students performed on the second common assessment.

The team identified students that scored at or above 80% at the mastery level; students scoring

between 79% - 60% as near mastery; and, any student scoring 59% or below as needing

remediation. Principal 4 facilitated a discussion with the teachers to compare how African

American students performed to that of White students. On the second common assessment,

African American students attained an 81% pass rate while White students attained an 85% pass

rate, showing a 4% gap in performance. When compared to the first common assessment,

African American students attained a 75% pass rate while White students attained an 82% pass

135

rate – a 7% gap. Principal 4 complimented the teachers on working to close achievement gaps;

however, she noted there was still in a gap in performance:

We still have a gap in performance. We will continue to examine this area throughout the

year and monitor whether the gap is closing as we give the next common assessment. I

also want us to compare our performance from the common assessments to the CSA at

the end of this nine weeks. (Principal 4, O2, l50-51).

Likewise, Principal 5 led her sixth grade mathematics teachers in a discussion about

additional ways to improve performance between African American and White students as the

SOL data indicated from the previous year that there was an 8% gap between African American

and White student performance. The consensus reached was to incorporate 15-20 minutes of

teacher small group intervention three times per week. Students would rotate back to the teacher

in a small group based on their lower-performing areas as dictated by the data from the second

common assessment. Principal 5 stated at the meeting’s conclusion:

After the third common assessment, I’d like for us to come back together to review the

data and assess whether the student performance groups demonstrated any movement and

closure in the gaps that we’ve noted. (Principal 5, O1, l80-81)

Principal 6 facilitated a data meeting with the Algebra I collaborative learning team. The

meeting was used to review the first common assessment that the students took on translating

and evaluating expressions; applying the properties of real numbers; and, solving multi-step

equations. Principal 1 used chart paper for each skill that was addressed in the common

assessment. The chart paper was divided into three sections – mastery, near mastery, and

remediation. Then, she provided each teacher with a stack of post-it notes to write down the

names of the students that took the test with each teacher being given a different color to track

136

whose students were in what class. Teachers then placed the names of the students that earned at

least an 80% response rate (4 out of 5 areas per skill correct) in either the mastery, near mastery,

or remediation rows. During such time, the teachers discussed the most-missed questions on the

common assessment and what skills were areas of strength. Principal 6 then engaged in driving

questions such as:

What patterns in the data do you notice? Do you think that has to do with how the content

was taught? What are you planning to do during classes next week to spiral review based

upon who we know needs what help? (Principal 5, O2, l60-61, 78, 92)

Principal 7 met with the eighth grade mathematics teachers during their collaborative

team meeting to identify the skills, learning intentions, and success criteria as they mapped out

lesson plans for the following week. Further, because the team agreed to assess students every

two weeks, the teachers worked together to craft the next common assessment consisting of ten

questions – five on describing the subsets of the real number system and five on estimating and

determining the two consecutive integers between which a square root could be placed. Principal

7 asked probing questions about the importance of utilizing essential questions and

understandings when not only creating mathematics lesson plans, but also assessments:

How are questions asked to students in order to develop their conceptual understanding?

What does our review of student work reveal to us? As you develop your lesson plans

this week, please clearly identify how you are going to have students demonstrate their

understanding conceptually. Are you planning to use pictures or models? When doing so,

you must also make sure that how you deliver instruction is reflected in the assessment.

(Principal 7, O2, l32-35)

137

Observations of High School and Middle School Mathematics Teachers (Phase 2b)

To answer Research Question 2 (RQ2), “To what extent, if any, do culturally responsive

teaching practices impact the mathematics performance of African American students at the high

school and middle school levels?” two 90-minute observations of the 23 high school and middle

school mathematics teachers that advanced to the primary study were conducted (46 total

observations). An observation was completed by the researcher once prior to the 4.5 weeks

assessment and once prior to the Critical Skills Assessment deployed by the urban school

division. The demographics of the mathematics teachers of the primary study are detailed below

in Table 16.

Table 16

Demographics of High School and Middle School Mathematics Teachers (Purposive Sample, n=23)

Teacher School Type Sex Range of Teaching Experience

Teacher Certification

Teacher 2a Middle School [Fundamental] F 6 – 10 Middle Ed. 6-8:

Mathematics

Teacher 6a High School F 1 – 5 Mathematics

Teacher 4a Combined PreK-8 F 6 – 10 Middle Ed. 6-8: Mathematics

Teacher 5a Middle School F 16 – 20 Middle Ed. 6-8: Mathematics

Teacher 6b High School F 6 – 10 Mathematics

Teacher 5b Middle School F 11 – 15 Middle Ed. 6-8: Mathematics

Teacher 6c High School F 20 – 25 Mathematics

Teacher 2b Middle School [Fundamental] F 1 – 5 Mathematics

Teacher 6d High School F 11 – 15 Mathematics

138

Teacher 7a Middle School F 6 – 10 Mathematics

Teacher 7b Middle School F 6 – 10 Mathematics

Teacher 1a Combined PreK-8 F 6 – 10 Middle Ed. 6-8: Mathematics

Teacher 1b Combined PreK-8 F 11 – 15 Middle Ed. 6-8: Mathematics

Teacher 7c Middle School F 16 – 20 Middle Ed. 6-8:

Mathematics

Teacher 5c Middle School M 6 – 10 Middle Ed. 6-8: Mathematics

Teacher 1c Combined PreK-8 M 6 – 10 Middle Ed. 6-8: Mathematics

Teacher 6e High School F 6 – 10 Mathematics

Teacher 6f High School F 1 – 5 Mathematics

Teacher 4b Combined PreK-8 M 6 – 10 Middle Ed. 6-8: Mathematics

Teacher 3a High School F 11 – 15 Mathematics

Teacher 3b High School F 11 – 15 Mathematics

Teacher 2c Middle School [Fundamental] F 6 – 10 Middle Ed. 6-8:

Mathematics

Teacher 5d Middle School F 20 – 25 Middle Ed. 6-8: Mathematics

The researcher used the Reformed Teaching Observation Protocol (RTOP) – a tool

expressly designed to measure culturally responsive mathematics teaching practices at the high

school and middle school levels (Piburn et al., 2000). Table 17, Reformed Teaching Observation

Protocol (RTOP) (Purposive Sample, n=23), has been provided to illustrate the culturally

responsive teaching practices ratings of the purposive sample of mathematics teachers based on

139

46 total observations. The item ratings range from 0 to 4. A rating of 0 indicated a descriptor did

not occur during the observation; and, a rating of 4 is interpreted as highly reflective of the

lesson observed. Ratings of 1, 2, or 3 indicated the degree to which an item characterized the

actions of the teachers and not the number of occurrences. These data were rounded to the

nearest hundredth.

140 Table 17

Reformed Teaching Observation Protocol (RTOP) (Purposive Sample, n=23)

Item Number Item Indicator

Never Occurred

[0] 1 2 3

Very Descriptive

[4]

Lesson Design and Implementation

1. The instructional strategies and activities respected students’ prior knowledge and preconceptions inherent therein. 0.00% 0.00% 0.00% 56.70% 41.30%

2. The lesson was designed to engage students as members of a learning community. 0.00% 0.00% 0.00% 54.30% 45.70%

3. In this lesson, student exploration preceded formal presentation. 0.00% 2.20% 2.20% 17.40% 78.30%

4. This lesson encouraged students to seek and value alternative modes of investigation or of problem solving. 6.50% 0.00% 2.20% 39.10% 52.20%

5. The focus and direction of the lesson was often determined by ideas originating with students. 23.90% 17.40% 15.20% 28.30% 15.20%

Content

6. Propositional Knowledge: The lesson involved fundamental concepts of the subject. 6.50% 0.00% 2.20% 50.00% 41.30%

7. Propositional Knowledge: The lesson promoted strongly coherent conceptual understanding. 0.00% 0.00% 4.30% 39.10% 56.50%

8. Propositional Knowledge: The teacher had a solid grasp of the subject matter content inherent in the lesson. 0.00% 0.00% 0.00% 6.50% 93.50%

9. Propositional Knowledge: Elements of abstraction (i.e., symbolic representations, theory building) were encouraged when it was important to do so.

0.00% 2.20% 2.20% 17.40% 78.30%

10. Propositional Knowledge: Connections with other content disciplines and/or real world phenomena were explored and valued. 58.70% 6.50% 6.50% 10.90% 17.40%

11. Procedural Knowledge: Students used a variety of means (models, drawings, graphs, concrete materials, manipulatives, etc.) to represent phenomena. 13.00% 0.00% 2.20% 26.10% 58.70%

141 12. Procedural Knowledge: Students made predictions, estimations and/or

hypotheses and devised means for testing them. 10.90% 2.20% 4.30% 32.60% 50.00%

13. Procedural Knowledge: Students were actively engaged in though-provoking activity that often involved the critical assessment of procedures.

0.00% 0.00% 2.20% 37.00% 60.90%

14. Procedural Knowledge: Students were reflective about their learning. 0.00% 0.00% 6.50% 47.80% 45.70%

15. Procedural Knowledge: Intellectual rigor, constructive criticism, and the challenging of ideas were valued. 0.00% 0.00% 4.30% 34.80% 60.90%

Classroom Culture

16. Communicative Interactions: Students were involved in the communication of their ideas to others using a variety of means and media.

0.00% 0.00% 2.20% 43.50% 54.30%

17. Communicative Interactions: The teacher's questions triggered divergent modes of thinking.

0.00% 0.00% 4.30% 47.80% 47.80%

18. Communicative Interactions: There was a high proportion of student talk and a significant amount of it occurred between and among students.

0.00% 0.00% 2.20% 37.00% 60.90%

19. Communicative Interactions: Student questions and comments often determined the focus and direction of classroom discourse.

0.00% 0.00% 13.00% 32.60% 54.30%

20. Communicative Interactions: There was a climate of respect for what others had to say.

0.00% 0.00% 2.20% 21.70% 76.10%

21. Student/Teacher Relationships: Active participation of students was encouraged and valued.

0.00% 0.00% 2.20% 13.00% 84.80%

22. Student/Teacher Relationships: Students were encouraged to generate conjectures, alternative solution strategies, and ways of interpreting evidence.

0.00% 0.00% 2.20% 30.40% 67.40%

23. Student/Teacher Relationships: In general, the teacher was patient with the students.

0.00% 0.00% 0.00% 8.70% 91.30%

24. Student/Teacher Relationships: The teacher acted as a resource person, working to support and enhance student investigations.

0.00% 0.00% 0.00% 15.20% 84.80%

25. Student/Teacher Relationships: The metaphor “teacher as listener” was very characteristic of this classroom.

0.00% 0.00% 0.00% 8.70% 91.30%

Note. From “Reformed Teaching Observation Tool (RTOP) (Technical Report No. IN00-3)” by M. Piburn, D. Sawanda, K. Falconer, J. Turley, R. Benford, and I. Bloom, 2000, Arizona State University. Retrieved from http://www.public.asu.edu/~anton1/AssessArticles/Assessments/Biology%20Assessments RTOP%20Reference%20Manual.pdf. Copyright 2000 by the Arizona Collaborative for Excellence in the Preparation of Teachers. Reprinted with permission.

142 The RTOP is comprised of three subsets – Lesson Design and Implementation, Content,

and Classroom Culture. These three subsets served as the initial overarching categories, thus

leading the researcher to glean and extrapolate from the data – (1) what consistent behaviors

were embodied by culturally responsive teachers; (2) what culturally responsive teachers did to

build conceptual understanding; and, (3) what culturally responsive teachers did to affect the

classroom environment.

Table 17, Reformed Teaching Observation Protocol (RTOP) (Purposive Sample, n=23),

indicated a level of consensus – when disaggregating the data using the Very Descriptive header

– between 76.10% to 93.50%, for items 3, 8, 9, 20, 21, 23, 24, and 25. As revealed by the data,

the purposive sample of mathematics teachers were strong in content knowledge and the content

in which they were observed teaching (I8). Due to strong foundational content knowledge,

teachers were able to make connections using multiple concrete and pictorial representations to

build conceptual understanding to move students to abstract algorithms that involved student

discovery and exploration (I3, I9). Classroom environments observed were such that respect was

evident and reciprocal between teachers and students inclusive of valuing multiple ideas and

methods to arrive at solutions (I20). Student engagement was expected (I21). Teachers served as

patient facilitators using guiding questions leading to rich, reflective math discourse causing the

teacher to actively listen to students as they justified their reasoning during checks for

understanding (I23, I24, I25).

Examination of High School and Middle School Mathematics Student Performance Data

(Phase 3)

To answer Research Question 2 (RQ2), “To what extent, if any, do culturally responsive

teaching practices impact the mathematics performance of African American students at the high

143 school and middle school levels?” results of the 4.5 weeks assessment and the Critical Skills

Assessment were collected and examined. The African American to White student performance

data of the purposive sample were compared to those that did not advance to the primary study to

see if there was a significant difference in achievement between them.

4.5 weeks assessment data. Table 18, 4.5 Weeks Assessment Content by Course,

provides an overview of standards specific to the essential knowledge and skills that were

addressed in each assessment by course. The grade levels where the 4.5 weeks assessment is

given have been included. The 4.5 weeks assessments at the high school and middle school

levels of the urban school division each have 20 questions; however, the number of standards

assessed was determined by course pacing guides. The content of the Course I and Course I

Honors assessments were identical. Course II Honors and Pre-Algebra are accelerated courses

where multiple grade-level standards are taught over the school year; these assessments were the

same.

144 Table 18

4.5 Weeks Assessment Content by Course

Course Grade

Level(s) Standards Essential Knowledge and Skills

Course I Course I Honors

6

6.5a Multiply and divide fractions (proper or improper) and mixed numbers.

6.5b Solve single-step and multistep practical problems that involve addition, subtraction, multiplication, and division with fractions (proper or improper) and mixed numbers, with and without regrouping, that include like and unlike denominators of 12 or less. Answers are expressed in simplest form.

6.5c Solve multistep practical problems involving addition, subtraction, multiplication and division with decimals. Divisors are limited to a three-digit number, with decimal divisors limited to hundredths.

Pre-Algebra Course II Honors

6 7

6.2a Represent and determine equivalencies among fractions, mixed numbers, decimals, and percents.

6.2b Order no more than four positive rational numbers expressed as fractions (proper or improper), mixed numbers, decimals, and percents (decimals through thousandths, fractions with denominators of 12 or less or factors of 100). Ordering may be in ascending or descending order.

7.1a Recognize powers of 10 with negative exponents by examining patterns; and, represent a power of 10 with a negative exponent in fraction and decimal form.

8.1 Compare and order real numbers.

8.2 Describe the relationships between the subsets of the real number system.

8.3a Estimate and determine the two consecutive integers between which a square root lies.

8.3b Determine both the positive and negative square roots of a given perfect square.

Course II 7

7.1d Determine square roots of perfect squares.

7.1e Determine the absolute value of a rational number.

7.11 Evaluate algebraic expressions for given replacement values of the variables.

7.12 Solve two-step linear equations in one variable, including practical problems that require the solution of a two-step linear equation in one variable.

145

Course III 8





8.14a Evaluate an algebraic expression for given replacement values of the variables.

8.14b Simplify algebraic expressions in one variable.

Algebra I 7 – 12

A.1a Represent verbal quantitative situations algebraically.

A.1b Evaluate algebraic expressions for given replacement values of the variables.

A.4a Solve multistep linear equations in one variable algebraically.

Geometry 8 – 12

G.1a Use deductive reasoning to construct and judge the validity of a logical argument consisting of a set of premises and a conclusion to include identifying the converse, inverse, and contrapositive o a conditional statement.

G.1b Use deductive reasoning to construct and judge the validity of a logical argument consisting of a set of premises and a conclusion to include translating a short verbal argument into symbolic form.

G.1c Use deductive reasoning to construct and judge the validity of a logical argument consisting of a set of premises and a conclusion to include determining the validity of a logical argument.

G.3a Investigate and use formulas to determine distance, midpoint, and slope.

G.3b Apply slope to verify and determine whether lines are parallel or perpendicular.

G.4a Construct and justify the construction of a line segment congruent to a given line.

G.4f Construct and justify the construction of an angle congruent to a given angle.

Algebra II 9 – 12

AII.3a Solve absolute value linear equations and inequalities.

AII.6a Recognize the general shape of function families.

AII.6b Use knowledge of transformations to convert between equations and the corresponding graphs of functions.

146

AII.7a Investigate and analyze function families algebraically and graphically by determining domain, range, and continuity.

AII.7b Investigate and analyze function families algebraically and graphically by determining the intervals in which a function is increasing or decreasing.

Note. Adapted from the “Virginia 2016 Mathematics Standards of Learning Curriculum Framework: Introduction” by the Virginia Department of Education. Retrieved from http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/2016/cf/algebra1-cf.pdf. Copyright 2016 by the Virginia Department of Education.

