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The positionality and power dynamics of high school math departments

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Content The Positionality and Power Dynamics of High School Math Departments Michael Watter Rossier School of Education University of Southern California A dissertation submitted to the faculty in partial fulfillment of the requirements for the degree of Doctor of Education May 2024 © Copyright by Michael Watter 2024 All Rights Reserved The Committee for Michael Watter certifies the approval of this Dissertation Dr. Rudolph Crew Dr. Wesley Smith Dr. David Cash, Committee Chair Rossier School of Education University of Southern California 2024 iv Abstract This study applies Critical Race Theory to develop an awareness of the positionality and power dynamics that exists among the math faculty at schools that serve high income and low-income communities to develop an understanding of the learning gap that exists among Southern California’s marginalized student populations. The purpose of this study is to uncover underlying biases and assumptions of the math faculty and understand how they describe their work with students, with each other, and with the content they teach. Also, the study looks to uncover what the perceptions of the math department are that exist among the school community. Additionally, it seeks to find out if math teachers believe there needs to be a change in how mathematics is taught and what evidence they have to support that belief. Qualitative data was gathered using interviews and observations at three different Southern California high schools to understand trends and commonalities. One school was populated by students from a high-income community, and two school were populated by students from low-income communities. The interviews were conducted with an administrator, math department head, math department member, and the department chair of another subject at each school site. The observations were of math department meetings at each school site. Findings show that data driven discussions need to be more present during departmental meetings. Strategies to develop cultural awareness and understanding towards students need to be developed. Collaboration and accountability need to be developed in departmental and schoolwide pursuits. This study begins to understand how math teachers perceive their roles as educators and offers suggestions to create a collaborative structure and improved student outcomes. v Dedication To Jacqueline, my wife. Thank you for supporting me more than I ever thought possible. I love you so much. To Levi and Jayden, my son and my nephew, may education create only opportunities for all your dreams to come true. To Emily, my younger sister, thank you for being the strongest person I know and giving me someone to always look up to. To Laurie, my mother, thank you for always staying up late with me to finish a project and pushing me to do my best work. To Daniel, my father, thank you for setting the example of everything that a father should be and allowing me to follow in your footsteps. I love you all and I hope that I continue to make you proud. vi Acknowledgments Eight years ago, earning a doctoral degree never seemed possible to me, but the life I have never seemed possible to me, either. Then, I met my wife, Jacqueline, and now anything seems possible. There are many people that I need to thank for helping and supporting me along this journey, but I know that none of this would be possible without her. Over the past three years, Jacqueline has encouraged me, supported me, and pushed me to accomplish this feat. Along the way, she managed to complete our family and bring us our son, Levi, as well. With the two of them in my life, I have experienced love and motivation like never before. I love you both. Additionally, I need to acknowledge my parents, who were my first teachers. They set an example for me of what hard work looks like, why education is important, and how to lead with love. I have learned everything from you two and have truly valued your guidance for 40 years – even if I have pushed back for 25 years. Education has always been important in my family from my grandparents, aunts and uncles, and cousins. I come from a family of educators, and I am proud to continue the tradition. I also must acknowledge my sister, who continues to strive and further her education, as well. It is inspiring to see her push for more and instill the same values in her son, Jayden. Getting through the last three years would have been a completely different experience was it not for my cohort. I have learned so much from their experiences and had the opportunity to engage in true collaboration with them. They pushed me to grow and build my capacity as an educational leader. I need to truly acknowledge Rudy, Janette, Alma, Kamale, and Kim who were constants throughout this entire process. I cannot wait to continue working with you all on the other side of this. vii Lastly, I need to thank Dr. Cash, Dr. Smith, and Dr. Crew for all your guidance through this process. You have brought insight and given advice throughout my research. Thank you for all of your support and resources to help me reach the end, and of course…FIGHT ON! viii Table of Contents Abstract.......................................................................................................................................... iv Dedication....................................................................................................................................... v Acknowledgments.......................................................................................................................... vi Table of Contents.........................................................................................................................viii List of Tables ................................................................................................................................ xii Chapter One: Overview of the Study.............................................................................................. 1 Introduction......................................................................................................................... 1 Background of the Problem ................................................................................................ 3 Statement of the Problem.................................................................................................... 4 Purpose of the Study ........................................................................................................... 5 Research Questions............................................................................................................. 5 Significance of the Study .................................................................................................... 6 Limitations and Delimitations of the Study........................................................................ 6 Definition of Terms............................................................................................................. 6 Organization of the Study ................................................................................................... 8 Chapter Two: Review of the Literature .......................................................................................... 9 The Power of Math Education ............................................................................................ 9 District Zoning.................................................................................................................. 15 Equitable Teaching ........................................................................................................... 20 Effective Collaboration..................................................................................................... 25 Conclusion ........................................................................................................................ 28 Chapter Three: Methodology........................................................................................................ 31 ix Statement of the Problem.................................................................................................. 31 Purpose of the Study ......................................................................................................... 31 Research Questions........................................................................................................... 32 Sample and Population ..................................................................................................... 32 Design Summary............................................................................................................... 33 Methodology..................................................................................................................... 34 Instrumentation ................................................................................................................. 35 Data Collection ................................................................................................................. 36 Data Analysis.................................................................................................................... 37 Trustworthiness and Credibility........................................................................................ 38 Reliability and Validity..................................................................................................... 38 Researcher Positionality.................................................................................................... 39 Summary........................................................................................................................... 40 Chapter Four: Results ................................................................................................................... 41 Participants........................................................................................................................ 41 Observation Data .............................................................................................................. 42 Results Research Question One ........................................................................................ 44 Discussion Research Question One .................................................................................. 50 Results Research Question Two ....................................................................................... 51 Discussion Research Question Two.................................................................................. 55 Results Research Question Three ..................................................................................... 56 Discussion Research Question Three................................................................................ 66 Summary........................................................................................................................... 66 x Chapter Five: Recommendations.................................................................................................. 69 Discussion of Findings...................................................................................................... 70 Limitations........................................................................................................................ 78 Implications for Practice ................................................................................................... 79 Future Research ................................................................................................................ 82 Conclusions....................................................................................................................... 83 References..................................................................................................................................... 85 Appendix A: Research Introduction Letter................................................................................... 98 Appendix B: Recruitment Letter (Teacher Interview).................................................................. 99 Appendix C: Recruitment Letter (Math Department Chair)....................................................... 100 Appendix D: Observation Protocol............................................................................................. 101 Appendix E: Interview Protocol (Math Teacher / Department Chair) ....................................... 103 Introduction..................................................................................................................... 103 Questions (with transitions)............................................................................................ 104 Closing ............................................................................................................................ 106 Appendix F: Interview Protocol (Other Department Chair)....................................................... 107 Introduction..................................................................................................................... 107 Questions (with transitions)............................................................................................ 108 Closing ............................................................................................................................ 110 Appendix G: Interview Protocol (Administrator)....................................................................... 111 Introduction..................................................................................................................... 111 Questions (with transitions)............................................................................................ 112 Closing ............................................................................................................................ 114 xi Appendix H: Informed Consent Form........................................................................................ 115 Appendix I: Conceptual Framework........................................................................................... 117 xii List of Tables Table 1: Interview and Observation Selection Criteria for High School Site Participants 33 Table 2: Research Question and Data Collection Method 35 Table 3: Participant and School Site Information (as of 2023) 42 Table 4: Median Household Incomes (as of 2020) 57 Table 5: Bayside High School CAASP and Demographic Data 59 1 Chapter One: Overview of the Study Introduction Math teachers can have an exceptional footprint on a student’s educational experience. All teachers have an opportunity to make an impact on a student’s life, but the influence and weight that educational success in mathematics has on a student’s achievement after graduation gives math teachers power among the school community. Wrong (1995) defines power as “the capacity of some persons to produce intended and foreseen effects on others (as cited in Domhoff, 1995).” Math teachers have the power to determine a student’s journey through school before they even enter high school. If a teacher perceives a student to have exceptional mathematical ability, they can promote students into Algebra during middle school. This perpetuates the classist system of tracking (Langston, 1988) without labeling it. A select group of students may have a perceived advantage over other students, because they are entering high school ahead of their peers. The ability to determine which students are allowed access to an advantage demonstrates Domhoff’s (1995) third axiom of power, where “leaders can stay in power by favoring some followers and punishing others.” The progression of some subject courses is dependent on a student’s grade level, but mathematics is dependent on a student’s perceived ability. Algebra plays a significant role as gatekeeper to the more advanced study in mathematics because of the belief that not everyone can be successful in the subject (NCSM & TODOS, 2016). “But because of how access to - the learning of - algebra was organized in the industrial era, its place in society under the old jurisdiction, it has become not a barrier to college entrance, but a barrier to citizenship (Moses & Cobb, 2002, p. 26).” Algebra 1 is the only official math class that is required to gain a high 2 school diploma (California Department of Education, 2021). Students that have been elevated to this class in middle school can enter high school already passing the requirement of Algebra 1. A comparison of the California Department of Education’s High School Graduation requirements and the A through G requirements for admittance to a University of California or California State University supports Ladson-Billings’ (2021) statement of, “although the ‘average’ American was thought to only need a rudimentary knowledge of mathematics (i.e., arithmetic), those who would be leaders and innovators would need knowledge and facility in advanced mathematics (p. 4).” In order to graduate high school, the state of California requires students to pass at least two years of mathematics courses. However, in order to qualify for admittance to an undergraduate education, students must pass three years of mathematics with a recommendation of four. To give a student the best chance of transitioning directly into a university from high school, they must pass two additional years of mathematics. All other courses have a difference of one year in their expectations (California Department of Education, 2021). Students that are good at math and put into advanced classes are viewed as academically elite, creating the “gatekeeper” status of mathematics. By playing the role of “gatekeeper”, mathematical ability has expanded its reach into the world and created a hierarchy among individuals that possess knowledge of its content. The mathematical achievement of students goes beyond individual experiences, though, as it affects the entire school community. In California, schools are evaluated on various factors, but the only academic classes highlighted are Math and English, so having strong mathematical performance is beneficial to the school’s rating (California School Dashboard). The higher rating that a school has, the more desirable it is to attend. “While wealthy families can choose affluent neighborhoods with good schools before going through the formal choice process, low-income 3 families are shut out of such residential choice (Hanushek et al, 2023. A severe drop in enrollment leaves the schools serving our marginalized student population at risk of closure (Bonta, 2023). Background of the Problem According to the California Assessment of Student Performance and Progress (CAASPP), high school students are struggling in mathematics. In the 2018-19 school year, there was a large gap in the number of Asian (70.4%), White (44.6%), and Filipino (50.9%) students scoring “Standard Met” or “Standard Exceeding” in comparison to the American Indian or Alaska Native (18.75%), Black or African American (14.27%), Hispanic or Latino (20.27%), and Native Hawaiian or Pacific Islander (25.57%) students (California Department of Education). Additionally, the demographic representation of math teachers in comparison to the student population of California is not representative of the students in the classroom. White teachers comprise 61% of the staff, but only 22% of the student population is white (California Department of Education). Our marginalized student population is struggling in math, but it is hard to believe in yourself when you do not see yourself reflected in school leadership. In the California public schools, 55% of the student population is Hispanic or Latino, 9.5% is Asian, and 5% is Black or African American and 21.5% of the teacher population is Hispanic or Latino, 5.7% are Asian, and 4% of the population is Black or African American (California Department of Education). Despite efforts to increase diversity in the teaching workforce, California does not seem to forecast much of a change in the demographics of math teachers. In the 2019-20 school year, only 5 African American teaching candidates and 47 Hispanic American candidates passed the CSET for Mathematics. Meanwhile, 109 White candidates passed, with a rate of 49.3%. African American candidates had a 23.8% passing rate 4 and Hispanic Americans had a 30.7%. Even though this was during the pandemic and numbers were low, from 2015-2020, African Americans had just 50 passing scores with a 30.1% passing rate and Hispanic Americans had 383 passing scores with a 44.1% passing rate. With 825 passing scores from White candidates and a 55.8% passing rate, the diversity of the math educators in California looks to remain steady (Commission on Teacher Credentialing). Utt and Tochluck (2020) discuss that very few teachers in urban school districts are from the communities that they teach in, and, as a result, a culture of White supremacy dominates the public school system in the United States. According to Lopez (2003), educators must “be prepared to work with individuals who are culturally different and help create learning environments that foster respect, tolerance, and intercultural understanding (p. 71).” In order to create an equitable learning environment and opportunities for success among the marginalized student populations, teachers must confront their own biases and develop a culture of understanding with their student population. Using a Critical Race Theory framework, this research study will conduct observations of department meetings and interviews of the school community to develop an awareness of the positionality and power dynamics that exists among the math faculty at schools that serve high income, middle income, and low-income communities in order to develop an understanding of the learning gap that exists among California’s marginalized student populations. Statement of the Problem The lack of diverse representation among teachers in math education is detrimental to the self-efficacy of non-white students. According to Wang et al. (2020) students that have negative experiences and social interactions in math classrooms are likely to develop math anxiety. According to the California Department of Education, 88% of the students in California are 5 nonwhite. However, between 2015 and 2020, only 23% of the teachers being credentialed in Foundational-Level Mathematics demographically identify as African American or Hispanic American (California Teaching Commission). The high school system is designed as a four-year program. Statistically, that means our Black and Brown students have less than a one in four chance of seeing themselves represented as an expert in math. That precedent sets a negative perception for the development of their identity in mathematics. This study will examine the conversations around students and student achievement in mathematics that exist among faculty to understand if there is a relationship to mathematical achievement among students. Purpose of the Study The purpose of this study is to uncover underlying biases and assumptions of the math faculty in relation to the students they teach. Through qualitative research, using interviews and observation, this study aims to understand the perceptions of mathematics. Interviews and observations will be conducted at three different high schools to understand trends and commonalities. One school will be high income and the other two schools will be low income. Interviews will also be conducted with members of the administration and department heads of other subjects to further understand the perceptions of mathematics at the school community. Research Questions The following research questions were used to guide this study: 1. During high school math department meetings, how do math teachers describe their work with students, with each other and with the content? 2. What are the perceptions of the math department that exist among the school community? 3. Do high school math teachers believe there needs to be a change in how mathematics is taught and what evidence do they have to support that belief? 6 This study uses a Critical Race Theory framework to explore the impact that the perceptions, biases, and immunities to change of math teachers has on a student’s educational journey. “Critical race methodology in education offers a way to understand the experiences of people of color along the educational pipeline. Such a methodology generates knowledge by looking to those who have been epistemologically marginalized, silenced, and disempowered (Solorzano & Yosso, 2002, p. 36).” If we are able to uncover biases and create understanding of our student population, we can lead to better outcomes for the students we serve. Significance of the Study This research study will provide insight into the attitudes, perceptions, and biases that exist among math education among the school community and develop an understanding of the causes of the achievement gap in math education. Limitations and Delimitations of the Study This study was limited to three public high schools in Los Angeles County in California, their math department’s openness to conduct department meetings under observation, and individual willingness to be interviewed. Interview questions related to math curriculum in the school are limited to the research participants’ epistemology. The delimitations of this study were limited to the teachers’ grade level taught (high school), geographic region (California), the school type (public) and the number of participants surveyed and interviewed. Definition of Terms Achievement Gap: The disparities in standardized test scores between the marginalized and white student populations (Ladson-Billings, 2006). 7 Anti-racism: The recognition of “racism as an institutionalized system of racial inequality that benefits White people (p. 127)” and seeking to interrupt this system (Utt and Tochluck, 2020). Defensiveness: The preventative response to new or challenging ideas that make it difficult to bring new ideas or ways of thinking to the group (Jones & Okun, 2001). Education Debt: According to Gloria Ladson-Billings (2006), the education debt is a “debt that has accumulated over time. This debt comprises historical, economic, sociopolitical, and moral components (p. 1).” Gatekeeper: A preventative measure that grants access to certain opportunities (Moses & Cobb, 2002). Immunity to Change: The unconscious resistance to making the change people desire. It can exist as an individual or as a collective group (Kegan & Lahey, 2009). Individualism: The isolation that results from lack of experience or comfort from working as a team that leads to a lack of accountability (Jones & Okun, 2001). Marginalization: “Relegation to or placement in an unimportant or a depowered position in society (APA, 2017a, as cited in APA, 2021, p. 4).” Math Anxiety: The “feelings of worry, tension, and fear that individuals experience when they anticipate or engage in mathematics activities (Wang, et al., 2020, p. 1).” Paternalism: An individual feels they are capable of making decisions for and in the interests of those without power (Jones & Okun, 2001). Positionality: According to Villaverde (2008), positionality is “how one is situated through the intersection of power and the politics of gender, race, class, sexuality, ethnicity, culture, language, and other social factors (p. 10, as cited in Douglas & Nganga, 2013, p. 60) 8 Power Hoarding: The response when anyone feels threatened from suggestions of change. “Those with power assume they have the best interests of the organization at heart and assume those wanting change are ill-informed (stupid), emotional, inexperienced (Jones & Okun, 2001, p. 5).” Unconscious Bias: aka implicit bias “refers to unconscious and automatic attitudes or stereotypes that effect our understanding, actions, and decision-making in daily life (Neitzel, 2018, p. 233).” White Supremacy: The systemic maintenance of the ideology of whiteness (Picower, 2009) Organization of the Study The Positionality and Power Dynamics of High School Math Departments is organized into five chapters. Chapter 1 presents an overview of the study, provides context to the urgency of uncovering the perceptions and biases of math teachers, and includes definitions of terms used in this study. Chapter 2 consists of a literature review in the following areas: credentialing process of teachers, the history of math education in school, equitable teaching strategies, and effective collaboration strategies. Chapter 3 describes the methodology selected for this research study and includes: sample and population selection, interview questions, data collection, and data analysis. Chapter 4 is a report of the research findings. Chapter 5 is composed of a summary of findings, implications for practice, conclusions and recommendations. References and appendices are included in the conclusion of this research study. 