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1 CULTURALLY RESPONSIVE TEACHING IN THE CONTEXT OF MATHEMATICS: A GROUNDED THEORY APPROACH By EMILY PETEREK A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009
2 2009 Emily Peterek
3 To Gloria Jean Merriex
4 ACKNOWLEDGMENTS Looking back on the past four years, I am truly amazed at the number of people who have shaped my experiences and, ultimately, this work. Each person and entity had an impact on the ways in which I see our educational system, society, and the dynamics therein. Most importantly, these individuals taught me that I must never stop learning, looking for new perspectives, and critically examining structures that drive education and affect students To each of them, I am truly grateful. I was fortunate to take several extremely formative courses in my first semest er as a doctoral student that fostered my interest s in culturally responsive teaching and equity in mathematics education and teacher education I would like to thank Dr. Dorene Ros s who inspired me to critically examine mathematics education and teacher education while engaging in meaningful activities to disseminate such work. I would also like to thank Dr. Cirece West Olatunji, who helped me to hone these interests in her course, and provided me with frameworks from counselor education that informed my work tremendously. I am also grateful for the guidance of Dr. Ruth Lowery, a supportive and foundational member of my doctoral committee who has encouraged my fascination with and commitment to culturally responsive teacher education I could not have done this work without the cooperation and support of the Duval Elementary School family. I am amazed by the dedication of the administration and faculty, and the candidness of the students and parents. I learned so much from each of you, and you truly made this research come to life. Thank you especially to Dr. Leanetta McNealy who was so generous with her time and insights, and Mrs. Angela Terrell, Ms. Lilliemarie Harvey, and Mr. Leonard Marshall, who gave a voice to Gloria when she could not do so he rself. I would also like to thank the Merriex family who let me into their lives during a difficult time of grieving.
5 Gloria Jean Merriex, the teacher on whom this entire work is based, also deserves the greatest of thanks. She was truly an inspiration to me, and I will never forget the way that I felt when watching her teach. I can only hope that she is proud of the work that follows. Along the way, there have also been friends and family members who have provided me with unwavering support. My wond erful husband Tim has always supported my commitment to this work. My parents and sister, Bob, Marie, and Cilla, have served as sounding boards and have put up with seeing less of me as I pursued this work. Lastly, a huge thank you to Dr. Thomasenia Lo tt Adams who has been my guide, rock, support system, and teacher, and who has taught me the value of hard work and determination. She has always verbalized her belief in my abilities while holding me to the highest standard and pushing me to the next lev el. She has taken me from dependent to independent, insecure to confident, and novice to researcher. I only hope that I can provide the same amount of encouragement, feedback, and care to my own graduate students in the future. I feel so lucky to have s uch an inspirational and supportive mentor wh o is so generous in so many ways
6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF FIGURES ................................ ................................ ................................ ....................... 10 ABSTRACT ................................ ................................ ................................ ................................ ... 11 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 13 Statement of the Problem ................................ ................................ ................................ ........ 13 Culture and Education ................................ ................................ ................................ ..... 15 Culture an d Mathematics ................................ ................................ ................................ 17 Purpose of the Study ................................ ................................ ................................ ............... 19 Research Questions ................................ ................................ ................................ ................. 20 Structure of the Dissertation ................................ ................................ ................................ ... 20 2 REVIEW OF THE LITERATURE ................................ ................................ ........................ 23 Schooling in an Oppressive Society ................................ ................................ ....................... 25 Cultural Incongruities in Mathematics Education ................................ ........................... 27 Responses from the Mathematics Education Community ................................ ............... 28 African American Culture ................................ ................................ ................................ ...... 31 Successful Teachers of African American Children ................................ .............................. 37 Culturally Responsive Teaching ................................ ................................ ............................. 42 Gaps in the Literature ................................ ................................ ................................ ............. 47 3 METHODOLOGY ................................ ................................ ................................ ................. 49 Nomination process ................................ ................................ ................................ ................ 50 Grounded Theor y ................................ ................................ ................................ .................... 52 Theoretical Perspective ................................ ................................ ................................ ... 54 Data Collection ................................ ................................ ................................ ................ 56 Simultaneous Dat a Collection and Analysis ................................ ................................ ... 57 Data Analysis Process ................................ ................................ ................................ ..... 58 Member Checks ................................ ................................ ................................ ............... 59 4 MONOGRAPH MANUSCRIPT ................................ ................................ ............................ 60 Phenomenon: The Life and Teaching of Gloria Jean Merriex ................................ ............... 60 Table of Contents ................................ ................................ ................................ .................... 61 Preface ................................ ................................ ................................ ................................ .... 62 Main Characters ................................ ................................ ................................ ...................... 67 Part I ................................ ................................ ................................ ................................ ........ 69
7 Chapter 1 ................................ ................................ ................................ ................................ 70 Chapter 2 ................................ ................................ ................................ ................................ 83 Chapter 3 ................................ ................................ ................................ ................................ 97 Part II ................................ ................................ ................................ ................................ .... 110 Chapter 4 ................................ ................................ ................................ ............................... 111 Culturally Responsive Teaching ................................ ................................ .................... 113 Culturally Responsive Mathematics Teaching (CRMT) ................................ ............... 117 Cornerstones and Interactions ................................ ................................ ....................... 121 Knowledge ................................ ................................ ................................ ............. 122 Communic ation ................................ ................................ ................................ ...... 123 Relationships/trust ................................ ................................ ................................ .. 124 Constant reflection and revision ................................ ................................ ............. 124 Cycle of Pedagogy and Discipline and Culturally Responsive Teaching Methods ...... 125 Communal learning ................................ ................................ ................................ 126 Rhythmic teaching ................................ ................................ ................................ .. 127 Storytelling ................................ ................................ ................................ ............. 129 Focus on review ................................ ................................ ................................ ..... 130 Improvisation ................................ ................................ ................................ ......... 131 Warm Demander Pedagogy ................................ ................................ ........................... 131 Outside Support ................................ ................................ ................................ ............. 136 Part III ................................ ................................ ................................ ................................ ... 142 Chapter 5 ................................ ................................ ................................ ............................... 143 Courtney ................................ ................................ ................................ ........................ 143 Lisa ................................ ................................ ................................ ................................ 147 Tim ................................ ................................ ................................ ................................ 148 Jennifer ................................ ................................ ................................ .......................... 150 Diana ................................ ................................ ................................ .............................. 151 Chapter 6 ................................ ................................ ................................ ............................... 156 Implications for Classroom Practice ................................ ................................ ............. 156 Implications for Mathematics Teacher Education Programs ................................ ........ 158 Implications for Future Research ................................ ................................ .................. 159 Appendix Formal Methodology ................................ ................................ ........................ 161 Research Questions ................................ ................................ ................................ ....... 161 Initial Stud y ................................ ................................ ................................ ................... 161 Nomination Process ................................ ................................ ................................ ....... 162 Grounded Theory ................................ ................................ ................................ ........... 164 Theoretical Perspective ................................ ................................ ................................ 165 Data Collection and Analysis ................................ ................................ ........................ 167 Member Checks ................................ ................................ ................................ ............. 170 Sample Interview Questions ................................ ................................ ................................ 171 5 JOURNAL ARTICLE 1 ................................ ................................ ................................ ....... 172 Meeting the Challenge of Engaging Students for Success in Mathematics by Using Culturally Responsive Methods ................................ ................................ ........................ 172 Setting the Stage ................................ ................................ ................................ ............ 173 Culturally Responsive Teaching ................................ ................................ .................... 175
8 A Brief Note on the Challenges That African American Students Face ....................... 177 Ms. Kay: Foundations in Comm unity ................................ ................................ ........... 177 ................... 179 Chants and movement ................................ ................................ ............................ 179 Real life ex amples ................................ ................................ ................................ .. 182 High standards through tough love ................................ ................................ ........ 183 Focusing student energy for mathematics learning ................................ ................ 184 Conclusion ................................ ................................ ................................ ............................ 185 6 JOURNAL ARTICLE 2 ................................ ................................ ................................ ....... 188 Achieving Su ccess with African American Learners: A Framework for Culturally Responsive Mathematics Teaching ................................ ................................ ................... 188 Summary ................................ ................................ ................................ ............................... 189 Introduction ................................ ................................ ................................ ........................... 189 Culturally Responsive Teaching ................................ ................................ ........................... 191 An Illustration of Culturally Responsive Mathematics Teaching (CRMT) ......................... 191 Knowledge ................................ ................................ ................................ ..................... 192 Communication ................................ ................................ ................................ ............. 193 Relationships/Trus t ................................ ................................ ................................ ........ 195 Constant Reflection and Revision ................................ ................................ ................. 196 The Cycle of Pedagogy and Discipline ................................ ................................ ......... 197 Setting the Stage for CRMT ................................ ................................ ................................ 198 7 CONCLUSIONS AND IMPLICATIONS ................................ ................................ ........... 199 Mathematics Classroom Practice ................................ ................................ .......................... 199 Mathematics Teacher Education Programs ................................ ................................ .......... 204 Future Research ................................ ................................ ................................ .................... 205 APPENDIX A GLORI A MERRIEX INTERVIEW PROTOCOLS ................................ ............................. 208 Interview #1 ................................ ................................ ................................ .......................... 208 Interview #2 ................................ ................................ ................................ .......................... 208 Interview #3 ................................ ................................ ................................ .......................... 209 B OUTSIDE PARTICIPANT INTERVIEW PROTOCOLS ................................ ................... 210 Merriex Family Protocol ................................ ................................ ................................ ....... 210 Leanetta McNealy Protocol ................................ ................................ ................................ .. 210 Buffy Bondy Protocol ................................ ................................ ................................ ........... 211 Leonard Marshall and Lilliemarie Harvey Protocol ................................ ............................. 211 Angela Terrell Protocol ................................ ................................ ................................ ........ 212 Former Student Protocol ................................ ................................ ................................ ....... 212 Former Student Parent(s) Protocol ................................ ................................ ....................... 212
9 LIST OF REFERENCES ................................ ................................ ................................ ............. 214 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 228
10 LIST OF FIGURES Figure page 4 1 Culturally Responsive Mathematics Teaching (CRMT) ................................ ................. 120 6 1 Culturally Responsive Mathematics Teaching (CRMT) ................................ ................. 192
11 Ab stract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CULTURALLY RESPONSIVE TEACHING IN THE CONTEXT OF MATHEMATICS: A GROUNDED THEORY APPROACH By Emily Peterek August 2009 Chair: Thomasenia Lott Adams Major: Curriculum and Instruction The achievement gap between African American students and their white counterparts is pervasive in elementary school mathematics classrooms (Lee, 2006). Too often, step by step methods of instruction are utilized in mathematics teaching, exacerbating cult ural incongruities that exist between teachers and students. Work in the area of culturally responsive teaching (Gay, 2000) provides a useful and powerful theoretical framework within which to explore these inequities while uncovering successful practices in classrooms that promote equity and access to mathematical knowledge. Within this framework, particular, culturally based pedagogies and effective styles of communication have been documented through the study of highly effective teachers of African Am erican students (Gay, 2000; Irvine, 2002; Ladson Billings, 1994), though very little of this work focuses on the unique work of mathematics teaching and learning. As such, mathematics teachers are struggling to help students of color succeed as inequitabl e tracking practices continue. This dissertation presents a working grounded theory meant to help teachers and teacher educators in the field of mathematics education conceptualize culturally responsive teaching in the context of mathematics. Grounded i n the work of Gloria Jean Merriex, a highly effective
12 mathematics teacher in a largely African American, high poverty elementary school, this theory can guide teacher efforts to help students of color succeed in mathematics classrooms. Results show that the work of culturally responsive mathematics teaching is complex and fluid, effecting student perceptions and supporting racial identity development among African American students. Specifically, there are four main, interconnected cornerstones of cultur ally responsive mathematics teaching that frame the everyday cycle of pedagogy and discipline and experiences of the student: communication, knowledge, trust, and constant reflection and revision. These cornerstones can be used to guide pre and in servic e teachers who are working to become more culturally responsive, teacher educators who are working with pre service mathematics teachers, and administrators and policy makers who seek to promote equity in mathematics classrooms.
13 CHAPTER 1 INTRODUCTION Statement of the Problem Schools in America are becomi ng increasingly diverse. The United States is on track to corroborate th e Census Bureau (2000) estimates that people of color will make up about 38 percent percent of the general 40 percent in 2000) is increasing each year, bringing linguistic and cultural diversity to the educational system (El Nasser, 2004). Ideally, this diversification of the student body would bring fresh perspectives and new waves of pedagogical and school p ractices that capitalize on the cultural knowledge and experiences of various groups as invaluable funds of knowledge. Statistics show, however, that schools are failing to meet the needs of students of color, who are falling behind in nearly every academ ic category (Ladson Billings, 1994; Gay, 2000; Delpit, 1995). Despite the racial breakdown of a school, students of color are often grossly overrepresented in lower tracks including special education settings (Gay, 2002; Townsend, 2003) and are repeatedly met with lower expectations by teachers and peers than their white counterparts (Irvine & York, 1993). This type of in school segregation results in achievement gaps that continue to grow even as the student body becomes more diverse (Lee, 2006). Betwee n school segregation is still rampant as well (Kozol, 2005) and contributes to academic struggles faced by students of color. Statistically, these children are more likely to be poor (Ladson Billings, 1994), and students in low income neighborhoods genera lly attend older, less maintained down schools that are often staffed with inexperienced or unqualified teachers
14 (Kozol, 1995, 2005). As a result of these in and between school practices, students of color are much more likely to dropout (Montecel, Co rtez, & Cortez, 2004). These types of data beg the question, are certain races academically superior to others? To some educators, the answer is a frightening yes, and data support their position that diversity in the student body is a detriment to the teaching and learning process that must be overcome rather than a strength that should be utilized in instruction (Gay, 2000). This belief is exacerbated by the fact that the majority of the teaching force is white and middle class (Howard, 2006) and that many traditionally trained white teachers have limited interactions with individuals from diverse backgrounds (Nieto, 1999). This leads to stereotyping, fear, and a desire to control every aspect of the teaching and learning process, thus stifling indivi dual student identities (Irvine, 2003). In this quest for control, many teachers turn to lecture style, teacher centered pedagogies that require students to sit quietly, take notes, and remain stoic. While some students may thrive in such cla ssroom settings, those that do not are often labeled as learning disabled or placed in lower tracks (Oakes, 1990) where step by step, teacher directed instruction is even the norm. Many teachers will argue that these types of traditional instruction, w hich rely heavily on with an equal opportunity to succeed. In treating all students in exactly the same manner, however, teachers are neglecting the various modalities, modes of communication, languages, norms, and values that exist in each classroom. Moreover, teachers who take this approach may not realize that they are acting within their own cultural norms, and may be forcing students to conform to an unf amiliar set of standards. This type of pedagogy, then, is highly cultural and favors only particular groups of students. Given the racial profile of the typical teacher as a
15 white, middle class, female (Howard, 2006), it is likely the cultural incongrui ties in the mathematics classroom that cause students of color to fall behind. Many teachers ignore these disconnects or attribute them to student shortcomings I nconsistencies in school versus home culture (i.e. how learning is assessed, how information is acquired) however, are often (Boykin, 1986; Spindler, 1987). Moreover, since school culture is so often based on white culture, students of color may not see school succes s as cultural success. This belief is often misunderstood as a lack of drive or apathy towards education. African American children however, formative cultural experiences and t hose imposed in school lead them to reject the modes of achievement avail able in classrooms (Marryshow, Hurley, Allen, Tyler, & Boykin, 2005 p. 603 ). Thus, African American students value achievement, but do not value mainstream achievement or achiever s, instead embracing Afro cultural success that is more consistent with their format ive cultural experience Culture and Education In order to understand how systemic issues of equity have permeated schools and classrooms, we can look to historical even ts that have shaped the structure, practices, and cultural fabric of American schooling. The significance of cultures, defined as pattern[s] of shared basic assumptions that [a] group learned as it solved its problems of external adaptation and internal i ntegration that has worked well enough to be considered valid and, therefore, to be taught to new members as the correct way to perceive, think, and feel in relation to those problems (Schein, 1991 p. 12), in schools is often overlooked Culture is the underc urrent that invisibly drives individual and group actions and reactions. It consciously and subconsciously shapes the ways in which we communicate, our daily rituals and practices, our sense of self, our beliefs, and our values. As
16 such, c ulture gr eatly influences every aspect of the teaching and learning process including the ways in which teachers enact pedagogies and children learn and develop as thinkers (Stoicovy, 2002). The American educational system itself, however, is based on dominant, Eu ro centric culture. In 2004, we celebrated the fiftieth anniversary of the 1954 Brown vs. Board of Education decision. This case dee med separate schools inherently unequal, thus mandating integration. This step towards racial equality was thwarted, how ever, by the e ntrenched racism that already existed in the United States (Ladson Billings, 2004; Tillman, 2004) Integration seemed like a fair solution on the surface, but African American students faced a new set of inequities as desegregation occurred. Schools were in compliance with the Brown verdict by simply allowing students of color to attend schoo ls that housed white students. The ways in which schools educated their new students, however, was not addressed, and n o further effort (in terms of p edagogy or otherwise) Billings, 2004, p. 3) and, in a sense, took a blatantly inequitable issue and simply made it indiscernible Many basic school practices have remained the same since 1954, and the statistics mentioned above stem from these initial occurrences. As a result, African American children were (and are) expected to conform home practices (Patterson, Hale, & Stessman, 2007). S tudents who do not conform are centric frame of refer (West Olatunji, 2004, p. 420)
17 Culture and Mathematics Perhaps the most damaging aspect of these inequities in the educational system is that the destructive facets are largely hidden. The culture of power (Delpit, 1995), which has always been at the base of every aspect of schooling, is now the norm. Teachers operate within this system unknowingly perpetuating the status quo, and students of color may be forced to participate in their own oppression (Hinchey, 2004) This is reflected in many aspects of schooling from behavioral expectations, such as the ways in which students are expected to behave while learni ng and dominant pedagogies in traditional mathematics classrooms to administrative treatment of students when enacting disciplinary procedures and the criminalization of particular behaviors (Skiba & Peterson, 2000). Mathematics is a subject matter tha t is often driven by such invisible practices. Unlike English, which explicitly requires particular language skills, or social studies, which is based on particular events, mathematics seems to be, for the most part, free from culture. This belief largely stems from the perception that students with linguistic differences may be able to understand mathematical symbols without learning English, or that mathematics is seemingly fixed and static, and does not seem relate to any historical or debatable perspec tive. Statistically, however, current mathematics pedagogy is failing students of color the achievement gaps in this subject are some of the most marked (Howard, 2006 ; Lee, 2006 ), and the teaching of students of color in mathematics is often wrought w ith lowered expectations, actions that reinforce racial stereotypes, and generally ineffective teaching (Irvine & York, (Stiff, 1990). These findings imply that th e learning of mathematics is h ighly political and cultural.
18 Historically speaking, the knowledge that is taught in schools today (beyond the basics needed to function in a society based on trade and capital) has been developed in our historically oppres sive society. Moreover, just as other curricula, the mathematics curriculum is largely written by and taught by white educators. Thus, the culture of power has determined what it is that we need to know mathematically and the best methods through which t his information should be taught and learned. This can cause tremendous struggles for students from other cultural backgrounds, and creates a disconnect between home and school expectations for these students. Pedagogically speaking, the universal symbo ls and notations that are used in mathematics, for example, must first be taught before they can be understood and used, and the importance and value of culture in this process of teaching and learning is undeniable. Mathematics is often taught using lect ure and strict direct instruction models where the teacher is the holder of the knowledge and the students brains are seen as depositories in which information is banked (Freire, 1970). S tudents are often not involved in the lesson; rather, teachers pas s out worksheets to test student knowledge, or teachers pose seemingly meaningless problems to encourage participation. In general, mathematics is not taught in a way that makes knowledge rele vant and accessible to students. made, and little pedagogical innovation is displayed, especially in lower level classes where students of color are overrepresented (Gay, 2000; Oakes, 1985). In these classes, teachers believe that students can on ly do mathematics when told step by step procedures for doing so (Paine, 1989). As such, the teacher perpetuates the deficit discourse that dominates mathematics education. Thus, from every angle, culture does play a major role in the teaching and learni ng of
19 mathematics. It is surprising, however, that the belief that mathematics itself is indeed free from culture has not resulted in the explicit incorporation of culture into mathematics curriculum and instruction. Purpose of the Study In recent yea rs, many educators have worked to combat the achievement gaps that have different from what is currently happening must occur in how large numbers of students of color There are many discussions in the literature that center on the needs of learners from diverse backgrounds, but reforms aimed at meeting these needs are not easi ly conceptualized, and require innovation, patience, and willingness to change at every level. Reinvented, empowering classroom instructional techniques are one part of this much needed systemic reform process. Culturally responsive teaching (CRT; Gay, 2000) is one such theoretical framework that focuses on the development of empowering teaching practice and instruction. Culturally responsive practices include (but are not limited to) improved and effective classroom interactions between students and t eachers (and students and students), continuous re thinking of the curriculum, community based learning projects, and investigations of the status quo (Gay, 2000; Ladson Billings, 1994) As such, CRT seeks to transform the teaching and learning experience providing positive, formative experiences for students. Further, CRT aims to improve racial (and cultural) relations among students. As such, these in class interactions and progressions will affect the entire school community, and will benefit white s tudents as much as students of color.
20 Research Questions In order to more readily conceptualize CRT as it relates to African American children, it is important that researchers study successful schools and teachers. Ladson Billings (1994) investigated such practices in The Dreamkeepers This work explored the conceptions, practices, beliefs, and outcomes of successful teachers of African American students, using classroom anecdotes and personal stories to convey the import of such work. This and relat ed work, however, remains general in terms of content, and highly theoretical. As such, this foundational work does not adequately inform the field of mathematics education in ways that specifically focus on race and power in mathematics settings. Furthe r, examples of successful mathematics teachers in high poverty, high minority schools are rare in the mathematics education literature, making it difficult for educators to conceptualize CRT in the context of mathematics. As such, the following research q uestions were posed: 1. How do effective mathematics teachers working in a high poverty, predominantly African American school context: a. structure instructional practices and interactions? b. establish a learning environment that results in mathematical success? 2. What are the interactions between these phenomena? 3. What part (if any) does culture play in these phenomena? Structure of the Dissertation The present work is in the form of a manuscript dissertation. This chapter (chapter 1) serves as an overall introduction to the body of work represented here, and gives context to the need for literature in the area. Chapter 2 is a review of pertinent li terature, and chapter 3 is a formal methodology section. Information from each of these chapters was used in the manuscripts that constitute chapters 4, 5, and 6, as the manuscripts (a monograph, a practitioner article, and a research article, respectivel y) are syntheses of the gathered information and
21 research. A cover page precedes each manuscript. This page gives the title of the manuscript, a short explanation of the work and its purpose, and a citation for reference. Lastly, Chapter 7 consists of c onclusions, implications, and possible future research directions. An appendix, which consists of sample interview protocols, and references are included at the end of the document. The focus of this dissertation document is the qualitative study that I rigorously completed in the spring of 2008. This case study, which adds to the literature on culturally responsive teaching practices in the context of mathematics, was done using grounded theory (see chapter 3), and is based solely on data (i.e. intervie ws with the teacher, artifacts, and observations of teaching) that were (e.g. students, parents, administrators) were conducted as specific pedagogies and practices of the teacher were the focus. T he results of this study appear in various forms in all three manuscripts, and this research constitutes the core of my formal dissertation work. As such, chapters 2, 3, 6, and 7 reflect this particular study. Chapter 4 includes additional data that nee ds explanation. Soon after the conclusion of my grounded theory study, the teacher/participant on whom the grounded theory work is focused passed away suddenly. In response to the call to incorporate my work into larger projects work, I began speaking to involved parties who were connected to this teacher (e.g. family, students, and administrators) in order to construct a monograph. This monograph is chapter 4 of this dissertation, and was only used to inform the work represented in that section. The remainder of the chapters (including the conclusions and implications) are based on the original grounded theory study. I make this distinction because the interviews that
22 ed rigorously or systematically, and therefore do not inform the research portion of this dissertation.