147

Table 19, 4.5 Weeks Assessment Results of African American Students Compared to

White Students (n=37), provides the percentage of the African American and White student

population that passed the 4.5 weeks assessment by the high school and middle school

mathematics teachers of the purposive sample (n = 23) and of those that did not advance to the

primary study (n = 14). These percentages are rounded to the nearest whole number. The total

number of African American and White students that passed the assessment out of the total

tested has been provided for context and comparability. These data are denoted by African

American passers to total African American students tested (PA/TA) and White passers to total

White students tested (PW/TW). The overall performance is denoted in bold at the end of each

column. Any student scoring at least 60% on the assessment is deemed a passing score per

division-wide equating measures designed by the urban school division’s Department of

Research, Planning, and Evaluation. The achievement gap percentage between African American

students (A) and White students (W) was calculated by finding the difference (A – W) with the

result given as either a positive or negative percent. A gray bar separates the purposive sample of

teachers (denoted in bold) from those who did not advance to the primary study.

148

Table 19

4.5 Weeks Assessment Results of African American Students Compared to White Students (n=37)

Teacher Course

Percentage of

African American

Students Passing

the 4.5 Weeks

Assessment

(A)

Number of

African American

Students Passing the

4.5 Weeks Assessment

Out of the Total Tested

(PA/TA)

Percentage of

White Students

Passing the 4.5

Weeks Assessment

(W)

Number of

White Students

Passing the



(PW/TW)

Achievement

Gap

Percentage

(A – W)

Teacher 2a Course I 96% 43/45 82% 14/17 14%

Teacher 6a Geometry 67%, 33/50 70% 7/10 -3%


Teacher 5a Course I Honors 88% 35/40 63% 7/11 25%

Teacher 6b Algebra I 88% 38/43 100% 5/5 -12%

Teacher 5b Course I Honors 88% 35/40 67% 10/15 21%

Teacher 6c Geometry 81% 53/65 80% 16/20 1%

Teacher 2b Algebra I 100% 32/32 100% 21/21 0%

Teacher 6d Geometry 73% 29/40 73% 21/29 0%

Teacher 7a Algebra I 100% 23/23 100% 28/28 0%



Teacher 1b Course II Honors 97% 28/29 100% 16/16 -3%

Teacher 7c Course I 92% 23/25 100% 30/30 -8%

Teacher 5c Course III 85% 36/43 67% 20/30 18%

Teacher 1c Pre-Algebra 90% 18/20 100% 32/32 -10%

Teacher 6e Geometry 77% 41/53 80% 16/20 -3%

149

Teacher 6f Algebra II 96% 48/50 93% 15/15 3%

Teacher 4b Course I Honors 86% 30/35 100% 14/14 -14%

Teacher 3a Algebra II 93% 27/29 93% 37/40 0%

Teacher 3b Algebra II 100% 28/28 100% 42/42 0%

Teacher 2c Course II Honors 100% 31/31 83% 15/18 17%

Teacher 5d Course I 80% 24/30 100% 19/19 -20%

88% 746/847 89% 448/500 -1%

Teacher 6a Algebra II 75% 33/44 86% 13/15 -11%

Teacher 5a Course III 60% 36/60 62% 8/13 -2%

Teacher 7a Course II 69% 29/42 100% 12/12 -31%

Teacher 1a Algebra I 92% 36/39 100% 13/13 -8%


Teacher 7b Course II 62% 18/29 67% 19/28 -5%

Teacher 3b Algebra II 76% 23/30 83% 20/24 -7%

Teacher 6b Algebra II 55% 22/55 40% 12/30 15%

Teacher 6c Algebra I 81% 36/44 100% 23/23 -19%

Teacher 2a Algebra I 96% 29/30 100% 24/24 -4%


Teacher 7c Course I Honors 42% 11/26 83% 29/35 -41%



72% 426/592 82% 224/273 -10%

150

Table 19, 4.5 Weeks Assessment Results of African American Students Compared to

White Students (n=37), illustrates that of the purposive sample of high school and middle school

mathematics teachers, 746 out of 847 (88%) African American students passed the 4.5 weeks

assessment. Of the 500 White students taking the 4.5 weeks assessment, 448 passed of the

purposive sample of mathematics teachers (89%). When reading the table from top to bottom,

African American students performed at or above the same rate as White students for 15 out of

the 23 purposive sample of mathematics teachers (65%) [Teachers 2a, 4a, 5a, 5b, 6c, 2b, 6d, 7a,

7b, 1a, 5c, 6f, 3a, 3b, 2c] with the percentage achievement gap ranging from 0 (equal rate to

White students) to 25%. Eight of the 23 teachers (35%) experienced an achievement gap with

African American students performing below that of White students [Teachers 6a, 6b, 1b, 7c, 1c,

6e, 4b, 5d] with the percentage achievement gap ranging from -20% to -3%. The overall

achievement gap was -1% when comparing African American students to White students.

Of the high school and middle school mathematics teachers not qualifying for the

primary study, 426 out of 392 (72%) African American students and 224 out of 273 (82%) White

students passed the 4.5 weeks assessment. When reading the table from top to bottom beginning

at the gray demarcation bar, African American students performed at or above the same rate as

White students for 1 out of the 14 mathematics teachers (7%) [Teacher 6b] with a percentage

achievement gap of 15%. Thirteen out of the 14 teachers (93%) had an achievement gap with

African American students performing below that of White students [Teachers 6a, 5a, 7a, 1a, 3a,

7b, 3b, 6c, 2a, 4a, 7c, 5b, 4b] with the percentage achievement gap ranging from -41% to -1%.

The high school and middle school mathematics teachers of the primary study had a

higher percentage of African American students passing the 4.5 weeks assessment by 16%; a

151

higher percentage of White students passing the 4.5 weeks assessment by 7%; and, an

achievement gap difference of 9%.

Critical Skills Assessment data. Table 20, Critical Skills Assessment Content by

Course, provides an overview of standards specific to the essential knowledge and skills that

were addressed in each assessment by course. The grade levels where the Critical Skills

Assessment is given have been included. The Critical Skills Assessments at the high school and

middle school levels of the urban school division each have 30 questions; however, the number

of standards assessed was determined by course pacing guides. The increase in questions from

the 4.5 weeks assessment is reflective of the content spanning the entirety of the first nine weeks

of instruction. Consistent with the 4.5 weeks assessment, the content of the Course I and Course

I Honors assessments were the same; and, the Course II Honors and Pre-Algebra assessments

were the same.

152 Table 20

Critical Skills Assessment Content by Course

Course Grade

Level(s) Standards Essential Knowledge and Skills

Course I Course I Honors

6

6.5a Multiply and divide fractions (proper or improper) and mixed numbers.

6.5b Solve single-step and multistep practical problems that involve addition, subtraction, multiplication, and division with fractions (proper or improper) and mixed numbers, with and without regrouping, that include like and unlike denominators of 12 or less. Answers are expressed in simplest form.

6.5c Solve multistep practical problems involving addition, subtraction, multiplication and division with decimals. Divisors are limited to a three-digit number, with decimal divisors limited to hundredths.



Pre-Algebra Course II Honors

6 7



7.1a Recognize powers of 10 with negative exponents by examining patterns; and, represent a power of 10 with a negative exponent in fraction and decimal form.





8.4 Solve practical problems involving consumer applications by using proportional reasoning and computation procedures for rational numbers.



153

Course II 7

7.1d Determine square roots of perfect squares.

7.1e Determine the absolute value of a rational number.

7.2 Solve practical problems involving addition, subtraction, multiplication, and division with rational numbers expressed as integers, fractions (proper or improper), mixed numbers, decimals, and percents. Fractions may be positive or negative. Decimals may be positive or negative and are limited to the thousandths place.

7.11 Evaluate algebraic expressions for given replacement values of the variables.

7.12 Solve two-step linear equations in one variable, including practical problems that require the solution of a two-step linear equation in one variable.

7.13 Solve two-step linear inequalities in one variable, including practical problems that require the solution of a two-step linear inequality in one variable.

Course III 8





8.4 Solve practical problems involving consumer applications by using proportional reasoning and computation procedures for rational numbers.



Algebra I 7 – 12

A.1a Represent verbal quantitative situations algebraically.

A.1b Evaluate algebraic expressions for given replacement values of the variables.

A.4a Solve multistep linear equations in one variable algebraically.

A.4c Solve a literal equation for a specified variable.

A.5a Solve multistep linear inequalities in one variable algebraically and represent the solution graphically.

A.5c Solve practical problems involving linear inequalities.

Geometry 8 – 12 G.1a Use deductive reasoning to construct and judge the validity of a logical argument consisting of a set of premises and a conclusion to include identifying the converse, inverse, and contrapositive o a conditional statement.

154

G.1b Use deductive reasoning to construct and judge the validity of a logical argument consisting of a set of premises and a conclusion to include translating a short verbal argument into symbolic form.

G.1c Use deductive reasoning to construct and judge the validity of a logical argument consisting of a set of premises and a conclusion to include determining the validity of a logical argument.

G.2a Prove two or more lines parallel given angle measurements expressed numerically or graphically.

G.2b Solve problems, including practical problems, involving angles formed when parallel lines are intersected by a transversal.

G.3a Investigate and use formulas to determine distance, midpoint, and slope.

G.3b Apply slope to verify and determine whether lines are parallel or perpendicular.

G.3c Determine whether a figure has point symmetry, line symmetry, both, or neither.

G.4a Construct and justify the construction of a line segment congruent to a given line.

G.4b Construct and justify the constructions of the perpendicular bisector of a line segment.

G.4f Construct and justify the construction of an angle congruent to a given angle.

Algebra II 9 – 12

AII.1c Factor polynomials completely in one or two variables.

AII.2 Perform operations on complex numbers and express the results in simplest form using patterns of the powers of i.

AII.3a Solve absolute value linear equations and inequalities.

AII.3b Solve a quadratic equation over the set of complex numbers algebraically.

AII.6a Recognize the general shape of function families.

AII.6b Use knowledge of transformations to convert between equations and the corresponding graphs of functions.

AII.7a Investigate and analyze function families algebraically and graphically by determining domain, range, and continuity.

AII.7b Investigate and analyze function families algebraically and graphically by determining the intervals in which a function is increasing or decreasing.

AII.7d Identify the zeros and intercepts of a function presented algebraically or graphically.

Note. Adapted from the “Virginia 2016 Mathematics Standards of Learning Curriculum Framework: Introduction” by the Virginia Department of Education. Retrieved from http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/2016/cf/algebra1-cf.pdf. Copyright 2016 by the Virginia Department of Education.

155 Table 21, Critical Skills Assessment Results of African American Students Compared to

White Students (n=37), provides the percentage of the African American and White student

population that passed the Critical Skills Assessment by the high school and middle school

mathematics teachers of the purposive sample (n = 23) and of those are not a part of the primary

study (n = 14). These percentages are rounded to the nearest whole number. For consistency,

context, and linearity to the 4.5 weeks assessment data presentation, the total number of African

American and White students that passed the assessment out of the total number tested has been

provided. As with the 4.5 weeks assessment, any student scoring at least 60% on the assessment

is deemed a passing score per division-wide equating measures designed by the urban school

division’s Department of Research, Planning, and Evaluation. The achievement gap percentage

between African American students and White students was calculated by finding the difference

(A – W) with the result given as either a positive or negative percent. A gray bar delineates the

purposive sample of teachers (denoted in bold) from those who did not move forward to the

primary study. It is to be noted that the total number of students tested slightly fluctuated

accounting for student attendance (absences) or student additions to class sizes during the testing

window from the 4.5 weeks assessment to the Critical Skills Assessment. A subscript lowercase

a denotes such occurrences when compared to the 4.5 weeks assessment data.

156

Table 21

Critical Skills Assessment Results of African American Students Compared to White Students (n=37)

Teacher Course

Percentage of

African American

Students Passing

the 4.5 Weeks

Assessment

[A]

Number of

African American

Students Passing the



[PA/TA]

Percentage of

White Students

Passing the 4.5

Weeks Assessment

[W]

Number of

White Students

Passing the



[PW/TW]

Achievement

Gap

Percentage

[A – W]


Teacher 6a Geometry 76%, 38/50 80% 8/10 -4%




Teacher 5b Course I Honors 95% 35/37a 73% 8/11a 22%

Teacher 6c Geometry 85% 55/65 84% 16/19a 1%

Teacher 2b Algebra I 100% 30/30a 100% 21/21 0%

Teacher 6d Geometry 75% 30/40 71% 20/28a 4%




Teacher 1b Course II Honors 93% 27/29 100% 16/16 -7%

Teacher 7c Course I 100% 25/25 100% 30/30 0%

Teacher 5c Course III 83% 33/40 a 71% 20/28a 12%

Teacher 1c Pre-Algebra 100% 20/20 100% 30/30a 0%

Teacher 6e Geometry 81% 43/53 85% 17/20 -4%

157

Teacher 6f Algebra II 96% 48/50 93% 15/15 3%

Teacher 4b Course I Honors 86% 30/35 93% 13/14 -7%


Teacher 3b Algebra II 100% 24/24a 100% 41/41a 0%

Teacher 2c Course II Honors 100% 31/31 89% 16/18 11%

Teacher 5d Course I 87% 26/30 100% 19/19 -13%

90% 754/835 91% 444/489 -1%


Teacher 5a Course III 57% 32/56 a 80% 8/10 a -23%



Teacher 3a Algebra II 66% 27/41a 80% 8/10 -14%

Teacher 7b Course II 69% 20/29 59% 17/29a 10%

Teacher 3b Algebra II 80% 24/30 83% 20/24 -3%

Teacher 6b Algebra II 38% 20/53a 37% 11/30 1%

Teacher 6c Algebra I 83% 35/42a 100% 23/23 -17%

Teacher 2a Algebra I 89% 25/28a 100% 23/23a -11%


Teacher 7c Course I Honors 34% 9/26 77% 27/35 -43%

Teacher 5b Course II 62% 36/58a 100% 15/16 -38%

Teacher 4b Course II 88% 44/50a 91% 10/11a -3%

70% 410/586 80% 215/269 -10% Note. a = total number of students tested slightly fluctuated accounting for student attendance (absences) or student additions to class sizes during the testing

window from the 4.5 weeks assessment to the Critical Skills Assessment.

158

Table 21, Critical Skills Assessment Results of African American Students Compared to

White Students (n=37), illustrates that of the purposive sample of high school and middle school

mathematics teachers, 754 out of 835 (90%) African American students passed the Critical Skills

Assessment. There were 444 out of 489 (91%) White students that passed the Critical Skills

Assessment of the purposive sample of mathematics teachers. When reading the table from top

to bottom, African American students performed at or above the same rate as White students for

17 out of the 23 purposive sample of mathematics teachers (74%) [Teachers 2a, 4a, 5a, 6b, 5b,

6c, 2b, 6d, 7a, 7b, 1a, 7c, 5c, 1c, 6f, 3b, 2c] with the percentage achievement gap ranging from 0

(equal rate to White students) to 22%. Six of the 23 teachers (26%) experienced an achievement

gap with African American students performing below that of White students [Teachers 6a, 1b,

6e, 4b, 3a, 5d] with the percentage achievement gap ranging from -13% to -2%. The overall

achievement gap was -1% when comparing African American students to White students.

Of the high school and middle school mathematics teachers not qualifying for the

primary study, 410 out of 586 (70%) African American students and 215 out of 269 (80%) White

students passed the Critical Skills Assessment. When reading the table from top to bottom

beginning at the gray demarcation bar, African American students performed at or above the

same rate as White students for three out of the 14 mathematics teachers (21%) [Teachers 1a, 6b,

7b] with a percentage achievement gap ranging from 0% to 10%. Eleven out of the 14 teachers

(79%) had an achievement gap with African American students performing below that of White

students [Teachers 6a, 5a, 7a, 3a, 3b, 6c, 2a, 4a, 7c, 5b, 4b] with the percentage achievement gap

ranging from -43% to -3%.

The high school and middle school mathematics teachers of the primary study had a

higher percentage of African American students passing the Critical Skills Assessment by 20%;

159

a higher percentage of White students passing the Critical Skills Assessment by 11%; and, an

achievement gap difference of 9%.

Statistical significance of student performance data. Table 22, Two-Proportions Z-

Test to Determine Statistical Significance of High School and Middle School Mathematics

Student Performance Data, captures the results from the two-proportions z-test used to test for

differences in proportions and if there was a statistical significance in the 4.5 weeks assessment

results and the Critical Skills Assessment results of the teachers within the primary study and to

those that did not advance to the primary study. Before the two-proportion z-test was used, a

significance level of 0.01 (!) was set. Notations for headers are explained directly below Table

22.