9 Chapter Two: Review of the Literature Being a member of a high school math department ingrains a teacher into the school community, as they are teaching one of the core subjects of a student’s educational journey. However, it is important to understand the positionality of the members of this department, because of the power and influence it holds over the school community. The math curriculum holds a disproportionate amount of weight over a student’s future educational pursuits, despite being only one class in a student’s schedule. Understanding this is beneficial to generating an equitable learning experience for students. This chapter, will review the power of math education in order to understand its role as a gatekeeper and its propensity to track students during their schooling. Then, it will address equitable teaching practices to see how teachers motivate students, and develop an understanding of their marginalized students. Next, will be an analysis of the lasting impact redlining had on school districts and creating funding inequities. Finally, there will be an analysis of developing a collaborative culture among individuals that are resistant to change. The Power of Math Education Math is the universal language. This is a belief that is widely accepted among our population. However, when the achievement scores of students in mathematics are broken down by demographics, the language does not seem to be universally acquired. In the 2018-19 school year, the year before the COVID-19 pandemic, only 18.75% of American Indian or Alaska Native, 14.27% of Black or African American, 20.27% of Hispanic or Latino, and 25.57% of Native Hawaiian or Pacific Islander students scored “Standard Met” or “Standard Exceeding” on the California Assessment of Student Performance and Progress (CAASPP). This is a large difference from the scores of the Asian (70.4%), Filipino (50.92%), and White (44.6%) student 10 populations (California Department of Education). When the California Common Core State Standards: Mathematics had been implemented, the goal was “to ensure universal access to highquality curriculum and instruction so that all students are college and career ready (Mathematics Framework for California Public Schools, K-12, 2015, p.28).” However, ten years after the new standards were adopted, there continues to be disproportionate results in achievement. In high school, a student’s math teacher has the power to not only influence their educational experience, but the trajectory of their life after high school. According to Wrong (1995), “power is the capacity of some persons to produce intended and foreseen effect on others (as cited in Domhoff, 2005, p. 1).” There is an expectation that in order to be purposeful people understand mathematics, and leaders and innovators understand advanced mathematics (LadsonBillings, 2021). However, many careers in this modern world do not require a knowledge of all the standards of our current math curriculum, yet a students’ perceived mathematical ability allows them to be given access to educational opportunities that lead to future success. This power of access inadvertently gives math teachers the unofficial role of “gatekeeper” among their students. Math as a Gatekeeper Mathematics has been deemed a “gatekeeper” because of the belief that if you do not do well in math, then you will not be successful later in life (NCSM and TODOS, 2016). Moses & Cobb (2002) compared people that are unable to do well in math to the people in the industrial age that cannot read or write. This belief is supported by the current California State University (CSU) requirements for admittance. Currently, the CSU system requires three years of mathematics for admission to undergraduate studies, an expectation that only 60% of California high school graduates are meeting (Smith, 2022). Additionally, the California state exams 11 “showed two out of three students did not meet state math standards, including 84% of Black, and 79% of Latino and low-income students (Smith, 2022).” With the subject of mathematics being an institutionally sanctioned gatekeeper to further education (NCSM & TODOS, 2016), math educators have a stake in helping to achieve equitable social outcomes (Ladson-Billings, 2021). To raise the achievement scores of non-white students, educators have a responsibility to make mathematics more accessible to their students of color. Traditionally, math education has been used to train an elite few (Moses & Cobb, 2002), but incorporating antiracist teaching in math classes can empower the historically marginalized student voice (Battey & Coleman, 2021). “By making the mathematics relevant to students’ lived experiences and analyzing their own community’s data, students are encouraged to continue taking mathematics and using it for their own purposes. The goal is not to make all students mathematicians, but it is to give them access to consciously use mathematics in their lives as a form of socially transformative participation (Battey & Coleman, 2021, p. 19).” More than likely, math teachers were students that excelled at math in high school, but the traditional model does not work for all. Math teachers and leaders must reflect on their own privileges and challenges in their personal histories (NCSM & TODOS, 2016), and work to build an understanding of their minoritized students. Accelerated / Advanced Classes Students enrolling in accelerated and advanced math classes are placed into an elite group of students, but the opportunities to participate in these classes comes with much bias. To participate in the class, students need to have good grades from their previous math courses and, often, the support or recommendation of a math teacher. According to Malcom Gladwell (2019), 12 the American education system rewards a certain kind of thinking that does not necessarily represent what you know, just how quickly you can recall information. Students that present as quick thinkers and meet the teacher’s unconscious biases will receive these recommendations. For Black and Latinx students, their teachers are a primary source of motivation for them to participate in accelerated math courses, however, “talking to a favorite teacher significantly lowers the likelihood of getting on the advanced track in ninth grade for black Latinxs (Irizarry, 2021).” Accelerated math courses are designed to get students through the high school math curriculum quickly so that they can reach college level math classes before they graduate. Students that can participate in these classes have privileged opportunities after high school, as this provides an opportunity to enroll at college with already earned credits. Additionally, there is a correlation between student’s math achievement and their decision to enter STEM fields (Bi et al, 2022). However, students that are enrolled in these classes also have a decline in their selfefficacy (Bi et al, 2022). Self-efficacies are developed form prior accomplishments, feedback from peers, teachers, and parents, and perceptions of where an individual compares to another (Bi et al, 2022). According to Irizarry (2021), black and Latinx students they are less likely to remain in the accelerated track in comparison to their white peers. Teachers can promote opportunities for success among their African American and Latinx students, but they need to understand any unconscious biases they may hold and the power they have over their students’ self-efficacy. Preparation for Future Having an acclivity in mathematical skill and knowledge not only creates opportunities for enrollment in college, but also for career opportunities. Careers in the STEM field, like data 13 science, are among the fastest growing employment ventures. However, currently students are not getting the proper exposure to these pathways in high school. Despite the increased demand for data literacy in the workforce, math teachers have put less emphasis on data analysis, opting to deliver lessons only from the essential standards (Schwartz, 2023). Additionally, in Black, Latinx, and low-income schools, where there is a lack of qualified math teachers, giving them inequitable opportunities for course completion (Agrawal, 2019). The lack of qualified teachers and quality instruction is creating an inequity among our student in math education. Teacher Shortage There is a shortage of credentialed teachers in the STEM field (Agrawal, 2019), especially in the K-12 schools that serve Black, Latinx, and low-income students (Smith, 2022). It is difficult to find teachers with mathematics backgrounds because other job opportunities can offer higher compensation (Sutcher, 2019). In the 2019-20 school year, 770 prospective teachers passed the English CSET in comparison to the 254 that passed the Math CSET (Commission on Teacher Credentialing). According to these numbers, there are three times more English teachers than Math teachers entering the workforce each year, meaning that the shortage of math teachers is going to continue. This is another area where there is power in being a math teacher. Under the “Who Benefits?” power indicator, possessing something of value creates power. Having a shortage of credentialed math teachers creates a level of power in the school community. Diversity in STEM Teaching Not only is there a critical need for more qualified math teachers, but there is also a need for more diversity in math and science teachers (Smith, 2022). According to the Commission on Teacher Credentialing (CTC), almost 50% of the teachers that earn their mathematics teaching credential are white. Additionally, between 2015 and 2020, only 23% of the teachers being 14 credentialed in Foundational-Level Mathematics demographically identify as African American or Hispanic American. Math teachers, the majority of which are white, “benefit from institutional racism irrespective of whether they are consciously aware of or actively support racist attitudes/practices/policies (Jayakumar et al., 2009, p. 555).” The lack of diversity among math educators in K-12 schooling creates a distributive power over the school that leads “to extreme hierarchy and social stratification (Domhoff, 2005, p. 1).” Maintaining the status quo of our current math curriculum and the lack of diversity among math teachers promotes settler futurity (Tuck & Gaztambide-Fernandez, 2013), because having a Black teacher increases the likelihood of going to college for Black high school students (Love, 2019). “Dark children need teachers who not only look like them, but who are engaged in an active, antiracist orientation (Love, 2019, p. 54).” For White teachers to engage in antiracist teaching, as well, they must reflect and understand their unconscious biases of their nonwhite students’ culture and background as preventative measures for success in school (Kumar et al, 2018). The experience a student has in mathematics can have a direct impact on their life. Therefore, it is imperative that our schools use this power to elevate the outcomes of our marginalized students, instead of maintaining the status quo. Current teachers need to develop an understanding of themselves, their positionality, and their students. Also, efforts must be made to make the curriculum relevant and engaging to students, so that they can access the material. Finally, it is crucial that initiatives to diversify the workforce for math teachers are implemented. Our schools have been using the same curriculum and pedagogy for mathematics for years without seeing any improvement in student outcomes. In order to improve the opportunities available to our Black and Latinx students, there needs to be an overhaul in the system. 15 District Zoning In 1954, Brown v. Board of Education ended segregation and set the expectation that public schools were to provide an equal educational experience for all children (Ravitch, 2021). However, seventy years later, forms of segregation still exist, creating inequitable outcomes in education. Although legally the public school system is designed to create the same opportunities for all students, there are historical circumstances that have created an educational debt in our country. Ladson-Billings (2006), who developed the concept of education debt, described these circumstances as “the historical, economic, sociopolitical, and moral decisions and policies that characterize our society (p. 5).” The policies in place that hinder the advancement of our marginalized demographics, manifests into “distrust and suspicion about what schools can and will do in communities serving the poor and children of color (Ladson-Billings, 2006, p. 9).” Urban school is a term unfairly applied to schools in a negative fashion, claiming to house unmotivated students and uninvolved parents regardless (Massey et al, 2014). However, the use of this term “conveniently subverts the focus on race because it fails to acknowledge the economic and societal inequities that produce systemic problems, such as increased dropout rates and high teacher turnover (Massey et al, 2014, p. 176).” There is a litany of policies and societal norms that produce these issues. Among the policies are redlining, funding inequities, and open enrollment. This section will investigate these issues and address the impact they have on student outcomes in public education. Redlining - (History of District Zoning) In the 1920s and 30s, during the New Deal era, the government outlined areas on maps – primarily areas with large populations of Black inhabitants – in red ink that they deemed were not worthy of inclusion in their new homeownership program (Legal Information Institute). This 16 practice came to be known as redlining, or “the practice of systematically denying various services (e.g., credit access) to specific neighborhoods, often based on race/ethnicity and primarily within urban communities (Egede et al, 2023, p. 1534).” Although redlining became illegal with the Fair Housing Act in 1968 (Nelson et al, 2023), it was during this time that the residential shift known as “White flight” occurred, as middle-class and white families began moving to the suburbs and leaving schools to address the needs of a mostly minority population (Massey et al, 2014). Almost 100 years later, the long-term effects and patterns of systemic racism are still around (Nelson et al, 2023). The “White flight” had immediate effects on the now integrated public schools. Historically, a significant portion of school revenue used to be derived from property taxes, so when white families moved to more suburban areas, families of color were left in schools with little funding (Pearcy, 2020). In addition to families moving away, districts struggled to keep staff. High-poverty and high-minority schools have the nation’s lowest teacher retention rates, and the lack of prepared teachers has affected the quality of education received in urban schools (Massey et al, 2014). Over time, deficit perspectives on urban students and education began to normalize, leading the “failure” of urban education (Massey et al, 2014). California is no exception. According to Pearcy (2020), “the most segregated states for public schools include southern states like Georgia, Mississippi, and Alabama, but topping the list are New York and California (p 47).” Currently, there are policies in place to try and create more equitable funding among the districts in California, but the debt has much to overcome. Funding Inequities According to research, there is a correlation between student achievement and the average income of the families enrolled in the school (Pearcy, 2020). This is likely because the 17 wealthier a family is, the more resources they can afford to support their child’s education. Additionally, historically, being able to live in a higher priced community, meant that the local schools would receive more funding. “Although the federal government kicks in a small portion, schools are financed primarily by local and state taxes, so the wealth of the community you live in will determine how well resourced your local schools are (McGhee, 2021, p. 179).” However, this is not necessarily the case in California, because in 1978 Proposition 13 was passed to limit property taxes at 1percent of the property’s purchase price. After this was passed, California went from the our country’s national leader in school funding to forty-first (McGhee, 2021). After Proposition 13 and Serrano v. Priest (I, II, and IIII), Proposition 98 was passed in 1988 to set the priorities of how the state would fund students attending primary school, secondary school, and community college. However, these decisions mostly allocated funding on a per pupil basis and did not factor in poverty levels (Rose, 2022). So, in an effort to enact school finance reform, California developed the Local Control Funding Formula (LCFF) in 2013-24 to increase funding for high-need students (Lafortune, 2019). Through LCFF, districts receive grants based on their number of high-need students (Lafortune, 2019), by factoring in grade level, participation in the free and reduced lunch program, English Learner status, and foster youths (Rose, 2022). With LCFF, districts receive the required amount to run a school, regardless of property taxes (Knight et al, 2022). LCFF has increased the per pupil state spending on students in districts with high poverty rates (Rose, 2022). Now, high-poverty districts receive 74% of their funding from California, while low poverty districts receive 37% (Knight, 2022). However, most of the funding has gone towards salaries and benefits of the staff, leaving only 25% to be spent on non-compensation categories (Rose, 2022). Since most of the funding goes to staffing needs, by filling these roles, 18 low-income schools have become staffed with more less experienced teachers (Lafortune, 2019), that usually have lower average salaries because of their lack of experience (Duplain et al, 2022). This creates not only a “salary gap” among districts, but an “experience gap” among the affluent and low-income schools. Research shows that targeted school funding on teacher quality has a measurable difference in student achievement (Duplain, 2022). The policies over funding facilities have created an inequitable outcome, as well (Rivera, 2018). According to Naqvi (2015), “…the existing program fails to treat school facility costs as an ongoing expense despite the recurring nature of facility needs, allows disparities based on school district property wealth, fails to target funding according to greatest need, results in excessive administrative complexity, and lacks adequate accountability mechanisms (p. 1 as cited in Rivera, 2018, p. 705).” According to research, in addition to teacher quality, safe and secure facilities enhance student achievement (Duplain et al, 2022). Since most of the state funding goes towards teacher salaries, to improve facilities, school districts need to pass bonds. Passing bonds is a way to utilize property taxes, because when voters approve a bond measure, they are agreeing to repay the bond through the necessary property taxes (Rivera, 2018). Levying local property taxes and the requirement of voters, “can lead to increasingly inequitable outcomes as districts in communities with supportive voters can pass bond after bond, raising large quantities of funding from their local taxpayers and from state matching funds, while other school districts fail to capture either state or local taxes (Rivera, 2018, p. 728).” Having a modernized, safe, and welcoming school campus creates an appealing facility for families to attend. Open Enrollment – Interdistrict / Intradistrict Enrollment 19 Open enrollment, also known as school choice, is a policy that allows students to attend a public school that is not the one designated to them by their home address (Brasington, 2014). The argument in favor of open enrollment is that it empowers parents and students to choose the school that best fits their academic needs, and it incentivizes schools to allocate funds in a manor to improve student achievement (Rothbart, 2020). However, school choice actually promotes greater social stratification and has not been shown to improve student achievement (Phillips, 2015). Open enrollment policies can increase segregation because of the tendencies of parents to choose schools based on class and racial composition in addition to academic standing (Prins, 2007). “White flight, vouchers, school choice, tracking, and advanced, honors, and gifted programs are the new mechanisms of exclusion, facilitating the withdrawal of resources from poor and minority schools (Prins, 2007, p. 289).” Additionally, the neutral, colorblind policies of school choice have discriminatory effects, especially on Latinx families – limited ability or availability because of workloads, work schedules, limited transportation, social networks not being made aware of the policy, or translation barriers (Prins, 2007). Through open enrollment, the wealthier, higher performing schools are taking resources and students from the poorer, lower performing schools. As a society, we need to establish policies and procedures to put resources back into our struggling schools. With private schools, charter schools, and school choice policies, there is a lot of competition for the local public schools. The education debt that Ladson-Billings (2006) describes, establishes that our “urban schools” are starting each year with a deficit in comparison to the wealthier, higher-performing schools. As the lower income schools continue to struggle to match the wealthier schools, the debt will continue to grow. This debt will not be repaid if 20 colorblind policies continue to exist. Educational leaders and policymakers must acknowledge this debt and work towards clearing it. Equitable Teaching A teacher’s job is to facilitate instruction and empower students to reach their full potential. Since every student is a unique individual, a teacher is expected to differentiate their instruction, or tailor learning activities to the individual needs of each student (Schunk, 2020). Differentiation is one way that a teacher can achieve equitable outcomes in their classroom. “Equity is achieved by raising the performance of all students and eliminating the predictability and disproportionality of student outcomes based on race, ethnicity, socioeconomic class, housing patterns, gender, home language, nation or origin, special needs, and other student characteristics (Roegman et al, 2019 p. 7).” Teaching for equity has become a critical component of education, as currently students of color that have family incomes comparable to white students, still have an achievement gap (Ladson-Billings, 2006). Through equitable practices, teachers build the capacity of all students. During teacher preparation programs, aspiring educators are exposed to the six Teaching Performance Expectations (TPEs). The TPEs are: Engaging and Supporting All Students in Learning, Creating and Maintaining Effective Environments for Student Learning, Understanding and Organizing Subject Matter for Student Learning, Planning Instruction and Designing Learning Experiences for All Students, Assessing Student Learning, and Developing as a Professional Educator (California Commission on Teacher Credentialing). When implementing these practices, teachers are not only able to build the capacity of their students, but they are able to build their own capacity as an educator. Embedded into these practices are concepts focusing on motivation and learning, assessment, and cultural understanding. This 21 section will demonstrate how implementing proper motivation and learning, assessment, and cultural understanding into instruction will lead to designing educational equity among math teachers. Learning and Motivation Achievement motivation theory says that students will not attempt or quit on an academic task if it is perceived as too difficult, but lowering the difficulty of the task and making it too easy will lead to lead to boredom (Schunk, 2020). Math anxiety, a negative response when having to solve math problems, affects students at all grade levels (Samuel & Warner, 2021). This is why being an effective teacher is integral to the development of student interest and engagement (Sinatra et al, 2017). “Lowering the fear of failure and raising hope for success enhance motivation, which can be done by conveying positive expectations for learning to students and by structuring tasks so students can successfully complete them with reasonable effort (Schunk, 2020, p. 374).” A student is motivated to learn a topic when they find interest and value in the content (Heddy et al, 2016), so it is a responsibility of the teacher to generate interest in the topic for students. Too often in math classes, students ask the question, “when are we ever going to use this?” However, building up the self-efficacy of students leads to greater interest and motivation in a subject (Sakellariou & Fang, 2021). If a math teacher can increase their students’ confidence in mathematics and make the material relatable, they will see an increase in motivation and learning. There is a correlation between self-efficacy and motivation. According to Rueda (2011), “individuals with higher self-efficacy, greater belief in their own competence, and higher expectancies for positive outcomes will be more motivated to engage in, persist at, and work hard at a task or activity (p. 41).” Increasing a student’s self-efficacy can reduce the negative 22 impact of math anxiety (Samuel & Warner, 2021). Through a humanistic teaching approach, teachers can develop self-efficacy in their students (Schunk, 2020). Humanistic teaching takes a holistic approach to dealing with students as individuals and understanding their perspective (Schunk, 2020). This approach requires teachers to: • “Show positive regard for students. • Separate students from their actions. • Encourage personal growth by providing students with choices and opportunities. • Facilitate learning by providing resources and encouragement (Schunk, 2020, p. 370).” Too often, this approach to teaching is overlooked, and teachers label their students as unmotivated. However, when a teacher disregards a student and labels them as unmotivated, the teacher needs to adopt a humanistic approach and realize that the student may be motivated by different objectives than what the teacher is motivated by (Rueda, 2011). Teachers are highly influential in generating interest and creating value, but teachers need to be motivated, as well. This is especially concerning among math teachers, as math scores always have a spotlight on them. In California, students perform worse on state testing than they do in English, with 65% of students not meeting standard in comparison to 53% (CA Dept of Education). During the pandemic, teachers were most concerned about their students falling behind in math, as our country has grown more dependent on mathematics for technology development and utilizing data to solve problems (Education Week, 2020). The same motivational principles that apply to students apply to teachers (Rueda, 2011), and negative teacher emotions and reactions lead to student disengagement and loss of interest (Sinatra et al, 2017). Consistently scoring low on tests will not only effect student motivation, but teacher motivation, as well. 23 Assessments The goal of assessment is to allow students the opportunity to demonstrate their knowledge, so the teacher can determine what was learned (Mayer, 2011) and offer clear feedback (Boaler, 2016). However, “most systems of assessment in U.S. classrooms do the opposite, communicating information to students that causes many of them to think they are a failure and they can never learn math (Boaler, 2016) p. 144).” According to the Self-Worth Theory, students want to be seen as capable, but failing creates a feeling of ineptitude (Schunk, 2020). Assessments, such as timed tests, have produced a perception in American schools that to be smart, you need to be fast (Boaler, 2019). However, organizing testing in this fashion rewards students for being quick to recall information, not to process their understanding (Gladwell, 2019). Good assessments allow students the opportunity explain and synthesize information (Schmoker, 2011), and provides a teacher an avenue to provide advice on how to further their learning to develop their confidence (Boaler, 2016). Assessments should also be used to guide lessons. By assessing students, teachers can gain an understanding of what was learned and use this information to decide where to go next (Mayer, 2011). Using assessments effectively can show knowledge gaps that should be targeted through instruction (Rueda, 2011). Additionally, data collected through assessments can be brought into department meetings for analysis and discussion (Schmoker, 2011). This process is valuable in recognizing effective teaching strategies and identifying inequitable opportunities and outcomes for students that can be addressed (Roegman et al, 2019). In mathematics, disaggregating data to identify inequities would be valuable, as there are consistently gaps in mathematical skills for students based on income, race, and ethnicity (Education Week, 2020). 