23 CHAPTER 2 REVIEW OF THE LITERA TURE In recent years, the demand for highly proficient mathematicians in the workplace has grown. Mathematically skilled workers are greatly sought after, as these individuals are needed to address national issues such as changing energy needs, financial crise s, national defense operations, evolving computer programming requirements, and scientific breakthroughs. As such, citizens with a strong mathematical background will have enhanced opportunities to impact their career trajectories; conversely, students wh o are not provided access to high level mathematics classrooms, this filtering process begins when students are very young through practices such as tracking which are r ealized when particular discourses, ways of speaking, and reasoning techniques are privileged (Diversity in Mathematics Education Center for Learning and Teaching [DMECLT], 2007) in these settings. In turn, certain funds of knowledge, ways of learning and knowing, and sociocultural norms provide specific students with capital in the mathematics classroom (Cobb & Hodge, 2002; Gutierrez, Baquedano Lopez, & Tajeda, 1999). Equitable access to mathematics education among students is imperative to counter this filter effect. Current, pervasive gaps in mathematics achievement between students of color and their white counterparts, however, imply that it is students of color who are more often denied access to mathematical knowledge and ultimately work in capaci ties that such knowledge affords. In 2005, for example, the National Assessment of Educational Progress ( NAEP ) report showed that 47 percent of white students versus 13 percent of black students were performing at or above proficiency in mathematics. Fur ther, researchers in the areas of equity and access in mathematics have extensively documented persistent gaps in mathematics achievement between students of color and white students using quantitative measures (Lee, 2006; National Center for
24 Education Sta tistics [NCES], 2003), while others have qualitatively explored specific mathematics curricula and pedagogies that provide or inhibit access to mathematics knowledge (Ladson Billings, 1994; Howard, 2006, for example), understanding that issues of power, ra ce, culture, and access are embedded in these contexts. Such studies have provided the field with important knowledge about the state of affairs in mathematics education, and highlight the need for more research that results in outcomes that are useful to mathematics teachers of students of color. The framework of culturally responsive teaching (CRT; Gay, 2000) has been explored to this end, and provides a construct that is useful in conceptualizing equitable educational practices. Many commentaries and articles and books that focus on theorizing CRT in general (Gay, 2000, 2002) and with a focus on mathematics (Greer, Mukhopadhyay, Powell, & Nelson Barber, 2009 theory, yet s tructured research specific to CRT in the context of mathematics remains piecemeal. Much related work has been done to identify home based ways of learning and knowing that students bring to the mathematics classroom and the ways in which certain types o f participation are valued or marginalized in such contexts (Boaler & Greeno, 2000; Cobb & Hodge, 2002; Martin, 2000; Moll, Amanti, Neff, & Gonzales, 1992; Nasir, 2002). This has led to a widened perspective (in the greater mathematics education community ) of what it means for a student to demonstrate mathematical proficiency or participate appropriately in the mathematics classroom, while feeding research that focuses on inconsistencies in classroom expectations versus home based practices (Hand, 2003; Na sir, 2004). These studies give rise to questions about racial identity development and negotiation in the classroom, an area which has been of focus in mathematics education research (Cobb & Hodge, 2002; Martin, 2000, 2006;
25 Nasir & Hand, 2006), culturally congruent learning opportunities for students in mathematics classrooms (Boaler 1998; Hiebert et al., 1997; Jacobs, 2002), how these opportunities differ for white students and students of color (Boaler, 2003, 2006), and ultimately perceptions and notions of mathematical proficiency (Saxe, 1988; Taylor, 2004). Research on CRT considers these issues holistically in classroom settings, and challenges teachers to empower students to examine societal structures through mathematics. This work focuses on key aspects of the classroom, and contributes to the overall theory of CRT (Frankenstein, 1997; Gutstein, 2003, 2006; Ladson Billings, 1994, 2001; Tate, 1995), but is not specific to mathematics education. Overall, in fact, the research base in areas relating to equity As such, this research in understanding the construct and complexities of CRT have framed the need for systematic research specific to holistic, culturally responsive mathematics teaching practices of students of color that a re explicitly contextualized in racial and cultural realities. In order to give context to the study presented in this dissertation, which attempts to address these shortcomings, the goals of this review of the literature are to (1) explore the school co ntexts and pertinent research that contribute to inequitable access in mathematics education; (2) discuss related research that focuses on racial/cultural identity development and practices of successful teachers of African American children; and (3) prese nt the theoretical construct of CRT in order to show the need for research specific to CRT in the context of mathematics. Schooling in an Oppressive Society educational realm As is evidenced by severe gaps in mathematics achievement among groups
26 of students ( Lee, 2006; NCES, 2003), learners from particular backgrounds experience systemic struggles in instructive settings such as higher dropout rates and significantly lower a cademic achievement scores (Pennington, 2000; Ladson Billings, 1994) than their white counterparts. Students of color are over represented in special education programs (Gay, 2002; Townsend, 2003), are more likely to be suspended from school (Ladson Billi ngs, 1997), and are less likely to receive a high school diploma (Greene & Winters, 2005) As Gay (2000) insists, why are students of color, who are successful in so many areas outside of school, failing in school settings? Hegemony, or of domination [of a group] not by the sheer exercise of force but primarily through consensual social practices, social forms and social structures is a driving force in inequitable educational access This implies that the s ystemic dominance and subjugation seen in society and schools are not a conscious arrangement by a dominant class, but social constructions that direct t he way we live. For example, i ndividuals are often intolerant of b latant act s of hate yet rarely question the way things are in our lifestyles and social practices. Ironically, the social norms we ignore are the most blatant, systematic and destructive sources of oppression (Hinchey, 2004) As such, hegemony, often in visible to those it subjugates, is allowed to remain in place without question. The silence of the dominant class condon es oppressive cycles, and the oppressed continue to perpetuate the social structures that favor the dominant class by accepting the sta tus quo. It is largely because of the historic and unquestioned hegemony of the dominant culture that schools enact and engage in oppressive practices. In exploring racist roots in America, landmark educational decisions, and current educational practice s, such hegemonic
27 practices become clear, showcasing obstacles that are (and always have been) in place, preventing culturally diverse children from feeling valued by the educational system. Cultural Incongruities in Mathematics Education The culture of sc hooling is based on historical precedents (such as Brown vs. Board of Education ) that were mandated with good intentions, but in the context of racism (Ladson Billings, 2004). Schools, therefore, were not designed to meet the needs of diverse populations; rather, white assump tions, practices, and values have silently and overtly dictated norm s in these settings (Howard, 2006) Often, i ndividuals from diverse backgrounds are expected to abandon their home culture and assimilate into the mainstream culture (Sleeter, 2001 b ). This mismatch causes struggles and resistance in and out of school among students and families whose home culture does not align with that of the school. These trends can be evidenced in many areas of schooling; namely specific dominant teaching practices (Howard, 2006) within and between school segregation (Gay, 2002; Kozol, 1995, 2005) and the lack of change in such pedagogies and the curricula that drive them over the past 50 years. Currently, urban schools are more seg regated than they were in 1968 (Orfield, Frankenberg, and Lee, 2003 ) especially in mathematics classrooms (Stiff, 1990) and equal education is not a reality for many students In neighborhoods with high populations of Black and Latino students, school buildings are m ore likely to have structural problems (in addition to staffing problems), thus providing worse conditions in general (Kozol, 2005; Oakes & Saudners, 2002). These schools also offer fewer advanced placement courses in mathematics, and employ fewer qualifi ed teachers (Darling Hammond & Sykes, 2003), many of whom are teaching outside of their field (Rogers, Jellison Holmes, & Silver, 2005). On the contrary, schools with large populations of white students are expected to have trained and qualified mathemat ics instructors teaching quality curricula in appropriate settings
28 (Rogers, Jellison Holmes, & Silver, 2005) and more advanced and pre college mathematics course offerings (Lee, Burkham, Chow Hoy, Smerdon, & Geverdt, 1998). Further, the normative aspects of mathematics education and school in general provide white students with a sense of cultural congruity. In the mathematics community, for example, discourse patterns seem to align with those of the culture of power (Gutierrez, 2002). As such, researche rs have found race to be a determining factor in the ways in which a student can expect to experience mathematics education (Hunter & Donahoo, 2003). Thus students of color can ultimately expect to face a substandard form of mathematics education. Conse quently the inferiority that students of color have lived with for centuries is still in place in the educational system particularly in mathematics classrooms This is especially dangerous in the school setting, as educational institutions perpetuate t he status quo by instilling these values and views in their students (Hinchey, 2004) As a result, student achievement data shows that students of color are falling behind in mathematics (Ferguson, 2000; Lee, 2006; Noguera, 2003) despite their socioeconom ic status. Responses from the Mathematics Education Community In response to realizations of inequities that exist in mathematics classrooms and the possible damages that such practices may do in terms of student self concept and racial identity, natio nal organizations have released statements, standards, and projects meant to help teachers promote equity in mathematics. The National Council of Teachers of Mathematics (NCTM), for example, published six guiding principles in its Principles and Standards for School Mathematics All students, regardless of their personal characteristics, backgrounds, or physical challenges, must have opportunities to study and support to learn does not mean that every student should receive identical instruction; instead, it demands that reasonable and appropriate accommodations be made as needed to promote access and year to a coherent, challenging
29 mathematics curriculum taught by competent and well supported mathematics program that provides solid support for their learning and is respo nsive to their prior documented examples demonstrate that all children, including those who have been traditionally underserved, can learn mathematics when they have access to high quality ins tructional programs that support their learning (pp. 11 13). Given the powerful and widely heard voice of NCTM, the publication of this principle did bring much needed attention to issues of equity and access in mathematics. The language, however, does co than the traditional norm and have needs to which teachers must adjust rather than challe nging call for systemic, enduring changes in perspectives. Cert ainly, the intention of this work is notable, though it is dominated by status quo discourse. Critical mathematics aims to challenge and discredit the deficit based views that dominate mathematics education discourse. Critical scholars, in fact, have th eorized that the culture of mathematics explicitly supports and perpetuates inequities while privileging particular groups (Delpit, 1988; Tate, 1994). Critical mathematics (Gutierrez, 2002) challenges this culture and provides a framework that encourages and empowers students to use mathematics to critically examine the schooling and social systems within which they operate (see Gutstein & Peterson, 2006, for example). Moreover, critical mathematics requires teachers to incorporate stronger, more meaningf ul connections between in school mathematics and out of school mathematical practices into the classroom, continuously situating such experiences in social realities. This type of instruction increases accessibility of mathematical knowledge to students f rom diverse backgrounds. This works to close the participation gap, wherein white students
30 participate in classroom activities more often and with more success than students of color, that exists in mathematics classrooms (Hand, 2006). A small number of other works, such as the Algebra Project (Moses & Cobb, 2001; Silva, Moses, Rivers, & Johnson, 1990), also center on issues of race and power while focusing on cultural relevancy in mathematics education. The Algebra Project endeavors to make algebra avai lable to middle school students at all achievement levels by explicitly connecting mathematical literacy to student communities. Students are engaged in inquiry projects that are developed out of local practices and issues, thus providing relevant, concre te contexts for the Project; as such, inquiry projects and contexts vary widely based on location, neighborhood, and other relevant factors. Students living in the inner city of Chicago, for example, may on bus or car speeds. In these ways, the Project addresses the issues of disproportionate access to mathematics in schools (Moses & Cobb, 2001) that have resulted in disproportionate access to college and certain career tracks. Other mandates that have aimed for similar success have been met with resistance by critical researchers, students, and teachers. Of ten, these programs and mandates are introduced as interventions meant to address a problem rather than reform efforts aimed at re thinking knowledge and mathematical literacy as keys to future success and access to college and competitive
31 eighth grade students take a first year algebra course. In implementing this mandate, however, California students were tracked into various levels of algebra classes (Paul, 2003), thus maintaining the inequities inherent in tracking that were in place before the mandate. Teacher dispositions towards groups of students remained largely unchanged (Oakes, Joseph, & Muir, 2003). As a result, instruction in the lower level class es remained procedural and inadequate; students in the classes assumed they were doing work that would prepare them for college debunk the myth that only a select group of students has the ability to complete an Algebra courses in middle school, these efforts have, in fact, perpetuated the deficit discourse and failed to explicitly address the underlying issues of race and power that have created the initial gaps in achievement. African American Culture It has been hypothesized that the educational system does not value or utilize the strengths and abilities of African American children that are gained through membership in their cultural group (Hale Benson, 1982). Moreover, many scholars argue that the African American experience that shapes cultural patterns is widely misunderstood, and that resulting norms and practices are often treated as inferior or damaging (Boykin, 1986). Thus, in order to gain meaningful insight into the learning styles of Afric an American children in ways that can dramatically affect school practices, researchers must work to understand African American culture, value and incorporate culturally based strengths of African American children, and 234). A large body of ethnographic, phenomenological, and quantitative data has shown that Benson, 1982) that is unique in
32 nature Within African American culture, common language patterns, distinctive ways of communicating, behaviors, learning skills, and expressive styles are universally revered and utilized (Baratz & Baratz, 1969) The culturally based norms that result f rom these practices, however, often do not align with status quo norms that dominate schools. The resulting situation fosters perceived inadequacies of African American children ( Boykin 1986); a position which neither helps to define the problem nor prod uces real results in affecting the existing achievement gaps (Ogbu, 1978). Many aspects of African American culture have been identified as hallmarks of the American black experience (Banks, 1 976; Levine, 1977). Boykin (198 3) identified and described ni ne interconnected dimensions of African American culture with the understanding that these common cultural practices and ways of being should not be used to categorize or stereotype all black Americans. Among these facets are spirituality and harmony, whi ch together encompass the beliefs that intangible forces have distinct impact s everyday life, and that such forces are strongly intertwined with personal fate. Movement in relation to body, music, and rhythm is also a key element of the African American experience, as is verve, which reflects a proclivity for high levels of such stimulation. Emotional connectedness to self and an emphasis on developing as an expressive, spontaneous individual are reflected in the dimensions of affect a nd expressive individualism, while a shared commitment to the good of the group and social interconnectedness is reflected in the dimension of communalism. This creates an interesting juxtaposition where material possessions belong to the community at lar ge, though individual eccentricity is valued. O ral tradition, or the use of metaphors and colorful language and the treatment of speaking and listening as a performance is prevalent in these communities, as is the adoption of a social time perspective (B oykin, 1983)
33 Hilliard (1976) also identified and described similar foundations of African American culture and cultural style concluding that: African American people understand and respond to things holistically instead of responding to parts that sum to a whole. This aspect of culture permeates key elements of the African American experience such as understanding of the arts musicality is not obtained through partitioning and counting, but as a cultural entity. African American people prefer infere ntial reasoning to deductive or inductive reasoning. African American people tend to approximate time and space instead of striving for accuracy. African American people prefer to focus on interactions, community, and people rather than material possession s and things. African American people have an ardent sense of justice and are perceptive to injustice. African American people tend to be altruistic. African American people prefer to be unique tending towards novelty and distinctiveness. African Ameri can people are highly proficient and sensitized to non verbal communication, and therefore rely less on words. Akbar (1975) drew similar ly themed but more specific conclusions, finding that the African American child: is highly affective uses specific lang uage that requires a wide use of many culturally based interjections (sometimes profanity) expresses herself or himself through body language and non verbal communication tends to use expressions that have connotations systematically use nuances of intonat ion and body language verbal cues and body language relies on words that have little meaning by themselves and ultimately depend upon context for meaning
34 prefers oral and aural modalities in learning and cognition seeks to be pe ople oriented is community oriented and sociocentric uses internal cues for problem solving is highly compassionate and empathetic prefers spontaneity and novel experiences adapts quickly and effectively to novel stimuli Additionally, the role of the a rt s in African American culture tends to be fluid and constant, with some form of art permeating nearly every aspect of everyday life. As such, arts integral an African American worldview. As a result, many African Americans are knowledgeable and skilled in the arts making performance a part of many communal activities (Bohanno n, 1964). These unique cultural characteristics are distinct from the more individualistic and less affective European culture that often dominates schools, and there are many commonalities between the three analyses. Overall, African American cultural styles are rooted in communal, interactive, and highly altruistic practices. Novelty and uniqueness are valued, though the overall good of the group is of utmost importance. Movement and arts are integrated into many aspects of everyday life, and accordi ngly non verbal cues and particular patterns of communication are valued and shared. A strong sense of faith and religious orientation is also a key element of the African American experience, as black churches serve as a venue for community, interaction, spirituality, performance, and socialization. A sense of holistic harmony and a view that all things human, spiritual, and artistic work together seems to drive cultural practice.
35 Child rearing in African American communities has also been sho wn to have distinctive characteristics that relate to these foundational underpinnings Robust kinship bonds exist between and among families, reflecting the strong sense of community that largely defines the African American experience (Hill 1972 ). Thi s kinship is outwardly expressed when African or other relational titles (Staples, 1974). Within African American families, a distinct and strong bond be tween mother and child is common (Nobles, 1974), with family matriarchs often described as strong and even domineering (Ladner, 1971) traits which are often perceived as authoritarian in the European American frame of reference This trait of strength an d stature in the family has been shown to easily pass from mother to daughter, with many African American females exhibiting a strong motherhood orientation from an early age (Hale Benson, 1986). This is partially due to the overall fluid ity and adaptabil ity of family roles wherein each member takes on responsibilities of work and child care, for example, as needed (Hill, 1972). As such, African American females are often given many domestic responsibilities from a young age. As a result, African Americ an girls have a strong proclivity for child care and an overall maternal maturity (Baumrind, 1972) traits which greatly benefit their families and communities. A strong educational and achievement orientation (Moos & Moos, 1976) and high personal expe ctations (Simmons, 1979) have also been identified as characteristics embedded in African American familial practices It has been found that many p arents in black neighborhoods understand that because of cultural dominance in educational and work setting s, children must learn to negotiate their African American cultural practices with those of mainstream culture (Boykin, 1986) For example, many parents of black children encourage culturally based
36 language patterns in the home, but prefer that their children use mainstream language outside of the community (Hoover 1978). In this and other ways, the African American experience is highly bicultural (Boykin, 1986). I n addition to mainstream American culture and African American culture, however, black Americans must also negotiate the role o f oppressed American ( Jones, 1979 ). This negotiation incompletely socialized the Euro American cultural system; they a re victimized by racial and economic oppression; [and] they participate in a culture that is sharply at odds with mainstream Ultimately, parents and families in African American communities have been charged with preparing their childre n to live and succeed among and within the dominant culture without becoming white (Nobles, 1975). This constant negotiation m ay result in resistance against the mainstream, coping techniques, anger and resentment, or even apathy towards the stat e of affa irs (Boykin, 1986) This may cause more visible issues for children when they move from life as a young child where they have largely been influenced by their community and familial practices, into a school setting where cultural incongruities are often e xacerbated. To this end, discrepancies in African American and European American culture have been success in a mainstream school. Many scholars view the two cultur es as nearly opposite, as vibrato he African tradition aims at circumlocution rather than exact Given the African American cultural proclivity for the arts, performer and audience styles have also been
37 con trasted. In European American culture the performer is seen as separate from the audience, analytic. In African American culture, on the other hand, the perf ormer draws his energy from the audience, and the audience fervently participates in the performance. The performance is relational in nature and provides an avenue for expression among the performers and the audience (Abrahams, 1970). This is especially insightful as it relates to the school experience when viewing teachers as performers and students as audience members. These distinguishing characteristics of life in African American communities are rooted in historical literature and the foundati onal aspects of African American culture have been maintained over time Past work in fact, has suggested that African American neighborhoods are sufficiently isolated so tion with other local Negro es, despite possible inter racial co n tacts in the ir work, school and shopping lif e ( Abrahams, 1970, p. 236) and therefore maintain and transmit unique cultural patterns from generation to generation (Williams, 1964). Though this work is dated, more recent research has shown strong patterns of re segregation in urban areas (Kozol, 2005; Ladson Billings, 1994; Walker, 2000) supporting the idea that African American culture is deeply rooted in history and is maintained through community interaction s while adapting to compensate for mainstream culture Successful Teachers of African American Children Children cultivate their cognitive styles through the socialization they receive in their community, family, and friend ship groups (Cohen, 1969), a fact that is important to the teaching of African American children. Some work which is couched in these historical discussions of African American culture, has focused on positive examples of effective pedagogy in classes la rgely populated by African American students Overall, these successful teachers effectively
38 incorporate key elements of the African American experience into classroom instruction, and effectively relate culture and cognition (Hale Benson, 1982; Boykin, 1 986). As such, these educators understand the uniqueness of the African American experience, the role of ways of life, society, oppression, and familial forces in the teaching and learning process, and that c s behaviors and ways of learning must b e understood within these contexts. Even before integration in schools was mandated, successful African American teachers dedication, and for their demanding teach been described as being intricately involved with students not only in this context of academics, but also in guiding learning about life and the world, and the dangers that faced them outside of scho segregation, unique perception of racism, and experiences within an oppressive system. to 260). As such, these educators were in a uniquely powerful position to influence student beliefs about self, racial identity development (Tatum, 1997), and to teach authentic content through which students were able to better understand the political and social situation of the country (Freire, 1998). Interestingly, while this work and the author recognize that separate is by no means equal because of the magn itude of other factors in the educational system, it is implied that some African American students were in academic contexts that provided more access to knowledge before integration, as they were better understood by their teachers and schools in terms o f cultural behavior.
39 Today, there is a severe shortage of African American teachers (and teachers of color in general, ( Howard, 2006 ) ) so students do not have the benefit of these types of role models in school. Moreover, much of the work in the field of education, and particularly in mathematics education, largely leaves out the voices of African American teachers (Agee, 2004; hooks, 1994) despite their distinctive and culturally based pedagogies and management strategies. As such, educators (and ult imately students) are missing perspectives and worldviews of African American teachers and curricula, dominant pedagogies, and even teacher preparation programs (Gay, 2000) reflect this void. Teacher beliefs about students of color are reinforced, and as a result, students of color often do not believe that the majority of teachers understand their sociopolitical struggles. This creates tension and conflict in classroom settings. Resistance is a common way that students act out against the resulting whit e hegemony (Miron & Lauria, 1998). Students recognize through verbal and non verbal cues that teachers do 200). Thus, white teachers are communicating to student that they are not capable of high achievement in academics and that they are not worth the effort of innovation. This is a far cry from African American tea More recently, other characteristics of successful teachers of students of color have been de scribed, as have the learning outcomes of their students. Howard (2001 descriptions of teachers to identify three key strategies of successful teaching as measured by student effort, engagement, and achievement. First, these teachers esta blished a family like
40 routines were key components of this practice as was explicit accountability for specific actions. Second, these teachers established cultur ally connected, caring relationships with students in and out of the classroom. Third, certain types of verbal communication and affirmation were valued of behavior communicated a sense of caring and high expectations. As such, students were able to decode familiar behavior that they might see at home. Other styles of communication such as call and response, Black English patterns (as used in classroom act ivities), and language expressions similar to those in church sermons or rap songs have also been common to several studies of successful African American teachers (Foster, 1989; Ladson Billings & Henry, 1990). These familiar communicative practices provi de verbal communication with students impacts success. In mathematics, for example, it has been stated can achieve success in ma king sense of complex term achievement ( Sleeter, 2001b ). Some researchers have exhibit an ethic of caring, positive beliefs about students and the community, and specific instructional practices. These African American teachers are viewed by students as authority figures and disciplinarians, caregivers, and pedagogues. Evidence of direct instruction and inquiry learning were identified teaching practices are multifaceted and complex. They take on many roles in an effort to push students acad emically.
41 Effective African American teachers have been shown to have strong ties to the black community (Ladson Billings, 1991, 1994), verbalizing and communicating this sense of belonging through their teaching. It is well documented that these teache rs often refer to metaphors and family ties when presenting material, and indicate a strong, almost familial relationship wi th their students (Foster, 1987; Ladson Billings, 1994). Similarly, effective black teachers have verbalized that their educational goals for students are more holistic, focusing not only on academic knowledge but also on developing self awareness, self confidence, and leadership skills (Foster, 1987). The learning context has also been shown to be central to academic success for st udents of color. African American students have been shown to perform at higher levels on mathematical estimation tasks when content is taught in a highly communal, collaborative setting (Hurley, Boykin, & Allen, 2005). African American children also per formed better on a specific task when taught in a context that allowed for and encouraged a high amount of movement and music while white children performed better on the same task when taught in a low movement environment (Allen & Boykin, 1991). It has b een suggested that this type of opportunity to engage in various modes of learning is helpful to African American children because it may align with historical cultural practices. This interconnection of culture and cognition is believed to lead to academ ic success and empowerment (Allen & Boykin, 1992). Though this area needs more development in terms of comparison across ethnic groups, such results imply that academic success is mediated by the context of the learning environment. Moreover, this work integrity model. As opposed to the aforementioned deficit model described by Delpit (1995),
42 comp lex and fluid (Boykin & Allen, 2004). If student realities are disregarded in academic contexts (for example, when home languages are stifled and suppressed in school), educational achievement and outcomes of learning are compromised and students are like ly to act out in resistance to the mainstream (Allen & Boykin, 1992). If students are given the opportunity to act within familiar cultural contexts, however, meaningful learning is more likely to occur and accessibility to higher order thinking skills su ch as problem solving is increased (Boykin & Allen, 2004). Culturally Responsive Teaching Some work that centers on successful models of teaching diverse learners focuses specifically on pedagogy, and has been studied under the umbrella term of culturally responsive teaching (CRT ; Gay, 2000 ). Research and dialogue in th is area is discussed within the American historical context, and gives a framework to much of the work of multicultural educators. Culturally responsive educators see student diversity as a strength in the classroom, and view the incorporation of cultural perspectives as a necessary educational commitment. Students are viewed as cultural beings with cultural filters (Gay, 2000) through which all information is sifted. In other words, cultural experiences and identities are seen as the foundations for all other experiences and behaviors (Ladson Billings, 2001). Culturally responsive teachers aim to capitalize on the fact that varying cultural filters exist among students and teachers. Moreover, these educators seek to resolve, through empowerment and validation, the dissonance this variation causes. As mentioned above, individual culture and experiences are the basis for all other actions (Gay, 2000; Ladson Billings, 2001). Often, s chool cultures (and teacher cultures) are not consistent with student cultures, causing student achievement to suffer. This implies that academic struggles are caused when inconsistencies in school versus home culture exist, though outcomes of such strugg les are not true reflections of
43 student ability (Boykin, 1986 [among students of color] are symptoms, not causes, of achievement 16). Too many current pedagogical solut ions in schools focus on standardized testing as the root of the problem and result in prescribed curricula focused around these assessments. Culturally responsive teachers are aware of this, recognizing cultural incongruities as the cause of the achievem ent gaps, and can therefore structure learning appropriately. When cultural discrepancies are considered as the root of the problem, it becomes clear these types of dictated pedagogy and curricula may actually exacerbate the achievemen t problems of studen ts of color. Culturally responsive teachers also recognize the strength in each studen different students (Gay, 2000, p. 33). This runs counter to or biased methods. Iron ically, in treating all students the same, teachers are enacting the very prejudices that they fear the most. One mode of instruction does not serve all students in the same way, and inherently favors one group. This is most likely to be the group that i s most like the teacher, as the teacher is likely to act out of his or her own cultural experiences. Since most of the teaching force is white, the students in this group are most likely to benefit. Culturally responsive teachers validate and affirm s tudent cultures by recognizing them as such in the classroom and paying tribute to each of them equally. These educators teach school ex 29) and supporting students to make sense of personally relevant information in and out of the classroom using various tools rather than memorized
44 formulas and procedures (Villegas & Lucas, 2000). In this way, CRT is multidimensional and comprehensive, en compassing many aspects of student and community lives. This validation and value placed on student lives is powerful and liberating. Culturally responsive teachers work for transformation through education. dents to develop the knowledge, skills, and values needed to become social critics who can make reflective decisions and implement their decisions In this way, CRT is e mancipatory and transformative for students, teachers, families, communities, and schools, re experiences (Ladson Billings, 1994), and engaging in a continuous effort to combat the status quo. Student cultures and familiarities become a part of the curriculum, and the norms of the classroom are re characterized based thereon. Specifically, modes of communication are made to benefit each child, ways of assessment and teaching a re re conceptualized, and a trusting and caring environment is emerged. This empowers students to believe that they can succeed in learning tasks, and motivates them to continue meeting challenges in and out of the classroom. Culturally responsive teache rs r ecognize and utilize the fact that other forces are at work in schools, and that pedagogy, though a powerful tool, cannot alone change societal perceptions (Gay, 2000). For example, these teachers recognize that academic achievement may be frowned upo n in particular cultural groups because of historical and social institutions and norms As a result, academic knowledge and attainment may be masked by a student as a defense against alienation from his or her cultural group (Fordham 1993, 1996). Again, this is illustrative of a severe discrepancy between student and school culture. The negative views of education held by certain cultural groups are understa ndable as the educational system has consistently asked
45 students of color to abandon their cultur e for the sake of education (Nieto, 2002). It makes sense that a delineation separating the two would emerge as a defense mechanism, a tool for resistance, or a way of simply denying what the school culture deems important. This undercurrent of cultural friction implies a school culture and, more widely, a societal issue relating to the Culturally responsive educators endeavor to change the face of education, helping students to realize th at they can control their own learning. These cultural beliefs and practices are at the forefront of instruction, and are viewed as individual strengths rather than collective weaknesses. In this way, CRT aims to transform traditional educational practic es and views of ethnic students of color (Gay, 2000). Thus, it is important to note that CRT cannot exist in isolation; rather, it must be a part of a larger, school and community transformation. CRT on its own can be helpful in educating diverse learner s, but only within a truly multicultural educational program can CRT be truly transformative and affect change on a grand scale. In bringing student knowledge and experience to the forefront of teaching, culturally responsive educators aim to develop stud cultural understanding. As such, CRT requires that teachers consider many factors within the educational setting, including curricula, learning environment, assessment techniques, patterns of communica tion, and relationship development. As such, culturally responsive teachers educate students holistically, allowing students to maintain their ethnic identities while developing a sense of shared responsibility in the learning environment (Gay, 2000). Th e multidimensional nature of CRT requires that it, and the teachers who enact it, are flexible and continuously evolving. If CRT were stagnant and rigid, it would inherently contradict its own purpose. Thus, perhaps the most important and distinctive cha racteristic of
46 CRT is its flexible nature. Indeed, CRT will not look the same in any classroom, and the enactment of the framework may vary widely. It is through this continual evolvement that CRT can change with the diversifying population. Moreover, i t is only through adaptable methods that educators can hope to meet the needs of various learners. Culturally responsive teaching is multifaceted and necessary in enabling students to be more active, productive, successful, and empowered human beings a nd learners. This type of educational practice is liberating and emancipatory for teachers, parents, community members, and learners, as teachers realize not only the importance of academic achievement, but also recognize the importance of maintaining and fostering a strong sense of heritage and culture. Culturally responsive teachers demonstrate lofty and appropriate expectations and exhibit As a result, stud ents in culturally responsive classrooms and schools believe they can succeed in learning tasks and have the drive to persist. There is no formula that a teacher or teacher education program can follow in order to address the needs of diverse learners. Rather, each educator must recognize the need for critical and culturally responsive mathematics teaching, understand the complexities that culture brings to learning environments, and engage in discussions and action plans that work to change inherent in equities in schools drawing on frameworks that have been proposed in the literature (Villegas & Lucas, 2000, for example). These changes in perspectives, perceptions and habits of mind among educators are not easy to make by any means. They are, however, possible and necessary if we are committed to providing equitable educational access to all learners. In providing educational experiences that strengthen, validate, and confirm student identities, we are enabling students to experience and change the wo rld in which they live.
47 Gaps in the Literature This framework of CRT is clearly sound and emerging, yet there is very little literature that directly investigates the phenomenon in the context of mathematics. Several scholars have written cohesive, i nformative books on the theoretical aspects of CRT (e.g. Gay, 2000; Gutstein, 2006), with some incorporating specific classroom practices (Ladson Billings, 1994). Further, more literature is emerging that is specific to culturally responsive mathematics t eaching (Greer, Mukhopadhyay, Nelson Barber, & Powell, 2009). This work, however, remains broad and theoretically based, making its accessibility to teachers a challenge. This type of work is made even more difficult by the fact that ideally, CRT would b e one part of systemic change efforts student achievement through w gain a more salient definition of CRT in the context of mathematics, it is important that we look to teachers who are highly successful with traditionally underserved populations of students in mathematics classrooms. Given this clear need for research based implications that relate to CRT in the context of mathematics, especially as they perta in to African American children in high poverty contexts, the following research focuses on exploring and documenting effective teaching practices of a mathematics teacher in one such setting. Explicit attention is given to the roles of power, race, cultu re, and interactions at every level. The need for a fresh perspective on these issues in addition to the lack of mathematics education literature in these areas led to the construction of a grounded theory study meant to help fill the existing gap. The r esults begin to inform the field
48 about specific, research based practices that illustrate culturally responsive teaching in the context of mathematics.