160 Table 22

Two-Proportions Z-Test to Determine Statistical Significance of High School and Middle School Mathematics Student Performance Data


! = 0.01 H0: AACR = AANCR H1: AACR > AANCR

! = 0.01 H0: WCR = WNCR H1: WCR > WNCR

! = 0.01 H0: TCR= TNCR H1: TCR > TNCR

African American Students of Culturally Responsive Teachers

African American Students of Non-Culturally Responsive Teachers

White Students of Culturally Responsive Teachers

White Students of Non-Culturally Responsive Teachers

Students of Culturally Responsive Teachers (Total)

Students of Non-Culturally Responsive Teachers (Total)

x1 = 746 x2 = 426 x1 = 448 x2 = 224 x1 = 1194 x2 = 650

n1 = 847 n2 = 592 n1 = 500 n2 = 273 n1 = 1347 n2 = 865

p = 5.06E-15* p = 0.001* p = 4.53E-17*

Critical Skills Assessment

! = 0.01 H0: AACR = AANCR H1: AACR > AANCR

! = 0.01 H0: WCR = WNCR H1: WCR > WNCR

! = 0.01 H0: TCR= TNCR H1: TCR > TNCR

African American Students of Culturally Responsive Teachers

African American Students of Non-Culturally Responsive Teachers

White Students of Culturally Responsive Teachers

White Students of Non-Culturally Responsive Teachers

Students of Culturally Responsive Teachers (Total)

Students of Non-Culturally Responsive Teachers (Total)

x1 = 754 x2 = 410 x1 = 444 x2 = 215 x1 = 1198 x2 = 625

n1 = 835 n2 = 586 n1 = 489 n2 = 269 n1 = 1324 n2 = 855

p = 5.57E-23* p = 1.07E-5* p = 4.32E-27*

Note. ! = significance level at 0.01; x1 = students passing the assessment of culturally responsive teachers; n1 = total number of students passing the assessment of culturally

161 responsive teachers; x2 = students passing the assessment of non-culturally responsive teachers; n2 = total number of students passing the assessment of non-culturally responsive teachers; H0 = null hypothesis; H2 = alternative hypothesis; AACR = African Americans students of culturally responsive teachers; AANCR = African Americans students of non-culturally responsive teachers; WCR = White students of culturally responsive teachers; WNCR = White students of non-culturally responsive teachers; TCR = Students of culturally responsive teachers (total); TNCR = Students of non-culturally responsive teachers (total) *p = calculated probability, p < 0.01.

162

Table 22, Two-Proportions Z-Test to Determine Statistical Significance of High School

and Middle School Mathematics Student Performance Data, illustrates that students with

culturally responsive teachers performed better on division-wide assessments, with the effect of

reducing the achievement gap between African American and White students compared to

teachers not self-identified as having high levels of cultural responsiveness with results

statistically significant at the 0.01 level after conducting a two-proportions z-test.

Culturally Responsive Leadership Practices Survey (Phase 4)

To answer Research Question 1 (RQ1), “To what extent, if any, do principals at the high

school and middle school levels that exemplify culturally responsive leadership influence

mathematics teachers’ use of culturally responsive teaching that results in building conceptual

understanding in mathematics?” the researcher-developed Culturally Responsive Leadership

Practices Survey (Appendix L) created from the culturally responsive leadership indicators

provided in the literature base, was deployed via Qualtrics. The purposive sample of

mathematics teachers (n = 23) and those that did not advance to the primary study (n = 14)

completed the survey with a 100% response rate. The survey was given to the mathematics

teachers to assist the researcher in understanding congruity or differences in perceptions of the

leadership practices of their principal; and, to help the researcher derive meaning and create

parallelism from the data yielded from the preliminary survey results and observations of the

purposive sample of principals. Eighteen indicators of culturally responsive leaders comprised

the survey, inclusive of a rating scale of 0 to 3 with 0 being none (no evidence), 1 (low), 2

(moderate), and 3 (high) to capture the principals’ level of culturally responsive leadership.

Because there are 18 indicators, the maximum point total would have resulted in 54 points.

163

Description and explanation of data. The data from the Culturally Responsive

Leadership Survey are presented by the overall response rate of the 37 mathematics teachers of

the urban school division of study; the 23 mathematics teachers who advanced to the primary

study (purposive sample); and, then the data of the 14 mathematics who did not advance to the

primary study (non-qualifiers).

Culturally responsive leadership survey results of high school and middle school

mathematics teachers (overall). The data from the survey are provided in Table 23, Culturally

Responsive Survey Results of High School and Middle School Mathematics Teachers by Item

(Overall, n=37), demonstrating the overall item response rate of each mathematics teacher.

Similar to the preliminary screening surveys, the mean and standard deviation of these data were

reported to illustrate consensus and the divergence of responses. The percent response rate,

mean, and standard deviation have been rounded to the nearest hundredth.

164 Table 23

Culturally Responsive Leadership Survey Results of High School and Middle School Mathematics Teachers by Item (Overall, n=37)


No evidence

[0]

Low [1]

Moderate [2]

High [3]

Mean ["#]

Standard Deviation

[SD]

1. Provides students with social, emotional, and academic supports. 2.70% 5.40% 43.24% 48.65% 2.38 0.72

2. Recognizes and celebrates the strengths of students. 0.00% 8.10% 29.73% 62.16% 2.54 0.65

3. Influences the school’s climate by being inclusive of cultural diversity. 8.10% 16.22% 29.73% 45.96% 2.14 0.98

4. Leverages rapport and relationships with families, community, and external partners to create inclusivity within the school.

10.81% 13.51% 35.14% 40.4% 2.05 0.99

5. Opposes and rejects deficit thinking about minority groups. Instead, exemplifies a warm, yet firm stance of high expectations for all students.

2.70% 2.70% 35.14% 59.46% 2.51 0.69

6. Promotes equality and advocates for the learning environment to reflect the multiculturalism that students bring to school.

8.10% 21.62% 18.92% 51.35% 2.14 1.03

7. Embraces restorative social justice in order to minimize exclusionary practices.

5.40% 10.81% 32.43% 51.35% 2.30 0.88

8. Hires qualified personnel having mastered their content, thereby having instructional staff that can provide experiences for their students that increase depth of mathematics understanding.

10.81% 2.70% 43.24% 43.24% 2.24 0.86

9. Matches students to the appropriate mathematics teacher and places the most experienced teachers with students in need of additional supports to master the content.

10.81% 13.51% 48.65% 27.03% 1.97 0.87

10. Recognizes the importance of mathematics teachers and sound mathematics teaching. 2.70% 2.70% 13.51% 81.08% 2.73 0.65

165

11. Communicates instructional expectations that are in alignment with high-quality and rigorous mathematics. 2.70% 2.70% 10.81% 83.78% 2.76 0.64

12. Ensures that teaching and learning are made relevant and meaningful to students. 0.00% 0.00% 37.84% 62.16% 2.62 0.49

13. Fosters and encourages mathematics teachers’ building of conceptual understanding in order to deepen mathematical thinking and problem solving as a process for students.

13.51% 5.40% 24.32% 56.76% 2.24 1.06

14. Frequently monitors and reviews mathematics student performance data individually and collaboratively with mathematics teachers in order to make just-in-time adjustments to set students up for success.

5.40% 10.81% 32.43% 51.35% 2.30 0.88

15. Frequently conducts observations of mathematics teachers and provides clear and timely feedback. 10.81% 8.10% 32.43% 48.65% 2.19 1.00

16. Constructs the master schedule to allow mathematics teachers to meet frequently (e.g., weekly, bi-weekly) to plan for instruction and to discuss mathematics student performance.

2.70% 0.00% 8.10% 89.19% 2.81 0.57

17.

Regularly attends mathematics teacher and/or team planning block(s) to hear how teachers plan for instruction; and, during such time, provides suggestions for instructional delivery and monitoring of student progress.

8.10% 13.51% 32.43% 45.96% 2.14 0.95

18. Persistent in the implementation of culturally responsive teaching through professional development to enhance teachers’ equity pedagogy.

13.51% 24.32% 32.43% 29.73% 1.78 1.03

166 Table 23, Culturally Responsive Leadership Survey Results of High School and Middle

School Mathematics Teachers by Item (Overall, n=37), indicated a level of consensus – when

disaggregating the data using the High header ordered from greatest to least – between 81.08% to

89.19%, a mean ranging from 2.73 to 2.81, and a standard deviation ranging from 0.65 to 0.57

respectively for items 10, 11, and 16. Respondents shared that the master schedule has been

constructed by their principal that allows mathematics teachers to meet to discuss instructional

practices and student performance data (I16). Instructional expectations are communicated that

reflect high-quality, cognitively appropriate mathematics and such mathematics instruction is

soundly delivered (I11, I10).

Items 2, 5, 6, 7, 12, 13, and 14 yielded a level of consensus between 51.35% to 62.16%, a

mean ranging from 2.30 to 2.62, and a standard deviation between 1.06 to 0.49. Data indicated a

somewhat larger spread in responses than the abovementioned. Respondents indicated that their

principals value and recognize students for their strengths and diverse backgrounds, thus

capitalizing on inclusionary practices with a nurturing nature while reducing deficit thinking that

adversely impact students of color (I2, I5, I6, I7). Regarding instructional leadership practices,

respondents shared that their principal works to ensure that teaching and learning are relatable to

students through problem-solving and the building of conceptual understanding to broaden the

scope of mathematical knowledge (I12, I13). As teachers create environments where building

conceptual understanding is expected, respondents specified that their principal monitored and

reviewed mathematics student performance data regularly and frequently so that intervention and

remediation are promptly leveraged (I14).

Items 1, 3, 4, 8, 15, and 17 yielded a level of consensus between 40.40% to 48.65%, a

mean ranging from 2.05 to 2.38, and a standard deviation between 1.00 to 0.72. Respondents

167 indicated their principal provided students with social, emotional, and academic supports due to

their influence on their school’s climate grounded in valued placed on cultural diversity (I1, I3).

Community partnerships and parental involvement are harnessed to support inclusive practices

(I4). The mathematics teachers shared that their principal regularly attended collaborative

learning team meetings and conducted frequent observations to help inform the next steps in

instructional behaviors (I15, I17). Respondents believed that their principal hired qualified staff

that could provide a depth of understanding of mathematics (I8).

The lowest consensus from the respondents was around the provision of culturally

responsive professional development to enhance equitable teaching practices (I18, 29.73%

response rate, !" of 1.78, and SD of 1.03) and consistent placement of students with the most

seasoned teacher that can move students forward (I9, 27.03% response rate, !" of 1.97, and SD of

0.87).

Table 24, Culturally Responsive Leadership Survey Results of High School and Middle

School Mathematics Teachers (Individual), provides the individual response rate of the 37 high

school and middle school mathematics teachers by item given by responses selected in numeral

form assessing the culturally leadership practices of their principal. The point total has been

included in the last column. A gray bar separates the mathematics teachers of the purposive

sample (denoted in bold) from those that did not move forward to the primary study.

168 Table 24

Culturally Responsive Leadership Survey Results of High School and Middle School Mathematics Teachers (Individual)

Teacher I 1

I 2

I 3

I 4

I 5

I 6

I 7

I 8

I 9

I 10

I 11

I 12

I 13

I 14

I 15

I 16

I 17

I 18 Total

Teacher 2a 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 53 Teacher 6a 3 3 3 2 3 3 3 2 2 3 3 3 2 3 3 3 2 1 47 Teacher 4a 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 3 53 Teacher 5a 2 2 2 2 3 3 3 2 3 3 3 3 3 3 3 3 3 3 49 Teacher 6b 3 3 3 3 3 3 2 2 2 3 3 3 3 3 2 3 2 3 49 Teacher 5b 3 3 2 3 3 3 3 3 3 3 3 2 3 3 3 2 3 2 50 Teacher 6c 1 2 1 1 3 1 2 2 2 3 3 2 2 1 1 3 2 1 33 Teacher 2b 3 3 3 3 1 1 1 2 2 3 3 3 3 3 3 3 3 2 45 Teacher 6d 3 3 2 2 2 3 3 2 1 3 3 2 2 3 3 3 1 2 43 Teacher 7a 2 3 3 2 3 3 2 2 2 3 3 3 3 2 2 3 2 2 45 Teacher 7b 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 53 Teacher 1a 2 2 3 2 3 3 3 2 2 3 3 3 3 3 3 3 3 2 48 Teacher 1b 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 3 51 Teacher 7c 3 3 2 3 2 2 3 3 3 3 3 3 3 3 3 3 3 2 50 Teacher 5c 2 3 1 1 2 1 2 2 2 3 3 3 3 3 3 3 3 2 42 Teacher 1c 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 53 Teacher 6e 2 3 2 2 3 2 2 0 0 3 3 3 2 2 0 0 0 2 31 Teacher 6f 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 53 Teacher 4b 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 54 Teacher 3a 2 2 2 2 2 1 2 3 2 0 3 2 1 0 0 3 0 1 28

169 Teacher 3b 2 2 1 0 2 0 2 0 0 2 0 2 0 1 0 3 0 0 17 Teacher 2c 2 3 1 1 2 1 1 0 2 3 3 2 3 1 1 3 1 1 31 Teacher 5d 0 1 0 2 0 0 1 2 2 2 2 2 0 2 0 3 1 0 20

Teacher 6a 2 2 3 2 3 2 2 3 2 3 3 2 3 2 2 3 2 2 43 Teacher 5a 3 1 1 0 2 2 3 2 3 1 3 2 0 1 2 3 3 3 35 Teacher 7a 3 3 3 3 3 3 3 3 0 3 3 3 0 0 3 3 2 3 44 Teacher 1a 3 3 2 2 3 2 2 2 2 3 3 3 3 2 3 3 1 1 43 Teacher 3a 2 2 3 1 3 3 3 2 2 2 2 2 1 2 2 3 2 0 37 Teacher 7b 3 3 3 3 3 3 3 2 2 3 2 3 2 3 3 3 3 1 48 Teacher 3b 2 2 2 2 3 3 2 3 2 2 3 3 2 2 2 3 2 1 41 Teacher 6b 3 3 3 3 2 3 3 3 2 3 3 3 3 3 3 3 3 1 50 Teacher 6c 2 3 2 2 3 1 0 1 1 3 2 3 2 2 3 3 3 2 38 Teacher 2a 2 2 0 0 2 0 0 3 2 3 3 2 3 3 3 3 2 0 30 Teacher 4a 2 2 2 2 2 2 2 2 1 2 1 3 2 2 2 2 2 2 35 Teacher 7c 2 3 2 3 3 2 2 3 2 3 3 2 3 2 2 3 3 2 45 Teacher 5b 1 1 0 0 2 1 3 2 1 3 3 2 0 2 1 3 1 0 26 Teacher 4b 2 2 1 1 2 1 1 2 1 3 3 2 2 2 2 2 2 1 32

170 Table 24, Culturally Responsive Leadership Survey Results of High School and Middle

School Mathematics Teachers (Individual), reflects the individual scores of the 37 high school

and middle school mathematics teachers by item and total point value assigned to each principal.


mathematics teachers (purposive sample). The data of the 23 mathematics teachers of the

purposive sample has been provided in Table 25, Culturally Responsive Leadership Survey

Results of High School and Middle School Mathematics Teachers (Purposive Sample, n =23).

Each response rate, mean, and standard deviation have been rounded to the nearest hundredth.


School Mathematics Teachers Rank Ordered by Consensus and Mean (Purposive Sample,

n=23), provides a rank ordered consensus to which the 23 high school and middle school

mathematics teachers considered and assessed the culturally responsive leadership practices

exhibited by their individual principal. Consensus was determined by at least an 80% percent

rating in the single category of High on the 3 point scale (i.e., 0, 1, 2, 3), and at least a mean of

2.75. The indicators meeting or exceeding these parameters have been denoted as such above the

gray bar and have been highlighted in bold.

171 Table 25

Culturally Responsive Survey Results of High School and Middle School Mathematics Teachers (Purposive Sample, n=23)


No evidence

[0]

Low [1]

Moderate [2]

High [3]

Mean ["#]

Standard Deviation

[SD]





4.35% 13.04% 34.78% 47.83% 2.26 0.86


4.35% 4.35% 30.43% 60.87% 2.48 0.79


8.70% 21.74% 8.70% 60.87% 2.22 1.09


0.00% 13.04% 30.43% 56.52% 2.43 0.73


13.04% 0.00% 43.48% 43.48% 2.17 0.98


8.70% 4.35% 47.83% 39.13% 2.17 0.89



172



4.35% 8.70% 17.39% 69.57% 2.47 0.95


4.35% 13.04% 13.04% 69.57% 2.47 0.90



4.35% 0.00% 8.70% 86.96% 2.78 0.67

17.


13.04% 13.04% 26.09% 47.83% 2.09 1.08


8.70% 17.39% 34.78% 39.13% 2.04 0.98

173 Table 26

Culturally Responsive Leadership Survey Results of High School and Middle School Mathematics Teachers Rank Ordered by Consensus and Mean (Purposive Sample, n=23)


No evidence

[0]

Low [1]

Moderate [2]

High [3]

Mean ["#]

Standard Deviation

[SD]




4.35% 0.00% 8.70% 86.96% 2.78 0.67




4.35% 8.70% 17.39% 69.57% 2.47 0.95


4.35% 13.04% 13.04% 69.57% 2.47 0.90


4.35% 4.35% 30.43% 60.87% 2.48 0.79

6. Promotes equality and advocates for the learning environment to reflect the multiculturalism that students bring to school. 8.70% 21.74% 8.70% 60.87% 2.22 1.09


7. Embraces restorative social justice in order to minimize exclusionary practices. 0.00% 13.04% 30.43% 56.52% 2.43 0.73


174 15. Frequently conducts observations of mathematics teachers and provides

clear and timely feedback. 17.39% 8.70% 21.74% 52.17% 2.09 1.16

4. Leverages rapport and relationships with families, community, and external partners to create inclusivity within the school. 4.35% 13.04% 34.78% 47.83% 2.26 0.86

17.