24 Utilizing this data for discussion and engaging in analysis can help learning communities develop an equity focus and develop a strategic plan (Roegman et al, 2019). Cultural Understanding According to Ladson-Billings (2021), “colleagues in what we deem the STEM fields (i.e., science, technology, engineering, and mathematics) often reject the notion that their subjects are amenable to what we consider racial, ethnic, or cultural issues… They make claims of objectivity or neutrality that should shield them from having to engage in conversations of diversity, equity, and inclusion (p. 1).” However, with the large achievement gap in mathematical achievement between white students and Black and Latinx students, it is imperative that mathematics teachers adopt culturally relevant pedagogy (NCSM & TODOS, 2016). Too often, teachers will blame students or families for low achievement, but having low expectations for students of color is a failure “to recognize or take responsibility for those students’ academic outcomes (Turner, 2020, p. 95).” With the societal advantages that come with quantitative knowledge, it is an ethical duty to engage these populations in the acquisition of mathematical understanding (Moses & Cobb, 2002). Teachers must develop an understanding of diverse worldviews and understand how their students learn (Germain-McCarthy, 2017). To be an equity-focused teacher, you must examine your own beliefs and life experiences in order to develop an understanding of how you perceive equity and race (Roegman et al, 2019). “Mathematics teachers and leaders must acknowledge that the current mathematics education system is unjust and grounded in a legacy of institutional discrimination based on race, ethnicity, class, and gender (NCSM & TODOS, 2016, p. 4).” In order to combat this history, math teachers need to reevaluate the way math has been historically taught in our classrooms. If mathematics teachers do not integrate issues of diversity and social justice into their curriculum, they limit the 25 opportunities for marginalized students to access to the material. Having a grasp on mathematics is becoming more crucial to having a successful career in the modern world (Ladson-Billings, 2021), and teachers have a moral obligation to give all of their students an opportunity to engage with the curriculum in a meaningful way (Germain-McCarthy, 2017). Effective Collaboration When implemented correctly, professional learning communities (PLCs) can show improvement in student outcomes, teacher development, and school reform (Cheng & Zhao, 2023). In 1998, Richard DuFour and Robert E. Eaker published Professional Learning Communities at Work, believing that “a highly effective PLC engages in an ongoing process in which educators work collaboratively in recurring cycles of collective inquiry and action research to achieve better results for the students they serve, and PLCs operate under the assumption that the key to improved learning for students is continuous job-embedded learning for educators (Eaker & Marzano, 2020, p. 2).” Although the concept has been extremely popular in education, it has not consistently shown improvement in student achievement because the implementation and purpose of collaboration has not properly been defined or established (Fullan & Quinn, 2016). For collaboration to be successful, the culture around collaboration must be developed (Fullan, 2020). This section will analyze the culture of collaboration, creating change, and immunity to change and how it relates to the school community. Culture of Collaboration For collaboration to be successful, schools must create an atmosphere of trust, honesty, consistency, and respect (Northouse, 2022). Having people meet in teams is not collaboration unless the proper culture is in place. According to Fullan (2020), “people can collaborate to do nothing or to do the wrong thing (p. 75).” Unsuccessful schools are critical of each other and 26 departments are misaligned or highly focused on improving tests scores, while successful school have administrators and teacher teams working together (Fullan, 2020). A positive collaborative culture exists when “members can stay problem focused, listen to and understand one another, feel free to take risks, and be willing to compensate for one another (Northouse, 2022, p. 469). The development of a culture of collaboration is difficult because it usually involves people changing their daily habits (Fullan, 2020). However, it is critical to establish a community, because in order to transform our schools to meet the needs of every student, we must work together (Aguilar, 2016). There are many routines and community-building activities that can be used to build relationships among team members, but they will not be effective without establishing community agreements and norms, first (Aguilar, 2016). As Peter Drucker said, “Culture eats strategy for breakfast (Aguilar, 2016, p. 96).” Norms are essential to not only help team members achieve their goals (Aguilar, 2016), but to maintain the momentum and focus of a group through transitions (Weddle, 2020). One positive thinking member of a team can impact an entire group in a productive way, but if the norms are not built into the culture, the productivity could vanish if the team member leaves for other opportunities (Weddle, 2020). Norms and agendas are most effective when developed by the team (Aguilar, 2016). When departments feel that norms or agendas are passed down from administrators, their engagement drops, feeling that the collaboration time is tedious (Weddle, 2020). When the proper foundations are in place, collaborative work will thrive (Fullan & Quinn, 2016). Creating Change To develop the adaptive mindset necessary for change in a school community, you must “use the group to change the group (Fullan & Quinn, 2016).” For an organization to reach its full 27 potential, the group must work cohesively, not as individuals (Achor, 2018), because change is created by the collective energy of the team (Northouse & Lee, 2022). Therefore, you must recognize the human capital that exists in our organization and build up their capacity. Fullan and Quinn (2016) talk about a shared understanding of purpose throughout an organization called “coherence.” The four principles of coherence, focusing direction, cultivating collaborative cultures, securing accountability, and deepening learning set the framework for developing a system of continuous improvement. Once a coherent system is established, we can address and correct the adaptive changes necessary for more equitable outcomes (Westover, 2020). The conversations to create the changes necessary for equity, requires everyone to be given an opportunity to have a voice, but this must be done in a nonthreatening manner (Fullan, 2020). Using different discussion protocols will create avenues to bring more voices into the conversation (Aguilar, 2016). By staying silent and not sharing perspectives, the school community is robbed of opportunities for growth and building understanding of how race affects education (Roegman et al, 2020). Through courageous conversations and addressing the elephants in the room, school sites develop a shared responsibility moving forward (Heifetz et al, 2009). Having a shared responsibility, trust, and mutual respect among a group of individuals allows the confidence to take risks and reach their full potential as change makers (Achor, 2018). Immunity to Change In education, it is crucial to adapt to the needs of your community. However, it is extremely common for teachers to resort to the methods that they were taught. It is more comfortable to maintain the status quo, than to learn new methods (Fullan, 2020). When people try to bring about change, they can be met with “skepticism and cynicism” (Beer, Eisenstat, & 28 Spector, 2011, p. 161). It can be extremely difficult to enact change among a group of people in education when they have an “Immunity to Change” (Kegan & Lahey, 2011). Employees with an immunity to change can be very upsetting to managers and colleagues (Kegan & Lahey, 2011), as negative behavior can lead to negative group thinking (Achor, 2018). However, change can be brought about. Competing commitments are an individual’s unwillingness to change, so to combat this, people need to be confronted with their competing commitments. It may take a long period of time, but leaders need to be persistent in these circumstances. On top of that, the leaders need to have an awareness of their own competing commitments, as they can have a change immunity, as well (Kegan & Lahey, 2011). Working towards educational equity is a team effort. It cannot be done alone and it is not a one change process. It is a continual effort of reflection and action that requires a culture of collaboration and accountability. “People are motivated to change through meaningful work done in collaboration with others. If we want to shift the organization, we need to pay attention to both the quality of the capacity building and the degree of collaborative learning (Fullan & Quinn, 2016, p. 60).” In order to have our students reach their full potential, we must work towards having our educators reach their full potential. Conclusion Being a math teacher comes with a lot of power and influence over a student’s academic journey because of the perception that if you do not do well in math, then you will struggle later in life (NCSM and TODOS, 2016). Therefore, it is the responsibility of the math teacher to make sure that the curriculum is accessible to all students (Battey & Coleman, 2021). Math teachers need to be aware of their biases, to build up the self-efficacy of their nonwhite students (Irizarry, 2021) and provide them equitable opportunities for learning (Agrawal, 2019). Understanding the 29 perspectives of diverse student populations and implementing antiracist is increasingly paramount to instruction, as there is a lack of diversity in STEM teaching (Love, 2019). Creating equitable opportunities for learning in mathematics will create equitable opportunities for life after high school. Historically, the inequities in public education have left a lasting impact on schooling today, 70 years after segregation ended (Nelson et al, 2023). The perception that comes with “urban schooling” creates a negative perception that permeates throughout the school site (Massey et all, 2014). The process of redlining and “white flight” robbed schools of the resources and funding that they had (Pearcy, 2020). Although LCFF has created a system of funding to bring more to high-need students (Lafortune, 2019), there are still funding inequities that are prevalent as the wealthier schools have less issues to address and access to more outside funding (Rivera, 2018). This makes it harder for the “urban schools” to compete with the wealthier schools, because open enrollment creates even more social stratification (Phillips, 2015). Inside the classroom, teachers have the ability to create equitable learning opportunities for all students, which is critical because there is an achievement gap among the races (LadsonBillings, 2006). Developing the self-efficacy of their students will lead to an increase in motivation and interest in learning a subject (Sakellariou & Fang, 2021). As much as a teacher can build the motivation of their students, teachers need to be motivated as well (Rueda, 2011), as negative teacher emotions can lead to disengaged students (Sinatra et al, 2017). Through assessment, teachers can continue to motivate students and build their capacity (Boaler, 2016). Additionally, teachers need to develop a cultural understanding of their students to understand how their students learn (Germain-McCarthy, 2017). 30 To maximize the potential of students, no teacher can do work alone. Through professional learning communities, both students and teachers can reach their full potential (Eaker & Marzano, 2020). For effective collaboration, schools must develop a culture of trust, honesty, and respect (Northouse, 2022), and departments must establish norms so that their collaborative efforts maintain focus (Weddle, 2020). Through group efforts, change can begin to occur (Achor, 2018), but courageous conversations must occur (Roegman et al, 2020). Additionally, people must put in efforts to combat any immunities to change to see progress through (Kegan & Lahey, 2011). 31 Chapter Three: Methodology Statement of the Problem The lack of diverse representation among teachers in math education is detrimental to the self-efficacy of non-white students. According to Wang et al. (2020) students that have negative experiences and social interactions in math classrooms are likely to develop math anxiety. According to the California Department of Education, 88% of the students in California are nonwhite. However, between 2015 and 2020, only 23% of the teachers being credentialed in Foundational-Level Mathematics demographically identify as African American or Hispanic American (California Teaching Commission). The high school system is designed as a four year program. Statistically, that means our Black and Brown students have less than a one in four chance of seeing themselves represented as an expert in math. That precedent sets a negative perception for the development of their identity in mathematics. This study will examine the conversations around students and student achievement in mathematics that exist among faculty to understand if there is a relationship to mathematical achievement among students. Purpose of the Study The purpose of this study is to uncover underlying biases and assumptions of the math faculty in relation to the students they teach. Through qualitative research, using interviews and observation, this study aims to understand the perceptions of mathematics. Interviews and observations will be conducted at three different high schools to understand trends and commonalities. One school will be high income and the other two schools will be low income. Interviews will also be conducted with members of the administration and department heads of other subjects to further understand the perceptions of mathematics at the school community. 32 Research Questions The following research questions were used to guide this study: 1. During high school math department meetings, how do math teachers describe their work with students, with each other and with the content? 2. What are the perceptions of the math department that exist among the school community? 3. Do high school math teachers believe there needs to be a change in how mathematics is taught and what evidence do they have to support that belief? Sample and Population In order to study trends among math faculty, the research for this study will engage in a purposeful sampling. A purposeful sampling is “when the researcher selects individuals or sites on the basis of specific criteria (Lochmiller and Lester, 2017, p. 141).” Among the criteria of the study, participants will be gathered from three different high schools in Southern California serving populations representative of different levels of income. One school will serve a high income population and two will serve a low income population. To determine income level, I will utilize the California Department of Education’s Dataquest website to look at the percentage of students that qualify for free and reduced lunch. Then, I will classify a high income school as a school site with less than 50% of the student body qualifying for free or reduced lunch, and the low income schools will have at least 50% of the student population qualifying for free or reduced lunch (California Department of Education). Selection of schools representative of different income levels was important because socioeconomic status is a strong predictor of how students will perform academically (Barr, 2015), and I wanted to avoid homogeneity in my research and “ensure that the conclusions adequately represent the entire range of variation (Maxwell, 2013, p. 98).” 33 At each school site, I will be observing the math department and interviewing faculty based on the specific criteria of their relationship to the math department. I am going to observe department meetings at each school site to see how they are facilitated and to recognize the differences in conversations that occur. Additionally, I will conduct interviews with the math department chair(s) and one other members of the department to understand their perspectives of the school, their department, and their work. Interviewing members of the department is critical to gathering relevant data for my research (Maxwell, 2013). Finally, I plan to interview the administrator that supervises the math department and one other educational leader at the school site that does not teach mathematics. Preferably, they would be department chairs or members of the Instructional Leadership Team of the school. The perceptions of the math department from faculty outside of the mathematics department would bring a new viewpoint to the study. Table 1 displays the interview and observation criteria for the high school faculty participants. Table 1 Interview and Observation Selection Criteria for High School Site Participants Interviews Observations Math Department Teacher Math Department Math Department Chair Administrator Overseeing Math Department Other Department Chair / Member of Instructional Leadership Team Design Summary Although statistical data is referenced in this study, my research will be following a qualitative methodology. Merriam and Tisdale (2016) describe qualitative research as “understanding how people interpret their experiences, how they construct their worlds, and what meaning they attribute to their experiences (p. 6).” In this study, I very much want to build an understanding of how members of the math department interpret their place in the school community. Additionally, I want to understand how the school community views the math 34 department and their influence on the school and educational outcomes. As a result, qualitative research will allow me to gather data through interviews and observation. Additionally, utilizing a constructivist approach will allow me to “capture the perspectives of different participants (Yin, 2018, p. 16)” and account for different epistemologies in the data I gather. This study will be following the Lochmiller and Lester’s (2017) guidelines for a research study. Chapter one of the study will establish the statement of the problem and the purpose of the study. This is followed by a literature review that influenced the study. Chapter three will explain the methodology utilized in the research. An analysis and recording of the data will be outlined in chapter four. Lastly, chapter five will establish a conclusion of the findings and provide recommendations for the future. Methodology This study’s methodology implements a qualitative approach to data collection by analyzing interviews procured from members of the school faculty and coordinating observations of school math department meetings. All three research questions will be addressed through both of these data collection methods to create the greatest opportunity to gather the perspectives, opinions, and biases of the participants. During observations, events could be interpreted differently by participants and researchers based on their positionalities and epistemologies (Milner, 2007). Therefore, combining interviews with observation provides participants avenues to clarify any misconceptions that were observed during the observation. Table 2 outlines the data collection method that was utilized for each research question. Table 2 Research Question and Data Collection Method Research Question Data Collection Method RQ1: During high school math department meetings, how do math teachers describe their work with students, with each other and with the content? Observation Interviews 35 RQ2: What are the perceptions of the math department that exist among the school community? Observation Interview RQ3: Do high school math teachers believe there needs to be a change in how mathematics is taught and what evidence do they have to support that belief? Observation Interview Qualitative Method A constructivist approach in qualitative data analysis will be used in this case study (Yin, 2018). I will utilize observational data and interview data to focus on different perspectives, positionalities, and unconscious biases. The literature review supports the credibility of the study (Merriam & Tisdell, 2016). A Critical Race Theory framework will be used to develop an understanding of the positionality and power dynamics of high school math teachers and the effect it has on the educational experiences of California’s marginalized student populations. Instrumentation Qualitative Instrument Participant interviews and department observations will be used as instruments to gather data for the study. The outline of the interview (see Appendices E, F, and G) was designed using Rubin & Rubin’s (2012) ethical responsibilities towards conversational partners. This was done to establish trust and mutual respect with the participants in order to get honest details in my data collection. The observation protocol was adopted from Merriam and Tisdell’s (2016) structure to record field notes. This format allows me to record my own perspective into the observation while recording the actions of the participants. Both protocols were built and tested in my Research Methods II class. The interview was developed and fine-tuned through a practice interview with a classmate and a follow-up interview with a colleague. The observation protocol was rehearsed through a department meeting found on YouTube. 36 Data Collection Interviews and observations will be conducted to collect data for the study. My interview protocol (see Appendices E, F, and G) was developed not necessarily to get to know someone, but rather to “allow us to enter into the other person’s perspective (Patton, 2002, p. 341).” This protocol supports my data collection by creating a level of purpose and thoughtfulness behind each question. Taking careful consideration in the development of questions, probes, and followup questions, creates opportunities to elicit thorough and descriptive responses from the participants (Merriam & Tisdell, 2016). Rubin & Rubin (2012) state that our first ethical obligation is to our interviewees, “to do them no harm and to keep promises you have made (p. 89).” Therefore, in my interview protocol I will be upfront with my respect towards confidentiality. If we build trust and honest communication with our interviewees, we produce honest and valuable data in our research. For the observation instrument, I place my research questions and conceptual framework at the top of my notes, so that the purpose of my observation is at the forefront. Additionally, I create prior timestamps for me to place in my observations. Although, I will have to modify the time stamps as the observation goes forward. Lastly, I will incorporate observer’s comments in my field notes to place my immediate thoughts and reactions throughout the observation. This is crucial, so that I will be reminded of my interpretation of the interactions that people had with one another when I review the notes. In order to create a more equitable and credible data source, I will ask permission to do an audio recording to clarify what was heard. Each interview should take 40 minutes on average and each observation will be estimated to be 60 minutes. Each school site will consist of 6 interviews and 1 observation, making a total of 18 interviews and 3 observations. I will exchange contact information with participants at the 37 end of each session, in case either one of us has follow-up questions or requests for more information. Participants will be given permission to ask that information not be included in the study. I plan to use a transcription service to record the interviews. After reviewing the transcripts for accuracy, I will delete the recordings and store the files on a password-protected hard drive. Data Analysis This study will consist of qualitative data gathered from interviews and observations. All three research questions will be addressed in both the observation and interview data. The research questions will guide the data analysis, and I will be using a Critical Race Theory framework to look for recurring themes and trends. In this world, we all bring our own experiences and perceptions. “Truth, or what is real and thus meaningful and ‘right,’ for researchers and participants, depends on how they have experienced the world. Researchers can acquire evidential truth in research when they value and listen to the self, to others, and to the self in relation to others (Milner, 2007, p. 395).” It is extremely difficult to conduct an observation, without carrying our personal biases with us. That is our epistemological design. My positionality, which will be addressed later in this study, certainly creates some biases that I am aware of. Our perspectives are built off of the life experiences that we have, and that influences how we interpret circumstances. Therefore, it is important to conduct interviews after the observation to clarify any comments and actions that stood out. Through interviews, we can develop knowledge for how individuals experience and understand the world. As Maxwell (2013) says, “an interpretation of someone’s perspective is inherently a matter of inference from descriptions of that person’s behavior.” A post interview will be conducted with the participants 38 to allow them the opportunity to share their perceptions and experiences. Not giving participants a voice in the process, and analyzing the data solely based on my perspective is extremely unethical. Trustworthiness and Credibility Bogdan & Biklen (2007) recommend good listening in order to allow participants to fully open up. This is how I will discipline my subjectivity, and develop an understanding of the participants I am learning from. “The goal of understanding how the person you are interviewing thinks is at the center of the interview (Bogdan & Biklen, 2007, p. 106).” I will avoid, to the best of my ability, pushing subjects to discuss topics that may be upsetting to them, being judgmental so as not to demean them, and trying to change anyone’s views. I am there to learn their values and encourage participants to share their views. To develop the best understanding, the participants must trust and feel comfortable sharing their perspectives with me. Reliability and Validity The observation and interview protocols were both established and field tested in my Research Methods II class to improve reliability. The interview was developed and fine-tuned through a practice interview with a classmate and a follow-up interview with a colleague. The interview is necessary to establish the construct validity of the observation. Construct validity “is based on some underlying construct or idea behind a test or measurement tool (Salkind, 2017, p. 171).” The observation is built purely to assess the events of the department meeting. It does not account for participants’ prior experiences that are brought into the meeting. The interview will work to build understanding of the events in the observation. 