49 CHAPTER 3 METHODOLOGY Because of the complex, fluid, and varied nature of CRT, it is nearly impossible to succinctly define the construct, and is even more difficult (and may be contradictory to the bases of CRT) to define a step by step model. Suggestions from the literature of what CRT is and the ways in which it might be enacted, however, should be used as a point from which educators can evaluate and begin to conceptualize changes in their own teaching style. The purpose of this study was to help in that conceptualization process so that the ideals of CRT are more accessible to mathematics teachers and mathematics teacher educators. Several authors have written cohesive books outlining and discussing the fundamental ideals of CRT (Gay, 2000) with some focusing on how it relates specifically to African American learners (Ladson Billings, 1994, for example). These discussions, however, have remained rather general. Though examples are given of specific subject area instruction at times (Greer, B., Mukhopadhyay, S., Powel l, A. B., & Nelson Barber, S., 2009 ; Ladson Billings, 1994 ), the overall vision for mathematics educators remains piecemeal and theoretical. Further, these ideals are difficult for teachers to enact, as there is (and should not be) no formula for CRT. Th e currently given framework is helpful in constructing ideas of what it means to be a culturally responsive educator. Given the fact that research on CRT is still developing, with theoretical and practical applications becoming more relevant to actual tea ching practice, my initial intent was to contribute to the field by seeking out specific culturally responsive pedagogical practices in mathematics classrooms. It is within the more general framework of CRT that I began this work. Spec ifically, I accept ed the present ideas about general CRT (largely from Gay, 2000 and Ladson Billings, 1994) while qualitatively zooming in on culturally responsive mathematics teaching (CRMT)
50 specific to African American learners in low income areas developing this concept more fully based on teacher practice. The intention was not to separate CRMT from CRT in general or in other academic areas, but rather to focus more specifically on mathematics instruction to reveal the characteristics of CRMT within the larger context of CRT. To do this, I initially chose to fully immerse myself in classrooms of successful mathematics teachers in largely African American, low income schools. The following research questions guided my methods, interactions, and data collection: 1. How do effective mathematics teachers working in a high poverty, predominantly African American school context: a. structure instructional practices and interactions? b. establish a learning environment that results in mathematical success? 2. What are the interactions between these phenomena? 3. What part (if any) does culture play in these phenome na ? Nomination process As a researcher in the field, it was important that I not let my own perceptions of CRT, poverty schools, and educational processes in general drive the b eginnings (or any part of) the study. I recognize that, though I have studied in the field of education for years, I do not have the lived experiences needed to identify successful practices in a particular neighborhood, and it was important that I not si tuate myself as the holder of knowledge about what makes a teacher in these communities successful. Moreover, if I were to choose teachers based on my own beliefs the entire purpose of the study would be contradicted. A complete omission of my viewpoint was not practically possible, as I have gained a solid knowledge base in these areas through immersion in the literature; however, my biases were greatly limited through the careful choosing of the ways in which I would go about identifying participants an d collecting data.
51 As such, o ne main objective of this research was to return the power of knowledge and nomination of successful teachers to the neighborhoods in which the work was done. Specifically, I asked community members, such as members of churc hes in the community, parents in the neighborhood, and local administrators, to identify the teachers who were to be included (i.e. those teachers who were successful with African American populations in these neighborhoods) rather than using predetermined ideals that have been set forth by previous literature. Informal conversations and written correspondence with students, parents, and community members began the nomination process and continued throughout the data collection and analysis period. These conversations drove the context of the initial data collection process, giving specific characteristics of mathematics educators on which to focus and particular names of teachers who largely embodied these attributes. It should be noted that the nomina tion process presented quite a challenge. Community mathematics teachers with whom these neighborhoods had come in contact. In fact, only one teacher, Gloria Me rriex, was identified. Ms. Merriex was recognized by many parents and administrators; it was surprising that no other teachers were touted as excellent mathematics instructors even when administrators were asked directly to do so. This anecdotally spoke to the need for improved mathematics instruction at the elementary school level in largely African American, high poverty communities. Moreover, several individuals who were asked for nominations indicated that they were not sure what made a particular teacher successful, and were unsure of my motives during initial meetings. This indicated that this type of information is rarely solicited from com munity members such as parents; this trend is evident in the literature. Since the nominations were so
52 lim ited As a result, the sole focus during the primary study was on Gloria Merriex, the only teacher to be nominated by her community. Thus, though the initial intention was to seek out other educators to corroborate research findings, the aforementioned c ircumstances, in addition to other extenuating events that were to happen later in the study, drove me to focus solely on Grounded Theory This study was meant to focus on and clarify the teaching practices of effective teachers in pred ominately African American, high poverty schools, and research methods were considered with this goal in mind. Data were collected in particular ways so that this end could be achieved, and my work with Gloria and my immersion in her classroom were constr ucted in an effort to support these objectives. An extensive review of the literature showed that there are very little research that deals directly with successful teaching practices of mathematics teachers in largely African American, low income elementa ry schools. There are even fewer that focus on the elements of such practice and the depths of student and teacher experiences. Virtually no studies attempt to deconstruct successful mathematics pedagogies in these settings. As such, there is a large ga p in the mathematics education literature when considering studies that focus on the successful mathematics teachers of African American children and the dynamics of mathematics classrooms in low income, high poverty schools. Through this investigation an d my experiences with the community, the need to clarify how successful teachers in these settings develop and enact practice became apparent. In order to give meaning to the social aspects of CRMT, it was important that all parts of e were considered and included in the data set. This meant that in addition to interviews and observations, natural occurrences such as interactions between people and with mathematical content, verbal and body language, physical settings, general behavio rs, and
53 individual constructions of reality needed to be included as key pieces of the overall setting. For these reasons, (i.e. the lack of existing literature on this topic and the need for a holistic, descriptive outcome), grounded theory was chosen a s the driving methodology for the study. A main goal of grounded theory is to develop flexible guidelines for colle data, the goal becomes the construction of a more general, middle range theory. This type of deconstruction allows for interpretations of social and practical complexities that are inherent in teaching, and should be built on and qualified over time. Further, this type of work does not position the researcher as an outside observer of phenomen a, but rather as a part of the world about which he or she is theorizing. The researcher is the lens through which all information is filtered, and must make decisions about the import of various data. Thus the work of grounded theorists is highly interp retive and interactive, and does not attempt to isolate data, but considers it as part of a relevant social context. Grounded theory gives qualitative researchers a means to construct a descriptive theory in 67 book, The Discovery of Grounded Theory the process of theory building was largely deductive in nature, producing grand theories meant to uncover universal laws of behavior (Glesne, 1999). Grounded theory is inductive in nature, allowing the researcher to produce a substantive theory that is situationally based and more useful to practice. This type of contextualized, classroom based theory became the goal of my study.
54 The analysis to be presented here is where the research began. The work focuses on my this deconstruction of pedagogy and relationships is sit uated historically, but it can and should also be taken separately, as it is intended to stand on its own as a theory about successful mathematics teaching in a largely African American classroom. Moreover, this specific piece of work serves as an importa nt model of analysis for the mathematics education field. It is meant to give a specific framework to successful mathematics teachers of African American students in t from data collected in her classroom. With emphasis, I note that the grounded theory data set was collected and analyzed before this occurrence. Theoretical Perspective In order to minimize bias and allow for truly novel ideas about these practices, I chose to enter the classroom setting free from the constraints of one particular theoretical perspective. This allowed me to not only deconstruct teaching practices, but also to let the data guide the framework of the study. Further, it allowed me, as a researcher, to genuinely generate new concepts and to treat all information (not only interviews, observations, and artifacts) as data. passing. In re framing her work and looking more broadly at her life, I was able to identify an appropriate theoretical stance. Teaching is a largely situational practice. Many stakeholders ( e.g. teachers, students, administrators, parents, community members, etc.) maintain a role in the day to day practices of schools, greatly influencing the teaching and learning processes that take place therein. Moreover, the culture of a school, which is determined by and influenced by these stakeholders
55 influences specific practice. That is, the realities that exist in schools are complex and not easily quantified. Further, the relationships that exist within these contexts are interactive and interdependent, and this complexity is mirrored in the researcher teacher relationship tha t is examined here. As can be seen in the data that follow the importance of culture and context in the teaching and learning process cannot be denied. Moreover, all of the stakeholders in and around the schooling context construct their realities with in and through the aforementioned relationships and their own interactions with the world. Specifically, the students involved in this attempt at grounded theory live in a low income neighborhood that is largely populated by African American individuals Much of what these students do and see in school is influenced by the fact that the city (or district) has not given them what their white counterparts have been given in terms of resources, physical environment, or cultural freedom. These types of inequ ities are y. in the creation of their social realities. Gloria communicated mathematics to her students in ways that are very much constructed meanings for culturally resp onsive mathematics instruction were seen as collaboration between teacher and researcher, each bringing a unique perspective and thought base to the discussion. These interactions were not limited to researcher and teacher, however. As is discussed above much of the meaning constructed and enacted in this setting is brought student relations, and numerous other sources. These meanings were developed by the involved stakeholders together,
56 embracing the meaningful realities that were constructed. This focus on the subjective parts of the social structure emerged as the context in which this work was done. in beliefs are paramount and are developed through these types of interactions and experiences. Individuals assign meaning to things and people based on such experi ences, and act toward things and people based on those meanings (Blumer, 1969). This is especially relevant to reactions. Data Collection Guided by ground ed theory methodologies, formal data collection occurred over the course of one semester (about four months) though I worked with Gloria informally for about two years before that time. Individual, semi structured interviews with Gloria were the foundatio n s of the data set with observations and artifacts serving as triangulating evidence. I spent at least three mornings each week (unless scheduling conflicts such as field trips or conferences interfered) in ents, visiting with co teachers and Gloria, and memoing. Observation notes were meant to be holistic, including information about various occurrences in the classroom but did focus on culturally based interactions T hese observations often generated guid ing questions for the next interview. Artifacts mainly consisted of student work and teacher made materials As an outside researcher, my role in the classroom was that of participant observer. This meant that I was a regular member of the class, and I often participated in the lessons. Sometimes I sat back and observed independently, other times I sat in with student groups or spoke with co teachers and parents in the back of the classroom. This allowed me to get a true
57 conversations with students, I was able to gain insights into their life histories and patterns of interaction. Over time, the students did not react to my presence and my sitting in with them did not seem to interrupt the flow of the class. This was helped by the fact that so many observers (pro fessors, other teachers, pre (because of the local attention that her teaching methods had drawn), so the students were used to the attention. Over the course of the data collection period, I conducted three formal interv iews 1 each between one and two hour s in length Often, the scripted questions were not needed in the course of conversation, but most main topics represented in these protocols were covered. I let these conversations go in w hatever direction Gloria wanted to take them. Many other informal conversations were considered when themes began emerging, as were observation data and artifacts. Data collection was driven by theoretical sampling, with each analysis of current data dri ving future data collection. In other words, holes in the data were identified, and the next interview and observation period were viewed as means to fill these holes. This process was to continue until saturation was reached. Simultaneous Data Collect ion and A nalysis In order to collect data in this manner, I employ ed simultaneous data collection and analysis practices (Glaser & Strauss, 1967) with the goal of eventual pattern and theme repetition through methodical coding I began by listening to coding, and anal yzing the first interview. These data were then triangulated and compared with observation notes and artifacts collected 1 Sample interview questions included at the end of this chapter to give the reader an idea of how theoretical sampling was used in this context
58 from the same time period, themes were emerged, and gaps in the data became evident. I then went back to the teacher and classroom and repeated the process, constantly comparing the new themes to those already emerged. Memos, which included personal notes and thoughts from observations and interviews, also served as a place to document emerging themes and beginning, imm ature theories. Data Analysis P rocess Interviews were analyzed according to grounded theory (Glaser 1998; Glaser & Strauss, 1967). I first listened to each interview, memoing to record initial ideas and thoughts. The interview was then transcribed in pr eparation for coding. Throughout these sessions memoing continued, with major themes that stood out being noted and these notes later being used to compare with other data from the interviews. Coding was done in three stages. First, open codes focusin g on identifying, naming, categorizing and describing phenomena in the text were determined. From the open codes, axial codes, which focused on relating open code categories, were determined. Lastly, selective codes, which focused on the combining of axi al codes into larger categories, emerged. From these codes, the major themes and core concepts contained in the data became apparent. Constant comparison was employed throughout this process. Specifically, all data were compared to the emerged themes an d to the rest of the data set. Moreover, all themes were compared with t he later (or earlier) raw data and themes, and all data were compared to the initial research questions. This helped to ensure that the emergent themes were true to the data, and tha t connections and intricacies were represented accurately. Data collection and analysis were still in progress when Gloria passed away, with the most recent interview occurring only two days before she died, and the final observation occurring the day be fore. Though data collection would have continued until the end of the school year (about
59 two weeks more) in order to truly achieve full overlap in themes, quite a bit of saturation was reached through the data that had already been collected. It is on t hese data that the results of this study are based. While one more interview and a few more observations may have changed several small details about the emerged theory, I believe that this representation does characterize the data set well. The graphic presented as figure 4 1 and figure 6 1 is representative of the results of this analysis. Member Checks As I conducted the initial research and eventually wrote the monograph, I continually went back to available participants to share my work. I did th is for several reasons. First, I wanted to ensure that I had represented their words appropriately and in the proper contexts. Second, it was important that the monograph tap into the interests of those who knew Gloria. As such, I asked them to validate the breadth and depth of the information. Lastly, I wanted to ensure that the message that I had intended was indeed being communicated effectively. To this end, I asked participants and scholars in the field to read parts or all of this work, especiall y the monograph, and state what they believed the message to be. This led to re writes and modifications, but I feel that it added a key element to the overall manuscript.
60 CHAPTER 4 MONOGRAPH MANUSCRIPT Phenomenon: The Life and Teaching of Gloria J ean Merriex By Emily Peterek The life and teaching practices of Gloria Jean Merriex provide an example of the ways in which culturally responsive teaching can improve low achievement in mathematics. Upon her passing, i t became necessary to not only share these methods, but also pay tribute to her legacy. As such, this monograph was written using the voices of those closest to her including family, friends, colleagues, and students. These voices, along with research da ta and literature, make the manuscript widely useful. Phenomenon is intended for teachers, administrators, students, teacher educators, and others who are interested in the subject matter. Citation Peterek, E. (in progress). Phenomenon: The life and teaching of Gloria Jean Merriex. To be submitted for publication as a standalone document.
61 Table of Contents I. Preface II. Introduction The Call III. Part I The Past Chapter 1 Chapter 2 What I Say Goes Chapter 3 IV. Part II Recent Life Chapter 4 V. Part III The Future Chapter 6 Chapter 7 VI. Appendix A Formal Methodology VII. References
62 Preface Th ey say I was made for teaching Gloria Jean Merriex Phenomenon (Phe nom e non) 1 : 1. an object or aspect known through the senses rather than by thought or intuition 2. a rare or significant fact or event If you look inside an anatomy textbook, you will find illustrations meant to show you the depth and complexity of particular parts of the human body. For example, on one page, you will find a large picture of a hand. The next few pages are transparent, o verlays for the initial picture, with each showing a different level of the anatomy. The first overlay will show you the bones in the hand, with the nerves being added with the next overlay. Next will come the tissue, followed by veins or skin layers. O nce all of the overlays are in place, the full complexity of the hand and all of its parts are shown. While at times it may be helpful to have the layers separated, it is when the picture is complete that the entire representation makes sense My work in writing this monograph has been similar, with layers upon layers of a story emerging to reveal something whole. The foundation, or initial outline, for this work came in 2005 when I was a first year doctoral student. As part of my research assistantsh ip, I was assigned to observe and take notes on the teaching practices of an elementary school mathematics teacher by the name of Gloria Jean Merriex. I will never forget the first time I visited her classroom I was stunned at her innovation and deeply inspired by the stories of the children she instructed. Her mathematics 1 Definition from Merriam
63 came to know Gloria over the next three years, I realized that her work went much de eper and much wide r than one could ever imagine. This was evidenced when Gloria was nominated by members of her community (who did not know that I even knew Gloria) to be a part of my dissertation study about highly successful mathematics teachers of Afri can American children. Over time, what began as a simple project meant to describe some of her mathematics teaching methods became a layered picture that culminated in significant ways. Gloria was a of himself as a learner, as an African American, and as a member of society. Starting in the classroom, the whole of her work impa cted a school and a community. When she suddenly passed away in May of 2008, these transformations became particularly evide nt. This sparred me to expand my work and share the practices of Gloria Merriex in an effort to pay tribute to her legacy. In speaking with her family, colleagues, administrators, students, and parents, a whole, layered picture of this phenomenal woman h as begun to materialize. Many people have a story about Gloria or her work, but her personal life was somewhat private. Individuals may have seen Gloria present at a conference, perform with students, or may teacher in Gainesville, Florida who used raps to teach mathematics and had remarkable standardized test scores even though she taught an underserved innovative techni excel. Using chants, choral responses, dances, and rhythms, Gloria was able to communicate mathematical ideas to children in a way that empowered them as learners and individual s. When
64 When in her classroom, I was inspired I I, and others, truly did feel her teaching with your senses and not only with your mi nd. In fact, one of my favorite parts engage her students. Whether an observer was a parent, professor, administrator, new student, or teacher, you could see the surprise and delight in their faces within the first five minutes. After watching her, observers would have a million questions: how was this possible? Did they rehearse? Did she always have this many students in her classroom? Can I see more? Th ese reactions came about for many reasons such as the high level of engagement among students and the sheer energy that Gloria constantly exhibited. Moreover, she worked in a largely African American school in a low incom e area with a population that has traditionally struggled in education. her family and the surrounding community, the school, the state, and the field of education as a whole. This was painfully evident at her funeral where the mix of people in attendance was staggering. These individuals were from a range of backgrounds and had varied interests in her work and life. To some, her life, demeanor, ideas, and general techniques were of interest. To others, the intricacies of her work, its impact on mathematics education practice, and implications for teaching mathematics in poverty schools was exciting. To some, she was just Jean. There are many reasons that I feel compelled to share the life, teaching practices, and soci al impacts of Gloria Merriex. Certainly, she was a master teacher who continuously went above and beyond for her students, and was passionate about their success. There was something bigger, however, on which her work made us focus. Despite the academic struggles faced by African American students she was determined to prove that economic status and race
65 were not central to academic excellence. She believed that learning was a matter of access, not ability, and it was up to teachers to make subjects su ch as mathematics, that have a reputation of being difficult, accessible to students who may have been told (verbally or otherwise) that they could not learn. At the same time, she would push these learners, who may have negative beliefs about their acade mic potential, to excellence, no matter who they were. She particularly focused realize their true ability. Often, she would guide these students from the special education classes that they had been taking into honors classes in which they excelled. her school Her determination and involvement in the community resonated with the entire neighborhood, transfor ming and empowering those with whom she came in contact. She was able to effectively interweave her artistic talents such as singing, dancing, sewing, and cooking, into her mathematics curricula, school events, and student performances. She believed that no child (or family) should be without resources and she worked tirelessly to provide for students who might need food, clothing, or even money. She was in touch with the parents of Duval, and the community at large. Over 30 years she taught generatio ns of students, and effectively helped to transform a school and a community. This work, which is far reaching and historically significant, needs to be shared. As a teacher of mathematics Gloria provided another level of success that existed within thi s larger framework. As someone who shared a childhood similar to that of many of her students, she was able to connect with learners at a deep level. Gloria used the culture of the community, which she lived in and learned about from her students, to gui de her mathematics lessons and teaching techniques. She was constantly revisiting her lessons and making
66 improvements based on student feedback She used culturally relevant language and disciplinary tactics that helped her students to excel. I n the f ield of mathematics education, there are very few specific examples of teachers who teach mathematics from a culturally responsive framework Gloria provides a subject specific model of this construct As such, as a researcher, there is a need to break down her specific pedagogical tools, using these ideas to conceptualize what culturally responsive mathematics teaching can look like in action. Of course, there is not (and there should not be) a form ula for this type of instruction, but the field will benefit by beginning to delve into specific teaching methods that might help to address the achievement gaps that exist in mathematics while including the voices of African American teachers and communit y members. In an effort to tell her story from these various points of interest, the main goal of this monograph is to deconstruct and generalize teaching methods from a research standpoint to identify key components of her work in an ef fort to help the field of mathematics education to gain a more solid understanding of culturally responsive mathematics teaching. Her story is told here through her own voice and through the voices of those who knew her best. This monograph allows the re ader to explore Gloria current state of affairs in mathematics education. The organization of the monograph reflects this goal Part I explores the past, focusing ildhood with an emphasis on developing several personality traits that were central to her character. Part II zooms in more specifically on that is meant to organize the complexities of her classroom and begin to generalize the key aspects of her mathematics instruction. In part III, I look to the future, discussing outcomes and
67 ll, as they are the er view of these ideas, tying the pieces of the theory together in ways that will help rethink key aspects of mathematics teacher preparation and mathematics ins truction in general. What you will not find in this monograph are specific instructions that dictate how to be an effective mathematics teacher in a largely African American school. Such laundry lists cannot possibly be helpful as each classroom and eac h teacher are different. Further, Gloria verbalized her distaste for scripted curricula on more than one occasion; it would be a dishonor to her if I then turned her methods into such a product. Rather, the theory presented is meant to give an idea of wh ere teachers may want to focus their efforts in becoming culturally responsive educators. Particular techniques may be useful to some, while other ideas will inspire innovation and a re thinking of the educational system. Main Characters Ms. Gloria Jean Merriex is the central figure of this story. She taught mathematics and reading at Duval Elementary school for 30 years, inspiring students, parents, and a community with her innovative teaching practice. Mrs. Cenia Merriex living in the same house for nearly 60 years. Ms. Jan Merriex two were growing up. Jan works with special needs childre n. Dr. Leanetta McNealy closely with Gloria, and the two traveled together to conferences, workshops, and performances all over the United States.
68 Dr. Buffy Bondy director of the School of Teaching and Learning at the University of Florida. For 9 years, Dr. Bondy was a Professor in Residence at Duval, and worked closely with the faculty, staff, and administration. She was a central figure in the fforts over the past years. Ms. Lilliemarie Harvey th year teacher at Duval Elementary School. Lilliemarie was a new teacher, Gloria served as he r mentor, and the two were close at work and in their personal lives ever since. Mr. Leonard Marshall member of the 3 rd grade team, Leon grew close with Gloria when he co taught with her duri ng his first year at the school. Mr. Marshall continues to teach using many of the techniques that he learned from Gloria. The two loved to sing together. Mrs. Angela Terrell retirement in 1999 to help the school infuse the arts throughout the curriculum, and has had much success in this role. Angie worked very closely with Gloria, helping her to plan and coordinate mathematics team performances and conference presentations. Emily Pete rek 2005 and continued my work with her until her passing in 2008. I had the pleasure of interviewing those whose words drive this story.
69 Part I Immediately after emancipation, Black educators assumed the unique task of enhancing opportunities for newly freed slaves. These racial uplift teachers, mostly women, taught in segregated schools to prepare Black children for freedom, respectability, independence, and self reliance. This same tradition of Black teachers as racial uplift professionals continued and thrived in segregated schools, particularly in the South. A key lesson to be derived from this research is how the oppressive circumstance of segregation result ed in a functional, semiautonomous Black community with its own peculiar set of rules, norms, sanctions, and rewards. Jacqueline Jordan Irvine, Educating Teachers for Diversity: Seeing with a Cultural Eye 2003, p. 56
70 Chapter 1 you can learn. I can understand it because of where I come from. I tell them about my house earn. But u can. Gloria Jean Merriex The city of Gainesville, Florida is located in north central Florida and is the largest city in the county of Alachua Pl aced between the panhandle and the tail of Florida, the city is roughly 80 miles southwest of Jacksonville and about 140 miles northeast of Tampa. More rural than urban, the popula tion currently hovers around 114,000, with close to 17 percent of families and 34 percent of individuals living below the povert y line 2 Though the city is relatively small, about 49 square miles in area, there are distinct cultural influences in various parts of the city Demog raphically, the city is about 67 percent white, 24 percent African American and 8 percent Hispanic; these populations are somewhat segregated, largely residing in different parts of the city The west side of Gainesville houses the University of Florida and most of the white residential population wit h a modest amount of diversity, while the east side of the city is home to several mostly African American communities. This distinction is evident not only in census numbers, but also in school populations, church congr egations, and neighborhood families In fact, it was not until several Brown vs. Board of Education decision that Gainesville public schools were desegregated. D espite years of integration, east side schools are still predominately populated by African American s tudents. 2 All Gainesville, FL demographic information is based on The Cen 2007 Community Survey 3 year Estimates (retrieved from www.census.gov )
71 In the years of official segregation, Lincoln High School (which actually housed seventh African American middle and high school population, while Gainesville High School, which i s located on the west side of town, served white students. In 1956, Lincoln High School was moved to a new building in southeast Gainesville, and the old campus came to house A. Quinn Jones Elementary School, which was also populated by young, black stude nts. After some restructuring over the years and the introduction of middle schools, Lincoln now exclusively serves students in grades 6 8, with Eastside High School serving high school students in the area. There are several other elementary schools a nd one other middle school in east Gainesville, and A. Quinn Jones is now a Center for Exceptional Students which serves severely emotionally disturbed students. Though schools on the east side of town have some ethnic diversity, many still have populatio ns that are overwhelmingly African American 3 Duval Elementary School, l ocated in the northeast portion of Gainesville in a community known as Duval Heights is just a few miles from the current Lincoln Middle School campus. Duval Heights is almost exclusively African American. There is a sense of community in the area that is evident as you drive down the main road. The many times I drove through the neighborhood to the school, I often saw people riding their bikes to and from the conve nience store, friends conversing outside of one of the many churches, children walking home from school together, and friends sitting on their porch chatting; there were always at people outside. The homes are quaint and older with colorful character and unique qualities, and many are shaded by the large trees that line the streets. 3 This information was retrieved through the School Board of Alachua County website and community relations staff: www.sbac.edu
72 About a minute off of the main turn into Duval Heights, after having passed numerous churches sitting on the avenue, is Duval Elementary School. The campus is modest and ol der, but not unkempt. This creates a sense of community that is evident the moment you walk through the doors. The front desk staff is always friendly, often chatting with parents or teachers while helping visitors find their way. This same kind demeano r is consistent throughout the work and newspaper clippings that document the accolades that the school has received. Student work consistently lined the hall ways outside of the main classroom corridor. The school draws most of its students from this neighborhood despite a district wide fine arts magnet program and recent success on state mandated tests such as the Florida Comprehensive Assessment Test (FCAT exclusively (about 98 percent) African American, with roughly 85 percent of students qualifying for free or reduced lunch programs in 2008 4 making it a Title I school Despite past struggles, over each o f the past 6 years, the school has earned 4 (in 2003, 2004, 2006, and 2008) and 2 (in 2005 and 2007) 5 as measured by the state of Florida accountability system, continually showing adequate yearly 6 progress in most areas. s in 5 th grade mathematics scores and gains was due in large part to Gloria Jean Merriex, a mathematics teacher who spent thirty years as a faculty member at the school. A native of Gainesville, Glori a was a th at 4 Demographic data retrieved from www.publicschoolreview.com and www.fldoe.org 5 Data retrieved from the School Board of Alachua County website ( www.sbac.edu ) 6 Adequate yearly progress (AYP) is one of the main components of No Child Left Behind (NCLB). The goal of AYP is to document steady student growth on standardized tests so that 100% of students are proficient in each tested area by 2014. The student body must show AYP as a whole and by disaggregated (by race, disabilities, limited English proficiency, and socioeconomic status) population gro ups.
73 were reflected in the continued segregation of schools Resulting experiences and others drove her belief in children, and historical cultural influences drove her teaching methods. What was exceptional about Gloria, however, was much more than her te aching. As this story will show, school, and the empowerment of generations of learners. The bustling, pink home of the Merriex family sits in the east part of town less than one mile from Duval Elementary and less than 3 miles from the University of Florida. Here, Cenia and Donal family...my daddy instilled that in us siblings, Donal Jr., Gloria Mary and Charles, have carried this va lue throughout their lives as became obvious when I began speaking with Jan, Charles, and Cenia Gloria the second child, entered the world on November 16, 1949 one day after her at 7 pounds, 2 ounces. Gloria was hrough with As a child, Gloria developed the strong personality that would make her so successful
74 we were growing up the older ones would have to take care of the younger ones, so no matter Gloria would also shield Jan from the realities of the day. When Jan was a little girl, loria would wake Jan and shop, Gloria would always direct Jan to the back door, which was often locked. This confused Jan, as the front door was always open. that to you ng Jan; rather, she would just wait for the door to be opened. She would never tell me well aware of such social rules, having attended A. Quinn Jones Elemen tary and Lincoln High School and ex periencing segregation firsthand The experiences that Gloria had while segregation was still officially in tact, and the attitudes she developed because of those experiences would later be one key to her success in th e classroom. This type of experience strongly informing teacher practice is not uncommon, though it presents several interesting moral contradictions. African American educators who have experienced the realities of formal segregation are somewhat rare b ecause of age and are often underrepresented in terms of voice and influence. Given their life history, however, these teachers are in unique positions to connect with African American children who might be affected by similar cultural struggles today wh ich are brought on by overt and systemic prejudice and racism These teachers are often intricately involved with students not only in this context of academics, but also in guiding learning about life and the world, and the dangers that faced them
75 outsid segregation, unique perception of racism, and experiences within an oppressive societal and educational system. lue orientations, and experiences to 260). As such, these educators were in a uniquely powerful position to influence student beliefs about self, racial identity development (Tatum, 1997), and to teach authentic content through which students were able to better understand the political and social situation of the country (Freire, 1998). Interestingly, while it is often recognized that separation by race creates an inherently unequal arrangement (due to the magnitude of other factors in the educational system), much of this work implies that before integration, some African American students were in academic contexts that provided more access to academic and cultu ral knowledge (Ladson Billings, 2004). In separate settings where students could learn from the struggles of African American teachers and familiar role models in edifying ways, le arners were better understood in terms of cultural behavior, were not forced to conform to Euro centric values, and were provided culturally relevant instruction. This is not meant to imply that desegregation was a bad idea, but is meant to highlight the fact that it was not the scho ols or teachers in black schools that caused an inequitable situation. Black students may have actually received a better education in separate schools where there were teachers of their race (Siddle system that defined [ Billings, 2004, p. 5) and the perceptions created by that system that made separate schools inherently unequal.