13.04% 13.04% 26.09% 47.83% 2.09 1.08


13.04% 0.00% 43.48% 43.48% 2.17 0.98


8.70% 4.35% 47.83% 39.13% 2.17 0.89


8.70% 17.39% 34.78% 39.13% 2.04 0.98

175

Tables 25 and 26, Culturally Responsive Leadership Survey Results of High School and

Middle School Mathematics Teachers (Purposive Sample, n=23) and the Culturally Responsive

Leadership Survey Results of High School and Middle School Mathematics Teachers Rank

Ordered by Consensus and Mean (Purposive Sample, n=23) correspond to the 23 high school

and middle school mathematics teachers that advanced to the primary study. As the data were

sorted using the High header from greatest to least, items 10, 11, and 16 had a response rate of

86.96% to 91.30%, a mean of 2.78 to 2.82, and a standard deviation of 0.65 to 0.67. Coalescence

around these three items was similar to the whole group (n = 37) selection (albeit in slightly

different rank order) with the whole group rank ordered by 16, 11 and 10 and the purposive

sample rank ordered by 11, 10, 16. Respondents provided that their principal communicates

instructional expectations (I11); recognizes aligned mathematics instruction (I10); and,

constructs the master schedule to allow mathematics teachers to collaborate on lesson design and

implementation as well as to review and to monitor student performance data (I16).

The second tier of responses – items 2, 5, 6, 12, 13, and 14 – yielded a level of consensus

between 60.87% to 73.91%, a mean ranging from 2.22 to 2.70, and a standard deviation between

1.09 to 0.47. These same items, except item 7, were ranked similarly from the whole group of

mathematics teachers (n = 37). The third tier of responses – items 1, 3, 4, 7, 8, 15, and 17 –

produced a level of consensus between 43.48% to 56.52%, a mean ranging from 2.09 to 2.43,

and a standard deviation between 1.00 to 0.72 – indicating even greater variance in responses

than the second tier of items. Similar to the whole group responses, the lowest consensus was

reflected for item 9 (39.13% response rate, !" of 2.17, and SD of 0.89) and item 18 (39.13%

response rate, !" of 2.04, and SD of 0.98).

176


mathematics teachers (non-qualifiers). Table 27, Culturally Responsive Leadership Survey

Results of High School and Middle School Mathematics Teachers (Non-Qualifiers, n=14), has

been constructed to provide the responses by percentage rate for each header along with the

mean and standard deviation all rounded to the nearest hundredth for those mathematics teachers

not within the purposive sample.


School Mathematics Teachers Rank Ordered by Consensus and Mean (Non-Qualifiers, n=14),

has been given to illustrate the assessment of culturally responsive leadership practices to which

the 14 high school and middle school mathematics teachers not moving forward to the primary

study identified of their individual principal. Consensus was determined by at least an 80%

percent rating in the single category of High on the 3 point scale (i.e., 0, 1, 2, 3), and at least a

mean of 2.75. The indicators meeting or exceeding these parameters have been denoted as such

above the gray bar and have been highlighted in bold.

177 Table 27

Culturally Responsive Leadership Survey Results of High School and Middle School Mathematics Teachers (Non-Qualifiers, n=14)


No evidence

[0]

Low [1]

Moderate [2]

High [3]

Mean ["#]

Standard Deviation

[SD]





21.42% 14.28% 35.71% 28.57% 1.71 1.14


0.00% 0.00% 42.86% 57.14% 2.57 0.51


7.14% 21.42% 35.71% 35.71% 2.00 0.96


14.28% 7.14% 35.71% 42.86% 2.07 1.07


0.00% 7.14% 50.00% 42.86% 2.36 0.63


7.14% 28.57% 57.14% 7.14% 1.64 0.74



178



21.42% 7.14% 35.71% 35.71% 1.85 1.17


7.14% 7.14% 64.23% 21.42% 2.00 0.78



0.00% 0.00% 14.28% 85.71% 2.85 0.36

17.


0.00% 14.28% 50.00% 35.71% 2.21 0.70


21.42% 35.71% 28.57% 14.28% 1.35 1.01

179 Table 28

Culturally Responsive Leadership Survey Results of High School and Middle School Mathematics Rank Ordered by Consensus and Mean (Non-Qualifiers, n=14)


No evidence

[0]

Low [1]

Moderate [2]

High [3]

Mean ["#]

Standard Deviation [SD]


0.00% 0.00% 14.28% 85.71% 2.85 0.36



5. Opposes and rejects deficit thinking about minority groups. Instead, exemplifies a warm, yet firm stance of high expectations for all students. 0.00% 0.00% 42.86% 57.14% 2.57 0.51



7. Embraces restorative social justice in order to minimize exclusionary practices. 14.28% 7.14% 35.71% 42.86% 2.07 1.07


0.00% 7.14% 50.00% 42.86% 2.36 0.63




180

6. Promotes equality and advocates for the learning environment to reflect the multiculturalism that students bring to school. 7.14% 21.42% 35.71% 35.71% 2.00 0.96


21.42% 7.14% 35.71% 35.71% 1.85 1.17

17. Regularly attends mathematics teacher and/or team planning block(s) to hear how teachers plan for instruction; and, during such time, provides suggestions for instructional delivery and monitoring of student progress.

0.00% 14.28% 50.00% 35.71% 2.21 0.70

4. Leverages rapport and relationships with families, community, and external partners to create inclusivity within the school. 21.42% 14.28% 35.71% 28.57% 1.71 1.14


7.14% 7.14% 64.23% 21.42% 2.00 0.78

18. Persistent in the implementation of culturally responsive teaching through professional development to enhance teachers’ equity pedagogy. 21.42% 35.71% 28.57% 14.28% 1.35 1.01


7.14% 28.57% 57.14% 7.14% 1.64 0.74

181 Tables 27 and 28, Culturally Responsive Leadership Survey Results of High School and

Middle School Mathematics Teachers (Non-Qualifiers, n=14) and the Culturally Responsive

Leadership Survey Results of High School and Middle School Mathematics Teachers Rank

Ordered by Consensus and Mean (Non-Qualifiers, n=14) reflect the responses of the 14 high

school and middle school mathematics teachers that did not advance to the primary study. As the

data were sorted using the High header from greatest to least, item 16 had a response rate of

85.71%, a mean of 2.85, and a standard deviation of 0.36. Item 16 remains a high consensus

indicator, reflective of the whole group and purposive sample responses.

Though not meeting the parameters of at least an 80% consensus response rate and mean

of at least 2.75, items 10 and 11 (comprising the upper second tier of responses) each had a

71.43% response rate, a mean of 2.64, and standard deviation of 0.63 – a reflection of two

indicators still particularly regarded as influential to and highly assessed by the non-qualifiers.

Within this tier, items 2, 5, 7, 8, 12, and 15 provided a level of consensus between 42.86% to

57.14%, a mean ranging from 2.07 to 2.57, and a standard deviation between 1.07 to 0.51. Items

2, 5, and 12 were similarly ranked to that of the whole group of mathematics teachers (n = 37)

and that of the purposive sample (n = 23).

The third tier of responses – items 1, 3, 4, 6, 13, 14 and 17 – produced a level of

consensus between 21.42% to 35.71%, a mean ranging from 1.71 to 2.28, and a standard

deviation between 1.17 to 0.61. Similar to the whole group and purposive sample responses, the

least consensus was reflected for items 9 (14.28% response rate, !" of 1.35, and SD of 1.01) and

18 (7.14% response rate, !" of 1.64, and SD of 0.74). The comparison of responses will be further

delineated and synthesized in Chapter 5 as a finding.

182 Data Analysis Summary

This chapter provided an analysis of the data collected from a qualitative study that began

with a preliminary screening survey measuring culturally responsive leadership and teaching

through a fixed criterion distributed to high school and middle school principals and mathematics

teachers of an urban school division. Observations of the purposive sample of principals and

mathematics teachers followed. An examination of student performance data from the 4.5 weeks

assessment and the Critical Skills Assessment occurred to see if there were any significant gaps

in achievement between the purposive sample of mathematics teachers to those who did not

advance to the primary study for African American students versus their White counterparts. A

culminating survey was deployed to the purposive sample of mathematics teachers and those not

within the purposive sample to provide insight into the culturally responsive leadership practices

of their principals. The summary of these analyzed data follows.

Preliminary screening survey of high school and middle school principals (Phase

1a). Seven of the 12 high school and middle school principals of the urban school division

earned at least 40 points or more on the culturally responsive leadership preliminary screening

tool, the Self-Assessment for School Administrators, thus comprising the purposive sample of

principals. The preliminary screening results of the purposive sample of principals illustrated a

unanimous consensus of self-awareness on the impact of racial, ethnic, and cultural differences

on one’s perceptions, values, behaviors, and interconnectedness with school stakeholders. The

seven high school and middle school principals self-identified with engaging in strategic,

frequent, and timely monitoring of student performance data to guide the next steps in

instruction, intervention, and remediation.

183 Preliminary screening survey of high school and middle school mathematics

teachers (Phase 1b). Of the seven high school and middle school principals that advanced to the

primary study, 70 mathematics teachers were contacted to participate in a preliminary screening

of culturally responsive teaching practices. Thirty-seven of the 70 mathematics teachers

responded to the preliminary screening survey, the Self-Assessment for School Teachers.

Twenty-three out of the 37 mathematics teachers earned 40 points or more on the preliminary

screening tool, thus advancing to the primary study and comprising the purposive sample of

mathematics teachers. The consensus in responses revealed a deep connection to students and

families by developing rapport and establishing partnerships between home and school with a

firm stance against racial and ethnic stereotypes and tropes in curriculum, instruction, and

assessments. Further, these teachers self-assessed that they intrinsically reflected on personal

biases and the impact on others while understanding that diversity bolsters and adds value to the

classroom environment. Because of such reflection and awareness, these teachers responded that

they have a keen understanding of how to differentiate and adjust instruction based on student

performance data.

Observations of high school and middle school principals (Phase 2a). The researcher

conducted two 90-minute observations of the seven high school and middle school principals (14

total) – once before the 4.5 weeks assessment and once before the Critical Skills Assessment.

Detailed field notes were used by the researcher. The field notes were reviewed by the researcher

in which to develop categories and emerging themes. Three themes – critical consciousness (self-

awareness) and interpersonal relationships amongst teachers and students; communication and

being present; and, data-driven decision-making rose to the fore.

184 Observations of high school and middle school mathematics teachers (Phase 2b).

Two 90-minute observations of the 23 high school and middle school mathematics teachers (46

total) were conducted using the Reformed Teaching Observation Protocol (RTOP) – once before

the 4.5 weeks assessment and once before the Critical Skills Assessment. Observations of the

purposive sample of mathematics teachers revealed teachers’ in-depth content knowledge and

the ability to draw on such knowledge to build conceptual understanding through concrete and

pictorial representations. The use of concrete and pictorial representations was observed by the

researcher to lead students through a purposeful problem-solving process that allowed students to

reason through and justify their solutions when solving abstract and complex algorithms. High

expectations and engagement cut across all observations with the teachers serving as facilitators

with minimal direct instruction – instead, employing scaffolding questions to enlighten and to

enhance the learning experience through mathematical discourse.

Examination of high school and middle school mathematics student performance

data (Phase 3). The high school and middle school mathematics teachers of the primary study

had a higher percentage of African American students passing the 4.5 weeks assessment by 16%

and the Critical Skills Assessment by 20%. The purposive sample of mathematics teachers had a

higher percentage of White students passing the 4.5 weeks assessment by 7% and the Critical

Skills Assessment by 11%. For both the 4.5 weeks assessment and the Critical Skills

Assessment, the achievement gap difference between the performance of African American

students versus White students of the purposive sample to those not within the primary study was

9%. The student performance data of African American and White students of the culturally

responsive teachers were statistically significant at the 0.01 level after conducting a two-

proportions z-test.

185 Culturally responsive leadership practices survey (Phase 4). The culminating

Culturally Responsive Leadership Practices Survey, developed by the researcher, was deployed

to the purposive sample of high school and middle school mathematics teachers (n = 23) and

those that did not advance to the primary study (n = 14). The data from the survey revealed

congruence with the preliminary self-assessment of the seven principals and the observations

conducted by the researcher. Triangulation of the articulated and observed emerged through the

consensus of three indicators: recognizes the importance of mathematics teachers and sound

mathematics teaching (I10 – critical consciousness and interpersonal relationships amongst

teachers and students); communicates instructional expectations that are in alignment with high-

quality and rigorous mathematics (I11 – communication and being present); and, constructs the

master schedule to allow mathematics teachers to meet frequently to plan for instruction and to

discuss mathematics student performance (I16 – data-driven decision-making).

Chapter 5 will provide a summary of the findings and implications drawn from these

data, recommendations for further research, conclusions, and, reflections.

186 Chapter 5

Findings, Summary, and Conclusion




actions impact the mathematics performance of African American students. Specifically, this

qualitative study examined the behaviors of a purposive sample of high school and middle school

principals and mathematics teachers self-identified as having high levels of cultural

responsiveness based on a preliminary screening tool. Observations of the purposive sample of

principals and mathematics teachers were conducted as well as an examination of student

performance data from two division-wide assessments to see if there were any gaps in

achievement between African American students and their White counterparts. A culminating

survey was provided to the purposive sample of mathematics teachers and those not within the

purposive sample assessing the culturally responsive leadership practices of their principals to

check the observed with the articulated bounded by what was practiced.

The research questions driving this study were:




mathematics?



levels?

187 Summary of Findings

Seven findings emerged after a review and analysis of the data collected from this

qualitative study. Item indicators referenced from deployed surveys are labeled with the letter I

and followed by the item number consistent with notations from Chapter 4. The findings will be

shared in the following section.

Finding One. Culturally responsive principals exhibit critical consciousness (self-

awareness) and interpersonal relationships amongst teachers and students. The preliminary

screening survey results illustrated the following item indicators applicable to this finding to

which the high school and middle school principals of the purposive sample self-identified at a

100% consensus, a mean of 2, and a standard deviation of 0:

• Item 1: I am aware of my own racial, ethnic, and cultural background and understand

how it affects my perceptions and values;

• Item 2: I seek opportunities to learn about the cultural practices in my school community,

including staff, families, and students;

• Item 3: I regularly reflect on my own bias and how I view and treat people with cultural

practices that are different than my own; and,

• Item 15: Artwork and photographs embedded in school communication and school décor

reflect the demographics of our student body and are age appropriate (CDOE, 2010, pp.

24-25).

Observations revealed that principals provided social, emotional, and academic supports

to students and teachers. Principals recognized and celebrated the strengths of students and

teachers; thus, the school climate was influenced by the principal exhibiting inclusivity.

188 The culminating culturally responsive leadership survey provided an overall consensus

by the purposive sample and those that did not advance to the primary study that the principal

recognized the importance of mathematics (I10, 81.08% consensus rate, !" of 2.73, SD of 0.65).

Respondents indicated at a consensus rate of 45.65% to 89.19%, a mean ranging from 2.14 to

2.81, and a standard deviation between 1.00 to 0.49 that their principals value and recognize

students for their strengths and diverse backgrounds; thus, capitalizing on inclusionary practices

with a nurturing nature while reducing deficit thinking that adversely impact students of color

(I2, I5, I6, I7).

Often, culturally responsive leaders embody what Gibson and Schinoff (2019) described

as “micromoves” – engaging behaviors that seem insignificant but have a larger, personal impact

(p. 1). Such leadership behaviors are those where the principal is connected to the culture and

integral to the dynamic of the school. Taliaferro (2011) shared that “the most successful leaders

are those that are in tune with the students, staff, and their communities. These leaders are

connected to his or her school community in a way that creates and sustains positive

relationships" (p. 9). Because of this connection, teachers feel supported and encouraged by their

principal and teacher's self-awareness, intrinsic biases, and ability to teach students of culturally

diverse backgrounds is strengthened by these behaviors being exhibited by the principal – thus,

transforming the classroom and ultimately the school environment to promote inclusivity and

diversity and the probability of increased student learning (Brown, 2007). The National Council

of Teachers of Mathematics (NCTM) (2014) concurred:

creating, supporting, and sustaining a culture of access and equity requires leaders and

teachers to be responsive to students’ backgrounds, experiences, cultural perspectives,

traditions, and knowledge when designing and implementing a mathematics program and

189 assessing its effectiveness. (p. 1).