39 Researcher Positionality During this research, I must be aware of my positionality, as it has strongly influenced the development of my problem statement and research questions. Currently, I am a high school math teacher enrolled in a doctoral program with a focus on educational leadership in k-12 urban schools. Additionally, I once served as chair of the math department at the first school I worked at. That tenure was fairly traumatic for me, as the interactions with members of my department left me disheartened and burnt-out. However, in my healing, I have searched for understanding about that chapter of my life, and it led to my interest in researching the dynamics of math department faculty. Certainly, my experiences have created certain biases about what I will be observing, but that is not necessarily a detriment to my research. Maxwell (2013) says that “separating your research from other aspects of your life cuts you off from a major source of insights, hypotheses, and validity checks (p. 45).” He also discusses Anselm Strauss’ theory of experiential data, or “the researcher’s technical knowledge, research background, and personal experiences (p. 45).” Where I was previously concerned about how my biases would affect my research, I now know that my prior knowledge can influence and shape the data that I collect. The school that I am currently employed at is the third math department that I have been a part of. All of the institutions that I have worked at were schools that served low income populations. Historically, these schools’ are primarily attended by racially marginalized populations, so I have to be reflective of my own positionality as a white male raised in an upper middle class family in the suburbs of New Jersey, and wonder if I have the understanding to fully interpret the data that I collect. I want to approach my research with the cultural understanding that I have developed in my eleven years in the classroom, but “the recognition of culturally sensitive research approaches has been minimized given the tendency of some researchers to 40 study people of color from deficit perspectives (Tillman, 2002, p. 4).” In order to counteract this, I will practice good listening to the best of my ability. Summary This study will use a constructivist approach with qualitative data gathered from interviews and observations. The interviews and observations will both address the three research questions: 1. During high school math department meetings, how do math teachers describe their work with students, with each other and with the content? 2. What are the perceptions of the math department that exist among the school community? 3. Do high school math teachers believe there needs to be a change in how mathematics is taught and what evidence do they have to support that belief? The findings will be analyzed in chapter four and recommendations will be given in chapter five. 41 Chapter Four: Results The purpose of this study is to examine the perceptions and biases of students and student achievement among secondary math department faculty to understand if there is a relationship to mathematical achievement among students. Additionally, this study intends to understand the perceptions of the secondary math department through internal and external perceptions. The following research questions were used to guide this study: 1. During high school math department meetings, how do math teachers describe their work with students, with each other and with the content? 2. What are the perceptions of the math department that exist among the school community? 3. Do high school math teachers believe there needs to be a change in how mathematics is taught and what evidence do they have to support that belief? This chapter will focus on the data gathered from three different Southern California public high schools. Two high schools serve lower income populations, and one serves a higher income student population. The results will be presented through data collected from interview responses from faculty at each school site, as well as an examination of trends in protocol present at each school sites’ math department collaboration meeting. The results from the research will be articulated by responding to each research question with supported research from literature. Additionally, recurring themes at the three school sites will be discussed. Finally, there will be a summary of the research to conclude the chapter. Participants The participants for this study were members of the faculty at three different high schools in Southern California. Two of the school sites serve lower income student populations and one site serves a student population from a high-income population. In order to determine the income 42 level of the student population, the California Department of Education’s Dataquest website was used to assess the percentage of students that qualify for free and reduced lunch. At each school site, I observed the math department collaboration meeting and interviewed school faculty based on their relationship to the math department. I conducted interviews with the math department chair, one other member of the math department, the administrator that supervises the math department, and a department chair outside of the math department. Although I was able to meet with everyone in person or through video conference, all names and identifying information will be kept confidential. Table 3 provides relevant information on the school sites and their participants, as well as their aliases. Table 3 Participant and School Site Information (as of 2023) School Site James Buchanan High School Ridgemont High School Bayside High School Total Population 3,437 873 2,807 Socioeconomically Disadvantaged 71.4% 69.4% 32.2% African American 3.9% 1.8% 0.6% Asian 1.3% 12.5% 12.1% Filipino 0.5% 4.8% 1.3% Hispanic 89.6% 74.8% 23.3% White 3.9% 2.7% 52.9% Teachers in Math Department 7* 10 17 Math Department Chair Wayne Jordan** Silvia Tatum Dr. Martha Triggs Math Department Member Felicity Jodene Emilia Jephson Rachael Appleton Administrator Oscar Devine Dr. Lindsey Jackson Todd Gates Other Department Chair Lillian Ware** Johnny Bennett Katie Martinson All names developed by online name generator * Department observed was an Integrated Math 1 PLC **Department Chair was a PLC Lead Observation Data At each school site, I was able to observe a departmental meeting in addition to interviewing the math department chair, another member of the math department, an 43 administrator that oversees the math department, and the department chair of another subject. James Buchanan High School’s meeting was focused on the alignment of district pacing, Ridgemont High School’s meeting was a working meeting with no agenda, and Bayside High School’s meeting was focused on the proposals for new Algebra 1 curriculum for next year. Although the structure and agenda of the meeting at each school site was different, there were three trends that I observed as being consistent among each department. In all three departments, there was a lack of data or protocol to discuss students work, sarcastic comments about students were made, and there was limited engagement among the departments. When contacting school sites to schedule time for observation, I requested to be in a departmental meeting where student work was discussed. However, each meeting was focused on procedural topics and planning future lessons or assessments. Although these are pertinent topics, no data was presented in any meeting, so all decisions were based on perception. In James Buchanan High School, there was discussion about procedures to gather data in the future, but the protocol was not currently in place. At Bayside High School, there were mentions and requests for data on student success, so it appears that it has been used in department meetings before, but it was not a regular practice. However, to effectively make equitable decisions on instruction and assess student needs without bias, data must be incorporated into the discussion so that “educators realize that reality may not support their assumptions (Roegman et al, 2019, p. 115).” Each school side had department members that were passionate about their subject and had a real desire for their students to be successful. However, sarcastic remarks made at the expense of their students still found their way into the departmental meeting, unconsciously demonstrating lowered expectations. At Bayside High School, an individual remarked that no 44 one is going to assume students at the next level will “actually know anything.” In James Buchanan High School, a teacher referred to their students as “idiots.” Ridgemont High School’s department had a teacher express frustration about a student because all they were expected to do was copy. Social cognitive theory tells us that the learning environment influences the selfefficacy of a student (Schunk, 2020), and if our unconscious biases come through our pedagogy, that can influence a student’s learning environment (Moore, 2017). Therefore, it is essential for educators to work towards uncovering their assumptions and beliefs about their students (Douglas & Nganga, 2013), so that they can believe in their own ability to succeed in a topic. The last trend to address was the lack of engagement from everyone in the room. Every meeting was run as a presentation. James Buchanan and Bayside had individuals present to in the front of the room towards the entire department, while Ridgemont had people broken up into groups for mini presentations. Although Ridgemont was grouped, it was experienced teachers telling their new faculty how to run their classroom, with very little back and forth. Every meeting also possessed individuals that did not speak unless they put themselves out there, and members that were working on their computers or cell phones. According to Aguilar (2016), these are all behaviors that undermine effective communication in meetings. These trends will be addressed through conversations I had with members of each school site through structured interviews, as well. This data was all collected from my perspective as an observer, whereas the conducted interviews were able to give the perspectives of the faculty, as well as historical and contextual data. Results Research Question One The first research question in the study focused on how members of the math department collaborated and focused their attention on improving student outcomes in mathematics. This 45 section analyzes the responses that answer the question, “During high school math department meetings, how do math teachers describe their work with students, with each other and with the content?” The data collected from faculty inside and outside of the math department was a mix of perspectives that showed some consistencies and inconsistence over the perception of how the departments are run. Overall, from this collection of data, there was very little difference between the departments of higher income public secondary schools and lower income public secondary schools. Among the themes that were presented are a lack of protocols during meetings, an absence of data, using the pacing guide as a bible, and a shortage of grading for purpose. Lack of Protocol When departments meet, the purpose of coming together must be centered around addressing the needs of students. However, sometimes student need can “get lost and buried beneath great ideas, strong personalities, adult needs, and competing agendas (Aguilar, 2019, p. 65).” Therefore, protocols are valuable because they can focus the group discussion and develop a structure for all members to participate in a meaningful way (Roegman et al, 2019). Although every department meeting that was observed did have a purpose, there was very little structure to ensure that everyone was engaged. Both James Buchanan and Bayside had an agenda displayed at the front of the room, and Ridgemont had teachers grouped by subject matter, but many people were disengaged in the discussion. Developing a structure to meetings is something that two administrators expressed a desire for. At James Buchanan, Oscar Devine admitted that there are no protocols in place at his math department’s meetings, and Dr. Lindsey Jackson at Ridgemont is hoping to inspire her 46 department to develop protocols but it has been difficult because “everybody has their different viewpoints.” The department chairs at each site expressed a different perspective on the structure of their meetings, though. All three school sites expressed a belief that everyone is always engaged in the department meetings, but that was not supported by my observations. At Ridgemont High, Sylvia Tatum said of her department: “Everybody’s always engaged. Yeah, there’s nobody who sits out. Um, and the person who sits out gets brought in or they don’t last very long, because we are an absolute collaborative group. Nobody works on their own.” However, during my observation, there were several people working by as silos. Wayne Jordan described his PLC once the serious talk starts as “there’s a switch that just, uh, turns around and then boom, we just, we just lock in.” During my observation, though, several members were interacting with them their devices during the meeting, and no one sat in a group setting. Oftentimes people may have chimed in with a question or opinion, but that does not translate to engagement. The structure of every department was reliant upon the department members’ autonomy to initiate input in the discussion. As Dr. Martha Triggs at Bayside said, “like generally, I’ll just kind of facilitate and if somebody wants to speak on something, they’ll raise their hand.” Without proper protocols and structure in place for collaboration and engagement, the work done in learning communities will not generate the impactful depth needed to bring meaningful experiences for students to the classroom (Fullan & Quinn, 2016). Absence of Data All three math departments were not currently implementing data analysis as a regular practice in their discussions. However, James Buchanan is currently working with the district and another high school in their district to form common assessments and data collection and 47 Bayside High spoke as though data is brought into their department discussions. These are great steps towards building this practice, but what stood out was that other departments have already been utilizing the practice of data analysis. At James Buchanan, Lillian Ware, the English department chair, has members of her PLC input data ahead of their meetings so that they can look at data and engage in an analysis. Johnny Bennett, the English department chair at Ridgemont High, has been incorporating the collection of data for the past five years. When data was brought into discussions, every department I spoke to did not disaggregate their data by race or gender, unless it was the SBAC test. The most common groups that data was organized by was classroom teacher, SPED, and ELs. Although it is not always easy or comfortable, in order to become equitable in the pursuit of improving student outcomes, educational leaders and stakeholders must talk about race, gender, and other marginalized populations in order to “identify and name the groups of students in their schools or districts whose educational experiences and outcome are inequitable (Roegman et al, 2019, p. 35).” If these difficult conversations to not occur when educators are doing the work, then the status quo will remain and student outcomes will remain consistent with history. Pacing Guide as a Bible The one topic that every math department brought up as a constant in their department meetings is the pacing guide. Sylvia Tatum said “it’s always about what is your pacing, where are we at?” Wayne Jordan brought up the calendar in James Buchanan’s PLC meeting to plan the pacing of future units. At Bayside High, although pacing is a regular discussion, according to faculty it usually occurs on the teacher’s own time. However, there is a recurring theme of having to get through the pacing at each school site, and the teacher’s let it be known. As Lillian Ware said: 48 “I hear a lot that the kids say that their teachers say, we're so behind, we're so behind <laugh>. Okay. And I'm like, behind what <laugh> Uh, but I understand, you know, I understand that the math, the math standards are different. You know, it's different than English and, you know, you have this, this expectation that you're gonna get your students to a certain point. …I've heard from some of my students that their teachers, you know, their answer to the block schedule is that they just, they teach two lessons. you know, so they cover in one day what they would've covered in two regular days, and then they give a quiz. So it's like two lessons and a quiz. two lessons and a quiz.” The pressure that math teacher’s feel to cover all of the standards is coming at the expense of students. As Dr. Lindsey Jackson said, “if we're not through the pacing guide, then they're not gonna be ready for next year. But yet we've got kids getting D's and Fs, which means they're not ready for next year anyway.” Grading for Purpose In addition to aligning their pacing, all three districts have implemented common assessments which is the first step in Collaborative Inquiry (Fullan & Quinn, 2016). However, once the assessment is administered, it does not seem as if many departments have calibrated their grading to provide equitable outcomes. At James Buchanan High School, Felicity Jodene is the only member of her department to implement Standards Based Grading, so the impact of the common assessment may hold different weight in her class as it would in a colleague’s class. That is, of course, if they grade the tests the same way. At Bayside, Katie Martinson’s students have expressed frustration about their math teachers’ grading: “There are a couple math teachers that I've heard about that are, that weigh classes and tests and quizzes and different things in a much different way than other teachers on 49 campus. And those teachers, the ones who weigh, for example, I know of a teacher who weighs tests at 99%. And so if you have a student who's a bad test taker and they're always, they have anxiety about it, whatever, they're not gonna do it in that class and that's it. And so as hard as they try, I mean, I had a student last year, he tried so, so, so hard at math, he did all of the homework. Mm-Hmm. And he got an F and he was really bummed and frustrated and didn't know what to do and talk to the counselor and talk to the teacher. And anything I saw in writing about the teacher was non-supportive. And so I think that with the teachers who really like, you know, I think that there are teachers who have expectations that are beyond what some students can do.” Grades are intended to be a form of feedback on their understanding (Nagel, 2015). As Hattie (2011) said, students want “to talk about their learning and how to improve (p. 33).” If every math teacher has different standards for what is expected from students to demonstrate their competencies, then students will struggle to find success in the classroom. At Ridgemont High, there are differing opinions on student grades. The department chair says: “This year we're seeing a lot of apathy. …I don't know. I think that there's a whole mind shift. That there's a lot of kids who really just don't care as much about their education. And, you know, we talk about it every day. Where does that come from? Why is that here? And does it come from home? Does it start from there? We don't, we don't have that answer. We can only, we can only control what's within our school day.” Meanwhile, the school administrator says: “Because our kids are failing. Our kids are failing, and the teachers are complaining and blaming the kids. It's not our kids' fault. You know, we have kids that are doing very well in other classes, but math is their failing grade, or math is their lowest grade, or is that . 50 And then when we're so rigid about allowing kids to make up a test or allow, you know, about having to turn in homework or whatever the case is, um, to the point where, where I have teachers that are willing to take a stance and not move on it, … we have teachers that would rather die on hills because their kids aren't gonna do homework and give them a failing grade because they're not, you know, the kids aren't doing the job, but we're not willing to change what we're doing in the classroom.” Discussion Research Question One The responses from the individuals interviewed revealed that the school faculty absolutely wants their students to succeed in mathematics, but they are not sure how to achieve this across the board. Many teachers continue to teach the curriculum the way they learned it in high school, because that is what is familiar to them. However, as Wayne Jordan said when he reflected on his high school experience, “It’s been 10 years. A lot has changed.” In the lower income schools, there is a push from administration to incorporate data analysis and reevaluate the way material is being taught and assessed. However, discussions and priorities among all the school sites seem to focus on pacing, curriculum, and logistics, instead of analysis of learning. As Rueda (2011) said, “often school debates center around what should be taught (curriculum and standards) and how it should be assessed, (which test is the best?) rather than how to teach it (p. 33).” When data is collected or incorporated into meetings, it takes a color blind approach when presented. None of the schools that were observed for data collection disaggregated their data by race or gender. The only subgroups that were ever identified were Special Education and English Learners. This makes sense at Bayside High, since according the California Dashboard, those are the only subgroups whose performance is in the red for mathematics. However, 51 avoiding data analysis by race or other difficult subgroups decreases the chances of identifying inequities that exist and could allow the challenges for success to persist in the classroom (Roegman et al, 2019). Results Research Question Two The second research question in the study addressed how members of the school community feel about mathematics and how math faculty feel they are perceived by the school community. The question guiding the analysis in this section is, “What are the perceptions of the math department that exist among the school community?” Through interviews, the data demonstrated trends of math being difficult to learn and hard to teach. Although there were trends among all three school sites, the deficit thinking was far more prevalent among the two lower income high schools. Math is a privileged subject, math is hard, and new hires since COVID were the tendencies that guided question two. Math is a Privileged Subject High school mathematics creates segregation among students that translates into life beyond high school, because there is a belief that you must be good at math to be successful in the modern world (Ladson-Billings, 2021). This reputation of mathematics creates a chasm in the educational opportunities presented to students in our educational system. “Secondary mathematics courses are often seen as gatekeepers to postsecondary education. Students who enroll and are successful in high-level mathematics courses in high school are more likely that their peers to graduate from high school, enter postsecondary education, and complete a college degree (Thompson, 2017.)” Unfortunately, there is a common belief that people are either good at math or they are not. As Emilia Jephson said: 52 “...so for some kids, like, depending again, who their teacher was, the teacher might have focused on something a little bit better than others. So they're really strong and, and other kids aren't. And so it takes 'em just a little bit longer to learn it, you know? Yeah. And then there's also just natural ability. I mean, that's true of any subject. Some kids are just naturally better at certain things, and so they'll get it the first time around and other kids just need a little bit more time.” Mathematical achievement can shape an individual’s educational experience. Differences in teacher expectations and grading, access to resources and intrinsic motivation can all impact student performance in mathematics (Thompson, 2017). With the current progression of math curriculum, if you fail or fall behind at the high school level it is challenging correct and close and knowledge gaps. As Rachael Appleton said: “And I don't think you can get away from that. Um, somewhere along the way they struggled, they fell, maybe they weren't helped to get back up. And since it's a building block subject. You know, it's just, they're constantly struggling. So if the kids that are in algebra two are a very, at our site, um, it's, they have only really a couple of options. You're either in algebra two. Or you're in algebra two honors. Okay. Now you can go to data science, but it's recommended that you take algebra two first. Um, so algebra two is a big melting pot of kids that struggle. Um, maybe they were passed through and shouldn't have been or the kids that are like, oh, I got this. Like I didn't wanna take honors, but I'm doing really well. Um, and so I think that mixture creates that negative environment at times.” Math is Hard 53 Math has a reputation of being hard, and this preconceived notion impacts the academic experience for both students and teachers. This section, will focus on the responses from teachers at James Buchanan High School, who’s school site has the highest numbers of Hispanic and African American students in terms of percentage and total enrollment numbers. According to Lillian Ware, math is “traditionally the hardest class for ninth graders.” This is echoed by her colleague and PLC math lead, Wayne Jordan. “…You hear the, the kids saying, oh, it's, it's, it's complicated. I've never been good