Authentic partnerships, advocacy and reflection : creating inclusive, culturally responsive community college mathematics classrooms

Material Information

Authentic partnerships, advocacy and reflection : creating inclusive, culturally responsive community college mathematics classrooms
Silverstein, Lisa M.
Place of Publication:
Denver, CO
University of Colorado Denver
Publication Date:

Thesis/Dissertation Information

Doctorate ( Doctor of philosophy)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
School of Education and Human Development
Degree Disciplines:
Education and human development
Committee Chair:
Hipolito-Delgado, Carlos
Committee Members:
Davis, Alan
Jefferson, Antwan
Hurtado, Sylvia


Community colleges are often considered an affordable entry point into postsecondary education for many students with a goal of earning a degree. As open access institutions, they accept any student who applies, including those considered to be below college level and in need of some level of remediation in the subjects of reading, writing and math. The need for remediation tends to be highest in the subject of math, with rates as high as 78%. Community colleges are also known to be the most diverse of higher education institutions, where students of color make up 90% of the student population requiring remediation. Students needing remediation contribute to higher attrition rates in community colleges, as remediation is considered a barrier to degree attainment. To address this issue, community colleges are revamping the ways in which remediation, commonly referred to as developmental education, is delivered. The purpose of this study was to learn how instructors who teach introductory mathematics courses in community colleges address attrition by creating inclusive environments that promote a perceived sense of belonging in their classrooms of diverse learners. The study was conducted at a diverse, urban community college with Hispanic Serving Institution status, addressing developmental education attrition by pairing a developmental course with an introductory college level course to accelerate the developmental sequence for students to earn college credit. The Multicontextual Model for Diverse Learning Environments, developed by Hurtado, Alvarez, Guillermo-Wann, Cuellar & Arellano (2012) was the conceptual framework, to first look at how students perceived their mathematics experiences and second, how instructors navigated the institutional learning environment to create a space of validation, belonging and engagement with and for their students. Students were surveyed in a variety of developmental mathematics courses in the spring semester. Measures of relationship with instructor, confidence and engagement, class structure and validation were averaged and ranked to identify the math instructors whom students rated highest as creating a space of validation, cultural inclusiveness and engagement. The four highest ranked math instructors were then observed and interviewed the following fall semester to understand how they create an inclusive environment in their courses and whether their practice contributed to higher persistence. Interview and observation data were synthesized using a thematic analysis. Findings determined that instructor authentic partnership, advocacy for students and reflective practice were key to creating an inclusive environment that fostered a strong sense of belonging and academic validation for students. Developmental courses paired with a college credit course, taught by instructors who are student-centered and culturally responsive, who authentically engage and partner with students, are shown to have impact on student persistence and perceived sense of belonging and validation in the initial step on the path to degree attainment for community college students needing remediation in math.

Record Information

Source Institution:
University of Colorado Denver
Holding Location:
Auraria Library
Rights Management:
Copyright Lisa M. Silverstein. Permission granted to University of Colorado Denver to digitize and display this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.


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LISA M SILVERSTEIN B.S., San Diego State University, 1996 M.A., University of Colorado Denver, 2001
A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy
Education and Human Development Program

This thesis for the Doctor of Philosophy degree by Lisa M Silverstein Has been approved for the Education and Human Development Program by
Carlos Hipolito-Delgado, Chair Alan Davis, Advisor Antwan Jefferson Sylvia Hurtado
Date: May 18, 2019

Silverstein, Lisa M (PhD, Education and Human Development)
Authentic Partnerships, Advocacy and Reflection: Creating Inclusive Community College
Mathematics Classrooms
Thesis directed by Professor Alan Davis
Community colleges are often considered an affordable entry point into postsecondary education for many students with a goal of earning a degree. As open access institutions, they accept any student who applies, including those considered to be below college level and in need of some level of remediation in the subjects of reading, writing and math. The need for remediation tends to be highest in the subject of math, with rates as high as 78%. Community colleges are also known to be the most diverse of higher education institutions, where students of color make up 90% of the student population requiring remediation. Students needing remediation contribute to higher attrition rates in community colleges, as remediation is considered a barrier to degree attainment. To address this issue, community colleges are revamping the ways in which remediation, commonly referred to as developmental education, is delivered. The purpose of this study was to learn how instructors who teach introductory mathematics courses in community colleges address attrition by creating inclusive environments that promote a perceived sense of belonging in their classrooms of diverse learners. The study was conducted at a diverse, urban community college with Hispanic Serving Institution status, addressing developmental education attrition by pairing a developmental course with an introductory college level course to accelerate the developmental sequence for students to earn college credit. The Multi contextual Model for Diverse Learning Environments, developed by Hurtado, Alvarez, Guillermo-Wann, Cuellar & Arellano (2012) was the conceptual framework,

to first look at how students perceived their mathematics experiences and second, how instructors navigated the institutional learning environment to create a space of validation, belonging and engagement with and for their students. Students were surveyed in a variety of developmental mathematics courses in the spring semester. Measures of relationship with instructor, confidence and engagement, class structure and validation were averaged and ranked to identify the math instructors whom students rated highest as creating a space of validation, cultural inclusiveness and engagement. The four highest ranked math instructors were then observed and interviewed the following fall semester to understand how they create an inclusive environment in their courses and whether their practice contributed to higher persistence. Interview and observation data were synthesized using a thematic analysis.
Findings determined that instructor authentic partnership, advocacy for students and reflective practice were key to creating an inclusive environment that fostered a strong sense of belonging and academic validation for students. Developmental courses paired with a college credit course, taught by instructors who are student-centered and culturally responsive, who authentically engage and partner with students, are shown to have impact on student persistence and perceived sense of belonging and validation in the initial step on the path to degree attainment for community college students needing remediation in math.
The form and content of this abstract are approved. I recommend its publication.
Approved: Alan Davis