Finding Two. Culturally responsive principals are present and communicate clear

instructional expectations for rigorous mathematics instruction. Preliminary screening

survey results illustrated the following indicator applicable to this finding to which the purposive

sample of high school and middle school principals self-identified at an 85.71% consensus rate, a

mean of 1.86, and a standard deviation of 0.38:

• Item 24: Teacher expectations and evaluations include culturally responsive teaching,

with a focus on equity and positive relationships (CDOE, 2010, p. 25).

During observations with the purposive sample of principals, each was specific in their

communication of high-level, cognitively rigorous, and engaging mathematical instructional

practices. Communication of such expectations was observed by the researcher to take place at

either collaborative learning team meetings that the principals attended routinely or by each

principals’ monitoring of the implementation of culturally responsive teaching practices during

instructional observations.

The culminating culturally responsive leadership survey provided an overall consensus

by the purposive sample of mathematics teachers and those mathematics teachers that did not

advance to the primary study that their principal communicated instructional expectations that

were in alignment with high-quality and rigorous mathematics (I11, 83.78% consensus, !" of

2.76, SD of 0.64). It is to be noted that item 16 remains a high consensus for the non-qualifiers,

reflective of the whole group and purposive sample responses. Though not meeting the

parameters of at least an 80% consensus response rate and mean of at least 2.75, items 10 and 11

(comprising the upper second tier of responses) each had a 71.43% response rate, a mean of 2.64,

190 and standard deviation of 0.63 – a reflection of two indicators still particularly regarded as

influential to and highly assessed by the non-qualifiers.

Gay and Kirkland (2003) asserted that culturally responsive leaders set the vision and the

learning environment for students of color. Mayfield and Garrison-Wade (2015) provided,

“leadership leads the charge for culturally responsive practices and creates greater opportunities

for students of color. Strong leadership is critical in transforming schools and disrupting

inequitable practices” (p. 13).

Finding Three. Culturally responsive principals use a systems approach and

organizational structure that allows for teachers to collaborate on lesson design and

implementation as well as to review and monitor student performance data. Preliminary

screening survey results revealed the following indicators applicable to this finding to which the

purposive sample of high school and middle school principals self-identified at a 100%

consensus, mean of 2, and a standard deviation of 0.

• Item 4: Our school regularly examines academic and behavioral data, and examines

achievement gaps by race, native language, socio‐economic status, and gender; and,

• Item 5: Strategic plans are put in place to address all achievement gaps (CDOE, 2010, p.

24).

During observations with the purposive sample of principals, each principal constructed

the master schedule to allow teachers to meet frequently (e.g., weekly, twice-weekly) to plan for

instruction while also giving way for them to provide recommendations for instructional

practices. Because of this organizational structure, each of the principals was able to maintain a

consistent presence in collaborative learning team planning sessions that focused on the review

of mathematics student performance data with specific references to student performance groups

191 (i.e., African American, White, etc.) while using data to drive curriculum implementation and to

adjust instructional delivery. Collaborative learning teams served as the systems approach

vehicle to create synergy designed around the power of the collective.

The culminating culturally responsive leadership survey provided an overall consensus

by the purposive sample of mathematics teachers and those mathematics teachers that did not

advance to the primary study that their principal constructs the master schedule to allow

mathematics teachers to meet frequently to plan for instruction and to discuss mathematics

student performance (I16, 89.19% consensus, !" of 2.81, SD of 0.57).

Strategic design of the master schedule provides opportunities for teachers to collaborate

to “implement the mathematics teaching practices that promote a growth mindset in their

classrooms and schools” (NCTM, 2014, p. 2). Creating a systems approach empowers teachers

to collaborate, thus motivating them to set ambitious learning goals for students (Taliaferro,

2011). Klotz (2006) asserted that culturally responsive principals use a data-driven model to

examine and monitor student performance frequently to make just in time adjustments so to set

students up for success.

Finding Four. Culturally responsive teachers capitalize on the diversity that

students bring to the classroom and exhibit an awareness of how their own racial, ethnic,

and cultural backgrounds, values, and perceptions impact the classroom environment. The

preliminary screening survey results provided the following indicators applicable to this finding

to which the purposive sample of high school and middle school mathematics teachers self-

identified at a consensus rate of 91.30% to 100%, a mean of 1.91 to 2, and a standard deviation

of 0.29 to 0:

192 • Item 1: I am aware of my own racial, ethnic, and cultural background and understand

how it affects my perceptions and values;

• Item 2: I seek opportunities to learn about the cultural practices in my school community,

including staff, families, and students;

• Item 3: I regularly reflect on my own bias and how I view and treat people with cultural

practices that are different than my own;

• Item 18: My behavioral expectations and policies have taken into account the varying

cultural expectations and norms in my student demographics;

• Item 23: I actively dispel racial and cultural stereotypes in my curriculum, assessments,

materials, and classroom décor; and,

• Item 25: I avoid imposing my personal values and opinions and assist students in learning

the difference between fact and opinion. I encourage the sharing of opinions that are

different than my own and looking at multiple perspectives (CDOE, 2010, pp. 27-28).

It is to be noted that the preliminary screening survey results for Item 1 of which the non-

qualifying mathematics teachers self-identified was at a consensus rate of 100%, a mean of

2, and a standard deviation of 0.

The Reformed Teaching Observation Tool (RTOP) was used during observations with the

purposive sample of mathematics teachers. Classroom environments observed were such that

respect was evident and reciprocal between teachers and students inclusive of valuing multiple

ideas and methods to arrive at solutions (I20, consensus rate of 76.16%).

Culturally responsive teaching extends beyond just good teaching – it respects, draws

from, and capitalizes on students’ culture, experiences, and acknowledges cultural identity

(Zeichner, 2003). Culturally responsive teaching seeks to encourage teachers to develop

193 culturally diverse understanding and demonstrate caring through the development of a familial or

a communal atmosphere filled with mutual respect of ideas and differences (Gay, 2002).

Finding Five. Culturally responsive teachers have sound content knowledge, thus

allowing them to differentiate instruction by making connections using multiple

representations to build conceptual understanding. Preliminary screening survey results

yielded the following indicator applicable to this finding to which the purposive sample of high

school and middle school mathematics teachers self-identified at a consensus rate of 91.30%, a

mean of 1.91, and a standard deviation of 0.29:

• Item 21: I differentiate to meet the needs of students from varying backgrounds and have

high expectations for all. I provide the support needed to reach expectations (CDOE,

2010, p. 27).

When using the Reformed Teaching Observation Tool (RTOP), the following indicators

were observed of the purposive sample of mathematics teachers applicable to this finding:

• Item 3: In this lesson, student exploration proceeded formal presentation;

• Item 8: (Propositional Knowledge) The teacher had a solid grasp of the subject matter

content inherent in the lesson; and,

• Item 9: (Propositional Knowledge) Elements of abstraction (i.e., symbolic

representations, theory building) were encouraged when it was important to do so (Piburn

et al., 2000, p. 29).

As revealed by the data, the purposive sample of mathematics teachers exhibited strong content

knowledge at a rate of 93.50% (I8). Because of strong content knowledge, these teachers were

able to shift from concrete representations to pictorial representations to abstract algorithms to

194 build conceptual understanding, to set contextual understanding, and to help students discover

the connections between the representations cohesively (I3, 78.30%; I9, 78.30%).

Building conceptual understanding is the doing of mathematics by enhancing

transference between multiple representations (Jackson & Wilson, 2012). Thomas, Santiago, and

Malloy (2002) indicated how essential building conceptual understanding and having a strong

knowledge of the content was to enhancing students’ desire to do mathematics, to foster a love of

mathematics, and to discover the interconnectedness of multiple representations. Ladson-Billings

(2009c, 2009d) stated that culturally responsive teachers critically examine their pedagogical

practices so that they can deliver content in such a manner that students develop transferable

strategies to apply to multiple contexts as students transition from multiple representations.

Finding Six. Culturally responsive teachers engage their students in mathematical

discourse that allow for students to reason and justify their solutions. The preliminary

screening survey results exemplified that the purposive sample of high school and middle school

mathematics teachers self-identified at a consensus rate of 91.30%, a mean of 1.91, and a

standard deviation of 0.29 for Item 5 – “I value diverse perspectives” (CDOE, 2010, p. 27).

The following indicators applied to this finding when assessing the purposive sample of

mathematics teachers using the Reformed Teaching Observation Tool (RTOP) with a consensus

ranging from 76.10% to 91.30%:

• Item 20: (Communicative Interactions) The teacher’s questions triggered divergent

modes of thinking;

• Item 21: (Student/Teacher Relationships) Active participation of students was

encouraged and valued;

195 • Item 23: (Student/Teacher Relationships) In general, the teacher was patient with the

students;

• Item 24: (Student/Teacher Relationships): The teacher acted as a resource person,

working to support and enhance student investigations; and,

• Item 25: Student/Teacher Relationships: The metaphor “teacher as listener” was very

characteristic of this classroom (Piburn et al., 2000, p. 29).

Teachers served as guides and facilitators – employing scaffolding questions that led to robust

and reflective mathematical discourse. Teachers had to listen intently to pose follow-up

questions to check for understanding as students justified their reasoning (I20, I21, I23, I24, I25).

Student engagement was the expectation set by the teachers and encouraged via mathematical

discourse (I21).

Teacher-facilitated, student-controlled discourse catalyzes high expectations by creating

relevant learning experiences with high cognitive demand. These high expectations reflect a

sense of value and belief that students can achieve at optimal levels in the classroom and can

conquer anything presented (Burns, Keyes, & Kusimo, 2005). Mathematical discourse creates

the avenue to drive justification and reasoning forward – made more powerful by the intentional

facilitation of the teacher that upholds a standard of student voice, thus valuing the students’

contribution to the class as a whole (Berry, 2019). The maximal potential of mathematics

instruction is unlocked when students can engage in a focused discussion that allows for

justifying and proving the reasonableness of solutions as teachers adjust instructional delivery to

match students’ needs and experiences (Walkowiak, Pinter, & Berry, 2017).

Finding Seven. Students with culturally responsive teachers performed better on

division-wide assessments and with a reduced achievement gap between African American

196 and White students compared to teachers not self-identified as having high levels of

cultural responsiveness. The mathematics teachers of the primary study had a higher percentage

of African American students passing the 4.5 weeks assessment by 16% and the Critical Skills

Assessment by 20% than the mathematics teachers not within the primary study. The purposive

sample of high school and middle school mathematics teachers had a higher percentage of White

students passing the 4.5 weeks assessment by 7% and the Critical Skills Assessment by 11% than

the mathematics teachers not within the primary study. For the 4.5 weeks assessment and the

Critical Skills Assessment the achievement gap difference between the performance of African

American students versus White students of the purposive sample to those not within the primary

was 9%, with the gap of the primary study group at -1%, and the gap of the group not within the

primary study at -10%. Student performance data of African American and White students of the

culturally responsive teachers was statistically significant at the 0.01 level when compared to the

African American and White students of the teachers having not advanced to the primary study.

Tate (1995) provided that African American students exemplify resilience and

achievement when contextual and conceptual understanding are connected. Further, Boaler

(1993) suggested that culturally responsive teachers experience success with African American

students due to their approach of acknowledging divergent methods of thinking that bring

meaning to the problems in which students are exposed.

Implications

The findings of this study have implications related to culturally responsive leadership

and culturally responsive teaching while building conceptual understanding in mathematics for

African American students. The following seven implications emanate from the findings of this

study.

197 Implication One. Principals should exercise a critical consciousness (self-awareness)

of one’s own racial, ethnic, and cultural background and how each of these impact

perceptions, values, and leadership behaviors. Finding One of this study indicates that

culturally responsive leaders understand how their values and cultural competence impact the

daily work of teachers and students. Sergiovanni (2007) dubs this as “heart, hand, and head

synergy” – a true understanding and self-assessment of the underlying beliefs that structure their

own behavior and practices (p. 3). Khalifa, Gooden, and Davis (2016) found that culturally

responsive leaders are continually reflective of their practices to influence the school’s climate to

accept often marginalized students by being inclusive of cultural diversity. Johnson (2006)

articulated that principals who are culturally responsive work to promote equality and advocate

for the learning environment to reflect the multiculturalism that the students bring to school –

these principals incorporate “students’ cultural knowledge as a vehicle for learning, fostering the

development of sociopolitical consciousness” (Johnson, 2006, p. 20).

Implication Two. Principals should clearly communicate their instructional

expectations for mathematics instruction of high cognitive demand and should be present

to monitor the implementation of those expectations. Linked to Finding Two, this implication

is reflective of Klotz (2006) with the provision that the goal of culturally competent school

leadership is to establish a culture and climate where all students are nurtured, comfortable,

engaged, and connected, captured in the essence of high expectations. Howard (2010) contended

that schools attaining high levels of student achievement and that consistently close achievement

gaps have visionary leaders that at their core are explicit in their acknowledgment of culture and

race while harnessing this awareness to define and then to continually elevate student

performance expectations. Tomlinson (2014) provided that the “cultural leader” maintains a

198 presence and in so doing honors and values “the learners in that community” and “dignifies the

contributions” of teachers (p. 1).

Implication Three. Principals should create an organizational structure that allows

teachers to plan for instruction and to monitor student performance data through a

systems approach. According to Finding Three of this study, creating such an organizational

structure develops reliable systems of trust and synergy with a collective focus on student

achievement and closure of achievement gaps. Khalifa, Gooden, and Davis (2016) provided that

culturally responsive leaders are consistently reflective of their practices, frequently monitor

student progress, and then course-correct when remediation, enhancement, or enrichment is

needed as dictated by student performance data.

Implication Four. High school and middle school mathematics teachers should be

aware of their own racial, ethnic, and cultural background and how each of these impact

perceptions, values, instructional behaviors, and classroom norms. In so doing, high school

and middle school mathematics teachers should create a classroom environment respective of

and attuned to the students in which they serve. Associated with Finding Four, high school and

middle school mathematics teachers should understand that their teaching has critical

consequences and an impact on students’ learning; therefore, it is imperative that teachers

“continuously question and monitor the impact of their teaching on student learning” (Almarode

et. al., 2019, p. 2). In particular, African American students respond favorably to a familial,

communal-like atmosphere with Mayfield and Garrison-Wade (2015) having stated,

“communalism denotes an interdependent, cooperative approach to learning where students can

readily learn with and from each other” (p. 4). Providing such an environment nurtures students’

cultural and mathematical identity (Mayfield & Garrison-Wade, 2015). Almarode et al. (2019)

199 described such a reciprocal classroom environment as one where “teachers see learning through

the eyes of their learners and learners see themselves as their own teachers results from specific,

intentional, and purposeful decisions about mathematics instruction critical for student growth

and development” (p. 2).

Implication Five. High school and middle school mathematics teachers should

connect the learning process through multiple representations and entry points to build

conceptual understanding (Rhodes, 2017). Aligned with Finding Five of this study, building

conceptual understanding sets the foundation for interconnectedness, divergent thinking, and

interdependence reflective of African American learning preferences (Boykin, Tyler, & Miller,

2005). Hammond (2015) added that creating an environment where building conceptual

understanding is the focus is integral for the physiological and cognitive development of African

American students to develop independent thinking and to build intellective capacity through the

transference and the applicability of knowledge and skills across mathematics content and

context.

Implication Six. High school and middle school mathematics teachers should

regularly engage students in mathematical discourse that requires them to reason and

justify their solutions. According to Finding Six, purposeful mathematical discourse allows the

teacher to construct questions before learning in anticipation of discoveries or misconceptions

while connecting students’ responses during instruction. Berry (2019) asserted that:

establishing norms that support student engagement positions students as competent in

discussing and making sense of their mathematical ideas whether working in pairs, small

groups, or as a whole class. This also builds students' mathematical agency. (p. 2)

200 Mathematical discourse should uplift and encourage multiple modes of thinking concerning

varying approaches to arrive at a solution (Smith & Sherin, 2019). Further, the use of

mathematical discourse to drive deep conceptual understanding and transfer in mathematics is

critical to students’ ability to “consolidate their understanding and apply and extend surface

learning knowledge to support deeper conceptual understanding” (Almarode et al., 2019, p. 23).

Culturally responsive teachers successful with the African American population of students

develop content by using students’ language and experiences to enhance the mathematical

discourse; therefore, allowing students to be comfortable in sharing their solutions to posed

scaffolding questions (Ukpokodu, 2011).

Implication Seven. School divisions should consider providing professional

development to teachers related to culturally responsive teaching strategies. Although, there

is a base of literature about culturally responsive (relevant, competent) pedagogy and teaching,

there is a persistent gap in the literature specific to culturally responsive mathematics instruction

and professional development designed to help teachers understand the concept as well as

distinguish it from “just good teaching” (National Association of School Principals, 2019, p. 17).