at it. Um, and, and then just the word math, it just can shut the student off just, or just shy them away from it.” When students come into the classroom with a belief that they will not do well in mathematics, then it reinforces “an institutional assumption that filters into the consciousness of local people, that kids are unable to do this work, will fail to gain the kind of math literacy we aim for. Perhaps a few can, the system says, but not everyone (Moses & Cobb, 2002, p. 155).” There is a power dynamic that exists in the math classrooms of schools in this country, and shuffling around the standards of curriculum is not going to correct the inequity that prevails. Students from our marginalized communities are struggling in mathematical achievement, but how can they believe in their abilities when they do not see themselves reflected in their classroom leaders. Felicity Jodene, a member of the math department at James Buchanan High School and a first generation Latina high school graduate on both sides of her family, did not believe that she was destined for college after high school, let alone being a math major. “And I looked around me and I noticed that I was not only one of the only Latinas in the classroom, I was also one of the few females in that classroom. Very much felt like I didn't belong. And I was like, how did I get here? I'm clearly not meant to be here. … 54 There's very, very few women in like STEM fields and so especially minority women. And so I was like, you know what? That's what I'm gonna teach. I'm gonna teach math for that reason.” New Hires Since COVID After the COVID-19 pandemic, many teachers across the country experienced “higher rates of depressive, anxious, and burnout symptoms (McLean et al, 2023)” and ultimately left the field of education. Of course, even before the pandemic, this was an issue across the country, especially in lower income school districts where there “a five-year turnover rate of 55% (Papay et al, 2017)” on average. This was an interesting trend that was held up in the data that I collected. Both Ridgemont and James Buchanan High School were dealing with a large number of new teachers in their math departments. However, Bayside High School was able to maintain consistency in their department, where the lowest teacher seniority is “five or six years” according to Rachael Appleton. There are two ways to view teacher turnover. According to Papay et al (2017), when teachers leave, they are usually replaced by inexperienced teachers that are less effective, as effectiveness improves over time. However, this could also be beneficial, as many times the reason a teacher leaves is due to ineffectiveness, and this creates room for new enthusiasm. It gives an opportunity for departments to shift the culture. At James Buchanan, Oscar Devine is using the newer teachers as an opportunity to reevaluate assessment and bring data into the department discussions. However, at Ridgemont, Dr. Lindsey Jackson is worried that the department is going to maintain the status quo: “…especially my new teachers, which many of them are new who won't say anything. I don't know, know that they will engage in conversation because you've got some very 55 strong personalities in that department who will tell the new people what they need to do and the new people will, because they wanna have a job next year, just go along with it. Um, and I know that's not good for kids.” Dr. Jackson’s concern was substantiated from my observations in the department meeting and by Sylvia Tatum’s interview: “…they're just, you know, they're coming into the department. We have like, just really strong, uh, procedures and for how we do things. Um, so I think a lot of times new teachers, they just wanna see how the department runs. And they might be a little bit more quiet the first year, but definitely by the second year they're expected to. To, uh, contribute more.” Discussion Research Question Two The effect that math education in K-12 has on the opportunities for students after high school graduation is substantial. Although countless efforts have been made to provide support to students that struggle in the curriculum, their effectiveness has been minimal. Math continues to be a “gatekeeper” for students looking to become contributing members of society. With the power and influence that mathematics holds over students, math teacher’s must develop an awareness of their positionality. “Mathematics teachers and leaders must self-reflect on privileges and obstacles in their own mathematics histories, build and exchange ideas, and expand the pool of knowledge resources by partnering with families and communities to make change (NCSM and TODOS, 2016, p. 4).” The attitudes and decisions of the math department impacts the culture of the entire school community. Math has a reputation for being hard, scary, and something that you are either good at or you are not. Students that suffer from math anxiety come into classes already 56 believing that they will not pass. “These negative emotional reactions can ultimately decrease academic performance and can even impact individual aspirations and choices later in life (Caviola et al, 2022).” According to University of California and California State University requirements, students must pass three years (four recommended) of mathematics to qualify for admission to the public universities in California (California Department of Education). If students struggle with mathematics throughout high school, their chances of attending a fouryear college decrease, limiting their appeal and opportunities in the workforce. Results Research Question Three Research question three sought to understand the perspective of math educators and supporting their students in the curriculum. The guiding question is, “Do high school math teachers believe there needs to be a change in how mathematics is taught and what evidence do they have to support that belief?” Through interviews, the data demonstrated that teachers want to see their students succeed, but they do not believe that the curriculum needs to be changed. After analyzing the trends from interviewing faculty, three trends stood out. District funding and access to resources, accountability, and a fear of change highlighted the data collected in this question. District Funding and Access to Resources For this section, the focus will primarily be on Bayside High School, as this is a school that historically enrolls students from higher income communities. The income level of the local communities directly impact the public schools in the area, because public schools are funded through a combination of Federal, State, and Local taxes. In California, state funding is based on a needs per student basis, so high-poverty districts “receive 74 percent of total funding from the state ($11,079) compared with 37 percent for low-poverty districts (Knight et al, 2022, p. 192).” 57 These funds are designed to support basic education, and create equity among the public school districts. However, anything beyond basic needs creates an inequity as “districts in communities with supportive voters can pass bond after bond, raising large quantities of funding from their local taxpayers (Rivera, 2018, p. 25).” As highlighted in Table 4, based off the median household income, the average residence in the Bayside High School community would likely be able to contribute more funds to support local school initiatives. Table 4 Median Household Incomes (as of 2020) James Buchanan High School Ridgemont High School Bayside High School Median Household Income $85,089 $84,663 $111,122 Families $95,411 $89,805 $129,041 Married-Couple Families $116,409 $109,089 $155,112 Nonfamily Households $63,314 $46,974 $81,201 Residents Under 18 Years 22.1% 23.1% 16.7% Data Collected from 2020 United States Census Through interviews with the faculty at Bayside High School, the availability of resources was revealed in several instances, implying that funding was not an issue. According to Rachael Appleton, the district assistant superintendent in charge of curriculum has been extremely supportive. “What do you guys need? Oh, you need this resource. Let me see if I can get it for you.” Bayside has been able to utilize this access to resources to finding a curriculum that works for their math classes. A major focus of the math department at Bayside is finding a curriculum that works for their Algebra 1 classes. Currently, Bayside offers four different variations of Algebra 1: Algebra 1, Algebra 1 by Design, Algebra 1 with Programming, and Algebra 1 with Support. Additionally, there is a class called Algebraic Mindsets to prepare students for Algebra 1. During the observation, teachers presented three more options for Algebra 1 curriculum to be implemented 58 next year, and each option received support from the department. Based off the interviews, there are several reasons that Bayside may offer such a variety of options. Rachael Appleton says: “…then our algebra one kiddos, how can we help them? Um, because granted the accelerated classes, that's a different kid, right? Like they're self-motivated, they, oh, I have a gap here, I know I need to work on this. And like, our, our lower kids don't have that self-driving force we'll say, or that self-initiative. Um, so really trying to create a stronger kid coming out of Algebra one, whatever that may look like for that individual student.” English Language Learners is also an area of focus for the math department to place their resources towards. Dr. Martha Triggs discussed: “So this year we have like a, an EL cohort. So our algebra one geometry and algebra two levels have an EL class. Um, that they're teaching and they've been trained to teach it with a lot of like scaffolding vocabulary and things like that. And then the students stay in their cohort throughout the day for other subjects as well. So they'll go to math, to English, to social science and so on. And that's to hope. That's one of our populations we're focusing on because they have the lowest scores Yeah. At our school, so.” Although the English Language Learners are one of the lowest performing populations at Bayside, the five year demographics highlighted in Table 5 show a different area of concern. Before the pandemic, Bayside performed very well in state testing, scoring 23.2 points above the standard. However, after the pandemic, the number of socioeconomically disadvantaged students almost doubled. Additionally, the scores in the state tests dropped to 18.1 points below the standard. Overall enrollment numbers stayed relatively the same, but the number of students identified as English Learners dropped. 59 Table 5 Bayside High School CAASP and Demographic Data Bayside High School – 5-Year Demographics Hispanic Students White Students Socioeconomically Disadvantaged English Learners CAASPP Scores (Compared to Standard) 2019 19.9% 57% 18.6% 3.3% 23.2 points above 2020 20.6% 56.4% 17.6% 3.6% n/a 2021 21.5% 55.7% 17.3% 3.2% n/a 2022 22.8% 54.4% 31.2% 3% 18.1 points below 2023 23.3% 52.9% 32.2% 2.4% 16.3 points below Data collected from California School Dashboard Table 5 also shows a decline in White students attending Bayside and a gradual increase in Hispanic students attending. Todd Gates, the assistant principal at Bayside, discussed some concerns in enrollment: “...many districts in California are facing declining enrollment, and we're in competition with, you know, parents, you know, electing to homeschool the kids, go private or to, uh, transfer out to other districts. And so, um, from, from my perspective, we have to be, you know, marketable and we have to offer what it is that not only what the kids need, but what, you know, what the kids want, you know?” The Bayside community is a very outspoken, conservative community. Additionally, the school offers inter-district and intra-district open enrollment options. Another reason that they may offer such a diverse curriculum and have taken focused measures to support English Language Learners, is to attract students to their school. Accountability Successful schools are not only accountable for their students’ success, but also for building the capacity of their faculty (Hitt, 2016). Accountability is not something to be feared, but rather a strengthening process. “Internal accountability occurs when individuals and groups willingly take on personal, professional, and collective responsibility for continuous 60 improvement and success for all students (Fullan & Quinn, 2016, p. 110).” In order to maximize the strength of the curriculum, teachers must be held accountable. There were three trends that were noticed to effect the accountability of the math department in terms of their curriculum: administrative involvement, difference in vision, and parental involvement. Administrative Involvement Across all three schools, there was a desire from the principals to be more involved in their departments. Oscar Devine tries to attend meetings as often as possible, but because of the PLC structure, he is only able to meet with each grade level team once or twice a month. Todd Gates is split between the math department and the special ed department and departments meet once a month. Therefore, he only sees the entire math department once every two months. Dr. Lindsey Jackson is in her first year at principal at Ridgemont, although she has been a principal before: “I have not attended the meetings this year yet. Um, part of the reason is where I came from in my former district, PLC time was sacred for teachers, and either you needed an invitation or you almost needed to ask to be a part of it as an administrator. And so as a new administrator here, um, just trying to get a grasp on everything that's going on in this school and the differences that, um, I'm experiencing in a different district. Um, in fact, I just, I just spoke to <REDACTED>. Um, and he, he wants the administrators to come in more to their PLC. And I said, I'd love to. I didn't realize that that was a thing here. Um, the other piece that's kept me from really getting in there is, um, I have 27 new teachers this year. First and second year. And I have to do three observations for each. So that's 81 observations, formal observations that I have to do. And the second set is due by December 15th. Okay. So, I've been spending a lot of time in new teacher classrooms, 61 which doesn't allow me the time typically to be able to go and attend PLCs. But my goal for second semester is to be in those PLC meetings at least once a week and if not twice, just so I could get to different departments.” To build a successful culture of student achievement, internal accountability must be at the forefront. “Internal accountability is based on the notion that individuals and the group in which they work can transparently hold themselves responsible for their performance (Fullan & Quinn, 2016, p. 112).” In order for administrators to see the shift in instructional practice that they desire, they must be involved in their department to model accountability and develop a shared vision. “If we want people to be excited about the direction we are taking them, we need to similarly elevate their collective vision of what a positive world can look like (Achor, 2018, p. 198).” Difference in Vision At Bayside High School, Todd Gates seem to have taken the approach of defaulting to Dr. Martha Triggs and allowing her to lead the math department. James Buchanan is currently entrenched in building a vision in collaboration with the other high school in the district. This section will focus on Ridgemont High School, as Dr. Lindsey Jackson and Sylvia Tatum have not formed a cohesive vision. Dr. Jackson is in her first year at Ridgemont and Sylvia Tatum, the department chair, has been there for fourteen years. Currently, Sylvia feels: “I think they want us to do better. I don't know that, I don't know how, I mean, they're sending us to a conference. I mean it, you know, I don't wanna feel like they're blaming us 'cause I don't think it's our fault, but it's important to them. District office looks at the D and F rates. So that's what we get judged on.” Meanwhile, Dr. Jackson said: 62 “I'm still learning a lot about everything in this school, but one thing that, um, I've noticed is that our teachers have not had a lot of professional development in the last few years since Covid. Um, and I think that's the, the most, that's what they need the most right now. Professional development on how to work with our kids since our kids are so behind. What do we do? How do we change what we do in the classroom? Our kids are not the same anymore. They're, our pre covid kids are not the same as our post covid kids complaining about the fact that kids don't do homework, but still assigning homework is the definition of insanity. Yeah. I mean, when, when I hear that these kids just won't do homework, so what are you doing differently? I, I, I just don't think that, you know, if they have, if they had gone to some kind of PD, which I'm now sending them to the math summit, the, um, PPLC solution tree, PLC Math Summit, I'm sending two high school and two middle school teachers to the summit. My hope is that, um, one of the consultants that I used for math in my former school is speaking that they will say, Hey man, I wish I, we could get one of these people to come work with us, because if they did, I'd hire 'em in a heartbeat. I want somebody to work with our math folks so that they can look at what they're doing in the classroom and attack it differently because what we're doing isn't working.” Currently, the administration and the department have different visions about the instruction, grading, and curriculum in the math department. There is a lot of distrust on both sides. Having differing perspectives is great, but having visions in opposition will cause a lot of friction and a lack of accountability. As Elmore (2005) said, “As schools become more coherent and effective as organizations, rather than collections of individuals, collective expectations are 63 more influential over individual teachers’ work, and the work of school leaders becomes defined as the explicit reinforcement of organizational values (p. 135).” Parental Involvement Parent involvement has a consistent correlation with student success (Chan et al, 2021). However, the only school that mentioned parents and the parent perspective in terms of the educational experience was Bayside High School. As Dr. Martha Triggs described their parent population as “extremely active.” This can be a good thing for school achievement, because in addition to administration monitoring student achievement, “Our parent population is very into it as well. Um, they're very involved. Yeah. Especially at the AP level and they're looking at us, which again makes the administration looking at us as well. Bayside being the only school to address parental input into decision making upholds negative stereotypes of marginalized communities in education. However, “a decolonial approach to parent involvement recognizes the need for a change in the economic structures that limit parents’ participation and decision making on behalf of their children…decolonizing approaches to parental inclsion in schools by necessity must point out and end all forms of epistemic, psychological, and physical violence as are experienced through silencing, linguicisms, segregation, tracking, and the dehumanizing effect of the stunted academic potentials of youth of color (Baquedano-López et al, 2013).” In order to maximize the potential of schooling, educators must make every effort to bring the voices of the parents and community into their classroom. Fear of Change It is extremely difficult to enact change among a group of people, and this holds true in education. Kegan & Lahey (2011) discuss the concept of an “Immunity to Change”. In order to 64 bring about change, people need to be confronted with their competing commitments and big assumptions. It also requires a manager to be persistent, as these changes will take long periods of time. Additionally, managers need to have awareness of their own competing commitments and big assumptions, as “managers are every bit as susceptible to change immunity as employees are (p. 91).” Every school site that was observed had an educational leader trying to enact change in their math departments curriculum, but each had a different approach in bringing about change among their colleagues. At James Buchanan, Oscar Devine is focusing on his younger teachers to develop a new culture among the department. Many of the teachers that have been there for awhile, are continuing to work within their comfort zone. “Veteran teachers are in this group, um, and they're really used to instruction the way they delivered it for the last five or 10 years. Every teacher has their own personality, right? So, um, there's that autonomy in the class, and they're used to that.” However, there is change supported from the district across the high schools to enact a change in their practice. By providing the departments with the tools to integrate new practices and facilitate a change in assessment, the district is utilizing a path-goal theory of leadership (Northouse & Lee, 2022). At Ridgemont, Dr. Jackson is trying to disrupt the status quo: “…for many teachers, they teach the way they were taught. Yeah. And that's the best way that they learned. So why don't you learn that way? I'm teaching it to you the way I learned it. We loved school. Not all of our kids love school. Not of all, all of our kids learn the way we learn. So to have them have to step out of where they're comfortable and to change the way that they've delivered information and to try something else is difficult.” 65 However, Sylvia Tatum is trying to integrate new members of the department by utilizing the leader-member exchange theory of leadership in her department (Northouse & Lee, 2022). Tatum feels strongly about the way that her department has been operating, “I like what we do. I like, I like our textbook. I like how we have it chunked up. I like how we offer, you know, different levels. So I don't, I don't think we need to change our curriculum. I like our curriculum.” However, Johnny Bennett, who has been teaching English at Ridgemont for 26 years, has noticed a change in the student population: “…our scores started to go down and the population changed. Not in unhealthy ways, it's just, it was different. But it seemed like some of us were still teaching or approaching it as if we were still a different school than we were. Like, our kids are supposed to be reading up here. That's not the kids we have now. What are we doing to face the actual kids we have?” At Bayside, Dr. Marth Triggs has implemented a transformational style of leadership. Transformational style “stresses that leaders need to understand and adapt to the needs and motives of followers (Northouse & Lee, 2022, p. 2020).” In the math department at Bayside, members are bringing new ideas on curriculum to help engage struggling students. According to Dr. Martha Triggs: “Um, I would love to see these new classes fly, um, that we're talking about. Um, kind of just moving into the, the current times. Right? I mean it seems like in a lot of classes they're being taught the same way they were, you know, 50 years ago. And so it's nice that we're, that we have younger teachers coming in that are innovative and trying new classes and trying to reach students. Um, also, and, and integrating technology has been a big focus. So I like to see that in continue. Yeah. Um, just, you know, older teachers like 66 myself are getting more comfortable with the technology and we're getting training and things like that. So, um, I would like to see that continue and get stronger. Just making it more relevant, the curriculum more relevant. I think we do that, like I said, at the upper levels really, really well. Yeah. Um, but it's just the, the other levels.” Discussion Research Question Three In order for students to become successful in a curriculum, educators must find ways to facilitate the acquisition of knowledge. “Teaching for mathematical proficiency is a responsibility that all schools bear (Doabler & Fien, 2013).” There are numerous theories on how this is best accomplished, but one thing is clear – it cannot be done in isolation. Focused collaboration and having a shared purpose, “helps to define purpose in practice and builds capacity that results in greater clarity and efficacy. More and more we see the education agenda being immersed with deep learning. This means innovation and continuous improvement coexist – always a difficult proposition (Fullan & Quinn, 2016, p. 129).” Departments and Professional Learning Communities exist in order develop common goals and spend time developing strategies to improve student learning. However, this is not always how the time is being utilized (Fullan & Quinn, 2016). According to the data collected, many decisions that are currently being made are found through perception and not concrete data. In order to create change, people must step out of their comfort zone and use intention to determine their next steps. Without change, the status quo will continue, and our marginalized student populations will continue to struggle in the subject of mathematics. Summary This chapter focused on answering three questions: 67 1. During high school math department meetings, how do math teachers describe their work with students, with each other and with the content? 2. What are the perceptions of the math department that exist among the school community? 3. Do high school math teachers believe there needs to be a change in how mathematics is taught and what evidence do they have to support that belief? Research question one focused primarily on how math departments and PLCs are organized in their meeting times. Most of the departmental meetings observed were focused around the practice of teaching, and did not incorporate the practice of analysis. There were no protocols for discussing student work and if data was brought into the meeting, it was very surface level. Therefore, many decisions made about best practices were developed from perceptions. Most discussions revolved around pacing and making sure that certain chapters would be covered by certain benchmarks throughout the school year. Additionally, many departments lack uniformity in grading practices. The second research question looked at how people perceive mathematics. Overall, the subject of math is considered difficult and finding success in the subject is reserved for a privileged group. Many students enter the class already believing that they will fail. Math is considered one of those subjects that you just have to get through. The pandemic did not alleviate any of the stress around the subject, with students returning to school with knowledge gaps in the subject matter. Even with many educators leaving the profession after the pandemic, new hires brought in are maintaining the status quo. Finding academic success for students was the overarching theme of the third question. Aside from being able to fund extra support outside of the classroom, students from wealthier neighborhoods have resources in the classroom to support academic success that students from 68 lower-income communities do not. However, after the pandemic, all schools need to reevaluate and shift their instructional practices in mathematics. Leadership is trying to find new solutions to students in a post-COVID-19 world, but many are still holding onto the way that things were done before the global pandemic. 