I dedicate this work to community college faculty who fearlessly and tirelessly advocate for and commit their hearts to students. To those faculty who believe that education is a right and that all
students can achieve their goals.
I also dedicate this to community college students, whose determination and drive to achieve their goals and be unapologetically themselves does not go unnoticed.

I want to first thank my committee for their guidance and belief in my work. Thank you to my advisor, Dr. Alan Davis, for his compassion, questioning and late-night emails with follow up thoughts and suggestions. I appreciate the conversations over coffee, I value those talks. Thank you to my chair, Dr. Carlos Hipolito-Delgado, whose influence and directness pushed me hard, making me a better writer and person. Thank you to Dr. Antwan Jefferson, for his understanding and sound advice; I am honored that he chose me to partner as a TA. This committee of men offered kindness, empathy and tissues when there were tears. I am grateful.
Thank you to Dr. Sylvia Hurtado for also serving on my committee; an inspiration and mentor, who understood and respected my love of the work, propelling my plans for a PhD. Thank you to Elaine Baker, who showed me what true advocacy and action looks like, no matter the cost. When people have compared me to Elaine, there is no greater honor; she will always hold a place in my heart. And to Ruth Brancard, who started FastStart, brought me in, and has been a support and guide. These three incredible women are the light and fire behind my work.
I also want to thank the FastStart team. The work we created together at the community college was magic and it lives on inside all of us. It will forever be one of my most treasured and meaningful times in my professional career.
Thank you to my family. To Justin, who stood by me as I perseverated over this work, taking time to understand. To Kellan, with deep compassion for humanity, challenging me in philosophical discussion, making me a better wonderer about society and life. To Raya, her intuition, motivation and determination is unlike anyone I know. I aspire to this. And to Hannah, who teaches me that sometimes things are better left alone, to move on and enjoy. I am still learning.

I. INTRODUCTION...............................................................1
Definitions and Terminology................................................4
Research Questions.........................................................9
Theoretical Framework.....................................................10
Literature Review.........................................................13
Sense of Belonging in Higher Education: Student-Faculty Interactions- Gender and
Sense of Belonging and Persistence.....................................19
Inclusive Practices by Faculty in Fostering Sense of Belonging.........20
The Practice of Inclusivity and Cultural Responsiveness in the Math Classroom.24
Sense of Belonging and Self Confidence in Math.........................27
Developmental Mathematics Courses......................................28
III. METHODS..................................................................31
Stage 1: Student Survey, Selection of Instructors.........................31
Setting and Participants...............................................31

Instrument: Student Survey...................................................33
Relationship with the Math Instructor....................................33
Confidence and Interest in Math..........................................34
Class Structure..........................................................34
Belonging and Validation.................................................35
Math History in Higher Education.........................................35
Demographic Information..................................................35
Data Collection..............................................................35
Stage 2: Case Study.............................................................38
Faculty Interviews and Observations..........................................39
Thematic Analysis............................................................42
IV. FINDINGS........................................................................45
Authentic Caring: A Student-Centered Practice...................................45
Advocacy: Students First, Going Above and Beyond, Shared Accountability......46
Students First

Education as a Right: Going Above and Beyond..............................
Shared Accountability.....................................................
Partnership: Reciprocity and Interdependence..................................
Relationships: Cultural Responsiveness, Valuing Individuals...............
Reciprocity: Learning Together............................................
Informal Interactions.....................................................
With Students..........................................................
Among Students.........................................................
Among Other Faculty....................................................
An Expression of Difference...................................................
Persistence and Passing Rates....................................................
V. DISCUSSION, IMPLICATIONS AND LIMITATIONS..........................................
Authentic Caring, Student Centered............................................
Inclusion, Cultural Responsiveness, Belonging and Validation as the Responsibility
of the Instructor.............................................................
Persistence and Passing Rates.................................................
Validating Faculty Identity and Reflection....................................
Flexibility in Supplemental Developmental Lab Courses.........................
Limitations and Future Research..................................................
72 72
78 80 80