Associated with Finding Seven, the purposive sample of principals responded to the

preliminary screening survey at a consensus rate of 85.71%, a mean of 1.86, and a standard

deviation of 0.38 that they “supported professional development for administrators and faculty to

examine their cultural awareness and to develop culturally responsive school-wide and

classroom practices” (CDOE, 2010, I7, p. 1). However, this contradicts the overall assessment of

the purposive sample of mathematics teachers and those not within the purposive sample from

the culminating culturally responsive leadership survey. The lowest consensus from the

respondents was around the provision of culturally responsive professional development to

201 enhance equitable teaching practices (I18, 29.73% response rate, of 1.78, and SD of 1.03). This

response rate could imply that teachers need more training to understand culturally responsive

practices to support student learning.

Recommendations for Future Research

The findings of this study have yielded several recommendations for future research.

These recommendations follow.

1. Future research should include the impact of culturally responsive professional

development to enhance teachers’ instructional practice. The data from the culminating

culturally responsive leadership survey revealed that there was a lack in this area from

their principal. This area should be explored further to see how such an implementation

of professional development would impact the instructional and behavioral practices of

teachers.

2. Future research should examine culturally responsive leadership and culturally

responsive teaching on other minority groups and the impact of both on student

achievement.

3. Future research could extend to observations of non-culturally responsive teachers within

schools with principals identified as having high levels of cultural responsiveness to see

how their teaching practices align with and compare to teachers exemplifying high levels

of cultural responsiveness.

Conclusion

The results of the preliminary screening survey, observations of the purposive sample of

high school and middle school principals and mathematics teachers, and the culminating

culturally responsive leadership practices survey yielded seven findings and seven implications.

202 Of the high school and middle school principals involved in the primary study (n = 7), the

themes of critical consciousness (self-awareness) and interpersonal relationships amongst

teachers and students; communication and being present; and, data-driven decision-making

emerged. These themes were supported by the preliminary survey results in which these

principals self-identified and from the culminating culturally responsive leadership practices

responses by high school and middle school mathematics teachers within and not a part of the

purposive sample. These culturally responsive leaders exhibited an awareness of self and how

such an awareness impacted the culture of the school; the relationships that define community

through their clear vision of teaching and learning inclusive of building conceptual

understanding in mathematics; the academic achievement of students; and, the closure of

achievement gaps between African American and White students as evidenced by two division-

wide assessments.

Twenty-three of the 37 high school and middle school mathematics teachers surveyed

during the preliminary phase of the study advanced to the primary study. These mathematics

teachers self-identified with developing students’ mathematical agency and identity through the

differentiation and the fusion of culture and content. These teachers exhibited a self-awareness of

their biases and values and the impact of both on instructional practices, all the while

understanding the richness that diversity brings to the classroom setting. These teachers used

mathematical discourse to create a culture of safety and sense of family, thus allowing their

students to gain confidence and exemplify their proficiency in mathematics through justification

and reasoning.

Because of such work, all students with culturally responsive teachers performed better

on division-wide assessments and with a reduced achievement gap between African American

203 and White students compared to teachers not self-identified as having high levels of cultural

responsiveness. Student performance data of African American and White students of the

culturally responsive teachers was statistically significant at the 0.01 level when compared to the

African American and White students of the teachers having not advanced to the primary study.

Reflection

This study provided me with a rich experience of a scholarly research process and an

investigation into the behaviors that both culturally responsive leaders and teachers sustained to

increase the achievement of African American students in mathematics. Throughout the study

process, the high school and middle school principals and teachers of the urban school division

promptly completed surveys and participated in observations. All were willing to avail

themselves – allowing me access to their honest self-reflections, schools, and classrooms to

complete the dissertation journey. If the dissertation study were extended, I would have

incorporated observations of non-culturally responsive teachers within schools with principals

identified as having high levels of cultural responsiveness to examine how their teaching

practices align with and compare to teachers exemplifying high levels of cultural responsiveness.

This study affirmed to me that there is an art to leadership and teaching is a craft – both

interweaving to design a distinctive learning experience for our children. Culturally responsive

leadership and teaching extend beyond these borders by creating a conducive learning

environment where all students are valued for the uniqueness that they bring to the tapestry;

where all students are nurtured and groomed for the talents that they possess; where deep and

transferable instruction is cultivated; and, where all students are able to thrive.

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Virginia Department of Education (2019b). Algebra Readiness Institute Presentation. SDBQ

Reports. Retrieved from http://www.doe.virginia.gov/home_files/search_results/vdoe- search.shtml?cx=000783915327965917031%3Aydjbl4xbjqo&cof=FORID%3A10&ie=U TF-8&q=sdbq&sa=Search

Virginia Department of Education (2019c). Urban School Division: Fall Membership.

Retrieved from

https://p1pe.doe.virginia.gov/apex/f?p=180:1:11347911110859:SHOW_REPORT:NO:::

Walkowiak, T. A., Pinter, H. H., Berry, III, R.Q. (2017). A reconceptualized framework for

‘opportunity to learn’ in school mathematics. Journal of Mathematics Education, 8(1), 7-

18.

Wlodkowski, R.J., & Ginsberg, M. (1995). Educational leadership, 53(1), 17-24. Retrieved from

http://go.galegroup.com.ezproxy.lib.vt.edu/ps/i.do?p=ITOF&u=viva_vpi&id=GALE|A17

533229&v=2.1&it=r&sid=summon&authCount=1

Woodson, C. G. (1933/1990). The mis-education of the Negro. Trenton, NJ: Africa World Press.

(Original work published 1933).

Zeichner, K. (2003). Educating teachers to close the achievement gap: Issues of pedagogy,

knowledge, and teacher preparation. In B. Williams (Ed.), Closing the achievement gap:

A vision for changing beliefs and practices. Alexandria, VA: Association for Supervision

and Curriculum Development.

220 APPENDICES

Appendix A: IRB Certificate of Completion in the Training of Human Subjects

Appendix B: Virginia Polytechnic and Institute University Institutional Review Board Approval

Appendix C: Western Institutional Review Board Determination Letter

Appendix D: Research Authorization Request

Appendix E: Research Authorization Committee Approval Letter

Appendix F: Participant Letter

Appendix G: Participant Response Letter

Appendix H: Informed Consent Agreement

Appendix I: Self-Assessment for School Administrators

Appendix J: Self-Assessment for School Teachers

Appendix K: Reformed Teaching Observation Protocol (RTOP)

Appendix L: Culturally Responsive Leadership Practices Survey

Appendix M: Survey Validation Instrument and Responses

221 Appendix A: IRB Certificate of Completion in the Training of Human Subjects

rm1 VIRGIN IATECHVI RGIN lATECHV IRGIN IATECHVIRGINlATEC HVlRGIN lATECH rm1 • ----------------------- • ~ § ~ ~ !!f~!etum, ~ ! ~ ;:'~-~ i ~ z ~ Has completed >. o Tra ining in Human Subj ects Protect ion ~

~ Oath• foll.,,.,g topira , :

.... Histor ical Basis for Regulating Human Subjects Research ~ ~ The Belmont Report z ~ Federal and Virginia Tech Regulatory Entities , Policies and Procedures ~

! ~;;, 2 01 8 i ~ z ~ ~ ~ Q !mt VIRG lN lATECHVlRGIN lATECHVlR'- ,,..:HVlRGIN lATECHVlRGIN lATECH !mt

222 Appendix B: Virginia Tech Institutional Review Board Approval

Wii' V ~~NIA I

MEMORANDUM

DATE:

TO:

FROM:

PROTOCOL TITLE :

IRB NUMBER :

July 1, 2019

lnsbttliOnal Review 8 06fd Nenh End Cen1er. Sulle 4120 (MC 0497) 300 TIITI., SttHl ~

Blacksburg, v.-gh • 24061 540/231-3732

[email protected] hltp:NWtNW.tese.-ch.vl edJJsl.rdhrpp

Ted $ Price, Angela Nicole Byrd-Wright

Virginia Tech lnstltutional Re\llew Board (FWA00000572 , expires January 29 , 2021)

The lnftuenoe and Impact of CuNural ly Responsive Leadersh ip on lhe Mathematics Performance of African American Studen ts at lhe Secondary Level

19-385

Effective July 1, 2019, the Virginia Tech Human Research Protection Program (HRPP) and lnstillrtional Review Board (IRS) determined lhat this protoco l meets lhe criteria for exemption from IRB review under 45 CFR 46 .104(d)c ategory(ies) 1.2Qi).

Ongoing tRB review and approval by this organization is no-I requ ired. This determination applies only to the activities described in lhe IRB submission and do-es not apply should any changes be made. If changes are made and there are questions about whether these activities Impact the exempt determinat ion, ple.ase submit a new request to lhe IRB for a determ ination .

This exempt determination do-es not apply to any collaborating lnstitution(s). The Virginia Tech HRPP and IRB cannot provide an exemption that overrides the jurisdiction of a local IRB or other institutiona l mechanism for determining exemptions.

All investigators (li sted above) are requi red to comply with the researcher requirements ouUined at

https·//secure research vt e<1u1externaMrb/resoonslbillt1es htm (Please review responsibilities before beginning your research,)

PROTOCOL INFORMATION :

Determined As: Protocol Determination Date :

ASSOCIATED FUNDING :

Exemp~ under 45 CFR 46.104(d) category (ies) 1,2(ii) April 25, 2019

The table on lhe follow ing page indicates whether grant pr~osa ls are related to this protoco l, and which of the listed proposals , ~ any, have been compared to this protocol , if requ ired.

'""''"' tit• Futur• VllltOINI A POlYTECMNIC INITlfUt( AMO ll A ll: UMIVlltl llY'

All ec,ual 01)p01'f(Jfhlf .,,,, •• ,,.,e •C:UMJ 1,/'14IJNt,o,.

223

IRB Number 19-385

SPECIAL INSTRUCTIONS :

page 2 of 2 Vlrginia Tech Institutional Review Board

This amendmenl , submitted June 24, 2019, changes lhe consent forms., data collection inslruments , and recruftment materials by replacing references to WIRB and their contacl information with the VT IRB and VT IRB contact information.

Drue• OSPNumber Sponsor Granr Compufi,,on Conducted'/

· Date this prope>sal numbtn was compared assessed as not requ -,g co"°"arrson, or comparison 1nformal10n was rev sed

If this protocol is to cover any other grant proposals. please contact the HRPP office ([email protected]) immed iately.

224 Appendix C: Western Institutional Review Board Determination Letter

April 25, 2019

Ted Price, PhD

Virginia Polytechnic Institute and State University, Richmond Center

2810 Parham Road, Suite 300

Richmond, Virginia 23294

Dear Dr. Price:

SUBJECT: IRB EXEMPTION—REGULATORY OPINION

Investigator: Ted Price, PhD

Protocol Title: The Influence and Impact of Culturally Responsive Leadership on the

Mathematics Performance of African American Students at the Secondary

Level

IRB Protocol No.: 19-385

This is in response to your request for an exempt status determination for the

above-referenced protocol. Western Institutional Review Board’s (WIRB’s) IRB Affairs

Department reviewed the study under the Common Rule and applicable guidance.

We believe the study is exempt under 45 CFR § 46.104 (d)(1), because The research is

conducted in established or commonly accepted educational settings. The research

specifically involves normal educational practices that are NOT likely to adversely

impact students’ opportunity to learn required educational content or the assessment of

educators who provide instruction.

We believe the study is exempt under 45 CFR § 46.104(d)(2), because the research

includes interactions involving educational tests, survey procedures, interview

procedures, or observation of public behavior (including visual or auditory recording).

Any disclosure of the human subjects’ responses outside the research would NOT

reasonably place the subjects at risk of criminal or civil liability or be damaging to the

subjects’ financial standing, employability, educational advancement, or reputation.

This exemption determination can apply to multiple sites, but it does not apply to any

institution that has an institutional policy of requiring an entity other than WIRB (such as

an internal IRB) to make exemption determinations. WIRB cannot provide an

Global Leader I Proven Expert

We s tern In s t itut ional Rev iew Board 1019 39thAv nu SE Surle 120 Puyallup , WA 98374-2115

omoe_ (360> 252-2500 F..: (360 ) 252-2498 HYPERLINK

·http ://www .wirt>.oom· www .wlriM::om

225

Ted Price, PhD 2 April 25, 2019

exemption that overrides the jurisdiction of a local IRB or other institutional mechanism

for determining exemptions. You are responsible for ensuring that each site to which

this exemption applies can and will accept WIRB’s exemption decision.

Please note that any future changes to the project may affect its exempt status, and you

may want to contact WIRB about the effect these changes may have on the exemption

status before implementing them. WIRB does not impose an expiration date on its IRB

exemption determinations.

If you have any questions, or if we can be of further assistance, please contact Amber

Billingham, BA, CIP, at 360-570-1299, or e-mail [email protected].

ALB:tb

D1 & D2-Exemption-Price (04-25-2019)

cc: Angela Byrd-Wright, Virginia Polytechnic Institute and State University

WIRB VA Tech, Virginia Tech

WIRB Accounting

WIRB Work Order # 1-1178670-1

226 Appendix D: Research Authorization Request

Academic Research

SUMMA RY

-

upports the con tinued scho larship o f adults in undergra duate and graduate programs and as a p ocess o sue individuals to app ly to conduct research using our facilities, data , em ployee expe rtise and

experience, and access to our students provided that such research does not interfere w ith our CO<e mission.

The fo llow ing factors are used in determ ining wh ethe r the schoo l system can accept a research proposa l: • The technica l soundness of tti e research design ; • The app ropriatene ss of the resea rch in a public schoo l setting; • The availa bilrty o f research sites and subjects : and • The need for the d ivision to protect the persona l and lega l rights o f students, pa rents, and staff .

Ind ividuals w ishing to cond uct research in are requ ired to submrt the requ est in wri t ing using the "Res ea rch Authoriz ation Re quesr to the Departme nt o f Resear ch, Planning & Eva luation . In addit ion to the form itself , applicants are asked to submrt an executive summ ary of the research proposal/prospectu s submrtted to the college or university . Applica nts are also asked to provide proof tha t their advisor and / or oommrttee and the Institutional Review Boa rd (IRB) have approved the research proj ect and met hodology.

The Research Authorization Commrtt.ee (RA C), chaired by the . Execut ive Director of Resea rch, Plann ing , and Evaluation , is comprised of executive level staff membe rs w ho can evaluate the like fy impac t of the study on schoo l ope rations and learn ing as we ll as the potential cont ribution to the scholarly bo. know1edge . This oommrttee is respo nsible fo r eva luating all requests for studies to be conducted with in Upon receipt o f the research request applica tion and all required supporting docume ntation , the RAC chairperson's signatur e is requ ired before a study may proceed to the Com mittee .

The decis ion of the committee is conveye d via letter to the individua l applicant and, when necess ary , the college or un iversity per any fom, s they requ ire . Unless specif ied in the approval letter. the re are no additiona l perm issions necessary , i.e. app licants do not have to secure the permission of principa ls to surv ey staff membe rs, or the IT depa rtment to use the d ivision ema il.

Participation of students, parents, and staff members in a study is completely voluntary. Ally ins trumen ts to be admin istered to resear ch subjects mu st d isp lay a clarifying stateme nt to th is effect . The identity o f any pa rticipant, schoo l. o r the division must be prese rved.

227

Academic Research Authorization Request

A. APPLICANT INFORMATION

1.

2.

""'Jl)\8 NiQOII) 8yt(S.\ 'l rtjfll Name: ___________________________________ _

2S I 5 Puidi Avcm11e. Newport New~. 'VA 23007

Address:-----------------------------------Street City S!"are Zip

3. Home Phone: ( 757 )3:i,:1-00:20u1s7}810.fis: (08r ) Business Phone: ( 757 ) 1214:4nx2~:J9

4 .

5.

6.

ab'jld ATq,l(ih;tmpl:l:n ,kl 2. \'a.W t,,.uk) ; WK I 1 1 SQ'o'lodll (~ 1) E-mail Address: ________________________________ _

Are you employed by

tf you are proposing this study in connection w ith the degree requirements of a college or university, please provide:

a. lnstitut ioo: Viror'l-a Po>,u,cm-c ln&i\ute ant1Vn""8rsl!y

D &lm;;dional l..coclcrsrip ~ Policy Stucl:es

b . epartment: _______________________________ _

c. What degree? 0 Maste( s 0 Doctoral O Other (specify) ___________ _

d. Course Name: ______________________________ _

Ot. Te<! S. Pl'le${1X8(17'8-.t_,U: (ec,4) 869·:2015) e. Name of your advisor or committee chairperson: __________________ _

7. What is the approval status of your proposal at your college or unWersity?

2f Formally approved 0 Approved by advisor, but not committee 0 Not approved yet

8. tf your study involves human subject s (e.g. students, parents. and/or staff), you must have prior approva l from your institution's review board. Have you receWed IRB approval?

0Yes □ No 0 Not Applicable

228

B. PROPOSED STUDY FEATURES

1. Tit le o f resea rch : Tt.o l11IU0nce UICI I~ ol eutu air, Ae::pon:,ivc l..cockm1hip en the M:!lhem:il:a PerllJC'rnance ol A!ric;in J\mcllic;jn Stuclonl:l at

2. Desired time schedule fOf carrying out the researc h: I I 20 19

From~/ 2019 to __ / __ Mo. Yr. Mo. Yr.