69 Chapter Five: Recommendations This chapter will discuss the findings of the research conducted in the context of the realm of education. The findings will connect the data collected to the literature used to guide the study, as well as acknowledging any limitations with the data. Additionally, this chapter will provide implications for practice and recommendations for future research. In the state of California, minoritized students are unlikely to see themselves represented in their teachers. Diversity among teachers, has direct benefits for students of color in terms of improved math scores, graduation rates, motivation, and feelings of inclusion (CA Dept of Education). In the United States, few teachers from urban school districts are from the communities that they teach, creating a culture of White Supremacy in public education (Utt and Tochluck, 2020). To create an educational experience that is equitable in the learning and opportunities given to students, teachers need to acknowledge their own biases and develop intercultural understanding in the classroom (Lopez, 2003). The purpose of this study was to understand the perspectives of math teachers in relation to the students they teach, and recognize any underlying biases and assumptions that exist in their practice. The following research questions guided this study: 1. During high school math department meetings, how do math teachers describe their work with students, with each other and with the content? 2. What are the perceptions of the math department that exist among the school community? 3. Do high school math teachers believe there needs to be a change in how mathematics is taught and what evidence do they have to support that belief? To collect data, this research study implemented a qualitative methodology utilizing interviews and conducting observations. Interviews and observations were conducted at three 70 school sites, two representing a student population from low-income families and one representing students from affluent family demographics. At each school site, the following staff members were interviewed: a math department chair or PLC lead, a member of the math department, a department chair from another subject, and an administrator that worked with the math department. Additionally, each school site allowed me to observe a math department or PLC meeting. Both methods were utilized so that the data would reflect a more thorough gathering of the participants’ perspectives. Discussion of Findings Through an analysis of the data collected, an answer to all three questions was able to form. Each school site demonstrated a desire for their students to be successful in mathematics, and there were commonalities and individualities that existed in their approaches. Departmental meetings tend to be curriculum and subject matter based, instead of focusing on data and student outcomes. Additionally, the subject of mathematics has a reputation for being difficult and not accessible for all. However, despite students having difficulties, not every teacher believes that there needs to be a reevaluation of the curriculum and teaching practices. After observing departmental meetings and interviewing members of each school site, ten themes that emerged from the three research questions that guided the study. In this section, the finding of the study will be connected to the literature and current practices. Research Question One Research Question One asked, During high school math department meetings, how do math teachers describe their work with students, with each other and with the content? The data collected from this study revealed four findings among the three secondary public school sites that were studied. The first finding that was revealed was a consistent lack of protocol to keep 71 members of the department engaged in discussions. This supports Aguilar’s (2016) recommendations for implementing protocols to create equitable voices in the discussion, as well as maintaining focus and reaching deeper conversations. Additionally, the lack of engagement supports Fullan’s (2020) criticism of Professional Learning Committees having “superficial and uneven (p. 70)” collaborations. From the data collected through observation, every department meeting I attended had members of the department that were disengaged or working on their own. Two of the department meetings were designed with an agenda displayed at the front of the room while one individual at a time would present to the group. This gave members of the department opportunities to disengage from the discussion and work on their electronic devices. The third observed meeting was a working meeting, where people were working in groups, but their was no agenda or common purpose. Several members of that meeting were working in isolation, as well. The observation data was contradictory to the data that was collected through interviews. During the interviews, although no department chair was able to identify a protocol used to engaged members of a discussion, there was a belief that during meetings everyone is engaged. The second finding was that there was a lack of data and actual student work brought into the meetings. By not incorporating disaggregated data into discussions, teachers are making decisions based purely on their assumptions and perceptions (Roeman et al, 2019). This goes against Love’s (2019) writing that children of color need teachers that promote antiracist education. Maintaining a color-blind approach to classroom outcomes promotes maintaining the status quo, while incorporating antiracist teaching in a math class can empower marginalized students (Battey & Coleman, 2021). Allowing students to low scores to continue without using 72 data to gather a true understanding of what is going on, supports Turner’s (2020) claim that teachers will not take accountability for students’ low achievement. In the observations I conducted, no data or student work samples were brought into the meetings. One of the departments did discuss the process to gather data for future meetings and another school alluded to data being brought into prior meetings, but the practice of data analysis was never observed. During interviews, every department mentioned that data has been brough into meetings on occasion, but it was not part of their regular practice at this time. Additionally, no department analyzed their student performance data by race or gender. The most common subgroups that were looked at were English Learner and Special Education. In the two lower income schools, there is a push from administration to incorporate data analysis and reevaluate the way material is being taught and assessed. However, discussions and priorities among all the school sites seem to focus on pacing, curriculum, and logistics, instead of analysis of learning. That leads into the third finding, where pacing guides dictate the use of collaboration time. A recurring theme in all the departments, is where the teachers are at in the pacing guide and where they need to get to. This supports Rueda’s (2011) claim, “often school debates center around what should be taught (curriculum and standards) and how it should be assessed, (which test is the best?) rather than how to teach it (p. 33).” There is the feeling of a ticking clock when the pacing is discussed. This could be a result of the lasting impact No Child Left Behind has had on education and instruction. Since schools were evaluated on student performance in mathematics and English, there was a lot of attention placed on meeting benchmarks and achieving yearly progress on standardized tests (Horn et al, 2015). That would support Schunk’s (2020) self-worth theory, forcing the thought, do low standardized test scores affect the 73 motivation of students or teachers? However, speeding through the curriculum in order to cover all of the topics, does not allow time for deeper learning and knowledge acquisition. Every department meeting I observed involved substantial time dedicated towards pacing or curriculum planning. One school site was pitching new curriculum for the next year, another school site did check-ins with everyone to see where they are in the pacing guide, and the third site was dedicated entirely towards planning the pacing out. Through interviews, members of each school site mentioned the importance of the pacing guide to their subject matter. At one site, an English teacher expressed how students hear their math teacher consistently express their concern about being behind in the pacing. At another school site, an administrator voiced her frustration that teachers were more concerned with staying on pace than whether their students demonstrated mastery of the curriculum. The final finding of this question was that demonstrating understanding of the subject matter depended on which teacher you have, because there are not common grading practices among the departments. This goes against Hattie’s belief that “what is needed to raise the bar and close the gap is consensus and skill development by all teachers engaged with groups of students around the most impactful strategies (Fullan & Quinn, 2016, p. 91).” Additionally, the purpose of grades should be used to provide feedback, not fear or motivation. According to the literature, feedback and accomplishments build the self-efficacy in students (Bi et al, 2022), and students that have higher self-efficacy will demonstrate greater motivation and expectations of positive outcomes (Rueda, 2011). If the expectation of teachers is unclear or change depending on who is assessing your knowledge, then students will struggle to understand how to be successful in the classroom. 74 Through qualitative data collected through interviews, members outside of the math departments expressed confusion about grading policies. One teacher expressed frustration that at their school site math teachers weighed tests and quizzes differently in each class. Additionally, one teacher weighs 99% of their grade on tests and did not provide supportive feedback towards a student that struggles with tests. At another school site, a math teacher mentioned that she was the only member of her PLC implementing standards-based grading. The third school site department chair mentioned that their department all use standards-based grading. However, the administrator at that site expressed that some teachers did not allow retakes on assessments and did not pass students because of missing homework. The department chair felt that students were unmotivated and showing apathy, but she was unsure where this trend was coming from. Research Question Two Research Question Two asked, What are the perceptions of the math department that exist among the school community? There were two findings that came about from this research question. The first finding showed that there is a perception that math is hard and being successful in the subject is only for a privilege group. This belief supports Moses & Cobb’s (2002) assertion that math is a gatekeeper subject, used to train an elite few. With accelerated and honors math classes, students are indirectly separated and tracked through their high school experience. According to Bi et al (2022), there is a correlation between a student’s achievement in mathematics and their decision to enter the STEM fields, where careers such as data science are among the fastest growing opportunities (Schwartz, 2023). Additionally, students that succeed in math are more likely complete a college degree (Thompson, 2017) 75 Two of the math departments that were observed, focused their meetings on improving outcomes for their Integrated Math 1 or Algebra 1 students, since this is where students tend to struggle the most. At these two schools, the departments are trying to get creative with their curriculum and teaching practices for these classes, while the higher and accelerated math courses are maintaining their traditional trajectory. Through interviews, teachers inside and outside of the math department echoed that math is the subject where students have the most difficulty. An English teacher, at one of the sites, stated that she lets her students know that she had difficulty with math, as well. The PLC lead (Latino) and department member (Latina) both expressed their efforts to connect and inspire their Latinx students based off their shared histories. This leads into the second finding of the question, regarding the staffing of the departments with vacancies post-COVID. Smtih (2022) stated that there is need for more diversity in math teachers, and this is true depending on the school site. Overall, the Latinx and Black teachers were a smaller percentage of the staff among the three school sites. However, one of the lower-income sites seems to have hired with intention, as only one member of the department meeting was not Latinx or Black. This supports Love’s (2019) imperative of students of color needing teachers that look like them in the classroom. According to the literature, there is a higher turnover rate in lower income schools (Papay et al, 2017). This was observed to be true, as there are several new teachers in the department at the two lower-income schools, while the higher-income school has had the same teachers for at least five years. Based off perceptions gathered from observation data, six out of ten teachers at Ridgemont High School were Black or Latinx, six out of seven teachers were Black or Latinx at James Buchanan High School, and 1 out of 19 teachers might have been Latinx at Bayside High 76 School. Fifteen of their teachers were White and 3 were Asian. During interviews, the department chairs at both Ridgemont and James Buchanan expressed an imperative to integrate the new teachers and get them comfortable with the dynamics of the department. A department member at James Buchanan expressed how well their district pays, however, there is still turnover. The principal at Ridgemont High is excited about her new hires, but worries that they will be too intimidated to speak up during the departmental meetings. Research Question Three Research Question Three asked, Do high school math teachers believe there needs to be a change in how mathematics is taught and what evidence do they have to support that belief? Three findings came out of the data collected from this research question. The first finding addressed the district funds and access to resources. The academic achievement at Bayside is higher than the scores at Ridgemont and James Buchanan, supporting Pearcy (2020) claim that there is a correlation between student achievement and the average income of the families enrolled at the school. The amount of new teachers at the lower income schools in contrast to Bayside proves Lafortune’s (2019) claim that most of LCFF funds for lower income schools goes towards staffing needs, leaving the schools with more novice teachers. Additionally, the facilities and extra curriculars available at the higher-income school supports Rivera’s (2018) claim that these schools are able to utilize bonds to maintain and build their facilities. Based off data collected from the California School Dashboard, all schools are performing below standard in math scores, but the higher income high school performs exponentially stronger than the other two schools and scores higher than the state average. Additionally, through interviews, faculty at Bayside expressed that there was not a funding issue when teachers needed support. During the departmental meeting, teachers were presenting new 77 alternative classes for Algebra 1 students, and they all seemed to have support. The administrator discussed the strong performing arts programs at the school, and the department chair I spoke with mentioned that she is able to teach her music production course in a recording studio at the school. Additional data shows that there is a declining enrollment of White students and a rising enrollment of Hispanic students over the last five years at Bayside, a community that has been very outspokenly conservative in the political beliefs the last five years. The second finding recognized the need for accountability to build academic success. Data collected from all the sites supports the claim that “unsuccessful” school were critical of each other, misaligned, and highly focused on improving test scores (Fullan, 2020). Data collected also supported that teams feel annoyed by agendas passed down from administrators was supported (Weddle, 2020). In order to develop a student-focused culture of collaboration, the stakeholders must come together to develop a shared vision. Once that vision is established, maintaining accountability with each other is crucial (Fullan & Quinn, 2016). Through interviews, all three administrators expressed a desire to be more involved in their math meetings. Each school site seemed to take a different approach to setting a vision and goals for this school year. At Bayside, the administrator said he give the department chair complete autonomy for the department. At James Buchanan, the administrator mentioned they were adopting a district vision, but it was only currently being implemented with the Integrated 1 PLC. He mentioned that the higher-level math classes had more tenured teachers that were not as willing to adopt new teaching practices. At Ridgemont, the administrator and department chair did not seem to be on the same at this time. The administrator is sending members of her department on a professional development to hopefully inspire them to investigate new practices. The department chair was annoyed at having to go on the trip. 78 The third finding was a fear of change among many members of the departments. Kegan & Lahey (2011)’s claim of an immunity to change being upsetting to managers was supported by the data. Achor (2018) says that change can be initiated by one individual, but ultimately it needs to worked on cohesively by the entire group. Organizations cannot reach its full potential when people work as individuals. At this point, the data does not support this claim. People are trying to initiate changes in culture at two of the school sites, but as of right now the status quo is maintained. This could change in the future, though. Through observation data, the only school that was enthusiastic about change was Bayside where they were looking at new curriculum opportunities. Even there, though, people still voiced their skepticism towards the ideas and the ability of the students. At Buchanan, there is a push to integrate new practices, but, according to interviews, the more veteran teachers have been resistant to change the way they have been teaching for the last ten years. At Ridgemont, nothing observed showed any steps towards change. The department meeting was all about maintaining the current culture. Through interviews, the department chair at Ridgemont expressed that there was no need to change the curriculum, because she likes what it offers. However, among the three school sites, they have the lowest average score in state testing according to the California Dashboard. Limitations The limitations of this study reside mainly in the samples that were used and the date and time in the field. Although the samples sites chosen were reflective of the income criteria established in the design of the study, the demographics of two of the sample sites were very similar. There was not a school site that implemented a significant African American population for this study. Therefore, much of the literature utilized for the study did not apply to the data 79 that was collected. Additionally, because of the time and availability of the participants, departmental meetings were only observed one time. This led to a very small sample size of observed teacher collaboration time and structure. The findings from this study were gathered from conducting one departmental observation and four individual interviews at each of three separate Southern California public high school sites (12 total interviews and 3 total observations). Implications for Practice This study addressed impact math teachers have on students and the school community at public Southern California high schools. The study acknowledged how members of the math department make informed decisions about their practice, and how those decisions translate to student outcomes. Additionally, high school math teachers need to develop a cultural understanding of their students and build an awareness of the effect math has on their students’ future. A third implication is that there needs to be a shared vision between math teachers and administrators to establish accountability for students finding success in their classes. Data collection and analysis must become a regular practice during department collaboration time. Without hard evidence, department decisions are made solely on perception and biases. This leads to unfair and prejudiced expectations in the classroom. According to the data collected, math teachers are making decisions based on time. Teachers are looking at the standards and determining where they will start and where they will finish at the end of the school year, but they do not look at what their students are understanding. When students are unable to keep pace with the teacher, they are left to repeat the same class the next year. Each school site is putting a major focus on improving the outcomes and supporting student in their freshman year math class, because so many are not passing and moving forward. However, 80 based off the data collected, these decisions appear to be made on the fact that students did not pass. At no point, is data used to answer the question, why did they not pass? Addressing this issue, begins with math departments and their school sites adopting and developing a culture of data driven decision making and true collaboration. Every school site that was observed already had PLC time built into the schedule for departments to meet, but the purpose had not fully been defined (Fullan & Quinn, 2016). There was a lot of focus on test scores and improving test scores, but there was very little discussion on what students were learning. With the support of administration, the departments need to develop their own norms and set their agenda with a focus on improving student outcomes (Weddle, 2020). Embedded in these norms should be protocols designed around data collection and analysis (Schmoker, 2011). Through this process, department members can develop a clarity in what works for their students and make equitable decisions on how to plan lessons and develop strategies to improve outcomes. The second implication is the need for teachers to develop an awareness and understanding of their students. Many teachers continue to teach the curriculum the way that they learned it in high school, because that is what is familiar to them. However, that does not mean that it is what is familiar to their students. According to data, it is unlikely that students from our marginalized populations will see themselves reflected in their math teacher. Additionally, teachers that continue to use the same strategies to teach curriculum are producing the same results. If students are consistently ending the year without understanding the material, that is setting them up for inequitable opportunities beyond high school. Students that show competencies in mathematics are given access to opportunities that students that struggle with 81 math do not. To create equity, math teachers must develop a sense of their students’ positionality and their own. Effective teaching is about understanding students. According to Roegman et al (2019), to become an equity focused teacher, you must begin with examining your own perception and understanding of equity and race. From there, teachers can begin to reevaluate the instruction and culture in their classroom and adopt antiracist teaching practices and culturally relevant pedagogy. However, this requires the support of administration through professional development. This is not something that can be corrected overnight, because it requires a shift in culture and for people to unlearn the way that they have learned how to do things. Whether they are aware of it or not, everyone bares competing commitments, and to challenge this and create change, we need to be confronted with this (Kegan & Lahey, 2011). Through collaborative learning, school sites can build the capacity of their math departments and create change that has a positive outcome on students (Fullan & Quinn, 2016) The third implication is that teachers and administrators need to establish a shared vision and develop a system of accountability. As much as teachers need to develop the self-efficacy and capacity of their students, they need to do the same with their colleagues. They should be empowered to try new things and step out of their comfort zone. Without this support, teachers will not develop and begin working in isolation. Additionally, when goals feel forced upon a department, resentment can build (Weddle, 2020). As much as faculty need to understand their students’ perspectives, they must understand and help develop the culture of the school. With the development of a shared vision, everyone feels involved with the outcomes and accountable for carrying out the goals. “Constantly improving and refining instructional practice so that students 82 can engage in deep learning tasks is perhaps the single most important responsibility of the teaching profession and educational systems as a whole (Fullan & Quinn, 2016, p. 110).” Accountability is developed through the relationships and culture of collaboration. Within departments, teachers need to develop a shared vision and focused community agreements. The relationship between team members and the culture of the department will set expectations of accountability for each member. If everyone feels supported and has a voice, then there will be increased engagement from all members. However, there needs to be engagement from the administration, as well, as transforming schools to meet student needs cannot be done alone (Aguilar, 2016). Securing accountability, focusing direction, and cultivating collaboration are just three of the principles of Fullan & Quinn’s (2016) “coherence”. There still needs the development of a system of continuous improvement, and with administrativ involvement and engagement, schools can truly create changes necessary to develop the capacity of both teacher and students. Future Research There are several avenues for continuing the research contained in this study. Students have struggled in mathematics for a long time, so improving outcomes will be a large endeavor. As research on this continues, more recommendations and solutions may develop, but for now there are three areas that should be addressed. It would be beneficial to try and establish a more generalized understanding of the impact of the math department. For starters, more perspectives should be gathered to build a stronger understanding. In order to do this, data needs to be collected at schools that serve demographics that were not evaluated in this study. Additionally, perspectives of other members of faculty would be beneficial. Currently, no guidance counselors or special education teachers were 83 interviewed. Also, no members of the classified staff were interviewed for their perspective. Lastly, since the purpose is to gather the impact on the school community, gathering data from parents and students would produce valuable results. The second recommendation would be to research professional development opportunities for math teachers in this realm. Everyone’s epistemology is developed from their own experiences throughout their life. They have their own perspectives and understandings of situations, so to change this would take very focused work. In order to build the capacity of teachers to uncover their unconscious biases and develop an understanding of their students’ perspectives, there needs to be coaching and practice. A one day professional development training will not produce the intended results, this must be a program designed for the long term. The third recommendation is to continue investigate and develop efforts to diversify the STEM teacher workforce. Our marginalized communities are grossly underrepresented not just as STEM teachers, but the entire field of STEM. This is very cyclical, as students will not believe that something is possible if they do not see people that look like them in that field. If we can bring more diverse representation into teaching math, diverse students will connect to the material more, producing greater outcomes for our minoritized students. Conclusions This study confirmed the belief that math teachers have a substantial impact on the culture, reputation, and outcomes of a school. Math teachers want their students to be successful in their academic pursuits, but not everyone knows how to do this, so it is imperative to develop their capacity to understand the students in their classroom. Additionally, improving student outcomes in mathematics is not a job to be done in isolation. Effective collaboration is crucial to accomplishing this feat, but, once again, the capacity to collaborate must be developed and 84 established in teachers and administrators, as well. Lastly, math has a very strong reputation for being difficult, and many students enter the classroom on day one with the mindset that they are going to fail. There are numerous studies conducted that show a correlation between success in mathematics and success after high school graduation. There is a moral obligation for math teachers to make their curriculum accessible to their students. You are not teaching math, you are teaching students. 