Community colleges play a crucial role in the landscape of higher education. They offer postsecondary opportunities for any student seeking academic degrees, vocational certificates, continuing education courses and more. Community colleges have the most diverse student bodies in higher education in every demographic dimension (Boggs, 2011) and half of the nation’s first year undergraduate population attends a community college (NCES, 2009). Fifty percent of Hispanic1, 31% of Black and 28% of White students entering college start at community colleges (NCES, 2009). The average age of community college students is 28, 36% of all students are students of color, 42% are first generation, roughly two thirds attend school part time and 16% are single parents (NCES, 2009). There are more non-traditional students of a wider age range in community colleges who most often commute to school with a larger percent who attend school part time (Bailey & Cho, 2010). This is particularly true in introductory courses, and in developmental mathematics courses, where attrition rates are highest (Bailey, 2009; Bailey & Cho, 2010; Boaler & Greeno, 2000).
Nearly 60% of community college students are required to take one or more developmental education, or remedial course, meaning that they are not considered “college level” in one or more content areas when they enroll. Of the students who need remediation in mathematics, rates are as high as 78% in some states (Bailey, 2009; NCES, 2009). For underrepresented populations such as low-income students and students of color, the percentage requiring remedial education can be as high as 90% at some colleges (Bailey & Cho, 2010). Of
1 Term used by NCES

the students who need remediation when they start college, fewer than 11% will complete a college degree (NCES, 2009).
Researchers at the Community College Research Center (CCRC) at Columbia University have conducted the most comprehensive studies on community colleges, including developmental education. Thomas Bailey and his team have found that students of color start college with the same commitment and goals as their white counterparts, but their expectations of the institution and their sense of belonging changes over time, and they do not persist at the same rate (Bailey, Jenkins & Leinbach, 2006). In 2006, 40% of first-time white community college students earned a degree or certificate within six years compared to 27% of Blacks and 31% of Hispanics (Bailey, et al., 2006). In this sample of students who had the goal of earning a bachelor’s degree, more white students transferred to a four- year institution and received their degree (12%) compared to Blacks (2%) and Hispanics (5%).
Developmental education mathematics courses in community colleges have the highest enrollment rates for students of color and the highest attrition rates (Bailey & Cho, 2010). In mathematics, the national average for students referred to a developmental mathematics course who complete and pass an introductory college mathematics course is 32 percent (Bailey, Jeong & Cho, 2015). Students who are referred to developmental courses start with the goal of earning a bachelor’s degree, yet only 11% attain this goal (NCES, 2009).
Many community colleges are working to improve the rates of degree attainment for students in developmental courses, with efforts that include acceleration of developmental courses where students spend less time and money in these courses, transitioning into their college credit courses sooner (Bailey, Jaggars & Jenkins, 2015). If students spend less time in developmental courses, attrition rates decrease (Bailey, et al., 2015). One example of an

accelerated developmental education model includes pairing the developmental course with a college level credit bearing course. The developmental course is labeled as a lab course, where students receive additional supports by the same instructor who teaches the paired college level course. This lab component is one additional credit for students instead of three credits. Students spend less time and money in the developmental course, investing instead in the college level course where their money and grade for the course count, with supports offered by their instructor (Bailey, et al., 2015). This model puts a responsibility on the instructor to retain their students and create a means by which the developmental student persists in the college level coursework. How do these community college faculty members consider their students in the developmental support lab courses, and how do these students consider their instructors?
The relationship between instructor and student is an essential component to student academic persistence (Alicea, Suarez-Orozco, Singh, Darbes & Abrica, 2016; Barnett, 2011; Chickering & Gamson, 1987; Kuh, Laird & Umbach, 2004; Laden, 1999; Myers & Bryant,
2002; Nadler & Nadler 2000; Nora, Barlow & Crisp, 2005; Pascarella & Terenzini, 1978; Schlossberg, 1989; Tinto, 1997). Faculty have a great deal of influence on their students in their interactions, both in and out of the classroom (Nadler & Nadler, 2000). Students who stay in college and do well in the classroom were found to have significantly more interaction with faculty out of the classroom than those who dropped out or stopped out (Barnett, 2011; Nadler & Nadler, 2000; Thompson, 2001). It is the responsibility of the institution to help students reach their goals, and this responsibility also lies on the shoulders of faculty (Alicea, Suarez-Orozco, Singh, Darbes & Abrica, 2016; Astin, 1984; Umbach & Wawrzynski, 2005). What happens in the classroom “may constitute the bulk of the nontraditional community college student

experience, making classrooms in these settings critical contexts to understand,” the influence of the faculty member on student outcomes (Alicea, et al., 2016, p. 758).
Definitions and Terminology
If the classroom is the critical context to understand the student, and community colleges have the most diverse student bodies in higher education, it is imperative that instructors create classroom learning environments that are inclusive. Inclusive classroom learning environments are ones where all students are accepted by the instructor and one another, and students perceive it to be this way (Bogg, 2011; Cole, 2007; Hurtado & Carter, 1997; Laird, 2005; Newman, Wood & Harris, 2015; Tinto, 1997). An inclusive environment increases a student’s sense of belonging and academic validation; if a student feels they belong and validated in a way that builds academic confidence, this is associated with the student’s decision to persist in the course (Alicea, et al., 2016; Barnett, 2011; Davidson & Wilson, 2016; Quaye & Chang, 2012). When students perceive themselves to be respected, their attendance and participation matter and they feel they belong, they experience a sense of belonging and validation of effort in their academic learning environment (Astin, 1984, 1993; Schlossberg, 1989).
In addition to creating an inclusive environment that promotes a sense of belonging and academic validation in a classroom of diverse students, it is important that the instructor is also culturally responsive, where students perceive their cultural backgrounds are of value, considered assets in the learning environment (Gutierrez, Morales & Martinez, 2009; Jett, 2014; Laden, 1999; Ladson-Billings, 1995; Sleeter, 2001). In classrooms that are inclusive and culturally responsive, where students feel they belong, students perceive interactions between the instructor and themselves, both in and out of the classroom, as meaningful and valuable (Davidson & Wilson, 2016; Moreno, 2015). It is also in these learning environments where