76 Many African American teachers lost their jobs when integration occurred, and the decl ine of teachers of color has been consistent ever since (Hudson & Holmes, 1994). Today this trend continues; there is a severe shortage of teachers of color in the teaching force (Howard, 2006 ) and in t eacher preparation programs. In 2000, of 3 million p ubli c school teachers, roughly 9 percent of those teachers were African American (Jorgensen, 2000; Snyder, 1999 ) and 87 percent were white while students of color constitute abou 40 percent of the student pop ulation (The American Association of Colleges f or Teacher Education [AACTE], 1999). Many schools (over 40 percent many students do not have the benefit of these types of role models in school. Teacher preparation programs show little hope for curbing this trend, as w hite females constituted over 80 percent of the population in colleges of education in 1999 while African Americans represented only 9 percent of prospective teachers in such programs (Yasin, 1999) As a result of the white dominance in the field, much of the research and literature in education, and particularly in mathematics education, largely leave out the voic es of African American teachers (Agee, 2004; hooks, 1994) despite their distinctive and culturally based pedagogies and management strategies. As such, educators (and ultimately students) are missing perspectives and worldviews of these women, and curricu la, dominant pedagogies, and teacher preparation programs (Gay, 2000) reflect this void; many teachers are compelled to teach specific material in particular, non cultural ways. Accordingly, African American students often do not believe that teachers un derstand their
77 gaps in mathematics by using culturally base d teaching methods and familiar communication patterns. Moreover, having lived as an African American through decades of blatant and invisible inequities in all parts of life, Gloria brought a realistic and understanding frame of reference to her students This historical context allowed her to educate students not only in mathematics, but also in strength of character and beliefs about self. Gloria achieved greatness through her own path of self discovery. She continually challenged her place in socie ty and worked to create opportunities for herself. After graduating from Lincoln High in 1967, she worked in the cafeteria of a local school as a cook. Her brother e barriers, Gloria found a way to change her life by going to college. Cenia recalls, have money to send our children to school, but [Gloria] was dete rmined that she was going to go. She got out and found out different things, how to get there, and she went on her own. She was determined that she was going to go to school and she had that drive. She had that In 1970, Gloria moved to Houston, Texas and began attending Texas Southern University, one of the largest historically black Universities in the U .S The University was established in education. It was there that Gloria Merriex began studying to be a teacher. After spending three years at Texas Southern, Gloria returned to Gainesville to earn her degree in teaching. She was an intern for a year after graduation, and began teaching a children, Toyana and Carl, still live in Texas and Gloria has two granddaughters, 9 year old Carla and 4 year old
78 grandch who considers Gloria to about how she used certain times I would see a little pie ce [of old Glo in a nega Mary all four of us would sing. [Gl oria] never did sing, but now she sings in the choir at [Hope to the World mber of who co there is a long bench and we would sing parents and the kids and other faculty members would gather around to listen because it was just
79 ines in [her room], she cooking She gets up and fixes breakfast. She knows [Charles] likes pork chops, so she would talent sho w where even the teachers had to get up and do something. [Gloria] must have been a drum majorette you talk about twirling a baton! All up and between her legs and catching it e come from her astside helping coordinate the Lilliemarie Harvey is in her fourth year teaching at Duval, and worked closely with Gloria during her first years a Ms. Merriex as a child. She knows how she needs to be talked to, she knows what will motivate
80 her, so she knows what to give [Duval] kids based on her background and how she grew up So Sometimes the kids had a hard time understanding the struggles that Gloria saw for them they beg and just talk to the kids and say this is how people view you. This i s why people view you like like 10 minutes and go to church with them you know like the preacher part of it, and then Leon Marshall agrees that it was her own personal experiences that shaped the ways in to work such, Gloria would not let her students believe that they could not do what she did. In order for the kids to appreciate this, ing their background as an excuse for failure. This mentality made believers out of children and, in turn, parents and the community. how to strive
81 same place that they did, and despite the struggles she faced, she was highly successful. Lilliem house who became this phenomenal, world renowned teacher. Anything is possible as long as othing is going to be Upon her passing, Gloria was on the verge of national acclaim. In the spring of 2008, a major foundation had approved a grant program that would spend $25,000 installing cameras in around the country to be able to wa development module based on her strategies, were also in development. Throughout her life, as is evidenced b y her record of personal and professional success es Gloria was invested in the things that were most important to her. These things, family, friends, everything and do es it not 100, but like 3,000 percent Given the amount of time that the two spent together, Ms. Harvey was able to see this energy in we hung out teaching. She planned parties and functions, and she worked just as hard for her church as she worked in that classroom. There was no running ou t of gas or halfway doing something, it was 100 percent on everything. I have never, ever met anybody like that. Some people slip in certain percent on everything
82 As such, Gloria left quite a pair of shoes to fill shoes which most people feel will never be filled.
83 Chapter 2 Understanding how they learn is one thing. Being a friend, being a momma, being a daddy, being an enemy, is another. You have to be the enemy at some time because you gotta get on e disrespectful I got to be their enemy...if they need me, if I can ge lot of them need a little love, but t hey understand what I say goes. Gloria Jean Merriex Lee McNealy has been the principal at Duval since 1994 but has roots as an element ary school teacher in Gainesville It was as a curriculum resource teacher at Duval, in fact, that she first met Gloria Merriex. At that time, Gloria was working as a first grade Gloria loved the children too. It was during these early years that Lee believes that Gloria b egan formulating ideas and lessons that grew to draw so much attention Though friendly, the two were not as close back then as they came to be. Over several years and after a stint as a teacher on special assignment (TSA) for the School Board of Alachua County Lee made her way back to Duval after completing her principal internship in various schools in the county, and spending another year as an administrator at a different school in the district. It was when she came to Duval as principal intertwined. Aside from their work at s chool, both were members of Hope to the World church, lived in the same community, and traveled all over the country as school leaders together. When Lee did return to Duval, Gloria was working as a part of the 4 th grade team of teachers, a group Lee close knit nature and varied
84 styles of teaching. Though the Three Amigos worked well together, Lee remembers that things this way at [a sch that Gloria could approach folk would just leave them taken aback, but Norma said after that encounter with Jea n that she was right she was no longer at the other elementary school. So outspoken and would say whate character istics, and realized that she did not shy away from the truth, even when it came off as This personality trait did not come and go as socially appr opriate as it does with many people. When a participant in a conference or in professional development seminar, for example, Gloria would not passively sit through a session if she felt the presenter was on the wrong track. At a math ematics conference to One session that she A pseudonym has been used
85 did it profe ery opinionated, and if back and being quiet Occasionally, Lee had to ng a particularly important year at Duval, a reading consultant, Sally was called in by Lee Though Sally told Lee that she was not able to help because of limited time, Lee talked her into coming to Duval on Saturdays to work with the faculty. Sally c ould have easily turned down the offer, but Lee pleaded her case, gaining sessions with Sally Jean piped up, saying she did not need a teacher and that she should be released to go back to her cla ssroom. When Sally told Lee about this incident, Lee pulled Jean aside and said Sally knew best at that point, but went along with the temporary structure as well as she could. woman, and her voice commanded the presence of a room. She took a ver y strict approach to discipline, having students without materials or with an attitude leave class and call their parents A pseudonym has been used
86 under her supervision. She did not tolerate any outside talking in class, though the children were so engaged in learning mathematics most of the time that there was little time or need for such behavior. She had high expectations for their mathematical ability and effort, and expected them to perform at all times. Her reputation was well known throughout the school. Up and coming fi fth graders knew what she expected, and she let them know as she passed them in the hallway that they had better be ready. Jan Merriex recalls the time that she put her own son class and how he experienced her toughness first hand. He was in fourth grade at the time, and writing. Those in fourth grade writing class, the teacher is my Auntie, and it i h! th her in 5 th grade too, then he was getting ready to go to [Howard] Bishop [Middle School] and you know what he says to om, you think that Auntie Jean can go with me to 6 th o h, wow. people judge people just because they see them at that As Jan knows from this experience and others, underneath the tough exterior, Gloria was d, but once they got to
87 fact, she and Sally the reading specialist who Gloria Sally would come [to the school] and it was lunch with her, or bring in some materials for Sally close with her tea m, the Three Amigos, and built an intense bond with Lee despite their not agree with her. But at the end of the day, we could always come back together and be on the It was almost as if she were cautious about showing her truly generous nature so that she would not be taken advantage of. Many people, including her family, other teachers, students, even researchers from the University, depended on Gloria. Lee was very aware of all that Gloria there wh en she interacted with her family. Cenia remembers sitting on the couch as Jean was walking
88 Though outwardly tough in the classroom, Gloria showed this sa me furtive and deep care would do anything for the children It went beyond the instructional practices because children who had no shoes or had no food or needed this, and she knew about it, then she last to the kids When you form that kind of bond, and that kind of rapport with a child, they know. Children know. They can decipher. They know who really, really cares, and who really students to do Lilliemarie saw things similarly, and found that strict rules of behavior and high You know how your family is hard on you backwar ike hey, baby. They knew that Buffy Bondy, a professor of education and director of the School of Teaching and Learning at the University of Florida has worked with the faculty at Duval for the past 9 y ears.
89 in s ome ways she was an open book like it is and let you know what she thinks about things but in other ways there was this very During her time at t he school, Buffy was officially a professor in residence, essentially serving as a consultant and part of the leadership team. Her job there as she describes it however, was not particularly well defined, and she often did whatever was needed at the time things which can be classroom management issue, but it can also [Lee] definition and solving work, and t hat could be academic, classroom based pedagogy sort of stuff, or professional development I was always involved with that. My theme was always to not do at on consulting with the principal. I would sometimes meet with the leadership team just to be part of ld just drop in on new to build the collaborative culture among teachers and leaders at Duval. would try to just sit on the stool by the door and just watch for a while. She might want to show eral papers focusing on various aspects of
90 was maybe a lit class perspective, not a warm and fuzzy someone who reaches out, though really very warm and e people thinking, including some student teachers, that she was intimidating. Then, if you really pay attention, you realize that you need to be watching how kids respond to that because your As pre service tea often made about what goes on in classrooms. Many times, this leads observers to draw conclusions about people, particularly teachers, which exist and work outside of our own cultural norms. Gloria, who was easily misunderstood and frequently described as intimidating and communicate expectations effectively and consistently. Because of her own background, she them [to do t their to be white Moreover, Gloria understood the struggles of the families in the neighborhood. Having lived through such perceptions of inadequacy herself, she knew that many of her students had been told in some form or another t hat they could not learn, thus hardening them to academic Lee even though she was the teacher, she had not forgotten from where she came. She could speak
91 their language [meaning] she could interface with the family, but did not demean them in any in close contact with members of the community, making the school central to the neighborhood. Lee Heights and, as we went from house to house, she was introducing me to the families and saying this is potential using a demanding style that could be perceived as harshness. Outside perceptions, however, are not necessarily impo reams them out over something, they may look down or a couple of those boys may grumble, but more o really cares about them who is going to make sure they are successful. She co mmunicates how committed she is to them and how much she cares about them from the beginning, so then, when she has to get tough, which she will not hesitate to do, they respond to that because they know that this is someone who has their very best interes ts at heart and really wants to see them excel. Given the tragedies in her life, it is not surprising that Gloria expected excellence from her students no matter what their situation. As someone who came from the same neighborhood and experienced mandated
92 Gloria who was typically consumed with her teaching, to come back to work after this trauma. Gloria experienced several other formative misfortunes in her life. After finding a way to get to college, she was faced with the challenge of staying the course when one of her good friends, Ricky, passed in 1972 during a visit to Gainesville. folks he was like family. [Gl the years following the tragedy, Gloria met another young man named Ricky, a basketball player sch These types of experiences may have hardened Gloria on the outside, making her appear to be confrontational and emotio I think she built up [her tough exterior] as a Moreover, as she began to gain notoriety later in her career, she would often speak about people from various places that might be taking advantage of her generous nature and willingness to share. This may have shaped her interactions with new observers, making her seem hardened on the outside. At the end of the day, however, she was happy to be helping children.
93 the kids, learning, and math. Then shopping! Lee McNealy going to Jacksonville, Tampa, and Orlando. take my e malls. Especially during the As a result, people at various stores knew Gloria and would contact her for special events and sales that might be happenin g. In return, she gave these stores her business. If she did not feel that she was treated properly by a store employee she would make her dissatisfaction on [Jean] walked in that store, they knew uh e i Ms. Gloria would not make her personal problems public. Her mother recalls that there were
94 ing me how his wife was real sick and [Gloria] would come to the house and do what she could do for his wife. We out you were sick, this is something she actu she would always always ; she was caring understand sometimes that little things are learned more recently. Jan thinks thi good in a way but its not good in says
95 will tell you off and keep Lee also worked to encourage Gloria to pay more attention to her health. During one particularly jarring episode after which Gloria ended up in the hospital because of the high glucose level of her blood Lee called h er own doctor and begged that she take Gloria on as a patient. In the short term, Gloria got much better. Over time, however, she stopped going to the time an her care because she could not be liable. Gloria was not following through and was not keeping was common for Gloria. She would be feeling bad, be forced to go to taking care of herself. Leon saw this as a side effect of her undying commitment to the school. hat made everything work, and she really denied herself so many times health of times in dealing wit need you at sch ool. And so you are not The only other person that could get her to move was her childhood neighbor and fellow make her go to
96 r like a little kid! His daughter lived in Atlanta and she would call the house and say cause he did l Thus, despite her seemingly tough exterior, Gloria was a very caring individual who cared deeply for those around her. There has been speculation in the community that because of her attention to want anyone making a fuss over her, and I think she knew that day [that she passed away] that it
97 Chapter 3 have on the kids and being proud of them once they finish and they understand. It makes you feel good ney! Gloria Jean Merriex When speaking to the faculty and staff at Duval Elementary, an overwhelming camaraderie is evident. This is largely due to a committed and inspirational leadership team coupled with the drive of each individu al teacher to work hard in educating this particular group of children. The school which is thriving now has not been without its struggles over the years. The No Child Left Behind Act (NCLB) 7 of 2001 introduced new accountability and grading systems i n public schools. These school assessments are meant to give the government a comparisons between institutions and between students. man dates that schools are scored on an alphabetical scale. Student test scores, based on tests that have been developed by state systems in accordance with NCLB, are the data from which these school scores are derived. These scores are used when publically evaluating schools students, and teachers. As such, these assessments greatly influence student retention, and inadequate performance can even keep a student from graduating high school. Further, the school as a whole is given a grade (A is the top scor e while F is the bottom score) based on such results. mediating school activities such as curriculum, instruction, funding, and special programs. 7 See http://www.ed.gov/nclb/landing.jhtml for more information on NCLB
98 Because o f the large amount of weight given to the scores that result from these assessments, they are often referred to as high stakes tests 8 In Florida, school grades are largely based on student performance on the Florida Comprehensive Assessment Test (FCA T) and also take into account adequate yearly progress ( AYP ) Essentially, the state looks for passing scores on the FCAT (a score of 3 out of a possible 5 is considered passing), and gains on the test particularly in the areas of mathematics and reading. Learning gains are made, for example, when a student who scores a 1 (out of 5) one year improves to a 2 (out of 5) the following year. The state also specially considers students who fall in the lowest 25 percent in terms of scores. Schools that do not make AYP are required to develop and submit a School Improvement Plan that outlines the ways in which these needs will be addressed and particular students receive and Individualize Education Plan (IEP) NCLB also includes many sub sections and specific plans for action. As outlined in the 9 Duval qualifies as a title I school, meaning that there are a high percentage of students in the school that qualify for the free or reduced lunch program. Essentially, the school o obtain a quality education and reach, at a minimum, proficiency on challenging State academic achieving children in our poverty 8 Several analyses (see Lee, 2006, for example) have used data gathered from NCLB driven tests to show that the 9 All school performance information, quotes, and data in this section were gathered from the national ( http://www.ed.gov/nclb/landing.jhtml ) and state ( http://www.fldoe.org/ ) Department of Education websites.
99 economically disadvantaged students do not receive the same quality of education as the economically advantaged. It has also been argued tha t the accountability grading system is unfair to these and other populations (students who do not speak English as their first language, for example), as the FCAT is written without regard for cultural or linguistic diversity (Jones, Jones, & Hargrove, 200 3). During the 2001 2002 school year, Duval earned a grade of F under the state rating system. Lee ter what had been a nd hugged me and s we made an F brought the morale of the school down. The school also faced the possibility of losing a large grant that they had just received as support for integrating the arts into the curriculum. After their initial hurt Lee o get the district, the state, our parents, the community that we were not failures The school immediately held a town hall meeting in the auditorium for parents. Gloria spo professional development facilitators, and the entire faculty at D uval. Gloria was also a large
100 part of that change, recalls Lee When we moved from [a school grade o f] F to A, and schools started coming wanting to see debriefing in the afte rnoon, questions would be asked, but it would always gravitate back to Ms. Fortunately the school was able to keep the grant that they had received to infuse the arts into the curriculum. Gloria, with her rhythmic teaching, chants, raps, and movement activities, was ahead of the curve on this front. As part of the grant, a team of representatives from the school was required go to a summer institute in Mississippi. These institutes were meant to help schools to find ways that the a rts could be incorporated and woven through all subjects. Gloria Briar Patch, because this was what she knew anyway. The Mississippi commission and the t eachers and educators, they were just budding with this, and we had already been taking that in her practice, so she just ran with it, and taught them one or two things when we were in rtise, many of her colleagues feel that she was under because she was employed by the school board they would not pay her [to consult with
101 driving source, she was the vehi cle that put Duval on the map. The community, the city of Gainesville, Alachua County, the state of Florida just had high admiration for her because she assess ment system gave Gloria a new goal: to help her students succeed in the eyes of the state without having to abandon their culture. Gloria worked tirelessly to this end, constantly thinking mathematics scores. Each successive year, her students showed the highest mathematics gains in the state, their overall scores at the top. In fact, Lee McNealy recalls how Jean thrived on working with the most were, I would say, the rough piece of coal and then became the diamond after she completed her kids who were [ labeled] ESE 10 loved the challenge of showing every child can learn. [Teachers] just have to be flexible, we Buffy rem deemed to have learning disabilities or kids who were supposed to be receiving special education services. It was kind of like she had something to prove there and they had somethin g to prove as well. So that whole thing, this belief in individual children and in a people to excel, because it 10 ho receives special education services from the school.
102 Lilliemarie remembers this same unwavering standard of excellence despite the varying There was no adjusting for [Gloria]. Her standards were way up here and you were either going life with midway through, all of the students are acting as though worked tirelessly to help such studen their schooling years, implying that they were mislabeled. She would always say that it is often the teac hing or teacher, not the learner, which is the source of any academic or behavioral problem. Gloria would spend hours observing her students and determining how they took in t makes mathematics lessons, her constant revisions, and her Leon remembers Gloria them, and they can remember a
103 Angie Terrell professional people would overlook. You know her Phillip 11 story he was a little boy that was an ESE student and right away when he came to her she knew that the kid was gifted. She spent many, many hours making sure that kid got out of the ESE program, and now he is at Eastside in the IB 12 program. Jan, who w orks with handicapped children, remembers that she and Gloria would often shove them to the side; she ma de sure that they got [the mathematics concepts]. She e ven put them on her Math Team can do this. I know it looks hard now but you know you can Just as Gloria would never tell Jan why they could not us Gloria would never tell a child that they were excused because of a label; rather, she pushed them to excel and accepted no excuses. FCAT testing gave her even more motivation to focus on these students, as she co uld see on the test itself that the child might need something more than had previously been provided. children that some people would put aside and say they c that they could learn if given the right instructional practices, the right nurturing. She would not FCAT scores were releas 2008], 80 % of the kids passed with a 3 or above 11 A pseudonym has been used 12 The IB, or International Baccalaureate, Program is similar to an Honors or Advanced Placement Program. It includes a challenging curriculum and is considered a gatewa y to college.
104 without choice, This attitude of persistence was likely instilled in Gloria many years before she was known for her innovative mathematics teaching. In the early years of Glori career, the T itle I schools had a pull out model. This meant that throughout the week, the kids who w ere identified as eligible for T itle I services would come into a separate lab classroom for extra support. Initially, Gloria worked to help children wh o struggled, working in the T itle I lab. Gloria also worked with students from other grade levels, teaching fifth grade math ematics during the year, but also continuing to teach reading in the mornings and younger children during summer scho not the age level or the grade level. She could take these children and make them feel so good Lee recalls. This empowerment and self confidence This determination and belief in children, no matter what their situation teaching methods, and drove her to continue on in pursuit of excellence. Gloria also wanted to help sustain the community surrounding the school. Because of the ore likely to have fewer th mo re years generation and a dying community because nothing is gonna come back to the community its
105 gonna die out, and th In other words, Gloria seed come up? No. But enough seeds came up so that we could be an A school, and tha t This focus on struggling students speaks to the theme of equity that resonated throughout would do everything she could to provide for children who needed food, clothing, or money. Jan remembers that Gloria would search high and low, even calling on her family, to find appropriate oes whatcha a resource for the students. If a child needed a shirt, pan ts, money, food, tutoring, she was there for them. Her pocket was just like a recycle bin. It was always going. So nobody could say I make that her business to make sure. And she did it looking for nothing in return. The journals, she went out and bought every child a journal at the beginning of the school year. She bought the journal, she bought the cover for that journal. It meant that much to her to know that every was that she did not directly address issues of societal perceptions based on ra ce and income directly. Though she might occasionally mention something to this end, such comments were few and far between. In other words, she did not constantly hit the children over the head with the idea that they had something to prove (though she occasionally made direct statements)
106 rather, she let her actions speak for her. Further, when she did help children acquire material anything Over time, teachers from the district began coming to Duval to watch Gloria in action. Soon, University faculty, doctoral students, preservice teachers, and grant organ izations from across the U.S. followed suit. Several groups began videotaping her lessons for various reasons, and using them for a multitude reasons such as preservice instruction, professional conferences, and inservice workshops. It was exciting that these sorts of projects were finally coming to was] kind of an interesting thing as a woman in this society where we often are underselling ourselves, she wasn At the time of her death, her notoriety was just beginning to reach another level, and several projects were set up and funded so that the sharing of her ideas would be more beneficial to everyone involved, especially Gloria. Le e believed that Leon gonna do the chicken wings, she was gonna do the rice, she was gonna do the green beans, she was gonna do the seafood salad. She made the pound cakes, she made the potato pie s. Why? Because she thought she was a good cook, and she was, but she wanted to make sure there was
107 recognition for her teaching because she knew she was special and gifted and wanted to show her skills, but also because she wanted no child to go without self confidence and excellent, relevant mathematics instruction. Gloria often stated to me that she was not sure of the sources of her motivation. What she did say was that she was influenced and driven in large part by her surroundings, namely her family, the children, the community, the school, and the church. Her passion seemed almost innate, and sh e believed that she was meant to teach children how to excel in academics and life. with fulfilling this role was enough for her. Lee oal to teach. And she her career. Though she rarely spoke abo ut outside sources of inspiration, Gloria was quite taken with well known educator Marva Collins; she is best known for her work and success with methods and ideas, lins speak. all Preparatory School, which was founded by Ms. Collins in 1975. Westside Preparatory School is located in a disadvantaged Chicago neighborhood called Garf ield Park. The opportunity for Gloria and Lee to visit the school arose while the two were in
108 ter compared notes from the day of observation, both women were flooded with ideas, but sat back and realized that Gloria both of us that she was on the right tr Though Gloria and Marva Collins shared similar aspirations and accomplishments, the two varied in style. Their work, however, seems to strive for the same end to encourage reasoning and thinking among traditionally underserved students. Ms. Coll ins utilizes the Socratic Method, using questioning techniques and abstract ideas to encourage thought and discussion. Gloria also introduced abstract concepts of mathematics, but used familiar cultural tools and practices to help children access the info rmation. Through this and with much repetition, she was able to encourage reasoning, questioning, and confidence in mastery. When made to read a passage, answer qu estions, and prove their answers to the class. The two were similar also in their beliefs about children in high poverty neighborhoods who had often received sub learning disabled child ren in my three decades of teaching. I have, however, discovered many and believed that all teachers should be accountable, though many shunned this resp onsibility got to move away from your old timey teaching and se
109 unwavering belief that each student is able to achieve was fundamental to her practice. John Dukes was another source of inspiration for Gloria. When Angie Terrell was in high school, Mr. Dukes was her class sponsor. She remembers Gloria speaking of him with high provided for them. She just had such high esteem f would make all the Lee I remember the same sentiment. I will never forget the first time that sh e told me about Mr. Dukes during my first year of working with her. She mentioned that he was a neighbor of hers who was a teacher when she was a young girl. She r things like air conditioning, and she made it her goal to somed County, but his influence at Duval Elementary is not forgotten. Several years ago a events for the children would be held in recent years.
110 Part II ond language to include other aspects of student and school culture. Thus culturally relevant teaching uses student culture in order to maintain it mary aim of culturally relevant teachi African American students to choose academic excellence yet still identify with African and African American culture. Gloria Ladson Billings, The Dreamkeepers 1994, p. 17
111 Chapter 4 I just sit and watch [the students] sometimes. I notice that kids can rattle off a song, even a new song, just rattle it off. I see it happen and think my God how can these kids learn a song so quick? Because they hear it all the time. They hear it every day. So I noticed this I said my teaching style is gonna be like that. So I teach [these concepts] every day. And even if I teach something new, I go back and reintroduce the old, an d combine the old and the new together. So understand the processes as well as ho w to how to solve the problems. Gloria Jean Merriex During my years as a graduate student I taught a mathematics methods course in the teacher preparation program. Essentially, this course was meant to teach teachers how to prepare and enact effective and engaging mathematics lessons in an elementary school sett ing. Pre service teachers take this course during the first semester of their fourth year in the program. In the fall of 2006 I taught the course for the first time, and the population of my class was representative of most teacher education courses at t he university : 28 white females, 2 African American females, and 1 Latina female. In subsequent semesters I taught the course three more times, and each time the percentages were similar. Several semesters I had one or two white males in place of one or two white females, but the overall population stayed quite constant. On the first day of the course, I always ask my students to respond to the following is the o classrooms are described as engaging, supportive, and student centered with a great variety of instructional techniques ( e.g. group work, direct instruction). Students are enga ged in whatever it is that they are supposed to be doing, and an appropriate level of noise is tolerated. If students are doing group work, the teacher walks around to help students, asking guiding questions and supporting interaction.
112 Phrases such as discipline, my students are careful to be sensitive, saying that they would ideally take a s oft tone My students have the best of intentions when describing these classro oms these are the ways in which they have been schooled, and the ways of communicating that they describe are consistent with their frame of reference. In fact, to most current teachers this may sound like the ideal environment for learning. They, and my students, think of this type of classroom as normal, and argue that they are just trying to be fair to all children. What is not as evident is that such classrooms are highly cultural and are based in the comfort zone of the teacher. In other words, w respond well to softer directives, for example, simply because such modes of communication mirror their culture at home. Such techniques, however, are not consistent with t he home culture of many African American children who are used to a more directive tone. This type of cultural incongruity may confuse an African American child, leading him to resist and act out. Teachers are quick to claim that they have set up a fair caring, and equitable classroom and that the African American children are in the wrong. In some cases, teachers will even go as far as to make an unfounded generality about the value of education in the eyes of the African American community. Such bel iefs only exacerbate the dominance of white culture in our schools and highlight the need to explore successful teaching practices in diverse classrooms.