3. Type of research or infom,ation reques ted:

4 .

Os tudent Records

□Teacher Records

□school Records

O s tudent Surveys

2f Admin Sti rveys

2f"Teacher Surveys

O Admin/Teacher Interviews

Os tudent Interviews

0 Focus Groups

f2'.fr est ResuJts

O o ther Data ____________ _

5>.,N(ly$ "' I I take 8PP'¢1Cffl$')9°¥ 2Q ffl illij\8$ II) (Xll'l"lpl$18, Time com mitments required of participants to complete survey/interview(s)? __________ _

5. tf data are requested from- to con duct the study, indicate the kind(s) and amount of data the request Slm:'cn! µcrlUl'IT\ar.ce d:!111 for midcle u1<1 hi;h m:nool ir~ ~nelt"~i c!I h:;u:l-,ec5 (4.!i mid•nno v.'Ccl:s Ulle!!!lllwnl :inOOI Cn!ic:dSlol'!$ kliic:t1!2'Tler.td:!!11

entails.~ = =====~= = ---------------------------{'llruc vs. An:::ln All"--Cric::ln mut±cn:~ .

C. REQUIRED ATTA CHMENTS

Check items you are attaching to this application:

E2J' Execut ive Summary/Abstract (3 page maximum) including:

• Proposal description, • Specific research obj ectives , and • De tailed data collection me thodology, including definition of and anticipated number of subj ec ts

E2f Cop ies of a ll data collection instrum ents used as a part of the study, including a copy of the informed co nsent

agreement detailing the subjects' vo luntary participation

E1 Copy of your Institutional Review Board (IRB) approval, if research proposal involves students or staff

D. RESEA RCH ACT IVITY REPORTS

I understand that when .. students, staff members , or parents are participants in a research study, the Resea rch Authorization Commrttee (RAC) requests that one complete copy of each report or product develo ped as a part or outcome of the ~ro vided to the Chairperson of the Resea rch Autho rization Committee at no charge to - within 30 days of the end of the study.

Signa ture, Ap plicant

229

E. SIGNATURE Of THESIS/DISSERTATION COMMITTEE CHAIRPERSON

n. following is 10 be signed by IN di;wperson of IN applc>nl'• iMM/d isser1atlon cormiittee (If eppl-) c,, course proteseor.

I hllve l9Vlewed tho enc:IOM<I ,. ... rc:1, p,oPoQI and flnd I., bo technlc:a'Y oompeConL t'-9tlcally """1d, and sjgnlllcant In loo.JS.

SUBMIT APPLICATION AND SUPPORTING DOCUMENTS TO:

DllfJ<lrtment of RN .. rch. Pt1Ming & EvOlue(;on

~te Forms Received:____} __ / __

1. INITIAL ,ocom.,.,cleUoo 10 p«1a1od to Commlt1ff ro. ,wlow: D ,Approval O Ol1approval

Recommendltion lo< /VJ hoc mombe<{s): ____________________ _

~oaturo. RAC Cllalrpo,- -'-' Dalt

2. FINAL AUtllef1utlon CommlUN - (lndlvlduol CommiflM !,(..,.bar responses all8Checl~

D Appn,vol O OlaapptOYOI O ProYl&lonal Appnml (00fltiogen1 on modlftcatlons below)

ROll\llb (- apec:lftc modlllc:otion1 -dod or rea,cn(1) lo< dlNpprova L 11 -opriole.)

Sig-nature, RAC Chairperson __ , __ , __

08to

230 Appendix E: Research Authorization Committee Approval Letter

ur ppr "i "i1hin irn d •r int th hth

n

231 Appendix F: Participant Letter

Angela N. Byrd-Wright 1 Franklin Street Hampton, VA 23669 Email: [email protected] (757) 810-6952 Date Participant’s Name Participant’s School Address Dear ______________________: I am a doctoral student within the Educational Leadership and Policy Studies Program at Virginia Polytechnic Institute and State University [Hampton Roads Cohort]. The title of my dissertation is: “How Culturally Responsive Leaders and Teachers Influence the Mathematics Performance of High School and Middle School African American Students in One Urban Virginia School Division.” The results from the study will be used in the researcher’s dissertation. Participation in the study is voluntary. Any decision not to participate has no bearing on your employment status with your current school division. Conclusions and recommendations from the study may be beneficial to this school division and others across the state. I have received permission to conduct research from the Research Authorization Committee of this school division and from the Institutional Review Board of Virginia Polytechnic Institute and State University. This qualitative study is comprised of a preliminary and a primary phase as described in detail below. Preliminary Study: Preliminary screening survey of school principals (Phase 1a). The purpose of this study was to determine if culturally responsive behaviors of high school and middle school principals influence the behaviors of mathematics teachers resulting in building conceptual understanding of their students. Phase 1a requires the completion of the 25-item preliminary screening survey, the Self-Assessment for School Administrators. Created by the Colorado Department of Education (CDOE), this survey will be used as it specifically measures culturally responsive leadership practices. The Self-Assessment for School Administrators is comprised of three distinct headers (e.g., most of the time, some of the time, and never) in relation to each culturally responsive leadership indicator. To establish a selection criterion baseline in order to choose the principals and thus their building sites to be studied, point values will be assigned to each header

232 as follows – most of the time (2 points), some of the time (1 point), and never (0 points). Because there are 25 indicators, the maximum point total will result in 50 points. For a principal to move to the next phase of the study, one must attain at least 40 points (or an 80% response rate). Principals scoring at least 40 points on the preliminary screening survey will make up the principal purposive sample of the primary study. The preliminary screening survey should take no more than 20 minutes to complete and will be provided to you via Qualtrics. Preliminary screening survey of high school and middle school mathematics teachers

(Phase 1b). This study also seeks to determine how teachers’ culturally responsive actions impact the mathematics performance of African American students. Therefore, of the principals that scored at least 40 points on the Self-Assessment for School Administrators, each high school and middle school mathematics teacher of the select principals’ sites will engage in the Self-Assessment for School Teachers. The preliminary screening survey for teachers was selected as it reflective of similar indicators and headers as the Self-Assessment for School Administrators; thusly, its inclusion as a selection criterion tool will assist the researcher in identifying the information-rich culturally responsive teacher cases reflective of the purpose of the study. In addition, the Self-Assessment for School Teachers will draw parallelism to the principal preliminary screening survey to which themes will be ascertained during the data collection process. Headers will be assigned the same point values as the previously described principal preliminary screening survey. Because there are 25 indicators, the maximum point total will result in 50 points. For a teacher to move to the next phase of the study, one must attain at least 40 points (or an 80% response rate). The teachers scoring at least 40 points on the preliminary screening survey will comprise the purposive sample of the primary study. The preliminary screening survey should take no more than 20 minutes to complete as it will be provided to you via Qualtrics. _______

Primary Study: Notifications to all preliminary screening survey participants will be provided by the researcher prior to the start of the primary survey. If you should you attain at least 40 points on the preliminary screening survey, then you will be notified via email in order to schedule time to engage in the following steps as described hereafter. Observations of high school and middle school principals (Phase 2a). The primary study involves two observations of the purposive sample of principals. I will conduct two 90-minute observations – once prior to the 4.5 weeks assessment and once prior to the Critical Skills Assessment of the first nine weeks of the 2019-20 school year. Field notes will be used to account for observations such as interactions with high school and middle school mathematics teachers and high school and middle school mathematics students (and in particular, students described as African American). Observations of high school and middle school teachers (Phase 2b). Developed by Piburn et al. (2000) of the Evaluation Facilitation Group of the Arizona Collaborative for Excellence in the Preparation of Teachers, the Reformed Teaching Observation Protocol (RTOP), was specifically developed to measure reformed or culturally responsive mathematics teaching practices specifically at the high school and middle school level. I will conduct two 90-minute

233 observations using the RTOP – once prior to the 4.5 weeks assessment and once prior to the Critical Skills Assessment of the first nine weeks of the 2019-20 school year. Examination of high school and middle school mathematics student performance data

(Phase 3). Directly following the 4.5 weeks assessment and Critical Skills Assessment, student performance data will be collected. The student performance data of each of the teachers in the purposive sample will be compared to the performance of those at the same grade level and content not within the sample. In addition, African American student performance will be compared to White students. This will be done to see if the variable application of culturally responsive teaching practices has an impact on the performance of African American students in comparison to their White counterparts and if there is a significant difference in achievement between the two groups. Culturally responsive leadership practices survey (Phase 4). The researcher-developed Culturally Responsive Leadership Practices Survey will be used to gather concluding responses from the purposive teacher sample and those not within the purposive sample regarding the culturally responsive leadership practices of their principal. This information will be mapped back to the data gleaned from having observed the principal in order to determine parallelism between the observed and the articulated responses, how culturally responsive leadership was performed, and its influence on instructional behaviors. This survey should take no more than 20 minutes to complete as it will be provided to you via Qualtrics. _______ I sincerely hope that you will agree to participate in this study. All identifying information such as your name and school will not be used. I appreciate your consideration and value your time in advance. If you should have any questions regarding this study, then you may either contact me via email or by phone; contact my Dissertation Chair, Dr. Ted Price, at [email protected]; or, the Virginia Tech Institutional Review Board (IRB) at (540) 231-3732 [[email protected]]. Enclosed you will find a participation response letter and an envelope for the returning response. Respectfully, Angela N. Byrd-Wright Doctoral Candidate Virginia Polytechnic Institute and State University Hampton Roads Cohort

Virginia Tech Institutional Review Board (IRB) Protocol Number #19-385 Virginia Tech Institutional Review Board (IRB), 540-231-3732 [[email protected]]

234 Appendix G: Participant Response Letter

Participant’s Name Participant’s Address Date: Angela N. Byrd-Wright 1 Franklin Street Hampton, VA 23669 Email: [email protected] (757) 810-6952 Dear Mrs. Byrd-Wright:

I agree to participate in the dissertation study explained on the cover letter of this mail correspondence. Please email me at the following email address ________________@________ to send the preliminary screening survey instrument to participate in your research study. I also understand that I should I attain at least 40 points (or an 80% response rate) on the preliminary screening survey instrument, that I will be notified of the option to participate in the primary study as described in your cover letter. Sincerely, Research Study Participant


235 Appendix H: Informed Consent Agreement

Research Title: How Culturally Responsive Leaders and Teachers Influence the Mathematics Performance of High School and Middle School African American Students in One Urban Virginia School Division Researcher: Angela N. Byrd-Wright, Doctoral Candidate, Virginia Polytechnic Institute and State University [Hampton Roads Ed.D. Cohort]

Contact email(s): [email protected]

Purpose of the research study: The purpose of this study was to determine if culturally responsive behaviors of high school and middle school principals influence the behaviors of mathematics teachers resulting in building conceptual understanding of their students; and, how teachers’ culturally responsive actions impact the mathematics performance of African American students. The results of this study will be used for the development of a dissertation. Participation in the preliminary screening survey (principals): As a participant in this study, you will spend approximately 20 minutes completing and submitting the Self-Assessment Survey for Administrators developed by the Colorado Department of Education and featured within its larger Equity Toolkit for Administrators. Your responses to the survey will be submitted electronically through Qualtrics. To establish a selection criterion baseline in order to choose the principals and thus their building sites to be studied, point values will be assigned to each header as follows – most of the time (2 points), some of the time (1 point), and never (0 points). Because there are 25 indicators, the maximum point total will result in 50 points. For a principal to move to the next phase of the study, one must attain at 40 points (or an 80% response rate). Principals scoring at least 40 points on the preliminary screening survey will make up the principal purposive sample of the primary study. Participation in the preliminary screening survey (teachers): As a participant in this study, you will spend approximately 20 minutes completing and submitting the Self-Assessment Survey for Teachers developed by the Colorado Department of Education and featured within its larger Equity Toolkit for Administrators. Your responses to the survey will be submitted electronically through Qualtrics. To establish a selection criterion baseline in order to choose the teachers that will participate in the primary study, point values will be assigned to each header as follows – most of the time (2 points), some of the time (1 point), and never (0 points). Because there are 25 indicators, the maximum point total will result in 50 points. For a teacher to move to the next phase of the study, one must attain at least 40 points (or an 80% response rate). Teachers scoring at least 40 points on the preliminary screening survey will make up the teacher purposive sample of the primary study.

Participation in the primary study (principals): Field notes will be used to capture the setting, activities and interactions, conversations using direct quotes or synopsis of discussions, and subtle factors (i.e., inferred meanings and connotations, nonverbal communication, etc.) while maintaining reflective comments in the margins and/or narrative using distinguishing font features [italicized bracketing and the initials “OC” to stand for observer comments]. Two 90-

236 minute observations will be conducted – once prior to the 4.5 weeks assessment and once prior to the Critical Skills Assessment of the first nine weeks of the 2019-20 school year.

Participation in the primary study (high school and middle school mathematics teachers):

• The Reformed Teaching Observation Protocol (RTOP) will be used to conduct two 90-minute observations – once prior to the 4.5 weeks assessment and once prior to the Critical Skills Assessment of the first nine weeks of the 2019-20 school year.

• Directly following the 4.5 weeks assessment and Critical Skills Assessment, student performance data will be collected. The student performance data of each of the teachers in the purposive sample will be compared to the performance of those at the same grade level and content not within the sample. In addition, African American student performance will be compared to White students. This will be done to see if the variable application of culturally responsive teaching practices has an impact or influence on the performance of African American students in comparison to their White counterparts and if there is a significant difference in achievement between the two groups.

• The researcher-developed Culturally Responsive Leadership Practices Survey will be used to gather concluding responses from the purposive teacher sample and teachers not involved in the purposive sample regarding the culturally responsive leadership practices of their principal. This information will be mapped back to the data gleaned from having observed the principal in order to determine parallelism between the observed and the articulated responses, how culturally responsive leadership was performed, and its impact on instructional behaviors. This survey should take no more than 20 minutes to complete as it will be provided to you via Qualtrics.

Anticipated Risks: There are no anticipated risks to persons who participate in the study.

Benefits: There are no direct benefits to participants in this study.

Time Period: All surveys should take approximately 20 minutes to complete and to submit your responses. Two 90-minute observations will be conducted.

Confidentiality: All information disclosed on the survey instruments will be held in strict confidence. The data generated from the surveys and observations included in the dissertation will contain no identifying information regarding the participants, the participants’ school or school division. Once the study has been completed and after successful defense of the dissertation, all electronic documents and hard copies will be maintained for one full year with accessibility only to the researcher. After one full year, all electronic documents and hard copies associated with the study will be purged and shredded.

Compensation: Participants will not be compensated for participating in this study.

Participation: Your participation is this research study is completely voluntary.

Right to withdraw from the study: As a participant in this study, you have the right to withdraw from the study at any time of your choosing. Your survey responses and observations

237 will be destroyed and deleted at the time of withdrawal and the data will not appear in the final dissertation.

Process for Withdrawal: If you elect to withdraw from the study, please notify the researcher at any time at the phone number, email address, and/or address provided within this Agreement.

Questions or Concerns: Should you have any questions or concerns regarding this study, please contact the researcher, Dissertation Chair, or the Virginia Polytechnic Institute and State University Institutional Review Board (IRB) Administrator at the contact information below:

Researcher:

Angela N. Byrd-Wright 1 Franklin Street Hampton, VA 23669 Phone: (757) 810-6952 Email: [email protected] Dissertation Chair:

Ted Price, Ph.D. Virginia Tech Richmond Center 2810 Parham Road, Suite 300 Richmond, VA 23294 Phone: (804) 869-2015 Email: [email protected] Virginia Tech Institutional Review Board (IRB):

Jennifer Farmer, Protocol Coordinator Email: [email protected], [email protected] (540) 231-3732 Participant Agreement: I have read the Informed Consent Agreement and conditions of this study. By signing below, I hereby acknowledge the above and give my voluntary consent: _______________________________________________ ___________________ Subject Signature Date _______________________________________________ Subject Printed Name _______________________________________________ Subject Email Address


238 Appendix I: Self-Assessment for School Administrators

Preliminary screening survey of high school and middle school principals (Phase 1a). This study seeks to determine if culturally responsive behaviors of high school and middle school principals influence the behaviors of mathematics teachers resulting in building conceptual understanding of their students. Phase 1a requires the completion of the 25-item preliminary screening survey, the Self-Assessment for School Administrators. Created by the Colorado Department of Education (CDOE), this survey will be used as it specifically measures culturally responsive leadership practices. The Self-Assessment for School Administrators is comprised of three distinct headers (e.g., most of the time, some of the time, and never) in relation to each culturally responsive leadership indicator. To establish a selection criterion baseline in order to choose the principals and thus their building sites to be studied, point values will be assigned to each header as follows – most of the time (2 points), some of the time (1 point), and never (0 points). Because there are 25 indicators, the maximum point total will result in 50 points. For a principal to move to the next phase of the study, one must attain at least a range of 40 points (or an 80% response rate). Principals scoring at least 40 points on the preliminary screening survey will make up the principal purposive sample of the primary study. The preliminary screening survey should take no more than 20 minutes to complete.