85 References Achor, S. (2018). 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Case study research and applications: Design and methods. SAGE Publications, Inc. 98 Appendix A: Research Introduction Letter Date Mr./Ms./Dr. _______________, My name is Michael Watter, and I am a Doctoral Candidate at the University of Southern California’s Rossier School of Education in the Educational Leadership program. I am currently conducting research for my dissertation: The Positionality and Power Dynamics of High School Math Departments. I am conducting a qualitative methods study examining the impact that the perceptions, beliefs, and attitudes of math teachers have on student outcomes. I will be using observation and structured interviews as my instruments. This study has been approved by the University of Southern California’s Institutional Review Board (attached). Based on your school community, I am inviting your school site to participate in the study. I would like to be able to interview your math department chair, the administrator that works with the math department, another teacher in the math department, and the chair of another subject’s department or member of your Instructional Leadership Team. Participation is voluntary, your school’s contributions will add to the growing literature surrounding the importance of students’ success in mathematics for future educational opportunities. If you are willing to allow me to collect data at your school site, please respond to this email and I will follow up with you the members of your math department regarding the completion of the Informed Consent Form (attached). You may contact me at watter@usc.edu. Thank you in advance for your consideration in participating in my study, Respectfully, Michael Watter University of Southern California Doctoral Candidate 99 Appendix B: Recruitment Letter (Teacher Interview) Date Mr./Ms./Dr. _______________, My name is Michael Watter, and I am a Doctoral Candidate at the University of Southern California’s Rossier School of Education in the Educational Leadership program. I am currently conducting research for my dissertation: The Positionality and Power Dynamics of High School Math Departments. I am conducting a qualitative methods study examining the impact that the perceptions, beliefs, and attitudes of math teachers have on student outcomes. I will be using observation and structured interviews as my instruments. This study has been approved by the University of Southern California’s Institutional Review Board (attached), and I have received permission from Mr./Ms./Dr. _______________ to reach out to you for participation in this study. I would like to be able to interview you about the impact the math department at your school has on students. Participation is voluntary, but your contribution will add to the growing literature surrounding the importance of students’ success in mathematics for future educational opportunities. If you are open to being interviewed, please respond to this email and I will follow up with you regarding the completion of the Informed Consent Form (attached). You may contact me at watter@usc.edu. Thank you in advance for your consideration in participating in my study, Respectfully, Michael Watter University of Southern California Doctoral Candidate 100 Appendix C: Recruitment Letter (Math Department Chair) Date Mr./Ms./Dr. _______________, My name is Michael Watter, and I am a Doctoral Candidate at the University of Southern California’s Rossier School of Education in the Educational Leadership program. I am currently conducting research for my dissertation: The Positionality and Power Dynamics of High School Math Departments. I am conducting a qualitative methods study examining the impact that the perceptions, beliefs, and attitudes of math teachers have on student outcomes. I will be using observation and structured interviews as my instruments. This study has been approved by the University of Southern California’s Institutional Review Board (attached), and I have received permission from Mr./Ms./Dr. _______________ to reach out to you for participation in this study. I would like to be able to observe one of your department meetings and interview you about the impact the math department at your school has on students. Participation is voluntary, but your contribution will add to the growing literature surrounding the importance of students’ success in mathematics for future educational opportunities. If you are open to being interviewed and having me observe department time, please respond to this email and I will follow up with you regarding the completion of the Informed Consent Form (attached). You may contact me at watter@usc.edu. Thank you in advance for your consideration in participating in my study, Respectfully, Michael Watter University of Southern California Doctoral Candidate 101 Appendix D: Observation Protocol Introduction Hello everyone, I’m Michael Watter. I’m currently working on my Ed. D at USC, but I have been a secondary math teacher for the last twelve years. However, for today I am only playing the role of researcher. Currently, I am working on my dissertation, and I’ve chosen to study high school math departments. I want to learn how the math department impacts that educational journey of students. Mr./Ms./Dr. _______________ invited me to observe your meeting today, so thank you so much for welcoming me. I’m going to sit off to the side and take notes today, but they are solely for myself, and all identities will be anonymous. Does anyone have any questions? (PAUSE) As long as you are comfortable with everything, I will be recording audio of the meeting, as well. If you want to participate in the meeting but wish to not be observed or recorded for research purposes, you are welcome to opt out of the process and no data will be recorded about you. If you wish to exercise this right, please let me know. (PAUSE) Thank you so much for welcoming me, and I did bring some coffee and treats from Porto’s, so please help yourself. Research Questions 1. During high school math department meetings, how do math teachers describe their work with students, with each other and with the content? 2. What are the perceptions of the math department that exist among the school community? 3. Do high school math teachers believe there needs to be a change in how mathematics is taught and what evidence do they have to support that belief? Conceptual Framework • Internal Perceptions of the Math Department o What conscious and unconscious biases exist among the members of the department, especially in relation to the student population. o What competing commitments exist among the math department, if any, that can create an immunity to change? 102 Map of the Space Notes – Times to be updated based on schedule and flow of department meeting. 1:00pm – 1:05pm – 1:10pm – 1:15pm – 1:20pm – 1:25pm – 1:30pm – 1:35pm – 1:40pm – 1:45pm – 1:50pm – 1:55pm – 2:00pm – 103 Appendix E: Interview Protocol (Math Teacher / Department Chair) Introduction Thank you so much for giving me your time and agreeing to participate in my study. As I mentioned in our correspondence, the interview should take about an hour, does that still work for you? Before we get started, I would like to remind you about the purpose of this study that was detailed in the Study Information Sheet, and answer any questions you might have. Currently, I am a doctoral student at USC conducting research on the perceptions and influence the math department has on the school community as a whole. I am particularly interested in understanding how department members feel about their students and their own positionality among the school. Additionally, I am talking to math departments from high-income high schools, middle-income high schools, and low-income high schools. I will also speak with faculty from another department, your department chair, and an administrator to gain further information from their perspective. Although I am currently working as a math teacher, as well, I want to assure you that today I am strictly playing the role of researcher. This means that my questions are not evaluative and I will not be making any judgments of you as a teacher. My goal is to understand your perspective. Additionally, as stated in the Study Information Sheet, this interview is confidential. Your name will not be shared with anyone outside of the research team. This includes not revealing your name to other teachers, the principal, or the district. The data for this study will be compiled into a report and, although I may use some of what you say as a direct quote, no data will be directly attributed to you. A pseudonym will be used to protect your confidentiality and I 104 will make every effort to de-identify any of the data I gather from you. The data will be kept in a password protected computer and will be destroyed after 3 years. If you would like, I would be happy to provide you with a copy of my paper once the study is completed. Are there any questions you may have about the study before we get started? I have an audio recording app on my cell phone so that I can accurately capture what you share with me. The recording is solely for my purposes to best capture your perspectives and will not be shared with anyone outside the research team. May I have your permission to record our conversation? Questions (with transitions) I’d like to begin by getting to know a little bit about your journey. 1. Please tell me about your teaching experiences. (Background / Demographic Questions) a. How long have you been teaching? b. What subject(s) do you teach? c. What involvement, if any, do you have with the school outside of the classroom? 2. What made you want to become a teacher? (Background / Demographic Questions) That is great information and thank you for sharing. I would now like to build an understanding of how your department operates. 3. How often, if at all, does your department meet? (Competing Commitments / Experience and Behavior Questions) a. How often, if at all, does your department meet by subjects taught? 4. What is generally discussed in the department meetings? (Biases / Knowledge Questions) a. Are there any recurring themes in the meetings? b. What, if any, are the department goals for this school year? 105 5. During department meetings, what protocols, if any, are used to discuss student work? (Biases / Experience and Behavior Questions) a. How is everyone engaged in discussions? b. Is data ever brought into the department meetings? 6. What populations, if any, is student work disaggregated by? (Biases / Experience and Behavior Questions) a. Do you ever organize student outcomes by race? b. Do you ever organize student outcomes by gender? Thank you so much for describing that for me. Next, I want to understand the perceptions of mathematics at your institution. 7. How do you feel about your students’ academic performance in mathematics? (Biases / Feeling Questions) a. Why do you feel that way? 8. How do you feel this school prioritizes academic achievement in math? (Biases / Feeling Questions) a. Why do you feel that way? 9. What adjustments, if any, would you like to see in the math curriculum that is being implemented here? (Biases, Competing Commitments / Opinion and Values Question) Finally, I would like to give you an opportunity to add any information that you feel is relevant to my research. 10. So, suppose that I was a new math teacher here at the school. What would you like me to know about the school before my first day of work? (Biases, Competing Commitments / Hypothetical Question) 106 Closing Thank you so much for inviting me into your classroom and sharing your perspective with me today! I really appreciate your time and honesty. Everything that you have shared will be beneficial for the development of my study. Additionally, If I suddenly have any follow-up questions, may I contact you, and if so, is email appropriate? Again, thank you for participating, and, as a thank you, please accept this Starbucks gift card as a small token of my appreciation. 107 Appendix F: Interview Protocol (Other Department Chair) Introduction Thank you so much for giving me your time and agreeing to participate in my study. As I mentioned in our correspondence, the interview should take about an hour, does that still work for you? Before we get started, I would like to remind you about the purpose of this study that was detailed in the Study Information Sheet, and answer any questions you might have. Currently, I am a doctoral student at USC conducting research on the perceptions and influence the math department has on the school community as a whole. I am particularly interested in understanding how department members feel about their students and their own positionality among the school. Additionally, I am talking to math departments from high-income high schools, middle-income high schools, and low-income high schools. I have spoken with members of the math department, but would also like to hear your perspective. Although I am currently working in education, as well, I want to assure you that today I am strictly playing the role of researcher. This means that my questions are not evaluative and I will not be making any judgments of you as a professional. My goal is to understand your perspective. Additionally, as stated in the Study Information Sheet, this interview is confidential. Your name will not be shared with anyone outside of the research team. This includes not revealing your name to other teachers, principals, or district personnel. The data for this study will be compiled into a report and, although I may use some of what you say as a direct quote, no data will be directly attributed to you. A pseudonym will be used to protect your confidentiality and I will make every effort to de-identify any of the data I gather from you. The data will be 108 kept in a password protected computer and will be destroyed after 3 years. If you would like, I would be happy to provide you with a copy of my paper once the study is completed. Are there any questions you may have about the study before we get started? I have an audio recording app on my cell phone so that I can accurately capture what you share with me. The recording is solely for my purposes to best capture your perspectives and will not be shared with anyone outside the research team. May I have your permission to record our conversation? Questions (with transitions) I’d like to begin by getting to know a little bit about your journey. 1. Please tell me about your teaching experiences. (Background / Demographic Questions) a. How long have you been teaching? b. What subject(s) do you teach? c. What involvement, if any, do you have with the school outside of the classroom? 2. What made you want to become a teacher? (Background / Demographic Questions) That is great information and thank you for sharing. I would now like to build an understanding of how your department operates. / school operates 3. How often, if at all, does your department meet? (Competing Commitments / Experience and Behavior Questions) a. How often, if at all, does your department meet by subjects taught? 4. What is generally discussed in the department meetings? (Biases / Knowledge Questions) a. Are there any recurring themes in the meetings? b. What, if any, are the department goals for this school year? 5. During department meetings, what protocols, if any, are used to discuss student work? 109 (Biases / Experience and Behavior Questions) a. How is everyone engaged in discussions? b. Is data ever brought into the department meetings? 6. What populations, if any, is student work disaggregated by? (Biases / Experience and Behavior Questions) a. Do you ever organize student outcomes by race? b. Do you ever organize student outcomes by gender? Thank you so much for describing that for me. Next, I want to understand the perceptions of mathematics at your institution. 7. How do you feel about your students’ academic performance in mathematics? (Biases / Feeling Questions) a. Why do you feel that way? 8. How do you feel this school prioritizes academic achievement in math? (Biases / Feeling Questions) a. Why do you feel that way? 9. What adjustments, if any, would you like to see in the math curriculum that is being implemented here? (Biases, Competing Commitments / Opinion and Values Question) Finally, I would like to give you an opportunity to add any information that you feel is relevant to my research. 10. So, suppose that I was a new teacher here at the school. What would you like me to know about the school before my first day of work? (Biases, Competing Commitments / Hypothetical Question) 110 Closing Thank you so much for inviting me into your classroom / school and sharing your perspective with me today! I really appreciate your time and honesty. Everything that you have shared will be beneficial for the development of my study. Additionally, If I suddenly have any follow-up questions, may I contact you, and if so, is email appropriate? Again, thank you for participating, and, as a thank you, please accept this Starbucks gift card as a small token of my appreciation. 111 Appendix G: Interview Protocol (Administrator) Introduction Thank you so much for giving me your time and agreeing to participate in my study. As I mentioned in our correspondence, the interview should take about an hour, does that still work for you? Before we get started, I would like to remind you about the purpose of this study that was detailed in the Study Information Sheet, and answer any questions you might have. Currently, I am a doctoral student at USC conducting research on the perceptions and influence the math department has on the school community as a whole. I am particularly interested in understanding how department members feel about their students and their own positionality among the school. Additionally, I am talking to math departments from high-income high schools, middle-income high schools, and low-income high schools. I have spoken with members of the math department, but would also like to hear your perspective. Although I am currently working in education, as well, I want to assure you that today I am strictly playing the role of researcher. This means that my questions are not evaluative and I will not be making any judgments of you as a professional. My goal is to understand your perspective. Additionally, as stated in the Study Information Sheet, this interview is confidential. Your name will not be shared with anyone outside of the research team. This includes not revealing your name to other teachers, principals, or district personnel. The data for this study will be compiled into a report and, although I may use some of what you say as a direct quote, no data will be directly attributed to you. A pseudonym will be used to protect your confidentiality and I will make every effort to de-identify any of the data I gather from you. The data will be 112 kept in a password protected computer and will be destroyed after 3 years. If you would like, I would be happy to provide you with a copy of my paper once the study is completed. Are there any questions you may have about the study before we get started? I have an audio recording app on my cell phone so that I can accurately capture what you share with me. The recording is solely for my purposes to best capture your perspectives and will not be shared with anyone outside the research team. May I have your permission to record our conversation? Questions (with transitions) I’d like to begin by getting to know a little bit about your journey. 1. Please tell me about your teaching experiences. (Background / Demographic Questions) a. How long have you worked in education? b. How did you become an administrator? c. What are your responsibilities here at ________ High School? 2. What made you want to become an administrator? (Background / Demographic Questions) That is great information and thank you for sharing. I would now like to build an understanding of how your department operates. / school operates 3. How often, if at all, does your school meet by subject? (Competing Commitments / Experience and Behavior Questions) a. How often, if at all, do you attend those meetings? 4. What is generally discussed in the department meetings? (Biases / Knowledge Questions) a. Are there any recurring themes in the meetings? b. What, if any, are the department goals for this school year? 113 5. During department meetings, what protocols, if any, are used to discuss student work? (Biases / Experience and Behavior Questions) a. How is everyone engaged in discussions? b. Is data ever brought into the department meetings? 6. What populations, if any, is student work disaggregated by? (Biases / Experience and Behavior Questions) a. Do you ever organize student outcomes by race? b. Do you ever organize student outcomes by gender? Thank you so much for describing that for me. Next, I want to understand the perceptions of mathematics at your institution. 7. How do you feel about your students’ academic performance in mathematics? (Biases / Feeling Questions) a. Why do you feel that way? 8. How do you feel this school prioritizes academic achievement in math? (Biases / Feeling Questions) a. Why do you feel that way? 9. What adjustments, if any, would you like to see in the math curriculum that is being implemented here? (Biases, Competing Commitments / Opinion and Values Question) Finally, I would like to give you an opportunity to add any information that you feel is relevant to my research. 10. So, suppose that I was a new teacher here at the school. What would you like me to know about the school before my first day of work? (Biases, Competing Commitments / Hypothetical Question) 114 Closing Thank you so much for inviting me into your classroom / school and sharing your perspective with me today! I really appreciate your time and honesty. Everything that you have shared will be beneficial for the development of my study. Additionally, If I suddenly have any follow-up questions, may I contact you, and if so, is email appropriate? Again, thank you for participating, and, as a thank you, please accept this Starbucks gift card as a small token of my appreciation. 115 Appendix H: Informed Consent Form University of Southern California Rossier School of Education 3470 Trousdale Parkway Los Angeles, CA 90089 INFORMATION/FACTS SHEET FOR EXEMPT NON-MEDICAL RESEARCH The Positionality and Power Dynamics of High School Math Departments You are invited to participate in a research study. Research studies include only people who voluntarily choose to take part. This document explains information about this study. You should ask questions about anything that is unclear to you. PURPOSE OF THE STUDY The purpose of this study is to examine the conversations around students and student achievement in mathematics that exist among high school faculty to provide insight into the impact the math faculty have on students’ educational outcomes and the school community. This study utilizes observation and interviews to collect data. This study is unique in that it will be collecting data from three different school sites serving different socio-economic status. The findings in this study might also be beneficial and relevant for other similar organizations. PARTICIPANT INVOLVEMENT If you agree to take part in this study, you will be asked to participate in a 60 minutes semistructured one-on-one interview. All interviews will be audio-taped with permission. You do not have to answer any questions you do not want to during the interviews. If you do not want to be taped during the interview, handwritten notes will be taken. ALTERNATIVES TO PARTICIPATION Your alternative is to not participate. Your relationship with your employer will not be affected whether you participate or not in this study. CONFIDENTIALITY Michael Watter will be the Principal Investigator of this study. Any identifiable information obtained in connection with this study will remain confidential. Your interview responses will be coded with a false name (pseudonym) and maintained separately. You will have the right to review and edit the audio recordings or transcripts of the one-on-one interviews. All audio-tapes related to this study will be destroyed once they have been transcribed. The transcripts will be stored on a password protected computer, which only the Principal Investigator can access. After three years, all files will be destroyed. The members of the research team and the University of Southern California’s Human Subjects Protection Program (HSPP) may access the data. The HSPP reviews and monitors research studies to protect the rights and welfare of research subjects. 116 INVESTIGATOR CONTACT INFORMATION If you have any questions or concerns about the study, please contact the following individuals: Principal Investigator Michael Watter watter@usc.edu Faculty Advisor David Cash dcash@usc.edu IRB CONTACT INFORMATION University Park Institutional Review Board (UPIRB), 3720 South Flower Street #301, Los Angeles, CA 90089-0702, (213) 821-5272 or upirb@usc.edu SIGNATURE OF RESEARCH PARTICIPANT I have read the information provided above. I have been informed and given a chance to ask questions. My questions, if any, have been answered to my satisfaction and I agree to participate in this study. I have been provided with a copy of this form. ______________________________________________ Printed Name of Participant Providing Consent ______________________________________________ __________________ Signature of Participant Providing Consent Date SIGNATURE OF INVESTIGATOR I have explained the research study to participants and answered all questions, if any. It is my judgement that this participant is knowingly and willingly agreeing to participate in this study. They have the legal right to give informed consent to their participation in this study in all various components. They have also been informed that participation in this study is voluntary and that participation can be stopped at any point in the data collection, for any reason. _______________________________________________ Printed Name of Principal Investigator Obtaining Consent _______________________________________________ _________________ Signature of Principal Investigator Obtaining Consent Date 117 Appendix I: Conceptual Framework