113 Culturally Responsive Teaching The teaching methods of Gloria are extremely complex and difficult to describe with words alone, but do provide insight into culturally based teaching methods. The transformative nature of her instructional practice, however, makes it necessary to use accepted research methodologies t o deconstruct her instructional practice in ways that are meaningful and relevant to schools, teachers, and administrators. Successful, African centered pedagogies have been studied (Ladson Billings, 1994; Irvine, 2003) in other contexts, largely under th e umbrella term of cult urally responsive teaching (CRT 13 ; sometimes referred to as culturally relevant teaching or cultura lly sensitive pedagogy). Culturally responsive teaching practices in largely African American contexts the education of African American Olatunji, Baker, & Brooks, 2006) using culturally based communication patterns, body language, and strategies to empower students. CRT provides a useful framework through which critical examinations of current ideas about culturally responsive pedagogy can be refined and expanded to include mathematical contexts. work and add to the existing literature, we will first take a look back to the general framework of cult urally responsive pedagogies and classrooms, largely in relation to African American learners. CRT is discussed within the American historical context, and gives a framework to much of the work of multicultural educators. Culturally responsive teachers view the incorporation of cultural perspectives as a necessary educational commitment. Students are viewed as cultural beings with cultural filters (Gay, 2000) through which all information is sifted. In other words, 13 The term CRT as it is used here is attributed to the work of Geneva Gay, especially as it pertains to her 2000 used by Glori a Ladson Billings to describe a similar framework.
114 cultural experiences and identities are seen as the foundations for all other experiences and behaviors (Ladson Billings, 2001). Educators who embrace CRT aim to capitalize on the fact that varying cultural filters exist among stude nts and teachers. Moreover, these educators aim to resolv e, through empowerment and validation, the dissonance this variation causes. As mentioned above, individual culture and experiences are the basis for all other actions (Gay, 2000; Ladson Billings, 2001). Often, school cultures (and teacher cultures) are not consistent with student cultures, causing student achievement to suffer. This implies that inconsistencies in school versus home culture ( e.g. how struggles a s lack of ability (Boykin, 1986; Spindler, 1987). Moreover, this indicates that poor Culturally responsive teachers recognize cultu ral incongruities as the cause of the achievement gaps, and can therefore intervene appropriately. Too many current pedagogical solutions in schools focus on standardized testing as the root of the problem and result in prescribed curricula focused around these assessments. When we consider that cultural discrepancies are at the root of the problem, it becomes clear these types of dictated pedagogy and curricula may actually exacerbate the achievement problems of students of color. Teachers who teach fro m a culturally responsive framework recognize the strength in
115 ethnicity they are enacting racist or biased methods. Ironically, in trea ting all students the same, teachers are enacting the very prejudices that they fear the most. One mode of instruction does not serve all students in the same way, and inherently favors one group. This is most likely to be the group that is most like the teacher, as the teacher is likely to act out of his or her own cultural experiences. Since most of the teaching force is white, the students in this group are most likely to benefit. Culturally responsive teachers validate and affirm student cultures by recognizing them as such in the classroom and paying tribute to each of them equally. These educators teach ay, CRT is multidimensional and comprehensive, encompassing many aspects of student and community lives. This validation and value placed on student lives is powerful and liberating. Culturally responsive teachers look to transform individual perceptions and actions through education. knowledge, skills, and values needed to become social critics who can make reflective decisions and implement their decisions in effective personal, social, (Banks, 1991, p. 131). In this way, CRT is emancipatory and transformative for students, teachers, families, communities, and schools, re defining what is considered important riences (Ladson Billings, 1994), and engaging in a continuous effort to combat the status quo. Student cultures and familiarities become a part of the curriculum, and the norms of the classroom are re characterized based thereon. Specifically, modes of c ommunication are made to benefit each child, ways of assessment and teaching are re conceptualized, and a trusting and caring environment is emerged. This empowers students to
116 believe that they can succeed in learning tasks, and motivates them to continue meeting challenges in and out of the classroom. Culturally responsive teachers recognize and utilize the fact that other forces are at work in schools, and that pedagogy, though a powerful tool, cannot alone change societal perceptions (Gay, 2000). For example, culturally responsive teachers recognize that academic achievement may be frowned upon in particular cultural groups because of historical and social institutions. As a result, academic knowledge and attainment may be masked by a student as a def ense against alienation from his or her cultural group (Fordham 1993, 1996). Again, this is illustrative of a severe discrepancy between student and school culture. The negative views of education held by certain cultural groups are understandable; the e ducational system has consistently asked students of color to abandon their culture for the sake of education (Nieto, 2002). It makes sense that a delineation separating the two would emerge as a defense mechanism, a tool for resistance, or a way of simpl y denying what the school culture deems important. This undercurrent of cultural friction implies a school culture and, more widely, a societal issue relating to the Culturally responsive educators aim to change the face of education, helping students to realize that they can control their own learning. C ultural beliefs and practices are at the forefront of instruction, and are viewed as individual strengths rather than collective weakness es. In this way, culturally responsive teachers aim to transform traditional educational practices and negative views of ethnic students of color (Gay, 2000). As such, CRT cannot achieve transformation, validation, and empowerment in isolation; rather i t must be a part of a larger school and community change in perspective As such, specific culturally responsive teaching practices vary widely between and among schools.
117 In bringing student knowledge and experience to the forefront of teaching, culturally responsive educators aim to cultural understanding. As such, CRT requires that teachers consider many f actors within the educational setting, including curricula, learning environment, assessment techniques, patterns of communication, and relationship development. As such, culturally responsive teachers aim to educate holistically, allowing students to mai ntain their ethnic identities while developing a sense of shared responsibility in the learning environment (Gay, 2000). The multidimensional nature of CRT requires that it, and the teachers who enact it, are flexible and continuously evolving. If CRT we re stagnant and rigid, it would inherently contradict its own purpose. Thus, perhaps the most important and distinctive characteristic of CRT is its flexible nature. Indeed, CRT will not look the same in any classroom, and the enactment of the framework may vary widely. It is through this continual evolvement that CRT can change with the diversifying population. Moreover, it is only through adaptable methods that educators can hope to meet the needs of various learners. Culturally Responsive Mathemat ics Teaching (CRMT) The framework of CRT has remained somewhat general in terms of subject specific strategies and theoretical foundations. Certainly, each subject should not be separated from the others as this would simply lead to more topical, cookie cutter solutions. The current framework of CRT, however, serves as a context within which culturally based mathematics teaching can be examined. In other words, this work is not meant to be divisive, but is meant to zoom in on one specific subject area w ithin the larger context of CRT. In adding to current ideas and revering successful models, this work becomes more prevalent and relevant to schools. Through interviews with Gloria, observations of her classroom, collection of artifacts such as teacher made tests and student work, and informal conversations that occurred naturally,
118 the theory represented in figure 4 1 14 was developed in an effort to generalize her practice into a working premise for culturally responsive mathematics teaching (CRMT). This model was constructed inductively using grounded theory methodology (Glaser & Strauss, 1967), and only was used in the analysis that led to these conclusion s. Given the limited research base (there are very few research based discussions of the construct) in the area of CRMT, grounded theory was an appropriate methodological choice. Subsequent interviews with other persons that are featured throughout this book have corroborated these findings, so all of these voices are useful Unlike traditional, hypothesis driven, deductive theory building, grounded theory aims to systematically generate a general theory from spe cific data (Glaser, 1992). While the former is based on the testing of a predetermined hypothesis, the latter is developed with no presupposition and is generated as data are collected. In this case, the specific data are the interviews, observations, an d artifacts mentioned above. It is important to note that in my work I treated all interactions (formal and informal), conversations, relationships, and perceptions of those involved as data. In doing so, I became the lens through which all data was sift ed. Though a systematic process was followed in sorting data, choosing what was important, and emerging the following theory, subjectivity is inherent in its development. The theory, however, is fully grounded in the data. As is implied by the choice of grounded theory as a methodology, this work is not meant aspect of her instruction. Indeed, the complexities of her classroom cannot possibly be capt ured 14 See appendix A for a full explanation of formal methods
119 in such a way, and the goal of this work is not to simply give guidelines and formulas so that others can duplicate particular practices. As such, figure 1 is not meant to be a grand theory; rather, the working theory is meant to serve as a substanti ve theory that is useful to practice because of its rooting in naturally occurring experiences. My main goal in presenting this theory, then, is to identify general, key aspects of her teaching and describe how such elements work together to create succes s in mathematics for underserved students. It is important to point out one major assumption that is inherent in this work relating to unwavering belief in the children with whom they work. As a culturally responsive teacher it is not enough to assume that you are not racist or do not hold skewed versions of reality based on the status quo. Rather, personal assumptions must be examined and the educator must truly believe that children can excel in mathematics without qualif iers. This type of belief in students because beliefs are tacit. Though they change with knowledge and communication, they must be in place to ensure success i n the classroom.
120 R E F L E C T I O N R E V I S I O N N R O I N T O C I E S L I F V E E R R R R E E F V L I E S C I T O I N O N Figure 4 1 Culturally Responsive Mathematics Teaching (CRMT) Figure 4 1 represents the dynamic and fluid nature of the teaching practices of Gloria and is meant to highlight the complex and fluid interactions that were inherent in her mathematics teaching model and the cycle of pedagogy and discipline exist within and are influenced by these ramparts. The student is at the center of all interactions and efforts and there is continual movement around the student obvious: knowledge, relationships/tru st, and communication. The fourth, constant revision and reflection, is represented in numerous ways, the main of which is the arrows between the three others in the model REFLECTION REVISION N R O I N T O C I E S L I F V E E R R R R E E F V L I E S C I T O I N O N R E F L E C T I O N R E V I S I O N N R O I N T O C I E S L I F V E E R R R R E E F V L I E S C I T O I N O N Relationships/ trust Communication Knowledge discipline STUDENT pedagogy
121 platfor m from which all of her success was possible. Strength and focus in these four areas were foundational to her mathematics instruction, serving as the bases from which lessons, interactions, attitudes, and pedagogy were constructed. Central to the figur e is the student who is constantly involved in the cycle of pedagogy and discipline. The pedagogy is always moving, in a sense, with unannounced jumps between concepts, varied teaching styles, and new material occurring at any time during her mathematics lessons Moreover, pedagogy and discipline are so closely t ied that one cannot be distinguished from the other. Her pedagogical and disciplinary actions were fluid and connected, and behavior was often controlled through pedagogy. Still driving the deci sions made in this cycle are the cornerstones, which are always present, stabilizing the student in learning mathematics. As the arrows also indicate, the cornerstones are not mutually exclusive, each informs the others, and they could not be in place without the others. Many communication techniques such as chants, choral responses, and direct, energetic instruction for example, are directly related to the knowledge Gloria has of her students. As such, they should not be taken independently. Furth er, within these foundational pieces are the intricacies of pedagogy and discipline, which are constantly intertwined and enacted continuously. Cornerstones and Interactions Each cornerstone has some unique qualities, but is most useful and interesting when considered in the context of the other three. These cornerstones were the foundation and support that drove environment. An explanation of each is given below and it will be obvious why each cannot be considered in isolation. Several interactions and outcomes of these foundational pieces is explored in the latter half of the section.
122 Knowledge Having 30 years of experience teaching at Duval, Gloria had a great deal of knowledge in many areas, and used all of this information together when designing techniques and lessons for mathematics teaching. As evidenced by her explanations of content and ability to improvise, Gloria had a great deal of content knowledge and pedagogical content knowledge. That is, she knew the mathematics that she was teaching at a deep level, allowing her to analyze student errors, deconstruct concepts, and present concepts in an accessible way. Moreover, this content knowledge was appl ied continuously in a teaching context, making it possible for Gloria to activate her mathematical knowledge in the course of teaching (Ball & Bass, 2000) in appropriate ways that allowed for greater student understanding of mathematical concepts. This strong knowledge base allowed Gloria to mai ntain a very academic focus her c lassroom with the ideas of accessibility and empowerment as key elements in her mathematics instruction. In order to mobilize this knowledge, however, she needed a great deal of knowledge spent a lot of time understanding their language, understanding their music, so she knew what it In order to gain this information, Gloria was in constant communication wi th students about their current interests, family lives, goals, and dreams. Moreover, she was an active member of the community and spoke with parents, formally and informally, on a continual basis. With this knowledge as a base, she worked continuously to design techniques that tap into student interests at a cultural level. Observation of students, as implied by the quote at the top of
123 to her kids and she Angie Communication In order to effectively present mathematics in ways that made sense to students, Gloria relied on several modes of co mmunication. Largely based in cultural practice, she carried familiar communication patterns into the classroom. This was especially effective because such patterns were also familiar to Gloria. In particular, she used call and response techniques integ rated with rhythms. For example, at the end of each problem involving a fraction (which eral times as the students studied the problem while chanting. After two or three repetitions, Gloria would keep the beat usually repeat two or three times. The students would then go on to reduce the fraction in unison using a similar technique. Cultural communication patterns were also evident when Gloria took disciplinary action learn ability and high expectations that drove her actions.
124 Relationships/trust Gloria was a teacher in the same community for nearly 30 years. Over time and after much success, she had built strong relationships with families in the neighborhood, the school community, and the students that the school served. Her no nonsense attitud e in the classroom and work that went beyond the school day earned her the trust of the community and the students. Moreover, her history as a member of the community allowed her to share the perspective of many of her students and their families this w as obvious in her commitment to sinker right there. And I think that Constant reflection and r evision it was sometimes hard to identify. When I would speak with her after a lesson, she would often use the co eventually deciding on ways to make the lesson more relevant and engaging. Many times, this type of process would occur during the lesson. Gloria had a way to feel the pulse of t he group and make adjustments as the lesson progressed. If she felt that the students did not understand a concept, she would stop and probe the class for misconceptions. She would explain the concept different ways, perhaps trying a new technique or cul tural connection, until the students were able to connect to the material. From year to year such revisions and reflections were also common. For example, in the 2005 2006 school year, students were generally not allowed out of their seat. By the 2007 2 008 school year, students were at the board working problems on an over, so it
125 This reflection proc re accountability is required of students. Also, she constantly changed cultural pieces, such as the music she used to teach mathematics concepts, in an effort to stay current and maintain student interest. Further, students inform the reflection process, with Gloria constantly asking herself, student cente red mathematics instruction cannot be effectively enacted without an effective, culturally responsive learning community. Cycle of Pedagogy and Discipline a nd Culturally Responsive Teaching Methods Together, these cornerstones were the foundation of G loria work. Though evidenced in her teaching, they were also cornerstones in her life, influencing her actions, interactions, ways of being, and attitudes. Within these strongholds was the cycle of pedagogy and discipline that specifically took place i n the classroom. The negotiation of pedagogy and discipline was almost students and belief in their ability, discipline was almost inherent. Moreover, students were expected to move quickly from concept to concept, often responding in unison, dancing, or chanting call and response methods, that there was little time to act out. This constant action is represented by the arrows in the interior of figure 1. If a student did act out, Gloria handled it quickly and directly, asking the student to stop talking or, in more severe cases, leave the classroom. All of the cornerstones shaped these types of interactions, thus the cycle exists within them.
126 Another way t o look at the model is to consider the placement of each component. The student is the focal point and is always c entral to the instruction. The student is most directly affected by the cycle of pedagogy and discipline and is, in a sense, caught in the m ovement and relevance of the classroom techniques represented in the cycle. Though less obvious, the student shaped these foundations. As the outermost part o f the model these serve as strongholds that work together to keep the student as the central model If a student has a difficult evening at home, for example, and comes in the next day distracted, he may slip out of the cycle of pedagogy, figuratively sp eaking. The cornerstones, however, will catch the student at a foundational level, as expectations of him and beliefs about him are communicated, thus keeping him from abandoning school altogether. Often, Gloria quickly re engaged the student Specific examples of this type of instruction involve communal learning, rhythmic teaching, improvisation, and a constant focus on review. These culturally responsive teaching methods provide familiar contexts for students and increased achievement. Communal learning The learning context is central to academic success for students of color. African American students have been shown to perform at higher levels on mathematical estimation tasks when content is taught in a highly communal, collaborative setting ( Boykin, 1994; Hurley, Boykin, & Allen, 2005). Gloria drew on this shared value, adopting a particular style that involved a lot of call and response, rhythmic strategies, peer teaching, and chants in unison. In many ways, the feel of the classroom mimic ked that of a community church. There was not an overtly religious tone, but the style was similar. Students were taught as a group, for example, and were expected to participate fully. If Gloria felt the energy in the room decline she would demand att
127 engaged and ready to learn. This was one major way that Gloria used shared cultura l practices in intensity of it that was all part of what she brought in cultural stuff that she shared with her st udents and it became part of how they did their work Rhythmic teaching African Americ an students perform better on specific tasks when taught in a context that allows for and encourages a high amount of movement and music (Allen & Boykin, 1 991). It has been suggested that this type of opportunity to engage in various modes of learning is helpful to African American children because it may align with historical cultural practices. This interconnection of culture and cognition is believed to lead to academic success and techniques allowed her students to make this connection be tween culture and mathematics. Gloria explained: I have always done a lot of, y ou know, rhythmic I guess teaching. Rhythmic all the time! When I taught the younger kids, I was doing a lot with vowels and the vowel songs, and I used to hit the floor all the time [motions like hitting the floor with a yard stick]. The kids reall y respond to that so I do it with the math t type esteem because they see that connection and yes you can learn, yes it is easy. Gloria also made use of student interest in dance. This not only helped them to make a physical connection to the mathematics, but al so allowed for more culturally based music and rhythm to be incorporated into the lesson. Gloria also used these connections as informal assessment tools. She shared:
128 The kids love to dance and if you can put math into action they can basically retain th e love to dance and they can recall the informatio when you might talk about a right angle you taught them the dance to learn right angle [puts arms in an a right angle ] they be sitting there trying to make the right angle while they take the test. The d ance really help the kids. It helps them to kinda exert their energy too at some point in time during the class time we have to get up an d just say hey we need to. ..let go. And definition for the mixed number on the board a nd we have the music. So once they finish they get up and just do a little rock [bac k and forth in rhythm in their chair]... and all the kids are involved and by THAT you can look around at a classroom and see who ecause y ou have total class participation. would give an answer or define a concept, she would require that they show that they understand what they are doing from a mathem atical perspective. This helped students to make connections mentally about a concept, what it might look like when illustrated, and its concise definition. Certainly, this focus on making sense of information while requiring that students use proper mat would tell them In later years, Gloria began calling on students to create their own beats, songs, and dances. Leon recalls that she wou ld indicate that she wanted a new beat for a particular set of helped to integrate their artistic talents into the mathematics curriculum.
129 Storytelling Gloria always used stories in her mathematics teaching to ensure that children could relate to the material. This was key to her success, as many children had a difficult time seeing how the mathematics related to them personally. These stories were sometimes meant to demonstrate meaning behind the material. For example, when teaching children how to find the least common multiple of two numbers, she would discuss relatio 10, or big brother, was the larger, ond, understanding that even though the numbers might not have the same name, they are in the same number family. A similar strategy was used when Gloria would introduce or review the concept of borrowing (trading in subtracting) Other times, stories were told as a way to help students remember facts or ways of doing problems. When do ing problems that required students to use the order of operations, for
130 clean inside the house, and then you move outside and clean there. Similarly in math ematic s you first look inside the parentheses and take care of the math ematics inside, then you move classroom, with new stories emerging continuously. Often, she would as k students for ways that they remembered concepts, helping them to come up with their own strategies and stories. Focus on review Review was review without mentioning music, dance chants, improvisation, or a combination of these techniques This focus, however, was truly unique to her classroom. While many teachers may do a quick review at the beginning of class before moving on to a new concept, Gloria would constantly go back to old m aterial, and she would do so on a moment to moment basis (which beginning and review everything you know, and that is not how I tend to see people teach Since definitions are learned communally and are communicated orally to the teacher in a call response fashion as a class, Gloria would ask for them at any point in the class. She learned that this type of repetition worked for her students by simply paying attention to student interests. By tying the definitions, and therefore review, in with music or communal learning, students were able to retain information over time. Gloria once said: At the beginning of the year I found my kids just c even around my house with my little grandbaby is 3 years ol d and I noticed that she can sing a song over and over, memorizing all said well let me come up with this idea. These kids understand THROUGH MUSIC, and through repetition, the Star Spangled Bann er So the music plays an important part with our kids, simply because our kids look at BET,
131 and everything is on BET f or them, and th ey strive just to look at BET so I am at that point now where I will do hours math...because it has to be repetitio n. We go over and over so now it just falls into place, and they understand. Now I call it rapping with math, and it is rapping with math, but do anybody can rap, but when I say perimeter do you understand what perimeter is? You know, anybody can just rap a song. Then I tell them too, even the song that you listen to understand the mean ing of song. [The math rap is] a lot of um definitions incorporated Improvisation Buffy ould try to figure out what exactly is she doing could be a little bit mystified. It was like she sort of felt the pulse of the group and would just blast off in any number of directions and then, almost like the old aspect of her teaching. With review, for example, she may begin the class by asking for the definition of a mixed number. If the class responded confidently, she might immediately begin a chant asking students to convert quarts to gallons in rhythm. If the response was solid, she might draw a figure on the board and ask them to find the area or perimeter. If she sensed a lack of confidence or hesitation in any individual, she would stop and dri ll. At any point, she might jump into new material. If the kids were not with her, she might change directions. As Buffy Warm Deman der P edagogy Particular types of pedagogy have been shown to be effective in bridging this school home gap for African American students. Teachers who enact such pedagogies maintain a firm,
132 directive, and demanding demeanor while communicating a deep sense of care for students. ut their expectations, exhibiting an ethic of caring, positive beliefs about students and the community, (Ross, Bondy, Gallingane, & Hambacher, 2008, p. 143). These teachers show respect for Students view warm demanders as authority figures and disciplinarian s, caregivers, and pedagogues. In research involving warm demanders, various examples of direct instruction and inquiry learning have been identified, as have specific examples of culturally relevant pedagogy and classroom management. Overall, this impli practices are multifaceted and complex, the teacher taking on many roles in an effort to push students academically. shown to have success with African American populati ons for decades. Even before integration in schools was mandated, successful African success, for their dedication, and for their de Wal ker, 2000, p p 264 265). This type of work is especially important for young, white women, the best speak softly and to be non d irect and non oss, Gallingane, & Hambacher, 2007 p. 146), making them less inclined to use a seemingly harsh tone with children. In a
133 largely African American setting, these attributes may communicate a lack of authority and weakness in discipline. how committed she is to them and how much she cares about them from the beginning so then when she has to get tough, which she will not hesitate to do, they respond to that because th ey know that this is someone who has their very best interests at heart and really wants to see them example, Jeffrey 15 had struggled on and off. This exchange took place in March, towards the end of the school year. G: Jeffrey, where is your math journal? J: [inaudible mumbling] G: Where is your math journal? J: G: [interrupting] Boy, look at my face when you talk to me and push that chair in. J: G: some body. J: I got nobody to call. G: Get yourself UP out of your seat and call someone they can either bring 15
134 your journal or bring themse l class unprepared. The second exam ple is illustrative of the type of force with which students were met if they were not on task. Many variations of this type of interaction were a regular occurrence. In parts of this example, the students are responding in unison as a whole class (denot ed by S) or by group (denoted by SG) during the course of a normal lesson. Students are seated in groups of 4 or 5 and there are 45 students in the classroom. They are working on changing mixed numbers to improper fractions using music and chants. One s tudent, Brittany, is eventually singled out. G: [starting music and snapping to the beat, points to the first in a line of mixed numbers on the board, 5 ] Go! S: [in rhythm] 5 times 2 equals 10 plus 1 equals 11 over 2. 11 over 2 [Gloria poi nts to the next problem, 3 ]. 3 times 4 equals 12 plus 3 equals 15 over 4. 15 over 4. G: [points to one group with one hand and the next problem, 2 3 / 5 with the other]. This group, go! SG1: 2 times 5 equals 10 plus 3 equals 13 over 5. 13 over 5. G: [pointing to next problem, 4 2 / 3 and next group] Go! SG2: 4 times 3 equals 12 plus 2 equals 14 over 3. 14 over 3. G: Stop, stop, stop! [stops the music] Brittany, you just moving your mo uth, B: Yes I am! G: [turns the music back on, resumes snapping to the beat, and points to the 4 2 / 3 problem]. Okay. Ready, go!
135 B: G: Go ahead! [continuing to snap] B: 4 times 3 equals 8 plus G: B: G: Look back here child. See this big piece of paper? [pointing to a large piece of poster paper]. During lunch your assignment is to write multiplication fa on the music, and resumes the whole class lesson] To outsiders I must admit that I was taken aback the first time th at I heard her use this tone in her classroom. th admit that w consistently responded to her no nonsense approach and, as was evidenced by the stories at her wake, believed that she was tough because she cared about them, wanted them to exc el, and believed that they could do so. This is illustrative of the focus that Gloria kept on the student outside norms and status quo practices did not guide her; rather, the particular learners in her classroom drove her instructional and disciplinary practices. These types of interactions showed dynamic interactions between the cornerstones. Each took place in the course of a lesson, was dealt with quickly, and did not interfere with the academic focus of the classroom. Through these interactions she communicated high expectations and care through culturally based verbal and nonverbal cues. She did this using
136 particular, familiar language and tones of voice which were based on the knowledge she had of to the students was evident through her communication style and attention to their interests and ways of knowing. This helped her to build strong relationships with the students, who trusted her as a caregiver and teacher. Student responses and continue As opposed to the deficit model described by Delpit (1995), this model is based on the idea th at 2004). If student realities are disregarded in academic contexts (for example, when home languages are stifled and suppressed in school), educational achiev ement and outcomes of learning are compromised and students are likely to act out in resistance to the mainstream (Allen & Boykin, 1992). If students are given the opportunity to act within familiar cultural contexts, however, meaningful learning is more likely to occur and accessibility to higher order thinking skills such as problem solving is increased (Boykin & Allen, 2004). Outside S upport pride in her life were r eal factors in her success. Each year, the fifth graders at Duval look forward to many opportunities for involvement and several special events. The most talked about of these was the opportunity to be a part of the Math Team. Gloria was in charge of th e organization, and any child that wished to be a part of it could try out ; the total number of students varied, but was generally around 30 A try out consisted of an oral testing, using the same methods taught in class, of concepts learned during school The result was a team of exemplary students who would showcase her methods ( e.g. chants, dances, etc.). It is also important to note that these were not necessarily the students who had always been at the top of
137 the class. Indeed, there were ESE kids on the team, though you would never know who they were. The Math Team began performing in churches and other community settings (they were usually invited) and after the word got out, they were invited to perform all over the country In 2007 and 2008, the team was invited to Atlanta, Georgia to perform. In 2007, Gloria and her team traveled with a team of researchers from the University of Florida to present a t the annual meeting of the Florida Council of Teachers of Mathematics Invitations were also accepted from groups in Tampa, Miami, and Gainesville. Audience members were always amazed by the performances, and often asked if we had t he Math Team became the spokesperson for wha t she did. She wanted to get [her mathematics teaching methods] out there i n a way that people could see [them] She felt like she could go to workshops and talk about things and d o a powerpoint, but she thought that nothing was more revealing and compelling than bringing the kids and let ting them showcase it for themselves. And she was right people would just be r showcase or her The Evening of Elegance, which is also only for 5 th graders, is a formal event that occurs here the kids get to wear their formal attire, and we introduce each student to their parents and family, introduce their parents if they are there, so it addition to a graduation ceremony that also occurred at the end of the school year, were almost exclusively organized by Gloria. The events served as rites of passage for the students in
138 Evening of Elegance as ear ly as January. This desire to be a part of these events not only motivated the children to work hard, but also gave them a reward for their work and persistence was the feeling that they were somehow empowered to go out on their own carrying with them what they had learned at Duval. Gloria also wrote and directed the 5 th grade play each year, parts of which were often performed at the Evening of Elegance. These types of events took time and effort to plan, as they often included a ceremony, a large dinner, decorations, and speakers. Leaders from the community and the university were invited as special guests. Gloria often took control of the planning, mai nly to make sure that each child was able to participate. With a formal event, the cost of clothing is often an issue that donations from different organizations, a nd I go out and find gowns for the ones who are having Lee she went out and bought all of the shirts and pants [for the boys] every child looked the same. containers of clothes that she purchased with her own money or made just so the kids could be her teaching was truly unique. Years ago, Gloria noticed that her students were not getting the help that they needed at home. As th e confident and outspoken woman that she was, Gloria
139 negative effect on all that s he was trying to accomplish at school. Rather than blame parents 16 however, she asked them what type of support they needed from her to help their student at kno other conversations, Gloria began to offer night classes to parents who wanted to learn the mathematics. Some parents wanted to learn the subject for themselv es and their own lives; to this offer were met with cynicism and a bit of reluctance, but over time attendance grew. As attendance grew, student enthusiasm grew, as did the quality of work produced at home. Gloria taught the adult classes using the same techniques that she had developed for her younger students, but with out the controlling overtone that is developmentally necessary for the children. Gloria believed that this type of interaction helped her to build trusting relationships with parents. In turn, these relationships directly impacted student achievement and gave Gloria explaining the problems to them, no put downs whatsoe ver. You know, we just come in here and talk and we talk about how to solve a problem and with that I have a good relationship with such as conferences in various cities that she would travel to with the Math Team that she could not offer the evening courses. She had planned to pick it back up this fall. 16 minority schools d home lives for the purpose of blame, but for the purpose of developing relevant instruction.