Never Some of

the time

Most of

the time

[0] [1] [2]

1 I am aware of my own racial, ethnic, and cultural background and understand how it affects my perceptions and values.

2 I seek opportunities to learn about the cultural practices in my school community, including staff, families, and students.

3 I regularly reflect on my own bias and how I view and treat people with cultural practices that are different than my own.

4 Our school regularly examines academic and behavioral data, and examines achievement gaps by race, native language, socio-economic status, and gender.

5 Strategic plans are put in place to address all achievement gaps.

6 Data is disseminated to families with procedures for them to offer support in improving our school for all students.

7 I support professional development for administrators and faculty to examine our own cultural awareness and develop culturally responsive school-wide and classroom practices.

8 I actively reach out to families from various backgrounds to give feedback and assist in the creation of school policies.

9 I actively recruit families to volunteer in the school and on committees so that volunteer pools reflect the student body.

10 Our school has clear procedures to report and respond to allegations of inequity. These issues are dealt with in a sensitive and timely manner.

239 11 I actively recruit applicants of diverse cultural backgrounds

and ethnicities to work in our school.

12 Our school has support systems in order to meet the needs of our staff from diverse backgrounds.

13 School communication with families is available in multiple languages and is sensitive to varying family structures as well as diverse cultural and socioeconomic backgrounds.

14 I make sure that translators are available to improve school and family communication.

15 Artwork and photographs embedded in school communication and school décor reflect the demographics of our student body and are age appropriate.

16 The books in our school library reflect our student body and depict varying cultural practices in a positive and anti-biased way.

17 I openly confront inequitable practices and have policies in place to hold staff accountable for their actions. I encourage staff to do the same.

18 School policies are created while consciously working towards equity for all students and families. Historical policies are reviewed for cultural sensitivity. Members representing the demographics of the community assist in this process.

19 Curricula and assessments used in our school are reviewed to make sure that materials are historically accurate, culturally responsive, and anti-bias.

20 Behavior expectations and policies have taken into account the varying cultural expectations and norms among students and families.

21 Curriculum guidelines reflect that culturally responsive lessons are embedded in day to day teaching, rather than isolated units.

22 Our school incorporates differentiation tools to meet the needs of students from varying backgrounds.

23 School policies include how to respect holidays in a manner that is sensitive to varying religions and cultural practices of the student population.

24 Teacher expectations and evaluations include culturally responsive teaching, with a focus on equity and positive relationships.

25 I am comfortable in leading discussions about race, culture, religion, ethnicity, class, gender, and sexual orientation with staff and students.



240 Appendix J: Self-Assessment for School Teachers

Preliminary screening survey of high school and middle school mathematics teachers

(Phase 1b). This study also seeks to determine how teachers’ culturally responsive actions impact the mathematics performance of African American students. Therefore, of the principals that scored at least 40 points on the Self-Assessment for School Administrators, each mathematics teacher of the select principals’ sites will engage in the Self-Assessment for School Teachers. The preliminary screening survey for teachers was selected as it reflective of similar indicators and headers as the Self-Assessment for School Administrators; thusly, its inclusion as a selection criterion tool will assist the researcher in identifying the information-rich culturally responsive teacher cases reflective of the purpose of the study. In addition, the Self-Assessment for School Teachers will draw parallelism to the principal preliminary screening survey to which themes will be ascertained during the data collection process. Point values will be assigned to each header as follows – most of the time (2 points), some of the time (1 point), and never (0 points). Because there are 25 indicators, the maximum point total will result in 50 points. For a teacher to move to the next phase of the study, one must attain at least 40 points (or an 80% response rate). The teachers scoring at least 40 points on the preliminary screening survey will comprise the purposive sample of the primary study. The preliminary screening survey should take no more than 20 minutes to complete.

Never Some of

the time

Most of

the time

[0] [1] [2]

1 I am aware of my own racial, ethnic, and cultural background and understand how it affects my perceptions and values.

2 I seek opportunities to learn about the cultural practices in my school community, including staff, families, and students.

3 I regularly reflect on my own bias and how I view and treat people with cultural practices that are different than my own.

4 As a faculty member, I feel supported and valued for my own identity and perspectives.

5 I value the diverse perspectives and cultural practices of my colleagues.

6 I regularly examine academic and behavioral data for achievement gaps by race, native language, socio-economic status, and gender.

7 I review data to inform instruction in ways that best meet the needs of individual learners, and collaborate with colleagues in data-based decision-making.

8 I create positive relationships with families so that we can work as a team to best meet their child’s needs.

9 I engage in professional development to examine my own cultural awareness and develop culturally responsive teaching practices.

10 I encourage all families to give me feedback and volunteer in the classroom.

241 11 I participate in action research focused on equity to better

meet my students’ needs and improve my instructional strategies. I monitor student engagement within this research.

12 Students and families feel comfortable when reporting inequitable practices are incidents, whether parties involved include me, students, or fellow colleagues.

13 Communication is available to families in multiple languages.

14 I make sure that translators are available to improve school and family communication.

15 Artwork and photographs embedded in school communication and school décor reflect the demographics of our student body and are age appropriate.

16 I act as a student and family advocate. I openly confront my colleagues if I see practices that I feel are inequitable.

17 I preview visual media to make sure that it is culturally responsive and anti-bias.

18 My behavioral expectations and policies have taken into account the varying cultural expectations and norms in my student demographics.

19 I review curriculum and assessments for historical accuracy, cultural responsiveness, multiple perspectives, and anti-bias.

20 Culturally responsive lessons are embedded in my day to day teaching, rather than taught in isolated units.

21 I differentiate to meet the needs of students from varying backgrounds and have high expectations for all. I provide the support needed to reach expectations.

22 Holidays are equally represented and celebrations are sensitive to the varying religions and cultural practices of my student population.

23 I actively dispel racial and cultural stereotypes in my curriculum, assessments, materials, and classroom décor.

24 I am comfortable in leading discussions about race, ethnicity, class, gender, sexual orientation, and religion with students.

25 I avoid imposing my personal values and opinions and assist students in learning the difference between fact and opinion. I encourage the sharing of opinions that are different than my own and looking at multiple perspectives.



242 Appendix K: Reformed Teaching Observation Protocol (RTOP)

I. BACKGROUND INFORMATION

Name of teacher Years of Teaching Subject observed Grade level Date of observation II. CONTEXTUAL BACKGROUND AND ACTIVITIES In the space provided below please give a brief description of the lesson observed, the classroom setting in which the lesson took place (space, seating arrangements, etc.), and any relevant details about the students (number, gender, ethnicity) and teacher that you think are important. Use diagrams if they seem appropriate. Record here the events that may help in documenting the ratings. TIME DESCRIPTION OF EVENTS

Notes:

III. LESSON DESIGN AND IMPLEMENTATION

Never Occurred Very

Descriptive

1

The instructional strategies and activities respected students’ prior knowledge and preconceptions inherent therein.

0 1 2 3 4

2

The lesson was designed to engage students as members of a learning community.

0 1 2 3 4

3

In this lesson, student exploration preceded formal presentation.

0 1 2 3 4

4

This lesson encouraged students to seek and value alternative modes of investigation or of problem solving.

0 1 2 3 4

5

The focus and direction of the lesson was often determined by ideas originating with students.

0 1 2 3 4

IV. CONTENT Propositional Knowledge

Never

Occurred Very Descriptive

6

The lesson involved fundamental concepts of the subject.

0 1 2 3 4

243

7

The lesson promoted strongly coherent conceptual understanding.

0 1 2 3 4

8

The teacher had a solid grasp of the subject matter content inherent in the lesson.

0 1 2 3 4

9

Elements of abstraction (i.e., symbolic representations, theory building) were encouraged when it was important to do so.

0 1 2 3 4

10

Connections with other content disciplines and/or real world phenomena were explored and valued.

0 1 2 3 4

Procedural Knowledge

Never Occurred Very

Descriptive

11

Students used a variety of means (models, drawings, graphs, concrete materials, manipulatives, etc.) to represent phenomena.

0 1 2 3 4

12

Students made predictions, estimations and/or hypotheses and devised means for testing them.

0 1 2 3 4

13

Students were actively engaged in though-provoking activity that often involved the critical assessment of procedures.

0 1 2 3 4

14 Students were reflective about their learning. 0 1 2 3 4

15

Intellectual rigor, constructive criticism, and the challenging of ideas were valued.

0 1 2 3 4

TIME DESCRIPTION OF EVENTS: Continue recording salient events here.

Notes:

V. CLASSROOM CULTURE Communicative Interactions

Never Occurred Very

Descriptive

16 Students were involved in the communication of their ideas to 0 1 2 3 4

244 others using a variety of means and media.

17

The teacher’s questions triggered divergent modes of thinking.

0 1 2 3 4

18

There was a high proportion of student talk and a significant amount of it occurred between and among students.

0 1 2 3 4

19

Student questions and comments often determined the focus and direction of classroom discourse.

0 1 2 3 4

20 There was a climate of respect for what others had to say. 0 1 2 3 4

Student/Teacher Relationships

Never Occurred Very

Descriptive

21 Active participation of students was encouraged and valued. 0 1 2 3 4

22

Students were encouraged to generate conjectures, alternative solution strategies, and ways of interpreting evidence.

0 1 2 3 4

23 In general, the teacher was patient with the students. 0 1 2 3 4

24

The teacher acted as a resource person, working to support and enhance student investigations.

0 1 2 3 4

25

The metaphor “teacher as listener” was very characteristic of this classroom.

0 1 2 3 4

TIME DESCRIPTION OF EVENTS:

Additional comments you may wish to make about this lesson.

Notes:

Note. From “Reformed Teaching Observation Tool (RTOP) (Technical Report No. IN00-3)” by M. Piburn, D. Sawanda, K. Falconer, J. Turley, R. Benford, and I. Bloom, 2000, Arizona State University. Retrieved from http://www.public.asu.edu/~anton1/AssessArticles/Assessments/Biology%20Assessments RTOP%20Reference%20Manual.pdf. Copyright 2000 by the Arizona Collaborative for Excellence in the Preparation of Teachers. Reprinted with permission.


245 Appendix L: Culturally Responsive Leadership Practices Survey

Description: The researcher-developed Culturally Responsive Leadership Practices Survey will be used to gather concluding responses from the purposive teacher sample and those not involved in the purposive sample regarding the culturally responsive leadership practices of their principal. This information will be mapped back to the data gleaned from having observed the principal in order to determine parallelism between the observed and the articulated responses, how culturally responsive leadership was performed, and its impact on instructional behaviors.

The survey tool is comprised of 18 indicators of culturally responsive leaders and a rating scale of 0 to 3 with 0 being none (no evidence), 1 being the lowest (low), 2 (moderate), and 3 (high) to capture the principals’ level of culturally responsive leadership.

Directions:

1. Please read each of the characteristics used to describe culturally responsive leadership. 2. Using a scale of 0 to 3, with 0 being the lowest and 3 being the highest, rate the

principal’s level of cultural responsiveness.

This survey should take no more than 20 minutes to complete.

BACKGROUND INFORMATION

Number of years teaching Number of years under the administration of current principal

I SCHOOL CULTURE, COMMUNICATIVE INTERACTIONS, AND

RELATIONSHIPS

No evidence Low Moderate High

1 Provides students with social, emotional, and academic supports. 0 1 2 3

2 Recognizes and celebrates the strengths of students. 0 1 2 3

3 Influences the school’s climate by being inclusive of cultural diversity. 0 1 2 3

4

Leverages rapport and relationships with families, community, and external partners to create inclusivity within the school.

0 1 2 3

II EQUITY No evidence Low Moderate High

5

Opposes and rejects deficit thinking about minority groups. Instead, exemplifies a warm, yet firm stance of high expectations for all students.

0 1 2 3

6

Promotes equality and advocates for the learning environment to reflect the multiculturalism that students bring to school.

0 1 2 3

7 Embraces restorative social justice in order to minimize exclusionary practices. 0 1 2 3

246 III INFLUENCE ON INSTRUCTIONAL BEHAVIORS AND PROCESSES

No evidence Low Moderate High

8

Hires qualified personnel having mastered their content, thereby having instructional staff that can provide experiences for their students that increase depth of mathematics understanding.

0 1 2 3

9

Matches students to the appropriate mathematics teacher and places the most experienced teachers with students in need of additional supports to master the content.

0 1 2 3

10 Recognizes the importance of mathematics teachers and sound mathematics teaching. 0 1 2 3

11

Communicates instructional expectations that are in alignment with high-quality and rigorous mathematics.

0 1 2 3

12 Ensures that teaching and learning are made relevant and meaningful to students. 0 1 2 3

13

Fosters and encourages mathematics teachers’ building of conceptual understanding in order to deepen mathematical thinking and problem solving as a process for students.

0 1 2 3

14

Frequently monitors and reviews mathematics student performance data individually and collaboratively with mathematics teachers in order to make just-in-time adjustments to set students up for success.

0 1 2 3

15 Frequently conducts observations of mathematics teachers and provides clear and timely feedback. 0 1 2 3

16

Constructs the master schedule to allow mathematics teachers to meet frequently (e.g., weekly, bi-weekly) to plan for instruction and to discuss mathematics student performance.

0 1 2 3

17


0 1 2 3

18

Persistent in the implementation of culturally responsive teaching through professional development to enhance teachers’ equity pedagogy.

0 1 2 3

Virginia Tech Institutional Review Board (IRB) Protocol Number #19-385 Virginia Tech Institutional Review Board (IRB), 540-231-3732 [[email protected]

247 Appendix M: Survey Validation Instrument and Responses

Description: Participants have been asked to provide feedback on each indicator to ensure the validity of the survey instrument. Two measures will be ascertained through this internal review – relevance of the survey indicators to the research questions and clarity (readability). A five-point ordinal Likert scale [strongly agree (5), agree (4), neither agree nor disagree (3), disagree (2), and strongly disagree (1)] will be used. The researcher’s goal for instrument validity is to obtain a greater than or equal to 80% (0.8) response rate, indicating an “improved conclusion validity and good statistical power” and an ability to “reach credible conclusions about relationships in [the] data” (Trochim, 2006, p. 1). Any survey indicator failing to reach the 80% threshold, will be revised and rewritten with a second review from the same group solicited to provide initial responses. Research Questions: The research questions to guide this investigation are –

1. To what extent, if any, do principals at the high school and middle school levels that exemplify culturally responsive leadership influence mathematics teachers’ use of culturally responsive teaching that results in building conceptual understanding in mathematics?

2. To what extent, if any, do culturally responsive teaching practices impact the mathematics performance of African American students at the high school and middle levels?

This survey should take no more than 20 minutes to complete. BACKGROUND INFORMATION

Number of years teaching (numeral only) Number of years under the administration of current principal (numeral only)

I SCHOOL CULTURE, COMMUNICATIVE INTERACTIONS, AND

RELATIONSHIPS

1

Provides students with social, emotional, and academic supports.

Strongly Disagree Disagree Neither Agree

or Disagree Agree Strongly Agree

Relevant to research questions 1 2 3 4 5 Clear (readability) 1 2 3 4 5

2

Recognizes and celebrates the strengths of students.




3

Influences the school’s climate by being inclusive of cultural diversity.




248

4

Leverages rapport and relationships with families, community, and external partners to create inclusivity within the school.




II EQUITY

5

Opposes and rejects deficit thinking about minority groups. Instead, exemplifies a warm, yet firm stance of high expectations for all students.




6

Promotes equality and advocates for the learning environment to reflect the multiculturalism that students bring to school.




7

Embraces restorative social justice in order to minimize exclusionary practices.




III INFLUENCE ON INSTRUCTIONAL BEHAVIORS

8

Hires qualified personnel having mastered their content, thereby having instructional staff that can provide experiences for their students that increase depth of mathematics understanding.




9

Matches students to the appropriate mathematics teacher and places the most experienced teachers with students in need of additional supports to master the content.




10

Recognizes the importance of mathematics teachers and sound mathematics teaching.




249

11

Communicates instructional expectations that are in alignment with high-quality and rigorous mathematics.




12

Ensures that teaching and learning are made relevant and meaningful to students.




13

Fosters and encourages mathematics teachers’ building of conceptual understanding in order to deepen mathematical thinking and problem solving as a process for students.




14

Frequently monitors and reviews mathematics student performance data individually and collaboratively with mathematics teachers in order to make just-in-time adjustments to set students up for success.




15

Frequently conducts observations of mathematics teachers and provides clear and timely feedback.




16

Constructs the master schedule to allow mathematics teachers to meet frequently (e.g., weekly, bi-weekly) to plan for instruction and to discuss mathematics student performance.




17




Relevant to research questions 1 2 3 4 5

250 Clear (readability) 1 2 3 4 5

18

Persistent in the implementation of culturally responsive teaching through professional development to enhance teachers’ equity pedagogy.




Virginia Tech Institutional Review Board (IRB) Protocol Number #19-385

Virginia Tech Institutional Review Board (IRB), 540-231-3732 [[email protected]]

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