Abstract (if available)

Abstract This study applies Critical Race Theory to develop an awareness of the positionality and power dynamics that exists among the math faculty at schools that serve high income and low-income communities to develop an understanding of the learning gap that exists among Southern California’s marginalized student populations. The purpose of this study is to uncover underlying biases and assumptions of the math faculty and understand how they describe their work with students, with each other, and with the content they teach. Also, the study looks to uncover what the perceptions of the math department are that exist among the school community. Additionally, it seeks to find out if math teachers believe there needs to be a change in how mathematics is taught and what evidence they have to support that belief. Qualitative data was gathered using interviews and observations at three different Southern California high schools to understand trends and commonalities. One school was populated by students from a high-income community, and two school were populated by students from low-income communities. The interviews were conducted with an administrator, math department head, math department member, and the department chair of another subject at each school site. The observations were of math department meetings at each school site. Findings show that data driven discussions need to be more present during departmental meetings. Strategies to develop cultural awareness and understanding towards students need to be developed. Collaboration and accountability need to be developed in departmental and schoolwide pursuits. This study begins to understand how math teachers perceive their roles as educators and offers suggestions to create a collaborative structure and improved student outcomes.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Watter, Michael Steven (author)

Core Title The positionality and power dynamics of high school math departments

School Rossier School of Education

Degree Doctor of Education

Degree Program Educational Leadership

Degree Conferral Date 2024-05

Publication Date 04/17/2024

Defense Date 03/29/2024

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

Tag achievement gap,building capacity,collaboration,departments,effective collaboration,equitable teaching,equity,faculty,gatekeeper,immunity to change,math,math anxiety,math education,mathematics,OAI-PMH Harvest,Secondary,student outcomes,unconscious biases

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Cash, David (committee chair), Crew, Rudolph (committee member), Smith, Wesley (committee member)

Creator Email mwatter@gmail.com,watter@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC113880189

Unique identifier UC113880189

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Legacy Identifier etd-WatterMich-12830

Document Type Dissertation

Format theses (aat)

Rights Watter, Michael Steven

Internet Media Type application/pdf

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Source 20240418-usctheses-batch-1142 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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