140 Angie understood The key components of communication, knowledge, relationships, and reflection served as supports and bases for all of her practices and commitments. The success academic endeavors, and academic achievement of students in general. The impact of her teaching on intangible and unquantifiable aspec lasting and transformative. Such results evidence and evidence the dynamic nature of the aforementioned theory of CRMT achieve phenome nal results. As students became a part of her classroom and life, their self perceptions were changed, and their understanding of societal practices and norms became more comprehensive. Student shifts in worldview was one of the most dramatic outcomes of work, and relates to all four cornerstones. developing racially and culturally. In other words, students were not forced to conform to a set of norms that did not a lign with their home culture; rather, their culture was used as an access point to mathematics and as a framework for learning. Shared cultural values and practices were central to the classroom, and success was defined in these terms. As such, students viewed mathematics learning in a new way that was meaningful, thus coming to see themselves as able and excellent mathematicians. Moreover, mathematical knowledge came to be seen in a more
141 positive light communally. To parents, students, and community me mbers, mathematical knowledge was no longer stigmatized as something unattainable or for which cultural values must be sacrificed; rather, it was seen as a vehicle through which racial identity development was enhanced became a shared value among school an d community members.
142 Part III it by placing it under scrutiny. In the classrooms, working in opposition to the system is the most likely road to succ ess for students who have been discounted and disregarded by the system. Gloria Ladson Billings, The Dreamkeepers 1994, p. 130
143 Chapter 5 need standing before you trying to help you. Whatever you get out of my teaching is the biggest reward you can ever get. [Some teachers are] so busy now [at the end of the school year] and are getting away from staying on the kid s. The kids check out. [Teachers] are so busy giving me. Gloria Jean Merriex Th e following pages solely consist of direct transcriptions of student stories about Gloria These narratives were gathered in December of 2008 from is a 6 th grader at a mid interview. Jennifer is a 7 th grade student at a middle school in Alachua County, and she interviewed alongside her sisters who were participated with Jennifer in rec iting the math rap These students represent the impact that CRMT can have on individual lives, and are a Further, student and parent voices are often absent from this typ e of work, or are altered to fit a theory or idea. I feel that these stories do corroborate my research findings, but leave this determination up to the reader. As such, these stories are left untouched and free from inter pretation. Courtney She taught more like by moving and singing and stuff rather than just sitting at a desk and working out of a book. Until 5 th grade I never knew my times tables, but she made me learn them by singing them and it was easy. Whenever I forgot to do my homework, or anyone forgot to do their homework, they would have to line up in the hallway and talk to Dr. [Lee] McNealy, Pseudonyms have been used for all participants mentioned in this section
144 the principal, and [Ms. Merriex] would kind of yell. One time, it was kind of scary, we were ally park the car all the way, so Ms. Merriex the day before she died. Sometimes she would just make something up on the spot because she just thought of something that came into her mind. Also sometimes the kids would do something is one day, I forgot which one it was, but these kids were kind of shaking their booty doing it, and she told everybody to do it that way. She made it feel easier to learn. I felt confident about math in her classroom and all the stuff she taught us she made us write down in that journal. Sometimes journal you could also sing it which helped. Even if you were really bad at math, [she showed me that] you co Actually before I went to Duval, I just went to Jefferson 17 and everyone there thoug ht it was just so cool to be stupid and dumb, but here [at Duval] people would brag all the time about, like, if they knew their times tables better than someone else or they could say them faster. At Jefferson that would be so nerdy, because at Jefferson everything, but most of the things that I see people bragging about were taught by Ms. Merriex. 17 Another elementary school in Alachua County; a p seudonym has been used
145 tell people to com lves, class, but once I saw she was picking around at people, I just quickly memorized them. When I at Jefferson in 3 rd grade, which was like my worst year I had a really bad teacher, th grade. Well, [this teacher] actually started to tell us ing. She just wrote the math rap on the board one day and we sang it once, and then we just stopped and she left it up there. And we actually watched the ma ke sense. We would perform it on the math team. Not everybody could be on the math team. You had to do your homework and stuff, but even if you forgot your homework for one time, she actually gave you like a week to turn it in, she gave you another ch ance. Sometimes I just forgot, she would at first just But there them they could be on the Math Team. It was like, if there was a trip, she gave permission slips
146 not to everybody, but sometimes I saw her give one do different probl ems, but in the same way she taught. Always at the end we always sang this Duval is good, and how it was good to be smart, and then it turned into saying your times tables. Some people thought the whole thing was memorized, like she had taught us before that was how we were saying it back that was how we knew it, and the technique of how to get the answer too. She would give us new problems [during performances] but she made it so you could get the answer really fast using her technique, so we were solving problems on the spot. Something like if this is the improper fraction, what is the mixed number on the spot. strategies in my mind. For graduation, we had this song that we were singing and we were just go ing to sing it normally like we always sing it, but after [Gloria] died they made it dedicated to her because it was a song about friendship. It seemed different without her. When we were practicing [the song] with her it seemed like the energy was reall y high, but when we actually did it without her it actually went down a little. She actually really increased the energy everywhere, like if people everyone st
1 47 e you stand up and do it by yourself, but I liked that. Lisa I was really impressed with what she did with the kids. So many kids just have so much eve rybody could do it and everybody could be good at it. She was really committed to that. She had this unusual method of teaching that was so effective. The body part of it [was unique]. The way if you had a ray [on a graph], you had a fist on one side, and on the other a ray kind of goes off like this. You kind of dance it out in your body so you really get a sense of infinity that way and a point here, and the angles, and the turning around. That getting it in the body was great, rather than just have Another thing that really struck me about Ms. Merriex is that she had so much passion for what she was doing and obviously had for such a long period of time. I really admire a teacher who is alwa ys trying to struggle to find a new way to get information across rather than just sticking with something that somebody else figured out or they tried 15 years ago and are just trying out with a new batch. She was always trying to find some new way to ge t through to her students. She has gone through a lot I would come in sometimes and she would have to hold the struggling through that and yet telling the st udents that they could achieve anything. But still she was so caring of all the kids, I mean she just cared so much about all of the kids. When they had her memorial service, the number of kids that just got up there just the caring she had I mean sh e made all of the graduation dresses.
148 She made math more cool even though she was tough. Like the way she kind of yelled something. She knew they could do bette people were stupid and she knew that everybody could do it and everybody could do math. carry out things in a really tense way. When you think of all the outfits she was sewing and all out or anything, she was just very relaxed about it like she knew what she was doing. She was just a very strong character, a very strong presence. Tim The ability to take a risk as a teacher is a great thing, and she extended the same kind of view to other teachers that she did to the students that anybody could do it. There was one of those films that had been made when she took [the Math Team] to Orla silent and had no idea what to do. That was fine for them to watch the Math Team do it, but not us. So getting the teachers to jump out of their comfort zone. So many times when you see a boring classroom it is because the teacher is so in their comfort zone how interesting can it thing t hat the students are afraid to show. You know the students are afraid to show you that ents to? Why should they lay
149 it on the line? Otherwise the teacher stays in that judging place and students are in that judged place is it any wonder why you want to get home? So many students said they looked forward to going to her class. I think its tricky though because somebody else could be doing something that looks the same and it not come across the same way. I say that because the way that she took the Math Team all over the place to teach and demonstrate what she was doing, and there was a very high standard to go on the trip. You had to have your uniform, you had to have not missed school, and turned in your homework, and it was a privilege to go on those trips even though it was also the way to teach the program. I think it made the s tudents realize that teaching was really important and that they could be part of that, and they were included in that. And the caring somehow came along with that package deal, like, we care not just about you but that other kids elsewhere are going to b e able to get to do this because you all know this is not the normal way of learning in other schools, you know. You can be a part of conveying that. I can easily see somebody else doing the same thing and it not coming across that way, so there is somet hing intangible in there. The other thing is that there is a lot of talk about integrating the arts with learning, and I think Ms. Merriex probably, because she was at Duval for so long as it was trying to become an arts infused school, had something to do with the fact that the arts actually did get integrated aching. In the school board and everything the arts are still funded separately. [the school board is] like, solution to that quandary is people like Ms. Merriex who made it one thing. You know, you
150 inspirational to other teacher s to try it, because there was an example of how to really do it, actually have an arts infused core curriculum classroom is not taught in the education schools, its not taught in college, not anything anyone really experienced as a student, so to have a real live example. [The D uval faculty and administration] re ally were committed to making [D uval] a school for this neighborhood. They kids that are here. You are the kids that And that was a huge part of [ there. You matter You know, M s. M erriex was from here and that played into that mentality. Jennifer She was a special teacher. Her math made her special. The way she taught math and rapped her math. She used the rap to help us understand the math. She danced it out so we could understand what we were doing. It was fun but serious. I remember some of the math rap. You remember? [In unison and in time with her two sisters]: Perimeter, distance around the figure. Area, length times width. Uh huh, uh huh! Vol ume, length times width times height. Hexagon, a six sides, Pentagon five sides, quadrilateral four sides, equilateral all sides equal. Get ready, get ready for t he sum of numbers divided by the group of numbers. Mode the number that occurs most often. Median, middle number. Octagon, eight sides. Ninety degrees, right angle; less than ninety, acute; more than ninety, obtuse; a hundred and eighty, line. Three s ixty, circle; translation, slide;
151 I still use some of [the math rap] in class now. Like mixed number, improper fractions. I still have my journal. Some days during afte r school she had kids in her math class so she could lot of it was in the math rap. We had to know the math really good to be on the Math Team. She chose who could be on Math Team, it depended on grades on tests and stuff, but anyone could be on it. We went to memorize the thing. She did what she did in class. She was hard but in a good way. She expected a lot from us. She cared. Her math was fun, I remember that, but she was serious [poster sized] piece of paper wri ting it over and over. Diana She was a great inspiration and a great math teacher. The way she taught the children personality plus, she was almost like a drill sergeant, but it was good for the children and they actually learned. The math rap, reading rap, just the different ideas and type of music she used. a daily basis. She could actually take that music and make it into something positive for the children when they were learning. All three of my girls were on her Math Team and they really enjoyed the math. It was p and see her standing in the back or the front of the school Even on weekends if she had Saturday school, they would look forward to being here with her. It wa
152 we would learn math from her. You know, for the math that these kids were learning, some of us needed a brush up course and she would actually help us understand the math that she was teaching. She was planning a [formal] parent class, but we never got the chance to do it. I actually went to Atlanta [with the Math Team] as a chaperone, what a month or two before her passing? They performed for a group at Georgia State University. These kids rapped math for an hour. That was my first time really seeing the children perform, and it actually brought tears to the eyes of some of the parents. It was just absolutely wonderful. The teachers that were at the c onference, they really enjoyed that. I mean, the way she worked it was just a miracle, you know? We still have a recording of that performance in Atlanta, which was the last it forever. And it was always something different. Sometimes you would hear them perform one thing, then the next time it was something else. Things like percent the stories she would tell to get to the answer. The kids were just into it. Class was like that too it was fun, they looked forward to class. It was always something new. She was an awesome individual. She just had her own style, and it worked for a lot of children. To see where mine started and where they ended up, it had a lot to do with her a whole lot. My girls were always quiet, but Ms. Merriex would always get them to open up. She math, I really do, because the kids knowing the math they need it everyday to survive. [My girls] still have their journal and its like a bible. She gave them each a journal, and believe it or not, they can always look back and find something they can use in middle school.
153 them to just think about some of the things she taught you and use it, and once they work it out in really do. up with a math question. And [the studen ts] were supposed to have an answer just like that! She come out with it. So they were really learning. So even though she was hard on them, it paid the price. It did. Like I say, they can use that math today. Whatever she taught them they can use today. That was an everyday thing. As soon as you stepped in her class, you knew what you needed to do, and she had order from day one. She let them know who she w as, she did not tolerate and she was down to business, and the children knew it. Respect was there, and hey, they knew it. She kept the kids in line, she really did. No, no, no nonsense. You better not be she comes back an d finds out her class was not all business? They their book. repeat herself. e Math Team and what Ms. Merriex was doing in her class, and how tough Ms. Merriex was. But, everyone wanted to be in With their education, their well being. When I dropped them at school I knew what they were coming to do. And they could show me what they were doing in school. I knew what type of
154 that was her, and the kids did too. They listened to her, no matter what it was, and if you had a problem, you could go to her and she would help them. With anything. If somebody did not have pants, she made sure they had some. She went beyond the call of duty as a teacher If a child needed to go home, she would take them home if they needed a ride. She was just all around. Everyone was so excited for graduation, you know this was her thing and she always happy time, but it was really, really sad because she was not there. But they carried it off in her her memory. Her plays, the 5 th grade play oh my gosh! For someone to come up with the danced with the heels on. The steps, and the music, I mean the time she put in, you know, you it was amazing. It was like where is she getting all of this from? Beautiful voice she could sing, and she would dance just unbelievable. The graduation dresses they all looked good, and she made sure all the children had shoes, slips, a tie, a shirt brag on what she did she knew what she was doing, and she knew she had it, and it just spoke for itself. It was always p ositive. She would not leave sometimes until the school is ready to lock down. She would be here doing something for the children. She would stay and work with it takes a dedicated person to do that, and that she was. She really was. [My children] learned a lot. Some things they are going to
155 her. When she left this world, she left a great part of her behind in all of her children. these stories indicate, a dedicated, culturally responsive teacher can truly empower students to become successful mathematicians while affecting the culture of a school.
156 Chapter 6 Yeah, I thi They come in th e first day of school and just look up They hear it through the grapevine where they too many options. Gloria Jean Merriex As we look to the future of mathematics education research and classroom practice, we can glean many ideas from the work and life of Gloria Merriex. There are implications of her work for various areas of mathematics education such as classroom practice a nd mathematics teaching, mathematics teacher education programs, and future research in the field of mathematics education. Impl ications for Classroom Practice 1. Culturally responsive mathematics teachers know their students. These teachers take time to get to know student cultures at all levels, and use this information in their instructional planning and in the course of teaching. Specifically, these educators understand the community culture (e.g. communication patterns, shared values) in addition to th graders think and feel, where they are emotionally and intellectually) and relevant pop culture (e.g. what types of music students listen to, who are the big names in entertainment). This informa tion comes from the students themselves, teacher involvement in the community, an overnight process; it takes years of personal involvement to build relationships t hat will allow a teacher to access this type of knowledge, particularly if he or she does not live in the neighborhood surrounding the school.
157 2. Culturally responsive mathematics teachers are supported by a particular belief system. Effective teachers belie ve that their students, no matter what statistics say, have the ability to be talented and gifted. Their job is to work to find ways in which students can express their talents while accessing mainstream knowledge. These beliefs are fundamental in provid ing effective non verbal communication and building relationships; as teachers we must realize that we are constantly communicating with students even if about her po pulation of students, on the other hand, she will communicate these non verbally and will struggle to build relationships. Students can see straight through words to what is underneath, and that is what is most important. Lastly, effective teachers are a ware of what they believe and continuously reflect and act on those beliefs. 3. Culturally responsive mathematics teachers do not ask students to abandon their home culture. As simple as this might sound, it is fundamental to the success of underrepresente d students. Many times, these students are asked to learn from traditional, individualistic, lecture type instruction, and are deemed disabled if this type of instruction does not provide them with a connection to the material. Culturally responsive teac hers are able to teach content, even mainstream content, without asking students to live, act, or learn differently than they would at home. This creates cultural congruity for students, and greatly increases their chances for success. Further, it allows for racial and cultural identity development in the course of teaching, and provides a safe context from which they can learn about societal pressures and misconceptions. Such an environment provides a solid foundation from which students can achieve aca demic success within their own cultural norms.
158 4. Constant reflection and revision is necessary for culturally responsive mathematics teaching. Children need to be challenged and engaged in mathematics. In refusing to change particular aspects of instruct ion, a teacher is not attending to the needs of her students. Reflection allows an educator to see what it is that needs revision while encouraging innovation and change. This reflection revision process is cyclical and should happen at the macro (i.e. r eflecting on entire lessons, units, or ways of teaching) and the micro (i.e. in the course of teaching on a moment to moment basis) levels. 5. Culturally responsive mathematics teachers work beyond the classroom. Specifically, these teachers provide resour ces to the community in proportion to their personal expectations. For example, if a teacher expects her students to receive help at home, she recognizes that parents might not be familiar with the material, and provides a class that will help them to hel p their children. If a teacher expects a student to have supplies, she provides them with the necessary materials so that each child has the same opportunity. belief system, knowledge of students, and relationships. Implications for Mathematics T eache r Education Programs 1. Multicultural mathematics curricula must be accessible and prevalent throughout teacher education programs. Too often, suggestions for being culturally responsive are tacked on to a curriculum rather than integrated throughout a program. By simply adding a multicultural piece to our existing programs, we are communicating to pre service teachers that culture is something extra we have to worry about rather than a resource that should be used in instruction. 2. Successful examples of culturally responsive mathematics teachers should be touted. We should use teachers who teach with a focus on culture as positive e xamples who enact the
159 beliefs that we preach in our programs. Further, more care should be taken when assigning pre service teachers to classrooms for student teaching experiences. By placing these students in traditional classrooms that are based Euro c entric norms, we are undoing all of the good that might have been done by multicultural coursework. Student teachers are likely to mold themselves to their mentor teachers (at least somewhat), so teacher educators must work to find such models. 3. Mathemat ics teacher educators should model and embody CRT. It is one thing to preach the theory, but quite another to enact it in the classroom. Again, we continuously communicate to our students in verbal and non verbal ways. If we are saying one thing and doi ng another (e.g. saying to get to know student culture but keeping a safe distance from our own students), our values lose credibility. If we enact CRT in our own classrooms, however, students are more likely to adopt such practices in their own teaching. I mplications for Future Research 1. Successful models of CRMT should be studied further. In the current literature, there are very few classroom examples of CRT in the context of mathematics. In theorizing about such models, we attain a certain level of un derstanding, but in discussing what we see in action we are able to more readily understand the relationship to practice. Further, such models can provide us with more salient definitions of CRMT while informing our teacher education programs. In turn, s uccessful multicultural teacher education programs should also be studied and used as models. 2. Student voices should be included in the literature. academic achievement, social interactions, and long term self concept sho uld be studied. This will help us to more easily evidence the effects of CRMT on students, parents, and
160 communities. Further, it will allow underrepresented student voices to infuse the literature base in the field. If our ultimate goal is improved stud ent achievement in particular populations, it is imperative that we include such voices. 3. Mathematics teacher beliefs should be examined in terms of student outcomes. This link seems to be strong and should be examined as such. This would be another ave nue through which student voices could be used, as they should be consulted about such developed. Examining the ways in which teacher education programs, for example shape such beliefs, and how these are then enacted in the classroom. 4. State and national accountability programs should be studied in relation to cultural bias. What effects do these systems, which deem particular topics to be the most important knowledg e to have, inhibit or encourage CRMT? Further, we should examine the effects of scripted curricula, many of which arise from state standards documents, on classroom practice, particularly in high poverty schools and schools with large populations of stude nts of color. It is important to remember that while there is no formula for CRMT, we can look to successful models like Gloria Merriex to guide our decisions in teaching mathematics. Through consistent examination of our own beliefs, a commitment to o ur students, and a willingness to constantly reflect and revise, we can provide each student with equal access to mathematics knowledge.
161 Appendix Formal Methodology Research Questions Given the need for successful models of African American learners, I chose to focus on bringing clarity to readers through an in in a high poverty, high minority school. Based on previous observations, I viewed this teacher as a successful model of CRT, her pract ices specific to mathematics instruction. As such, the research questions were: 1. How do effective mathematics teachers working in a high poverty, predominantly African American school context: a. Structure instructional practices and interactions? b. Establish a learning environment that results in mathematical success? 2. What are the interactions between these phenomena? 3. What part (i f any) does culture play in these phenomena ? The current study is a case study meant to shed light on the above questions. Certainly, more teachers are to be included in the refinement of the resulting theory in the future. Because of the complex, fluid, and varied nature of CRT, it is nearly impossible to succinctly define the construct, and is even more difficult (and may b e contradictory to the bases of CRT) to define a step by step model. Suggestions from the literature, however, should be used as a point from which educators can evaluate and begin to conceptualize changes in their own teaching style. This study is meant to help in that conceptualization process. Initial Study Several authors have written cohesive books outlining and discussing the fundamental ideals of CRT (Gay, 2000) with some focusing on how it relates specifically to African American learners (Ladson Billings, 1994, for example). These discussions, however, have remained rather general. Though examples are given of specific subject area instruction at times,
162 the overall vision for mathematics educators remains piecemeal. Further, these ideals are di fficult teachers to enact, as there is (and should not be) no formula for CRT. The given framework is helpful in constructing ideas of what it means to be a culturally responsive educator. Given the fact that research on CRT is still developing, with the oretical and practical applications becoming more relevant to actual teaching practice, my initial intent was to contribute to the field by seeking out specific culturally responsive pedagogical practices in mathematics classrooms. It is within this more general framework of CRT that I began this work. Specifically, I accepted the present ideas about general CRT (largely from Gay and Ladson Billings) while qualitatively zooming in on culturally responsive mathematics teaching (CRMT) specific to African A merican learners, developing this concept more fully based on teacher practice. The intention was not to separate CRMT from CRT in general or in other academic areas, but rather to focus more specifically on mathematics instruction to reveal the character istics of CRMT within the larger context of CRT. To do this, I initially chose to fully immerse myself in classrooms of successful mathematics teachers in largely African American, low income schools. Nomination P rocess As a researcher in the field, it wa s important that I not let my own perceptions of CRT, poverty schools, and educational processes in general drive the beginnings (or any part of) the study. I recognize that, though I have studied in the field of education for years, I do not have the liv ed experiences needed to identify successful practices in a particular neighborhood, and it was important that I not situate myself as the holder of knowledge about what makes a teacher in these communities successful. Moreover, if I were to choose teache rs based on my own beliefs the entire purpose of the study would be contradicted. A complete omission of my viewpoint was not practically possible, as I do have a solid knowledge base in these areas; however, my
163 biases were greatly limited through the car eful choosing of the ways in which I would go about identifying participants and collecting data. One main objective of this research was to return the power of knowledge and nomination of successful teachers to the neighborhoods in which the work was do ne. Specifically, I asked community members to identify the teachers who were to be included rather than using predetermined ideals that have been set forth by previous literature. Informal conversations and written correspondence with students, parents, and leaders began the nomination process and continued throughout the data collection and analysis period. These conversations drove the initial data collection process, giving the researcher specific characteristics of mathematics educators on which to focus and particular names of teachers who largely embodied these attributes. It should be noted that the nomination process presented quite a challenge. Community mathematics teachers with whom these neighborhoods had come in contact. In fact, only one teacher, Gloria Merriex, was identified. Though she was identified by many, it was surprising tors even when administrators were asked directly to do so. This spoke to the need high poverty communities have for improved mathematics instruction at the elementary school level. Moreover, several individuals with whom I spoke indicated that they were not sure what made a particular teacher successful, and were unsure of my motives during initial meetings. This indicated that this type of information is rarely solicited from community members such as parents. Since the nominations were so limited, th e sole focus was on Gloria.
164 Grounded Theory Initially, this study was meant to focus on and clarify the teaching practices of Ms. Merriex, and research methods were considered with this goal in mind. Further, data were collected in particular ways so tha t this end could be achieved, and my work with Gloria and my immersion in her classroom began in an effort to achieve these objectives. Initially, an extensive review of the literature showed that there are very few studies that deal directly with success ful teaching practices of mathematics teachers in largely African American elementary schools. There are even fewer that attempt to deconstruct such teaching practices, focusing on the elements of practice and the depths of student and teacher experiences Further, it was important that all parts of practice were considered and included in the data set. This meant that in addition to interviews and observations, natural occurrences such as interactions between people and with mathematical content, verbal and body language, physical settings, general behaviors, and individual constructions of reality were sought out and included as key pieces of the overall setting. Given the lack of existing data and the need to clarify how successful teachers in thes e settings develop and enact practice, grounded theory was chosen as the data analysis method for this portion of the study. A main goal of grounded theory is to develop 67, p. 2). Over time and with comparison to other sets of data, the goal becomes the construction of a more general, grand theory. This type of deconstruction allows for interpretations of social and practical complexities that are inherent in teaching, and should be built on and qualified over time. The following analysis is where the research began, and focuses mainly on experiences in interviewing. In the larger wor k, this deconstruction of pedagogy and relationships is situated
165 historically, but it can and should also be taken separately, as it is intended to stand on its own as a theory about successful mathematics teaching in a largely African American classroom. Moreover, this specific piece of work serves as an important model of analysis for the mathematics education field. It is meant to give a specific framework to successful mathematics teachers of African American students in any setting, not as a simple d practice, though the theory was built from data collected in her classroom. It is also important to grounded theory data set was co llected and analyzed before this occurrence. Theoretical Perspective In order to minimize bias and allow for truly novel ideas about these practices, I chose to enter the classroom setting free from the constraints of one particular theoretical perspect ive. This allowed me to not only deconstruct teaching practices, but also to let the data guide the framework of the study. Further, it allowed me, as a researcher, to genuinely generate new concepts and to treat all information (not only interviews, obs ervations, and artifacts) as data. passing. In re framing her work and looking more broadly at her life, I was able to identify an appropriate theoretical stanc e. Teaching is a largely situational practice. Many stakeholders ( e.g. teachers, students, administrators, parents, community members, etc.) maintain a role in the day to day practices of schools, greatly influencing the teaching and learning processes t hat take place therein. Moreover, the culture of a school, which is determined by and influenced by these stakeholders influences specific practice. That is, the realities that exist in schools are complex and not easily quantified. Further, the relati onships that exist within these contexts are interactive and
166 interdependent, and this complexity is mirrored in the researcher teacher relationship that is examined here. As can be seen in the data that follow the importance of culture and context in th e teaching and learning process cannot be denied. Moreover, all of the stakeholders in and around the schooling context construct their realities within and through the aforementioned relationships and their own interactions with the world. Specifically, the students involved in this attempt at grounded theory live in a low income, high minority neighborhood. Much of what they do and see in school is influenced by the fact that the city (or district) has not given them what their white counterparts have been given in terms of resources, physical environment, or cultural social realit y. ulture we could not social realities. Gloria communicated mathematics to her students in ways that are very much based in traditional African American c constructed meanings for culturally responsive mathematics instruction were seen as collaboration between teacher and researcher, each bringing a unique perspective and thought base to the discussio n. These interactions were not limited to researcher and teacher, however. As is discussed above, much of the meaning constructed and enacted in this setting is brought student relations, and numerous other sources. These meanings were developed by the involved stakeholders together, embracing the meaningful realities that were constructed. This focus on the subjective parts of the social structure emerged as the context in which this wor k was done.