positive interactions occur that build a student’s confidence. When a student feels a sense of belonging and can interact positively with their instructor, academic validation and confidence is built in the subject area and as a valued member in the classroom community resulting in higher persistence rates (Barnett, 2011; Benken, Ramirez, Li & Wetendorf, 2015; Mesa, Celis & Lande, 2014; Prasad, 2014; Tinto, 2012).
Persistence is often defined as a student continuing to stay enrolled in college semester to semester (Bailey, et al., 2015; Barnett, 2011; Tinto, 1987). For this study, persistence refers to students continuing to attend their mathematics course for the entire semester, whether they passed the course or not. Passing rates refer to students who completed the duration of the course with a passing grade of a C or better. Attrition rates, when students stop attending class for a variety of reasons, are higher for students enrolled in community college introductory mathematics courses. Rather than use the term attrition, that focuses on students not completing courses, the term persistence was intentionally used in this study to focus on students who completed their mathematics course.
There are few studies on what community college mathematics instructors actually do to create inclusive learning environments that promote persistence, particularly for students in developmental mathematics courses, a subject traditionally known to be less likely to promote discussion and group sharing of personal experiences (Boaler & Greeno, 2000). This study aimed to attend to this gap in the research. Mathematics instructors who create inclusive, culturally responsive classroom environments, encouraging positive interactions, belonging and validation at one urban community college, from the perspective of the student, were observed and interviewed. Persistence and passing rates were analyzed to determine whether the inclusive
environment influenced student outcomes.

The classroom environment consisting of students and instructor is at the core of higher education institutions (Hurtado, Alvarez, Guillermo-Wann, Cuellar & Arellano, 2012). The Multi contextual Model for Diverse Learning Environments (DLE model; Hurtado, et al., 2012) is a framework that focuses on how the organization of higher education institutions affects the identity of the student, who they are and what experiences they bring, and how they are served in the classroom and beyond at the institution. Students are shown in the center of the model as they are at the core of the institution. Faculty are also acknowledged in the center of the model as they are closely related to the student, to show how they influence one another. Interactions between students and instructors both in and out of the classroom have been found to correlate with higher GPAs, degree attainment, career plans and intellectual and personal development (Benken, Ramirez, Li & Wetendorf, 2015; Pascarella & Terenzini, 1978; Prasad, 2014; Thompson, 2001). According to the DLE model, it is the processes and relationship between faculty and student that drive the other functions of the institutions. With administrative supports and resources dedicated to an inclusive campus culture, for both faculty and students, positive relationships are fostered, creating senses of belonging that are interlinked. This communicates to the student that what happens in the classroom and life out of the classroom are related not only through the shared knowledge, but through the importance of both and how they interact and support each other (Davidson & Wilson, 2016; Hurtado, et al, 2012).
Using the DLE model, I show the importance of how an inclusive environment, created by mathematics instructors both in and out of classroom, where the cultural backgrounds of students are acknowledged, is essential to developing a sense of belonging, academic validation and student confidence that lead to higher persistence.

In Hurtado et al.’s Multicontextual Model for Diverse Learning Environments (2012), the primary focus is on the identity of the student in the context of their learning environment. From a holistic standpoint, the student cannot help but bring their whole unique, individual self into the classroom (Davidson & Wilson, 2016; Quaye & Chang, 2012; Moreno, 2015; Yosso, et al,
2009). In this frame, it is imperative that instructors also understand who they are and how they navigate in society to better understand their students (Jett, 2014; Quaye & Chang, 2012).
As the researcher for this study, I too have to understand who I am holistically and how I navigate in society as I can bring unintended biases into my work based on my experiences. My positionality plays a role in my research and motivation to conduct this study. This includes the choice of the student survey items to measure the classroom environment, the qualitative information about the instructors and the learning environments they created, and my interactions and relationships built with the instructors. As a constructivist, a facilitator and learner within various interdependent learning communities, I view my research, personal and professional experience as interrelated (Shenton, 2004).
I grew up in Los Angeles, one of the largest cities in the country, educated in a diverse school district wrought with dysfunction in the 1980’s. We had weeks at a time when school was not in session due to teacher strikes. When a large fight broke out in high school, all students were instructed to evacuate the campus. During the Rodney King riots, school closed, and when we came back, it was supposed to be business as usual. The tension among faculty, and among students was palpable, but not addressed. There were many people in my city, my school, my classes. We all had our own stories, as well as the narratives society told for us, shaping us as we matured, but there was not enough time or energy for individuals. I persisted but did not perform

well. I did enough to get by so attention was not put on me. Instead, I watched and observed, as a white, heterosexual female, considered middle class, navigating the world through a quiet awareness. There was so much happening that was much larger than me.
The first true sense of community I felt was when I worked at an outdoor camp in adventure and experiential education. Those years in adventure education taught me that building relationships and feeling part of a community can have lasting effects in persistence and confidence, a central component to learning and taking risks. It was this experience that brought me back into the classroom as a professional. I did not have a sense of community in my school environments and did not want other young people in their formative years to experience school that way. In my professional career as a middle school language arts teacher, community college instructor and eventually a director who worked with faculty, the foundation of my experiential practices and participation in diverse environments set the stage in how I focused on each individual who made up each unique learning community, and how I showed up as a white, heterosexual, middle class female participant in each of those spaces.
In my position at the community college, I worked with community college mathematics faculty, observing their classrooms and practices. I found myself drawn to how concepts were taught and how they were received by students. In developmental mathematics courses specifically, I noticed the strengths of the students were often times language based, and the strengths of the instructors were more conceptual. In an English and mathematics learning community I co-taught, we discovered through student input and questions, that they wanted the language of the math concept written or discussed along with the numerical computations. I wrote the concepts as text, while the mathematics instructor wrote them numerically. As coinstructors, we had to navigate our pedagogical practices, relationship, backgrounds and

identities, along with our students, in order to create a community of engaged learners in two very different subject areas. This experience further piqued my interests about mathematics courses in community colleges. How does a mathematics instructor create sense of belonging in a subject area that does not necessarily revolve around language, but is rather conceptual, with higher attrition rates than other subject areas (Bailey, 2009; Boaler & Greeno, 2000)?
My idea of an instructor who builds a strong community in the classroom was someone who practiced experiential techniques, with contextualized activities and opportunities for students to experience the material through inquiry and discussion, where student ideas are valued, and they do not feel like a number. This study was created to research these practices to provide a deeper understanding of this phenomenon in the math classroom.
Research Questions
The purpose of this study was to learn how community college mathematics faculty develop a sense of belonging within their courses and the degree to which their engagement with their students might foster validation in an inclusive environment, both in and out of the classroom. The research questions for this study are:
1. How do mathematics faculty co-create a culturally responsive and inclusive environment with students at community colleges?
2. How does a faculty member’s engagement with students both in and out of the classroom affect the classroom environment, relative to connectedness with students, and student

Sylvia Hurtado and her colleagues developed the Multi contextual Model for Diverse Learning Environments (DLE model, 2012) as a tangible way to view and analyze diversity in higher education learning environments by looking at the campus climate. Hurtado and her team needed a model to guide their research that was taking place at multiple higher education institutions. They wanted to use a model that brought attention to how the structure of an institution, both through sociohistorical and policy contexts influence students of diverse backgrounds. This model suggests that institutions can “possess historical legacies of inclusion and exclusion, as well as a psychological dimension based on different perceptions associated with the positionality of individuals within the institution, and a behavioral dimension based on interactions or intergroup contact experiences on campus” (Hurtado, Alvarez, Guillermo-Wann, Cuellar & Arellano, 2012, p. 43). The model has been revised over time as a necessity for institutions to recognize themselves as “Diverse Learning Environments” (p.46), including Predominately White Institutions to bring a greater awareness to underrepresented groups at higher education institutions. It frames the institutional environment for diverse learners, including marginalized students and students of color. The model is a way to spur discussion about how institutions discuss and reflect on the organizational aspect with respect to diverse student populations.
The DLE model draws on social identity theory (Tajfel, 1974). At the center of the model is the “Institutional Context” composed of the student and the institutional components that influence the learner. This context is also referred to as the “Climate for Diversity.” Faculty and

staff are included in the Institutional Context as they are students’ touch points and directly affect the student. The curricular (classroom) components are central to the model as “diversity is embedded in who we teach (student identities), who teaches (instructor identities), what is taught (content) and how it is taught (pedagogies)” (Hurtado, et al., 2012, p. 49). Like Hurtado and her colleagues, several other researchers also describe the classroom as a social environment created by how students and instructors position themselves relative to one another and interpret the interactions occurring between them (Davidson & Wilson, 2016; Gutierrez, Morales & Martinez, 2009, Jett, 2014; Ladson-Billings, 1995; Sleeter, 2001).
The bottom of the model “Community Context and External Commitments” shows the direct influence of community on student, faculty and staff. The model reflects that “institutions do not exist in a vacuum” (Hurtado, et al., 2012, p. 49) but are part of communities and individual external commitments and “contextual forces outside the institution” (p. 49). Institutions are entities that “shape and are shaped by their environment” (p. 49) essential to what they are as organizations. This focus can accommodate faculty, and their understanding of their students (Ladson-Billings, 1995, 2009). This includes their community/ies, so that not only can they better serve and meet student need but also understand their vital role and identity as they navigate as facilitators (Gutierrez, et al., 2009; Jett, 2014).
The intersection of community interfacing with student, faculty and staff roles in the DLE model is where a common cultural connection or shared activity and understanding take place (Gutierrez, 2008; Ladson-Billings, 1995; Jett, 2014). The focus of the model is the student and how their identity as a student is impacted by the contexts that surround them on a college campus. It is the faculty who interact most directly with students on campus. These interactions create a stronger sense of academic validation for students that positively affect their retention