167 beliefs are paramount and are developed through these types of i nteractions and experiences. Individuals assign meaning to things and people based on such experiences, and act toward things and people based on those meanings (Blumer, 1969). This is especially relevant to related to students upheld and drove her actions and reactions. Data Collection and Analysis Guided by grounded theory methodologies, formal data collection occurred over the course of one semester (about four months) though I worked with Gloria informal ly for about two years before that time. Individual, semi structured interviews with Ms. Merriex were the foundation of the data set, with observations and artifacts serving as triangulating evidence. At least three mornings each week (unless scheduling conflicts such as field trips or conferences interfered) teachers and Gloria, and memoing. Observation notes were meant to be holistic, including information about various occurrences in the classroom. Further, these observations often generated guiding questions for the next interview. Artifacts mainly consisted of student work and teacher made materials. As an outside researcher, my role in the classroom was that of participant observer. This meant that I was a regular member of the class, and I often participated in the lessons. Sometimes I sat back and observed independently, other times I sat in with student groups or spoke with co teachers and parents in the back of the classroom. This allowed me to get a true conversations with students, I was able to gain insights into their life histories and patterns of
168 interaction. Over time, the students did not react to my presence and my sitting in with them did not seem to interrupt the flow of the class. This was helped by the fact that so many observers (profess ors, other teachers, pre the students were used to the attention. Over the course of the data collection period, three formal interviews 18 were conducted, each roughly one hour in length. Often, the scripted questions were not needed in the course of conversation, but most main topics were covered. I let these conversations go in whatever direction Gloria wanted to take them. Many other informal conversations were considered when themes b egan emerging, as were observation data and artifacts. Data collection was driven by theoretical sampling, with each analysis of current data driving future data collection. In other words, holes in the data were identified, and the next interview and ob servation period were viewed as means to fill these holes. This process was to continue until saturation was reached. In order to collect data in this manner, I employed simultaneous data collection and analysis practices (Glaser & Strauss, 1967) with t he goal of eventual pattern and theme repetition through methodical coding. I began by listening to, coding, and analyzing the first interview. These data was then triangulated and compared with observation notes and artifacts collected from the same tim e period, themes were emerged, and gaps in the data became evident. I then went back to the teacher and classroom and repeated the process, constantly comparing the new themes to those already emerged. Memos, which included personal notes and thoughts fr om observations and interviews, also served as a place to document emerging themes and beginning, immature theories. 18 Sample interview questions included at the end of this appendix to show a bit about how theoretical sampling worked
169 Interviews were analyzed according to grounded theory (Glaser, 1998; Glaser & Strauss, 1967). I first listened to each interview, memoing to record initial ideas and thoughts. The interview was then transcribed it in preparation for coding. Throughout these sessions, memoing continued, with major themes that stood out being noted, and these notes later being used to compare with other data from the interviews. Coding was done in three stages. First, open codes focusing on identifying, naming, categorizing and describing phenomena in the text were determined. From the open codes, axial codes, which focused on relating open code categories were determined. Lastly, selective codes, which focused on the combining of axial codes into larger categories, were emerged. From these codes, the major themes and core concepts contained in the data became apparent. Constant comparison was employed throughout this process. Specifically, all data were compared to the emerged themes and to the rest of the data set. Moreover, all themes were compared with the later (or earlier) raw data and themes, and all data were compared to the initial research qu estions. This helped to ensure that the emergent themes were true to the data, and that connections and intricacies were represented accurately. Data collection and analysis were still in progress when Gloria passed away, with the most recent interview occurring only two days before she died, and the final observation occurring the day before. Though data collection would have continued until the end of the school year (about two weeks more) in order to truly achieve full overlap in themes, quite a bit of saturation was reached through the data that had already been collected. It is on these data that this analysis is based. While one more interview and a few more observations may have changed several small details about the emerged theory, I believe t hat this representation does characterize the data set
170 well. The graphic presented as figure 1 (in chapter 4) is representative of the results of this analysis. Member Checks As I conducted the initial research and eventually wrote this book, I continu ally went back to available participants to share my work. I did this for several reasons. First, I wanted to ensure that I had represented their words appropriately and in the proper contexts. Second, it was important that the book tap into the interes ts of those who knew Gloria. As such, I asked them to validate the breadth and depth of the information. Lastly, I wanted to ensure that the message that I had intended was indeed being communicated effectively. To this end, I asked participants and sch olars in the field to read parts or all of this work and state what they believed the message to be. This led to re writes and modifications, but I feel that it added a key element to the overall manuscript.
171 S ample Interview Questions Interview #1 ( Sample Q uestions): Tell me about your background. What was school like for you? When did you decide that you wanted to be a teacher? Where were you prepared to become a teacher? How would you describe your way of teaching? Have you always taught this w ay? Does your role in the community influence your teaching? How do you use what you know about students in the course of teaching? What types of teaching methods have given you the most success with this population? As a group, what do you feel it is th at they need from a teacher? How do you handle the various ability levels of children in your classroom? Can you tell me about a student who is struggling or has struggled in your class? How did you handle it? How do you handle discipline in your classroo m? What do you consider to be misbehavior in the classroom? What types of support (from administration, parents, etc.) are key to your success as a teacher? Interview #2 (Sample Q uestions): Can you tell me more about the Math Team ? Tell me more about t he Evening of Elegance and the 5 th grade Graduation. How do rites of passage events like these benefit kids? You talked about cultural influences during our last interview. How does being in your class help students develop racially? When a student acts of the room, might have them call home, and always address them directly with a particular tone. Why does this work with this group of students? You communicate with students in very spe cific ways. Can you talk about that? You mentioned that as a product of this community, you understand where students are coming from. In what other ways does your background influence your teaching? Interview #3 (Sample Q uestions): Last week a new student came into your classroom and was almost immediately sent out. Can you talk about why you handled the situation in this particular way? this? How does that relate You have said several times that you believe that your teaching has an impact on generations and the entire community. How do you feel that the successes at Duval have transformed the community? What are the main outcomes of your teaching? How can we better prepare teachers to work in schools like Duval?
172 CHAPTER 5 JOURNAL ARTICLE 1 Meeting the Challenge of Engaging Students for Success in Mathematics by Using Culturally Responsive Methods By Emily Pe terek and Thomasenia Lott Adams, Ph.D. The information obtained in doing research must be made accessible to teachers if we hope to truly transform educational practices in an effort to close the achievement gap. In an effort to provide such work, I co authored the following manuscript. This piece, which is based in work with Ms. Kay 1 a successful teacher of mathematics in a high poverty, with a large population of African American students, is being published in a practitioner journal by the National Council of Teachers of Mathematics. As such, the style of writing is accessible to teachers, and suggestions are given as to how teachers can become more culturally responsive. Further, supportive literature is provided as to support the conclusions pres ented while providing suggestions for further reading. My hope is that this manuscript will provide an overview of the basics of culturally responsive mathematics teaching through modeling, while encouraging teachers to find their own path to personal, re sponsive styles of teaching 2 Citation: Peterek, E. & Adams, T. L. ( 2009 ). Meeting the challenge of engaging students for success in mathematics by using culturally respons ive methods. In D. Y. White & J. S. Spitzer (Eds.), Mathematics for every student : Responding to diversity (pp. 149 159 ) Reston, VA: National Council of Teachers of Mathematics. 1 A pseudonym has been used to protect the identity of the participant, the school, and the community 2 The follow ing is a re print of the article which was published in February, 2009
173 Meeting the Challenge of Engaging Students for Success in Mathematics by Using Culturally Responsive Methods By Emily P eterek Thomasenia Lott Adams Setting the Stage Welcome to Oaklane Elementary School. Oaklane is located in the northeast section of an officially rural yet college town community. In t his section of town o ne of the oldest African American communities in the ci ty and a recently established African American community have merged because of the addition of a new, affordable housing development. Oaklane Elementary is central t o this merged neighborhood and serv es a population of students primari ly from the local co mmunity, which is 99 percent African American. The school has a Title I classification, with 92 percent of the students receiv ing free or reduced price lunch es Many of the students live in a nearby large subsidized housing development owned and operated b y an African American church located just a few blocks from the school. Oaklane offers a n arts magnet program that is open to any elementary school child in the district though the curriculum brings little diversity to the school In previous years, Oakl such labels as achieving risk the district administration consider ed clos ing Oaklane, but support from the local community kept the doors open. However, the school ha s recently experienced a change in building administration, a change of philosophy in teaching, and an improvement in parental involvement. These changes have led to a dramatic increase in student achievement and a campus wide boost in morale. In just five years, the school went from a grade of F to a grade of A in it is currently s
174 and achievement s in mathematics are not able We wanted to find out for ourselves what was happening at Oaklane that produce d such dramatic results. In particular, we wanted to know how the teachers at Oaklane were reach ing students in mathematics. Thus, we established a s principal and the lead mathematics teacher. After some time and many conversations, we decided to pay Oaklane a visit. We were not sure what to expect when we walked into what would be one of the most eye opening experiences of our lives as mathematics educators. As we entered the classroom of Ms. Kay 3 we heard the twenty African American fifth graders say in unison with rhythm and enthusiasm. When we entered, we saw several fraction s on the whiteboard. The students were focusing on a problem for which they had attained an answer of three Ms. Kay ask ed, to a beat that she kept by snapping her fingers, followed by th singing voice, answered with a very audible choral response T hree on she asked in her half While Ms. Kay continued, she led the students through many other mathematical concepts including measurement, measures of central tendency, least common multiple s prime and com posite numbers, and geometry. The class reviewed e very idea by using this oral chant, call response, and rhythmic technique. We asked her about this style of instruction, and she said, d test], but they leave me as a 4 or 5 [out of 5] 3 Pseudonyms have been used throughout this chapter.
175 and a chance to see how she established mathematics learning as a priority for her students. Week after week, we observed Ms. Kay teaching fifth grade mathematics classes We partially expect ed that would wane. We also realized that we might return to find that what we had seen was a rehearsed and memorized presentation that lacked real support for conceptual understanding. Yet we always found consistency in her instruction, with the same level of whole class involvement regardless of the math ematics topic. I tell a id as if it is the simplest thing in the world to do to tell a story with mathematics in a way that the story captures students and they can relate it to daily life activities so that they can learn the mathematics. Ms. Kay is in a unique environment at Oaklane because many in the community had given up on the school yet she has used her teaching craft effectively to support her stu success. She has learned how to respond to the learning needs of her students. Indeed, our observations of Ms. Kay confirm that she attends to the cultural characteristics of her students as a means of reaching them. We see her as successfully facil itating culturally responsive mathematics teaching. The aim of this article is to present a brief snapshot of the foundation for the pedagogical tools that Ms. Kay uses to teach mathematics. Culturally Responsive Teaching M any discussions in the literatur e center on the needs of learners from diverse backgrounds Conceptualizing r eforms ( for teachers and schools to enact ) that a ttempt to meet these needs, however, is not eas y and requir es innovation, patience, and willingness to change at every level. Oakl ane Elementary has accomplished such reform, which has been led largely by
176 reinvented and empowering instructional techniques that reflect culturally responsive teaching ( CRT). These practices are a crucial part of this critically needed systemic process o f reform. CRT, which has emerged largely from multicultural assumptions and theoretical underpinnings, is at the core of multicultural education I ts basis is that many current schooling and teaching environments stifle cultural practices, perspectives, a nd experiences Culturally responsive educators, however, consider student diversity as a strength in the classroom rather than a challenge that they must overcome, and they see the incorporation of cultural perspectives as a necessary educational commitme nt. They view students and teachers as cultural beings with cultural filters (Gay 2000) that sift all information They see c ultural experiences and identities as the foundations for all other experiences and behaviors (Ladson Billings 1994 ) CRT creates learning communities in which members validate cultural practices and values and revere them as funds of student knowledge. S tudents of culturally responsive teachers embrace their own culture while learning to respect the cultures of others For the student and the teacher, the educational experience is liberating and empowering in every sense (Gay 2000). In the process, the student and teacher transcend Eurocentric values on which much of the curricula, disciplinary practices, and pedagogy ar e based, allowing the use of home cultures as a learning tool in school. CRT establishes a culturally relevant community endeavor that addresses student needs culture in orde r to [and] the primary aim of culturally relevant teaching is to assist in the development of a relevant black personality that allows African American students to choose academic excellence yet s till identify with African Billings 1994, p. 17) Culturally responsive mathematics
177 teaching (CRMT) is a natural extension of this theory. This article focus es on this emerging concept and us es an example of success to illustrate our findings A Brief Note on the Challenges That African American Students Face As indicated by statistical evidence, African American students are currently experiencing struggles that prevent success in instructive settings They include d ropout rates that are higher than those in the past, as well as lower academic achievement scores and increased incarceration rates (Pennington 2000; Ladson Billings 1994) Further, students of color are grossly overrepresented in special education program s (Gay 2002; Townsend 2003), are more likely to be suspended from school (Ladson Billings 1997), and are less likely to receive a standard high school diploma. Gay (2000) asks a very poignant question: W hy are students of color, who are successful in so ma ny areas outside school, failing in school? This question is worthy of investigation, particularly in the context of mathematics, where the achievement gaps are some of the most marked (Howard 2006) T he need for CRMT is undeniable. Ms. Kay: Foundations in Community As previously described, we have been fortunate to work with a teacher whose instructional practices mirror many core ideals of CRT. As with all great teachers, the attributes and routines of her instruction are holistic and multifaceted, makin g them difficult to identify and discuss briefly. Moreover, classroom dynamics are distinct and unique, making our task of sharing this story even more challenging. C lear ly however, Ms. Kay uses her understanding of student needs and interests as a foun dation to make the learning experience meaningful for her eaves with every aspect of her life. Ms. Kay not only help s her mathematics students with academics, confidence, and self perception but also involves herself in many aspects of the school and community, th ereby putting herself in a position to learn about the cultural context of the community. For
178 example, Ms. Kay offers a night class for par ents who are interested in improving their own mathematical skills. Teaching this class gives her an opportunity to (1) motivate parents for parental involvement, (2) learn more about the home and community lives of her students so that she can use this in formation to connect with students and to use as contexts for mathematics problems that students can explore, and (3) show the students that she cares about them beyond th e boundaries of the classroom. Similarly, Ms. Kay is visible in the religious communi ty; she realizes and respects that this involvement is also important to the students at Oaklane and their families. Many weeks, she has invited us to attend her church, an experience that has been enlightening to us as researchers and inspiring to us as e instruction with her students closely resembles the way that the minister of her African American church facilitate s the service: active participation of the whole audience, le ader audience dialogue, leader audience call and re sponse rhythm in repetitions and clap ping, and other indications from the leader that he expects an audience response. This same level of expectation centered, stru ctured classroom. This type of congruence between home and school culture is fascinating to watch and has been immensely successful in her classroom. hall marks of Ms. Kay s style. As a result, she is well respected, visible in the community, and knowledgeable about her students lives outside school. Her involvement is important to the students because it illustrates that children and families are cared for, looked after, and respecte d in every aspect of their lives Moreover, as we subsequently describe in more detail, her involvement enables Ms.
179 Kay to recognize cultural practices and values that help her design effective, empowering mathematics instruction. As extensive involvement in the community indicates she stays in touch with her students as evidenced in her instruction through the use of such cultural practices gleaned to teach mathematics. Further, she knows what and how much her students are able to engage in, so that each learner reaches the level of knowledge that Ms. Kay is seeking for her or him Standardized test scores, al though a focus and a goal are not the o nly facets of education with which she is concerned. She wants students to understand what they are doing and to be able to make sense of it in their own lives. She wants students to relate to and interact with the material so that they are able to use i t, retain it, and be confident in their abilities Ms. Kay empowers students as learners of mathematics. This article next attempts to put into words specific mathematics teaching practices that Ms. Kay exhibits. Teaching of Mathematics Ms. Kay is a strong and respected teacher H er peers, school administrators, parents, and teacher educators praise her because of her ability to reach for and touch the stars with her students. F ully captur ing the unique and dynamic pedagogical practices that have produced remarkable results for her students is challenging but this section attempt s to describe phases of her mathematics instruction Chants and m ovement Consistent with the culture of the local community wher e the students play in the features choral responses, requiring the vocal, physical, mental, and personal involvement of each student. She rarely sits down during class and is constan tly walking among the students to encourage
180 participation and engagement in mathematics She is relentlessly moving, snapping, clapping, leading chants and encouraging enthusiasm. Her energy and passion are contagious as evidenced by the full engagement of her students. To further the effectiveness of these chants and choral responses, Ms. Kay uses her vocal talent to engage students, creating rhythms that teach mathematics through musical modalities. Students come to realize that singing mathematics is a n enjoyable way to learn concepts and is effective for retention. Further, because Ms. Kay knows that her students enjoy the music of the hip hop culture, she uses this music as an inspiration for various rhythms and songs and allow s students to sing alon g to their favorite tunes. She has found that through hearing and participating in chants every day, students retain information and constantly refine their knowledge. Several students have reported to us that when they hear a song or rhythm on the radio, T he information is therefore accessible and relevant to students, and receives reinforce ment daily outside the classroom. In addition to the chants, Ms. Kay assigns specific movements to concepts to give students another way to retain the information. For example, Ms. Kay may ask the class to show her a line. First, all student s extend one arm fully (open Stude nts do these movements way (open palmed that they make the arm movements. Eventually, students use these movements and others for such related
181 concepts as right angle, acute angle, and so on music and order. This type of movement activity engages the students, builds their confidence in the material, and substantially increases the c hances of ret aining the information In addition it gives learners a physical representation that enhances understanding. This involvement is the type that Ms. Kay requires and encourages. Students are in the rhythm of the mathematical content with her, learning through music, movement, and rhythm: matters that are very much a part of their lives outside th e classroom. Additionally, she varies the topics, the order of topics, and the responses that she solicits so that students do not have a way and they must reach a place of comfort knowing that she is interested their learning. The students are acquiring sophisticated math ematical knowledge in the context of cultural consistency, accepting that Ms. Kay challenge s them to do their best, even in the midst of having a good time. Incorporating rhythms, songs, and movements into her lessons is one way that this teacher encourage s her students to be full participants in lessons; using specific songs as the basis for projects is another. For example, Ms. Kay grew concerned that her students were spending so much time listening to hip hop music at home and in other venues that they were not accomplishing as much as they could at school, specifically in mathematics. T o address th at problem, she assigned a weeklong project at the end of class one day. Because she had noticed that many of her students knew all the words to the hip hop them to keep track of how many times they heard the song each day for a week. She t hen required the students to organize these data into a bar graph, complete with title and appropriate labels. The results were amazing. Not on ly did students produce colorful and artistic bar graphs, but they
182 were also able to analyze the data that they collected, group it in different ways, and discuss why they may have heard the song more on one day than on another day. This type of constant a ttention to student engagement supports goal to interest students and keep them interested and invested in mathematics During class, she encourages students to answer questions in unison, using a strong voice so that they feel empowered by their s to ask for an answer until she hears a powerful refrain. The result is truly amazing and unconventional: learners are constantly clapping, stomping their feet, drumming on their desks, moving, dancing, and marching in time during mathematics lessons Moreover, students engage in mathematics at home when listening to their favorite song or when the familiar beat of the geometry dance comes on the radio. One might expect chaos from this type of behavior, but the mood in the classroom is extremely positive, organized, and goal oriented. Ms. Kay is clearly in control of the situation, but she is like an orchestra conductor who purposefully draws out the best from tho se she is leading Real l if e e xamples T eachers receive constant encourage ment to relate the material that they teach to the real instruction is a challenge in and of itself. Ms. Kay, however, is deeply in touch with the culture of the school and community and mak es storytelling a naturally occurring medium through which she convey s real life contexts. fifths and one say per sists asks. There is a pause and then the students answer
183 to which more then uses a familiar story to access ch existing knowledge of finding the least common multiple as a means to finding the least common denominator. She proceeds to tell this story about five and king down the street, who do you see coming first? A ll the students respond Ten! So who decides what denominator we use? A ll answer, laughs, clearly understanding the point that the teacher is making and th e underlying mathematical idea. Ms. Kay has realized that the students in this school are part of a walking community. Many students walk to school with their brothers, sisters, cousins, and neighbors, so n addition, she asks them to explain concepts to her as if they were explaining them to their little brother or sister. This type of focus on family and interaction is important to this specific population, and students respond with hard work and determina tion. High standards through tough l ove on her first day of class S he entered the room with a visibly negative attitude and a smug expression on her face. She sat in the back of the room ; and as Ms. Kay quickly discovered, Brandy was unprepared. Ms. Kay tried to be accommodating, asking Brandy what she had done at her previous school and how comfortable she was with the current material. From this brief interaction, Ms. Kay learned that Brandy had not enjoyed her previous school and the idea of having to do such energetic work in did not thrill her Further, when another student lent Brandy a pencil and paper, Brandy snatched it from his hands and rolled her eyes. T his type of behav ior pushed Ms. Kay to her limit The teacher stopped what she was doing and made clear to Brandy that her attitude and
184 actions were unacceptable. S he then explained that her students do not disrespect one an other, especially when one is trying to help another. Brandy looked angry when Ms. Kay walked away and continued with her instruction. About a month later, we returned to watch the same class. Brandy, who had been resistant in the beginning, was one of th e loudest chanters. She was helping students around her, taking When we discussed this incident with Ms. Kay, she indicated that for these students, community acco untability goes a long way in helping individual students do the right thing. Brandy rose to expectations and became a more confident learner. Such relationships with students are of particular interest to the authors. Throughout the year Ms. Kay makes demand s on her students; her expectations for their mathematics learning are clear, high, and unwavering. At the same time, however, she conveys a sense of care for being and success in school. For example, when a student shows that h e or she understands a mathematics concept so well that he or she can explain it to the entire class, Ms. Kay praises the student enthusiastically. However she does not tolerate wandering attention. She often calls out s tudents who are not engaged and dir ect s them back on task. She tells s tudents who forget their mathematics journal to call home so that someone can bring it to them Students respond to these lofty expectations by meeting the standard and in some cases, exceeding it. Ms. Kay responds with v isible pride in her students, a reward for which they work very hard. Focusing student e nergy for mathematics l earning What does the perfect classroom look like? Many people believe that it should be full of silent students. However, this definition of no rmal or perfect is not consistent across cultures. In other words, traditional school practices are considered normal even if they do not work for students of diverse backgrounds. In turn, student achievement suffers, appropriate behavior that
185 is accepta ble at home is not acceptable at school, and the educational setting devalues household language patterns and practices. Thus, the school setting deems certain cultural behaviors inappropriate, dooming some groups of students to a life of conformation or a life of unfulfilled potential. Ms. Kay has found her niche in incorporating cultural behaviors into her classroom She engage s students musically through chants and rhythms ; she encourages students to speak with loud, confident voices. Students know tha t they are to respect themselves, their classmates and s on mathematics and the empowerment that they believe keeps them engaged. Ms. Kay empowers students to be confident learners. When she spea ks precisely and forcefully with the mathematics through chanting and recalling, the students engage in the same and the students appear to be developing their own confidence about the mathematics that they are learning. Conclusion What can teacher educators and teachers learn from Ms. Kay? They can take Ms. Kay s ideas and successes and begin to evaluate their own practices. She shows teachers that accept ing and car ing for students as they are is important [Teachers should not forc e students to conform to values that do not acknowledge their power as learners and as human beings. Rather, educators must remember that each student has a cultural background. In the context of that background, students will make the most progress.] Th e previous statement does not mean that students should not follow rules or think outside their home culture, but it is a call for educators instruction, behavioral interv ention, and assessments for him or her Because each classroom and each teacher are different, no one formula can unlock the secrets of cultural responsiveness; yet each teacher can think about how her or his instructional style affects students. Further, each
186 teacher can engage in conversations about the topic of diversity, sharing ideas and continuously improving his or her own craft These conversations may include colleagues, parents, and students The question for you is H ow can you empower students a s learners of mathematics? Although no one size fits all approach to CRMT exists we have gleaned several ideas from Ms. Kay that have been helpful to practicing teachers Chants and rhythm are a n important about and notices and us es the m as a basic component in creating engaging mathematics lessons. She sets v ocabulary t o music sets definitions to music and sets procedures and algorithms to music. Rhythmic motions punctuate recitation. T he class accomplishes p ractice within the meter of musical accompaniment. Ms. Kay constantly communicates h igh expectations built on tough love to her students. She accepts no excuses and does not tolerate failure. Students must rise to the occasion. She expects all students to participate in every lesson and she does n o t allow students to do otherwise. She say s t participate excuses policy and her endless praise of successful students evidence her tough love. Students learn that this praise, however, does not come easily and that they must earn it Teacher m entor is a way to describe Ms. Kay overall. She provides students with what they need to learn and become successful mathematicians. She addresses their attitudes about, and responsibilities for, schoolwork and she encourages with them with praise. Storytelling is a means through which Ms. Kay connects mathematical ideas with her students. She uses practical examples from the daily lives of the children (e.g., walking to school or borrowing from a neighbor). Review happens in every mathematics lesson. Ms. Kay actually buil ds this review into the songs and chants that she leads throughout class. She believes that hearing or seeing mathematics one time is simply not enough for students to learn it thoroughly. For Ms. Kay, c ommunity involvement is a n important component in pos ition ing herself to stay in touch with her students and their families. She realizes that the community in which students live greatly influences their culture, and she stays close to the community by offering mathematics instruction to parents and by orga nizing rite of passage programs for her fifth grade students. Empowerment that is, mathematics empowerment is what Ms. Kay wants for the students. For example, when the class stud ies percents, Ms. Kay create s scenarios about the students planning a shoppi ng budget and shopping She instructs the students to pay close attention to percent off sales so that the y can make certain that they receiv e the appropriate discount on purchases. Ms. Kay warns the students that without mathematics empowerment, others ca n cheat and take advantage of them
187 The language of mathematics is an essential component of as evidenced requirement that students justify their thin king and give articulate explanations for their solutions. As the large gaps in achievement among students of various backgrounds illustrate culture is essential to learning. Specifically, heritage, personal perceptions, experiences, and societal norms play role s in processing information and shap ing individual thinking processes CRMT presents a necessary intervention. Through empowering pedagogical practices such as those previously described, educators must bridge the gaps sustained by the status quo while empowering students to bridge the same gaps What we need now is action that address es the reasons that teachers are failing to reach much of the minority population in schools. No one proposing that other teachers can also help their students reach for and touch the stars
188 C HAPTER 6 JOURNAL ARTICLE 2 Achieving Success with African Am erican Learners: A Framework for Culturally Responsive Mathematics Teaching By Emily Peterek Given the lack of research based information on successful teachers of African American children in the context of mathematics, it is important that information about this study is disseminated to teacher educators and researchers. This manuscript was written from a research angle in order to encourage more work of this type that can build on the produced theory. Further, this manuscript is meant to encourage cl assroom based, qualitative research in mathematics classrooms, and brings attention to the achievement gaps in this context. Citation : Peterek, E. (accepted). Achieving success with African American learners: A framework for culturally responsive mathematics teaching. Childhood Education.
189 Summary The black white achievement gap is pervasive in elementary school mathematics classr ooms. Too often, step by step methods of instruction are utilized in instruction, exacerbating cultural incongruities that exist between teachers and students. Particular, culturally based teaching techniques and effective styles of communication have be en documented through the study of highly effective teachers of African American students (Gay, 2000; Irvine, 2002; Ladson Billings, 1994), though very little of this work focuses on mathematics pedagogy. This paper presents a working theory meant to help teachers and teacher educators conceptualize culturally responsive mathematics teaching. Grounded in the work of Ms. Johnson 1 a highly effective mathematics teacher in a largely African American, high poverty school, this theory can guide teacher effort s to help students of color succeed in mathematics classrooms. Introduction For decades, the biggest challenge facing our nation has been that of providing equitable education for all students. Today, over fifty years after the famous Brown vs. Board of Educ ation decision that legally ended school segregation based on race, urban schools are more segregated than ever (Ladson Billings, 2004). Impoverished neighborhoods with large populations of minority students endure the greatest injustices, still s uffering in unkempt school buildings with fewer resources while experiencing lowered student achievement and higher dropout rates. Each year, these schools receive fewer qualified teachers, and seem to become more invisible to the school system (Kozol, 19 95, 2005). Student achievement data show the 1 A pseudonym has been used to protect the participant
190 effects of this negligence, illustrating that students of color, particularly African American males, are falling behind in nearly every category ( Ferguson, 2000; Noguera, 2003 ) despite their socioeconomic stat us. Within schools, dominant norms and ways of teaching are often based in white culture, mirroring Euro centric norms. The resulting practices contribute to cultural incongruities in classrooms and schools, leading students of color to perform below th eir potential. In turn, teachers assume deficits in students of color (Delpit, 1992) and, over time, varied ethnic practices and ways of learning are deemed inappropriate. These negative beliefs may be validated, reinforced, and even exacerbated among co lleagues, as the majority of the teaching force, particularly at the elementary level, is white, female, and middle class (Howard, 2006), and most have limited interactions with individuals from diverse backgrounds (Nieto, 1999). Inconsistencies in school versus home culture (i.e. how learning is assessed, how information is g 2000, p. 16). In response to low achievement among particular groups, inequitable tracking practices are adopted, and students who do not conform to a particular s et of cultural behaviors are often punished, being placed in the lowest tracks. This trend is evidenced through the overrepresentation of students of color in special education (Gay, 2002), increased drop out rates among students of color ( Montecel, Corte z, & Cortez, 2004 ), and growing achievement gaps that exist between these groups and their white (European American) counterparts. In mathematics, these gaps are particularly marked (Howard, 2006), and the teaching of students of color in
191 mathematics is o ften wrought with lowered expectations, actions that reinforce racial Culturally Re sponsive Teaching family histories, value orientations, and experiences to students in the classroom, attributes often Pang & Gibson, 2001, p. 260 ) helping students to bridge the home school cultural gap. These educators have strong ties to the black community (Ladson Billings, 1994) and maintain a strong academic focus while helping students to develop self awareness, self confidence, and leadersh ip skills ( Foster, 1987 ). Further, African American children have Ware, 2006 ) or teachers who engage students through the use of high expectations, firm and authoritative classroom management and culturally familiar communication patterns (Ross, Bondy, etc., 2008). Identifying these attributes is helpful; however, it has remained difficult to describe the whole practice of a culturally responsive teacher in the context of mathematics. An Illustration of Culturally Responsive Mathematics Teaching (CRMT) Given the complexity of mathematics classrooms, it is difficult to capture every detail of throu gh observations, interviews, and artifact collection, have been organized into the following graphic (figure 6 1 ) in an effort to capture the complex and fluid nature of CRMT.