and persistence rates (Hurtado, et al., 2012; Nora, Barlow & Crisp, 2005, Rendon, 1994). Within the climate of diversity context in the DLE model, interactions and processes between faculty and students has an effect on the academic validation of the student. Confidence and persistence increase when a student feels validated for who they are and the educational experiences they bring to the class (Hurtado, et al., 2012, Rendon, 1994). It is important to note that in the DLE model, a student can feel validation in their academic courses by the instructor and belonging among students in the classroom, that leads to persistence and success, however, this does not always translate into a feeling of belonging within the larger context of the institution (Hurtado, etal., 2012).
The model considers the organizational factors as well. “Policy Context” and Sociohistorical Context” are layered above the Institutional Context to show their influence on the institutional context and climate for diversity along with the Community Context and External Commitments. When the community and institution partner, relationships are built and an idea of a “college going culture” (Hurtado, et al., p. 88) is woven into the fabric of the community. If the institution is committed to partnering with the local community, the climate of both the community and the institution is a rich place for diverse learning environments to be fostered (Hurtado, et al., 2012).
Policies, including education policies at the local, state and federal levels as well as degree attainment, financial aid and access at each institution constitute an “important external context that shapes campuses and student outcomes” (Hurtado, et al., 2012, p. 93). These contexts are represented in the model as they have implications to student outcomes and sense of belonging (Astin, 1984; Tinto, 1987). The sociohistorical context and changes within this context of the institution are considered as well with respect to diverse learning environments.

This shapes the organizational structure of the institution, which plays a role in how students and community perceive a sense of belonging.
The praxis of education is a fluid dance of who the instructor and student are, both in and out of the classroom. With inclusiveness and sense of belonging at the core, participants work together in an inclusive community where they are valued and validated (Jett, 2014; Ladson-Billings, 1995; Soja, 1989). Students draw from their experiences, in environments facilitated by faculty who also bring their own experiences to the classroom and institution. Student and faculty identities are fostered, coming to their own conclusions based on what they learn and what they have experienced (Ladson-Billings, 1995, 2009; Quaye & Chang, 2012).
Validation and sense of belonging, from within the classroom to the other areas of the institution outside of the classroom, are important factors for students to persist in their higher education pursuits (Astin, 1984; Hurtado,, 2012; Schlossberg, 1989). When institutions provide opportunities for inclusivity through faculty connection, teaching, campus and community activities and events that represent all types of students, there is a feeling of self-worth and that they matter (Astin, 1984). Institutions need to note and understand the commonalities of students, but it is vital to acknowledge individuality (Schlossberg, 1989). Environments that clearly indicate to all students that they matter will urge them to greater involvement; students are motivated to learn, and retention is higher (Astin, 1984; Hurtado & Carter, 1997; Ladson-Billing, 1995, 2009; Schlossberg, 1989). How do faculty create this environment in their classrooms for their students and for themselves?
Literature Review
There is an underrepresentation of students of color in STEM majors and an overrepresentation of students of color in remedial courses (Bailey, et al., 2015; Hurtado, Eagan,

Tran, Newman, Chang, & Velasco, 2011). Many studies have been conducted to address this issue by looking at student math and science knowledge, attitude about math and efficacy in undergraduate as well as developmental math courses (Bailey, et al., 2015; Benken, et al., 2015; Mesa, Celis & Lande, 2014; Peters, 2013). However, relationships with instructors and how they foster validation and belonging for students of color in developmental mathematics classrooms specifically, has not been an area of focus. As mentioned in the introduction, developmental math courses have the highest enrollment rates of students of color and the highest attrition rates (Bailey & Cho, 2010). When a sense of belonging is created and fostered between professors and students of color, does this affect the possibility of students staying in college and perhaps pursuing a degree in a STEM major?
Sense of Belonging in Higher Education: Student-Faculty Interactions- Gender and Race Sense of belonging has long been studied, and continues to be built upon in higher education, starting with the early work of Chickering (1969), Spady (1970), Tinto (1975) and Pascarella and Terenzini (1979) where student- faculty2 contact both inside and outside of the classroom as it related to student retention and success from the students’ point of view and campus wide supports were of most focus. Pascarella and Terenzini (1978, 1979) found that frequency of contact had a direct influence on student academic performance, perceptions and intellectual growth, also influencing students’ perceptions of faculty instructional quality (Theophilides & Terenzini, 1981). Pascarella and Terenzini’s (1978, 1979) contributions in this area of study built upon the work of Chickering (1969) and Spady (1970) to show the relationship between faculty-student connections and student persistence. Their studies built
2 The phrases student-faculty interaction and faculty-student interaction are intentionally used interchangeably throughout this document to highlight the importance of both entities in the interaction.

upon one another based on the freshman year outcomes they found in a sample of students from a private university in New York (Pascarella & Terenzini, 1978). They found partial correlations between student-faculty relationship variables based on types of informal contact with faculty and the criterion variables: academic performance, personal development and student intellectual development. They found a stronger correlation when students reached out to faculty for support in academic and course information. With further research at the same institution Pascarella and Terenzini (1979) looked at factors such as race/ethnic origin, high school achievement, family background and other pre-enrollment information as related to student faculty connections. They used voluntary persistence/withdrawal decisions as the dependent variable.
When controlling gender along with these variables, they noticed a difference between men and women in relation to how often they connected with faculty (Pascarella & Terenzini, 1979). When men had more frequent contact with faculty about careers, courses and academic programs, this was positively related to their first-year persistence. For women, interactions with faculty were directed more toward intrinsic, personal outcomes. Pascarella and Terenzini (1979) suggest that academic outcomes for first year students are better predicted by the frequency of student faculty contact than their characteristics prior to entering college. If a student has more informal contact with faculty in the first year, this practice is likely to continue into their subsequent years of college, reducing attrition rates (Pascarella & Terenzini, 1979; Tinto, 1975). This is important to note, as a student’s experience in their first year of college can have an effect on how often a student will reach out to faculty. If we use Pascarella and Terenzini’s (1979) findings on student faculty contact, this relates to a sense of belonging for the students. If a student feels a stronger sense of belonging early in their college going experience, such as when a developmental course is taken, they are more likely to persist in this first year.

Pascarella and Terenzini’s findings were based on data collected on students. Nadler and Nadler (2000) studied the faculty perspective on student-faculty communications to better understand the process. In their literature review, they found that female instructors were visited by, and had more informal interactions with, students than their male counterparts, leading to their study on whether instructor sex affects student and faculty contact outside of the classroom and faculty perception of empathy. The sample consisted of 89 randomly selected full-time faculty, 46 males and 43 females, from Miami University, where all students are undergraduates, and where faculty are expected to do academic advising. A questionnaire was sent to the faculty focused on their out of class interactions with students. Findings showed that female faculty spent more time with students outside of class, with longer average meeting times (Nadler & Nadler, 2000). Students were found to initiate the out of class contact equally with male and female instructors, though they spent more time, an average of seven minutes longer, with the female instructors than their male instructors (Nadler & Nadler, 2000). Students were more likely to share personal information with female instructors, than with their male instructors, which Nadler and Nadler (2000) relate to greater empathy that female instructors show with their students. Findings also showed that students expected women instructors to be more empathetic, though they had lower evaluations than males (Nadler & Nadler, 2000). Based on these findings, do students perceive a sense of belonging to be generally fostered by their female instructors? Students tend to evaluate their male instructors higher (Nadler & Nadler, 2000). Does a sense of belonging from a student perspective only relate to their interactions in the classroom, or are out of classroom interactions factored into a student’s idea of sense of belonging as well?
Not only does gender influence relationships, race and prior academic experiences influence relationships as well (Hurtado & Carter, 1997; Laird, 2005; Nora, Cabrera, Hagedorn

& Pascarella, 1996; Pascarella & Terenzini, 1979; Tinto, 1997). Pascarella’s (1980) extensive review of the literature, for example, reported that students who feel they have similar interests and aspirations as their instructors, are more likely to seek faculty mentorship and determine the frequency and quality of their contact with faculty. Based on this evidence, Darnell Cole (2007) looked at how race impacts student- faculty interactions as more students of color entered the college landscape. In Cole’s (2007) review of the literature, findings suggest that race/ethnicity is a significant factor to student- faculty contact and intellectual development. Students of color felt that faculty were “less willing to interact with them, even concerning academic issues” (p. 251) resulting in significantly less faculty contact, where race was described as the determining factor. However, when college campuses are focused on diversity and creating an inclusive environment, with a diverse student and faculty population, where faculty are an integral part of this commitment, student intellectual development and interactions with faculty increase (Cole, 2007; Gurin, Dey, Hurtado & Gurin, 2002; Hurtado, et al., 2012).
Cole contributed to the field by examining the effects of interracial interactions on faculty-student interactions and on the students' intellectual self-concept, in higher education learning environments, both in and out of the classroom. He studied 119 predominately white institutions (PWIs), controlling for institutional type, number of enrolled students, number of faculty and racial/ethnic demographics. Outcome variables were student-faculty interactions and intellectual self-concept. Background characteristics and environment variables at the college were also examined for effect on student-faculty interaction and intellectual self-concept (Cole, 2007). He included four year and two-year colleges in his study, surveyed students over four years, using Astin’s IEO model (1993) as his framework. He found that while the percent of American Indian and Hispanic students and institution type were positive predictors of more