192 Figure 6 1: Culturally Responsive Mathematics Teaching (CRMT) Knowledge Clearly, teachers must have vast funds of knowledge. In mathematics, pedagogical content knowledge is essential. Ms. Johnson exhibits a deep understanding of mathematics, making it possible for her to deconstruct difficult concepts, analyze student error s, and contextualize mathematical knowledge is activated in the course of teaching (Ball & Bass, 2000) in appropriate ways that allow for student driven changes in d irection and maximum student understanding. teachers of African American students of ten use their cultural knowledge to refer to metaphors and family ties when presenting material, indicating a strong, almost familial relationship with their students ( Foster, Relationships/ trust Communication Knowledge discipline STUDENT pedagogy
193 1997 ; Ladson Billings, 1994). A product of the neighborhood in which she teaches, Ms. Johnson is able to relate mathematics to student lives in a non superficial manner. For example, when describing to students how to find a least common multiple or denominator, she refers to the two then relays a story about big brother coming to the school to pick up little brother and the two Here, Ms. Johnson has tapped into several cultural realities of her student in this neighborhood, the older siblings frequently care for the younger siblings. She has based lives. Connecting related numbers to r elated family members is effective for this population, and strategy repetition helps students to make this connection often. Further, Ms. Johnson has employed a call response structure, engaging the whole class at once and maintaining a clear academic fo cus. Communication students. Not only does she use a specific vernacular when speaking with students, she utilizes familiar patterns of interaction in her mathematics l essons. This helps to lessen the cultural disconnect that many African American students face in school. As can be seen in the above example, this includes extensive use of chants and call response techniques. Ms. Johnson also
194 uses rhythms, music, and d ance in her teaching, helping students to remember mathematical concepts in culturally relevant ways. In order to choose music for her lessons, Ms. Johnson with This interconnection of culture and cognition is believed to lead to academic success and empowerment (Allen & Boykin, 1992). Deeper societal issues are also communi each student in her class that she genuinely cares for them and has their best interests in mind. This is made clear in several ways, and is complemented by a demanding and strict environment. This type o Ware, 2006 ), and has been shown to be highly effective in evoking positive responses from African American students. These communication patterns mirror parent child relationships that studen ts experience in their own homes. High expectations are clearly set from the first day of school (Ms. Johnson begins teaching from the back of the book so that students will encounter the most difficult concepts first), and students who are not striving f or excellence are immediately set immediately walks the child to the office to call home. The student then has a choice when calling home. If they know where the bi nder is, they must ask someone to come bring it to the school. If they do not, they must tell their parent that they came to school unprepared and then hand the phone to Ms. Johnson. Students respond to this type of demanding behavior because they reali ze that Ms. Johnson believes that they can do more and can excel. In turn, students begin to think of themselves as people who can excel.
195 can achieve success in making sense of c term achievement (Love & Kruger, 2005). confidence throughout the school year, and often leave fifth grade as empowered learners and individuals. Such trans formations are hallmarks of culturally responsive teaching (Gay, 2000). Relationships/Trust Over time, Ms. Johnson has built relationships in the community surrounding the school. She has taught several generations from some neighborhood families, and of ten visits student homes. She is also very active in her church which draws from the same population. Moreover, her record of success has brought a new sense of empowerment to the community. Students who have been placed in lower tracks throughout their education are suddenly in honors classes, and students who have never spoken in class before are singing and chanting along with Ms. Johnson. She demands a lot from her students, but the pride she shows in return alters individual student self perception s. Successful practices in the classroom coupled with community involvement and familial relationships have resulted in an immensely trusting relationship between the neighborhood and Ms. Johnson. Parents trust that Ms. Johnson will do whatever is necess ary to help the children succeed, and know that their student will emerge from the demanding environment as a stronger individual and learner. Further, Ms. Johnson ensures students will be able to get help with math homework at home by holding evening cla sses for parents. She teaches the parents using similar mathematical strategies so that they will be on the same page as their child when working at home. Further, parents gain essential knowledge that they might not have otherwise had access to, creatin g a more academic focus in individual homes. Relationships are built with students at various points as well. Each year, Ms. Johnson is in charge of the fifth grade play, which she writes, directs, and choreographs. She has also
196 created a rite of passage event called the Evening of Elegance. Students are asked to dress formally, and each is presented to parents and community members by their homeroom teacher. A large meal is shared and students often perform their class song. Ms. Johnson und erstands that such rituals are important to students, and enjoys the pride they show when involved. Further, since many students at the school are from low income families, Ms. Johnson will provide dresses or suits to those in need. Constant Reflection and Revision Successful teachers are always looking for new and improved ways to make mathematics accessible to students, and Ms. Johnson is no exception. The rate at which this reflection and revision process takes place is astonishing; the process is c onstant and ongoing. For example, Ms. Johnson might try out a strategy with her first class of the morning. If she feels the pulse of the group is positive and responsive, she might deem the strategy a success, but slightly tweak it for the second class. By the end of the day, she has perfected her technique and shares the revisions with her early classes the following day. Other days, she makes adjustments on the spot. If she tries out a certain rhythm, for example, but the students are not fully conn ected, she will tweak the rhythm or strategy until she feels their full engagement. Standardized test scores and teacher made assessments are also utilized in this revision process. In grading, if Ms. Johnson sees that many students have missed a con cept that she taught in a particular way, she will go back and re teach until she discovers a method that makes the concept accessible to all students. The strategy may change from class to class or year to year, but her commitment to the children drives her to continuously engage in this process. In which have been used to indicate constant movement.
197 The Cycle of Pedagogy and Discipline When observing in Ms. discipline and instruction as distinct entities. The two are so intertwined that they become based teaching techniques largely control dis cipline, and any issues that arise are immediately dealt with. This cycle is central to her practice, and, as indicated by the graphic, is focused on the needs of the students. In classroom practice, this cycle allows Ms. Johnson to maintain a strict academic focus in her classroom, instilling in her students a drive to succeed. One hallmark of her instruction that contributes to the cyclical nature of her practice is constant concept review. Each day, Ms. Johnson teaches a new mathematical idea and orally (using call response, chants, movement, etc.) reviews many of those that have been covered in previous days. At any point in the class, she might ask students for an old definition or for the solution to a problem relating to any of the past conce pts they have covered, keeping all content at the forefront. Students might learn the concept of decimal addition on a given day then briefly review mixed numbers, area, and perimeter, only to end class by doing the geometry dance. This continuous review process allows students to immediately and internally access information at any time. This is especially important on high stakes tests. When students are taking such assessments, an observer may see a student bobbing his head in order to remember a rhy thm or a pair of hands slightly moving to remember a concept taught through movement. Student results on such assessments have been some of the best in the state for many years. The various arrows in the figure are meant to show movement and connections. As discipline most immediately affecting the learner. The student is constantly engaged in some
198 cornerstones of communication, relationships, knowledge, and reflection represents the larger environment created by Ms. Johnson. In this setting, stude nts continually encounter cultural familiarities and may experience a change in self concept. These cornerstones serve as walls, keeping students engaged in the cycle of learning. Setting the Stage for CRMT It would be impossible for any teacher to exa ctly emulate Ms. Johnson, and the goal of this research is not to simply clone someone who is successful with a particular population. Rather, this beginning theory about CRMT can help teachers to find their own teaching styles and practices, keeping in m ind the overarching ideals that create responsive and academically focused mathematics classrooms in largely African American schools. Such guidelines might help educators to bridge gaps between home and school that exist for students of color. Moreover, given the complicated, fluid nature of culturally sensitive mathematics classrooms, it is imperative that we put forth what such environments (and the educators who create them) might look like in action. Ultimately, the theoretical underpinnings of CR MT allow teachers to recognize cultural incongruities as the cause of the achievement gaps, thus providing appropriate interventions. Too many current pedagogical solutions in schools focus on standardized testing as the root of the problem and result in prescribed curricula focused around these assessments. When we consider that cultural discrepancies are at the source of the problem, it becomes clear that dictated pedagogy and curricula may actually exacerbate the achievement problems of students of col or. In altering current practice, however, we may begin to bring equity bac k to mathematics classrooms.
199 CHAPTER 7 CONCLUSIONS AND IMPL ICATIONS The purpose of this work wa s to explore the practices of highly successful mathematics teacher s of Africa n American children. Though th e results obtained through the resulting case study cannot be widely generalized because of the unique nature of classroom practices and interactions, many ideas pertaining to various areas of mathematics teaching are informe d by this work. In deconstructing techniques and practices of such teachers, the field of mathematics education can begin to take strides in providing an equitable, culturally responsive education across color lines. Further, in allowing children to main tain and enhance their cultural and racial identities in the mathematics classroom, educators can work to re define the static notions of mathematical competence while relating mathematics to community practices. As such, the implications of this work and the success of Gloria Merriex impact many areas including classroom practice, teacher education programs, and future research in the field. Most importantly, this work brings much needed attention to issues of culture and equity in schools while providin g research based suggestions that greatly inform the mathematics education literature. Mathematics Classroom P ractice While it would be impossible, impractical, and possibly ineffective for any teacher to emulate Gloria Merriex, there are certain prac tices and ideas that can be gleaned from her work and put into practice in mathematics classrooms. When considered with current literature about effective teachers of African American students, generalizations can be made that directly inform classroom pr actice and immediate action. Much of this work with Gloria corroborates what historical literature has indicated over time. Mainly, if African American students are taught in documented culturally congruent ways
200 (using movement, the arts, performance, a nd communal learning, for example), they are more likely to succeed. Gloria Merriex showed that this is not only true in general education, but also in mathematics classrooms. Thus, mathematics teachers in diverse classrooms should constantly reflect on the knowledge they have of their students, the ways in which they are communicating (verbally and non verbally) with students, and the relationships and trust (or lack thereof) that result from these foundations as they are enacted in the classroom. This work shows and extends that idea, indicating that ways in which teachers use culturally congruent methods in addition to the interactions and dynamics that connect classroom practice to teacher beliefs directly affect student achievement. This study con tributes to the literature significantly as it provides a working theory that will help teachers to take the informative and foundational literature on CRT and put it into action in mathematics classrooms. As such, this work bridges mathematics education theory and practice through field based research. This contribution is far reaching, as in informing teaching practice the theory can also help teacher education programs to re define the ways in which they prepare teachers for diversity in the mathematic s classroom. Further, this theory is not prescriptive, but interpretive, meant to guide teachers in their quest to become more culturally responsive rather than providing a list of rules to follow. In this way, the theory is applicable to various setting s with diverse populations and teachers, and provides a practical (rather than theoretical) framework within which to work. Moreover, inherent in this work is the notion that mathematics teaching, and not students of color, should be adjusted in efforts t o affect the achievement gap, thus rejecting the deficit language that has largely dominated mathematics education literature.
201 The theory presented in this work is more accessible to educators than theoretical and hypothetical works of the past. Spec ifically, the theory is interpretive, fluid, and general, implying that it can be utilized to guide mathematics teachers who are struggling to be more culturally responsive. This is especially important for white teachers (as the majority of the teaching force is white, middle class females, Howard, 2006) in diverse classrooms who do not feel that they can comfortably embody or even adopt culturally specific practices gleaned from a talented singer with internal rhythm and a harsh tone; rather, each teacher should be aware of the ways in which his or her students learn, their backgrounds, interests, and cultural practices, and should utilize this knowledge to inform their unique pr actice. Thus, one important goal of this work is to empower all teachers to respond effectively to diversity in the mathematics classroom while giving them the tools to do so. Culturally responsive mathematics teachers know their students and use this knowledge to build strong, foundational relationships. More specifically, these teachers take time to get to know student cultures at all levels, and use this information in their instructional planning and in the course of teaching. This type of k nowledge is multilayered and complex, and involves understanding the community culture (e.g. communication patterns, shared values) in addition to th graders think and feel, where they are emotionall y and intellectually), and relevant pop culture (e.g. what types of music students listen to, who are the big names in entertainment). Teachers gain this information by communicating with the students themselves, maintaining involvement in the community living. Given the intricacies of culture and identity, this type of knowledge is not gained quickly,
202 nor can one acquire it superficially; it takes years of personal involvement to build relationship s that will allow a teacher to access this type of knowledge, particularly if he or she does not live in the neighborhood surrounding the school. Acquisition of such knowledge is certainly possible, however, but requires a high level of commitment and wil lingness to work beyond the school day. As can be inferred by the vast amount of knowledge needed to effectively teach mathematics in an enriching manner, c ulturally responsive educators continually work beyond the classroom. Specifically, these teachers provide resources to the community in proportion to their personal expectations. For example, if a teacher expects her students to receive help at home, she recognizes that parents might not be familiar with the material, an d provides a class that will help them to help their children. If a teacher expects a student to have supplies, she provides them with the necessary materials so that each child has the same opportunity. This type of commitment is a hallmark of successfu system, knowledge of students, and relationships. Further, such work provides additional information that can be used in practice, providing the teacher with a meaningful perspective. This deep understanding of student needs, goals, culture, and ways of living informs classroom practice and provides the teacher with an informed perspective. In c ulturally responsive mathematics classrooms where this interest is a driving force, teachers do not require that stu dents abandon their home culture in order to be successful Many times, students of color are asked to learn from traditional, individualistic, lecture type instruction, and are deemed disabled if this type of instruction does not provide them with a conn ection to the material. Culturally responsive teachers are able to teach content, even mainstream content, without asking students to live, act, or learn differently because of social norms; rather, these teachers try to
203 provide cultural congruity for stu dents in the mathematics classroom. Further, these teachers are attentive to racial and cultural identity, and often develop these constructs in the course of teaching. As a result, these teachers provide a safe context from which students can learn abou t societal pressures and misconceptions. Such an environment provides a solid foundation from which students can achieve academic success within their own cultural norms. Students are empowered as disciplined individuals. In order to maintain such hig h expectations while providing a culturally congruent education, effective mathematics teachers engage in c onstant reflection and revision. This allows teachers challenge and engage students in relevant mathematics. In refusing to change particular aspec ts of instruction despite the outcomes, a teacher is not attending to the individual needs of her students; rather, she is providing the same instruction to all students, a practice which inherently favors particular learners. Reflection allows an educato r to see what it is that needs revision while encouraging pedagogical innovation and change. This reflection revision process is cyclical and should happen at the macro (i.e. reflecting on entire lessons, units, or ways of teaching) and the micro (i.e. in the course of teaching on a moment to moment basis) levels. The vested interest that is required of culturally responsive teachers is driven by foundational principles and ideas. These teachers are supporte d by a particular belief system based on the idea that their students, no matter what statistics say, have the ability to be talented and gifted mathematicians. Their job is to work to find ways in which students can express their talents while accessing mainstream knowledge. These beliefs are fund amental in providing effective non verbal communication and building relationships; as teachers we must realize that
204 a teacher does not truly hold positive bel iefs about her population of students, on the other hand, she will communicate these non verbally and will struggle to build relationships. Mathematics Teacher Education P rograms Many teacher education programs have taken strides in preparing teachers fo r work in diverse classrooms. Successes of the Teach for Diversity (TFD) graduate program for pre service teachers at the University of Wisconsin (Ladson Billings, 1994), and the CULTURES (Center for Urban Learning/Teaching and Urban Research in Education ) program at Emory University (Irvine, 2003), which focuses on preparing experienced teachers for work in urban schools, have been documented. Programs such as TFD and CULTURES prepare teachers for work with diverse populations, making issues of culture, race, and power an integral part of the curriculum. Too often in other programs, however, suggestions for being culturally responsive are presented as addenda to curricula rather than integrated throughout a program. As such, multicultural curricula mus t be accessible and prevalent throu ghout teacher education programs, and content and methods courses must be reconceptualized In simply adding a multicultural piece to our existing programs, we are communicating to pre service teachers that culture is s omething extra we have to worry about rather than a resource that should be used in instruction. This full integration of multicultural theory should also be applied to internship, student teaching, and practicum settings. As such, s uccessful examples o f culturally responsive teachers should be touted and employed as mentor teachers By placing these students in traditional classrooms that are based Euro centric norms, we are undoing all of the good that might have been done by multicultural coursework. Student teachers are likely to mold themselves to their mentor teachers (at least somewhat), so teacher educators must work to find such models. In focusing on in service teachers who teach with a focus on culture, however, we can provide
205 positive examp les for pre service teachers while showcasing the ways in which successful teachers enact the beliefs that we preach in our programs. These successful models should be acknowledged and included in the literature, as should the voices of pre service teach ers with whom they work. In general, the field of mathematics education should publish the success stories of such teachers and their students in an effort to re define the concept of competence in mathematics. This type of modeling is influential at the university level as well. As such, mathematics t eacher educators should model and embody CR M T. It is one thing to preach the theoretical underpinnings of CRMT and CRT, but quite another to enact these ideals in the classroom. We continuously communi cate to our students in verbal and non verbal ways, however, so our commitment to providing equitable instruction should be tangible. If we are saying one thing and doing another (e.g. saying to get to know student culture but keeping a safe distance from our own students), our values and voices lose credibility. If we enact CRMT in our own classrooms and take care when placing future teachers in appropriate placements, however, students are more likely to adopt such practices in their own teaching. Fut ure R esearch Currently, there is a large gap in critical mathematics education literature, especially as it pertains to culturally responsive teaching. Researchers in the field must work to address issues of equity, culture, and race, keeping in mind the sociopolitical realities of our schools. This research should employ innovative methodologies that account for social influences on the mathematics classroom, and can contribute heavily to teacher practice, mathematics curricula, and teacher education pro grams. In order to more readily conceptualize equitable and culturally responsive mathematics teaching, we should continue to study successful models In the current literature, there are very
206 few classroom examples of CRT in the context of mathematics. In theorizing about such models, we attain a certain level of understanding, but in discussing what we see in action we are able to more readily understand the relationship to practice. Further, such models can provide us with more salient definitions of CRMT while informing our teacher education programs. In turn, successful multicultural teacher education programs should also be studied and used as models. Moreover, while the prevalence of racial segregation makes culturally specific mathematics teachi ng important, successful models of CRMT in truly diverse classrooms are still largely missing from the mathematics education literature. As such, this is an arena in which research should also be focused. Further, while we strive to recruit and retain mo re teachers of color, specific implications of this type of work for white teachers working with diverse populations should also be examined in mathematics classrooms, as these teachers have a profound impact opment. Perhaps the most important outcomes of CRMT can only be communicated by students who have experienced such classrooms. Thus, holistic descriptions of such models should include s tudent voices. hievement, social interactions, and long term self concept should be studied through interviews, observations, and follow up data. This will help us to more easily evidence the effects of CRMT on students, parents, and communities. Further, it will allow underrepresented student voices to infuse the literature base in the field. If our ultimate goal is improved student achievement in particular populations, it is imperative that we include such voices. On the other hand, s tate and national accountabili ty programs should be studied in relation to cultural bias. What effects do these systems, which deem particular topics to be the most important knowledge to have, inhibit or encourage CRMT? Further, we should examine the
207 effects of scripted curricula, m any of which arise from state standards documents, on classroom practice, particularly in high poverty schools and schools with large populations of students of color. These curricula, teaching practices, and research methods all hinge on the beliefs of the individual who has produced them. As such, t eacher and researcher beliefs should be examined in terms of student or research outcomes. This link seems to be strong and should be examined as such. This would be another avenue through which student vo ices could be used, as they should be consulted about such beliefs. It would be interesting to look also at the ways in which example, shape such beliefs, and ho w these are then enacted in the classroom. Given the interpretive nature of grounded theory research and results, the hope is that the reader will find freedom to come to his or her own conclusions about the nature of CRMT. Further, individuals should foc us on areas of this work that are particularly interesting or relevant to their own work.
208 APPENDIX A GLORIA MERRIEX INTERVIEW PROTOCOLS The following interview protocols were guides for interviews that occurred while Gloria Merriex was still alive and teaching. Intervie ws between her and I were long and semi structured, meaning that they often veered off of the course provided by the protocols. As such, many questions that came up during interviews and subsequently i mpacted the data are not included in the lists. The following questions are provided as samples however, to give the reader an id ea of how theoretical sampling wa s used in the interview process. The protocol for interview #1 was designed from questions generated by a few observations and literature. Each successive interview protocol was constructed subsequently from perceived holes in the data at the time of the interview. Here the reader can follow the progression of questions that were generated in this manner. Interview #1 1. Tell me about your background. What was school like for you? When did you decide that you wanted to be a teacher? Where and how were you prepared to become a teacher? 2. How would you describe your way of teaching? Have you al ways taught this way? 3. Does your role in the community influence your teaching? How do you use what you know about students in the course of teaching? 4. What types of teaching methods have given you the most success with this population? As a group, what do you feel it is that they need from a teacher? 5. How do you handle the various ability levels of children in your classroom? 6. Can you tell me about a student who is struggling or has struggled in your class? How did you handle it? 7. How do you handle disciplin e in your classroom? What do you consider to be misbehavior in the classroom? 8. What types of support (from administration, parents, etc.) are key to your success as a teacher? Interview #2 1. Can you tell me more about the math team? 2. Tell me more about the Evening of Elegance and the 5 th grade Graduation. How do rites of passage events like these benefit kids?
209 3. You talked about cultural influences during our last interview. How does being in your class help students develop racially? 4. When a student acts up out of the room, might have them call home, and always address them directly with a particular tone. Why does this work with this group of students? 5. You communicate with students in very speci fic ways. Can you talk about that? 6. You mentioned that as a product of this community, you understand where students are coming from. In what other ways does your background influence your teaching? Interview #3 1. Last week a new student came into your cla ssroom and was almost immediately sent out. Can you talk about why you handled the situation in this particular way? 2. identity development? 3. You have said several times that you believe that your teaching has an impact on generations and the entire community. How do you feel that the successes at Duval have transformed the community? 4. What are the main outcomes of your teaching? 5. How can we better prepare teachers to work in schools like Duval?
210 APPENDIX B OUTSIDE PARTICIPANT INTERVIEW PROTOCOLS Protocols are listed by interviewee. Gloria Merriex was the only participant who was interviewed more than once, and everyone except Gloria was contacted during member checks. conversations with outside participants were semi structured, and the following protocols provide only a sample of questions. It is important to note that each of the followi ng protocol s was constructed p rior to the relevant interview though ultimately discussions often deviated from the set list of questions. In this way, I let the interviewee guide the direction of the conversation. If there was a point or idea that I wanted to probe, I tried to do so at a fitting, appropriate time. Lastly, the larger project that is documented in the book student, colle a gue, and friend in terviews (represented by the following protocols) were conducted retrospectively and were not used in my formal analysis or methodology. Merriex Family Protocol 1. What is your name and what is your relationship to Gloria? 2. When/where was Gloria born? 3. What w as she like as a child and young woman? 4. Tell me about her children and grandchildren. 5. What do you remember about her most from those days? 6. When did you know Gloria wanted to be a teacher? 7. What influenced and/or inspired her in her life and work? 8. What do yo u believe that her goals were? 9. 10. What do you want people to remember about Gloria? About her work? 11. What made Gloria so good at what she did? 12. Do you believe that Gloria would have done anything differently in the fu ture? 13. Who else should I interview for this project? Leanetta McNealy Protocol 1. What was your relationship to Gloria? How did this relationship come to be? 2.
211 3. work influential? If yes, in what ways and to whom? 4. What should people know about Gloria Jean Merriex and her work as a mathematics teacher? What should people know about Ms. Merriex as a person? 5. One thing that Gloria and I were beginning to discuss in d epth was the role of culture in her classroom. She always talked about relating to the students and playing many roles (mother, father, enemy, friend). Can you comment on this? a. devel opment classroom had an impact on this sort of identity development among students? b. What role do you believe communication played in her teaching? 6. Relationships (with children, parent s, administrators, aides, etc.) seemed to be another 7. Are there any anecdotes that you might be able to share that exemplify what made Gloria so special? 8. Who else should I interview for th is project? Buffy Bondy Protocol 1. Please tell me your name and tell me about your relationship with Gloria Merriex. What was your role at Duval Elementary School? 2. 3. Why were her teaching methods so successful? a. What else made her so successful? b. What evidence is there that she was successful? 4. a. in their development (i.e. cu ltural identity development, etc.)? b. Was communication important in her classroom? How? 5. 6. What can other teachers, administrators, and teacher educators learn from Gloria? 7. What were her relationships at school like? How did her personality help or hinder these relationships? 8. 9. What would you like people to remember about Gloria Merriex? 10. Is there anything el se that you wo uld like to share? Leonard Marshall and Lilliemarie Harvey Protocol 1. Please tell me your name and about your relationship with Gloria Merriex. How did your relationship develop? 2. 3. What evidenced her success? Why was she so successful? 4. What were her relationships at school like? 5. How did Gloria work with students of various levels? Can you provide an anecdote? 6. ial development?
212 7. What do you believe inspired her? 8. What did you learn from Gloria? What can others learn from Gloria? 9. What do you want people to remember about Gloria Merriex? 10. Is there anything else that stands out in your mind about Gloria and her work o r her life? Angela Terrell Protocol 1. Please tell me your name and about your relationship with Gloria Merriex. How did your relationship develop? 2. 3. What evidenced her success? Why was she so su ccessful? 4. Can you talk about your collaborative work with the math team? Why was this important (to students, the school)? 5. How was her involvement in the community influential in her teaching practice? 6. You have said before the you believe that Gloria inspired her students. How? What effect or effects did this have on the school and community? 7. What do you believe inspired her? 8. What did you learn from Gloria? What can others learn from Gloria? 9. What do you want people to remember about Gloria Merriex? 10. Is there anything else that stands out in your mind about Gloria and her work or her life? Former Student Protocol 1. Please tell me your name, where you currently attend school, and one special thing about yourself. 2. When did you have Ms. Merriex as a teacher? 3. Do you think that Ms. Merriex was a special teacher? Why or why not? 4. What do you remember about being in her classroom? Can you tell me a story about a day in her classroom? 5. How did being in Ms. Merri got to middle school in terms of your math abilities? 6. Did any of you travel with the math team? What was that like? 7. How did your experiences with Ms. Merriex help you as a mathematician? Do you fe el that she influenced you in any way? How? 8. do to help you learn? 9. When I am preparing teachers to come teach at Duval, what kinds of things should I tell them about you and your needs as learners? 10. What else would you like to tell me about Ms. Merriex? Former Student Parent (s) Protocol 1. Merriex as a teacher? 2. How did you know Gloria? 3. Do you fe accomplish this?
213 4. What stands out in your mind about Gloria Merriex? How was the community impacted by her work? 5. 6. What should people know about Gloria Jean Merriex and her work as a mathematics teacher? 7.
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BIOGRAPHICAL SKETCH Emily Peterek was born in Austin, Texas in 1979. She began her education at a public, neighborhood school about a mile from her childhood home in Austin. Emily attended seventh and eighth grades at Martin Junior High School, a public school in East Austin to which she and other neighborhood children were bused. It was here that Emily had her first, formative experiences w ith diversity and poverty. These experiences coupled with the fact that her father also wor interests about equity. In 1993, Emily began high school, attending Stephen F. Austin High, also a public school. She graduated from Austin High in 1997. In the fall of 19 97 Emily began college, attending Trinity University in San Antonio, Texas. Here she majored in mathematics, and entered the secondary education program as a sophomore. This education program requires that students obtain an undergraduate degree in a su bject area, but enrollment in the program requires undergraduate coursework and involvement in several practicum placements. The program culminates with a 5 th which students engage in a full time teaching internship and work towards certification. Emily graduated with a Bachelor of Arts in Mathematics in 2001, and a Master of Arts in Teaching in 2002. By the end of 2002, she was certi fied to teach sixth through twelfth grade mathematics and special education at all levels from kindergarten through twelfth grade. In 2002, Emily began her teaching career as an Algebra I teacher at Westside High School, a three year old public school in Houston, Texas. Though located in a middle class suburb, Westside was diverse in terms of ethnicity and socioeconomic status as students were bused from various areas of the city. This diversity was not reflected in the faculty; most teachers and adminis trators were white. Emily taught several Pre AP (Honors) Algebra I courses and several Prep (Regular) Algebra I courses during this first year. She noticed that her Pre AP courses were
mostly populated by white or Asian students, while most African Ameri can and Hispanic students were in the lower tracks. Moreover, of the students in her courses who were labeled ESE (Exceptional Student Education), 85 percent were African American. In her second and third years of teaching, Emily taught Pre AP and Prep A lgebra II courses. These tracking trends became even more evident and marked. In the fall of 2005, Emily left Westside and entered the doctoral program at The University of Florida (UF). As a student at UF, Emily was involved in a multitude of projects including teaching a mathematics methods course for pre service elementary school teachers, teaching a field based practicum course for pre service secondary mathematics teachers, working ical content knowledge, and developing a professional development model based on observations of a successful teacher in a high poverty school. Emily also became active in several professional organizations such as the National Council of Teachers of Math ematics, the American Educational Research Association, and the Association of Mathematics Teacher Educators, and has been a presenter at each of these Emily is interested in continuing her work in the areas of equit y and access in mathematics education. To this end, Emily would like to continue working with pre service and in service teachers in identifying successful models in schools with large populations of underserved students