student- faculty interaction, the number of students enrolled and percentage of Asian students were negative predictors of student faculty interactions for students of color (Cole, 2007). Students of color were more likely to interact across racial lines and white students could avoid interracial interactions (Cole, 2007). Cole (2007) recognizes that minority student representation is necessary for interracial contact on campus but does not mean the interactions are meaningful. He suggests that it is essential to increase white student’s diversity involvement through structural diversity practices among the institutions as a whole (Cole, 2007). Cole’s (2007) findings showed that with more peer involvement among students on the campus, including in the classroom, there is an increase in student-faculty interactions and on students’ intellectual self-concept.
According to Yosso, Smith, Ceja and Solorzano (2009), minority students often bear the responsibility to integrate with their college campus, including in their courses. Cole (2007) addresses this by stating that it is not the responsibility of the students, it is the responsibility of the institutions, including that of the faculty to make the effort to address a “more diverse higher education community and shifting racial ideologies across ethnic groups” (Cole, 2007, p. 253, Hurtado, et al., 2012). This need could also be said for faculty cultural responsiveness in classrooms (Ladson-Billings, 1995). What we know from Pascarella and Terenzini (1978, 1979, 1980), and Cole (2007) is that student faculty interaction and involvement is important for student persistence in their first year of college and beyond, particularly for students of color, to feel a sense of belonging. As Yosso, (2009) find, minority students see the responsibility as theirs to integrate in with the college environment and in their classes. How might faculty bear more of this responsibility through student-faculty interactions to create a stronger sense of belonging?

Sense of Belonging and Persistence
Tinto’s (1987) initial groundwork to understand college attrition, found that a student’s sense of belonging and importance of building community are vital to success and student persistence. Other scholars have contributed to Tinto’s work by including non-traditional students, most of whom attend community colleges and are students of color. These scholars added that faculty cultural responsiveness is vital to student persistence, particularly for students of color and students from underrepresented communities (Davidson & Wilson, 2016; Jett, 2014; Newman, Wood & Harris, 2015). Demcho (2011) and Davidson and Wilson (2016) focused on the responsibility of the institution to better understand and facilitate minority student retention, rather than put the responsibility on the individual student to bring the institution to a cultural understanding.
Monica Demcho (2011) conducted her dissertation study on sense of belonging among first year commuter students at a four-year Hispanic Serving Institution (HSI) to explore non-academic factors that affect retention rates. Demcho drew from the works of Pascarella and Terenzini, Astin and Hurtado, using Tinto’s model of institutional departure (1993) to analyze the perceptions of first year commuter students, most of whom were minority students, of their sense of belonging and integration at the institution. Cross-racial peer interaction, campus involvement, driving distance and institutional commitment were the variables assessed in this quantitative study. Demcho found that cross-racial peer interaction was a predictor of a student’s sense of belonging and driving distance had an effect on institutional commitment and campus involvement. Her study supports previous research findings that show the importance and need for social integration of students, particularly first year, minority commuter students, on college campuses. She also describes that this responsibility lies on the shoulders of the institution,

showing a commitment to the non-academic factors of students and their success by the faculty and staff employed by the institution (Astin, 1984; Demcho, 2011; Tinto, 1987, 1993; Yosso,, 2009). Though Demcho’s study was conducted with students at a four-year HSI, the demographics of the students she surveyed also closely match the demographics of many community colleges with the HSI designation, and closely match the institution of my study.
In their study on students who drop out of community colleges, Davidson and Wilson (2016) found that sense of belonging is critical to persistence rates. Students’ academic and social elements are not compartmentalized, they are holistically integrated. Students’ relationships within family, work and school are blended, without differentiating their influences on persistence. Collective affiliation, where a person’s sense of belonging among the various communities in which they participate function cohesively needs to be understood and fostered by community colleges so the student can maintain their engagement in each of these communities. A student’s “many senses of belonging are not separate from the student’s decision to persist” (Davidson & Wilson, 2016, p. 11). Creating a sense of belonging by relating what happens in the classroom to work, family and the community creates a shared knowledge for the student, that they matter, and the parts of their lives are equally important and that they interact and support one another (Davidson & Wilson, 2016).
Inclusive Practices by Faculty in Fostering Sense of Belonging
Faculty play a role in student success based on best practices that are engaging, perceived as supportive within the classroom and provide students feel a gain of overall knowledge that enhance their college experiences (Umbach & Wawrzynski, 2005). Drawing on the work of Tinto, Chickering, Astin, and Pascarella and Terenzini on student engagement and faculty-student interactions, Umbach and Wawrzynski (2005) studied the behaviors and attitudes faculty

exhibited related to student behaviors and the environment created by these faculty members to support self- reported gains by undergraduates using a Hierarchical Linear Model (HLM). The sample for this study came from roughly 20,000 seniors and 22,000 first-year students, as well as 14,000 faculty members who completed the National Survey of Student Engagement (NSSE) in Spring 2003 from 137 institutions. Gains in personal, social and intellectual development for students were positively related with course-related interactions with faculty. Active and collaborative learning techniques and levels of challenge for students by faculty on also showed evidence of positive gains in students and increased student-faculty interactions (Umbach & Wawrzynski, 2005). Faculty also had an influence on student participation in co-curricular activities on college campuses, leading to an increase in student gains as well. Faculty at liberal arts colleges were significantly more likely to engage in collaborative learning techniques and interact with students, creating an environment of student engagement and learning (Umbach & Wawrzynski, 2005). One of the limitations Umbach and Wawrzynski (2005) mention is that they could not match students with faculty directly. In my study, surveys completed by students will indicate which faculty in particular create a sense of belonging and engage in the practices identified by Umbach and Wawrzynski (2005). Umbach and Wawrzynski (2005) did not find significant results for out of class interactions among faculty and students as a way to increase student engagement and learning, rather they found that it is the attitudes and behaviors of the faculty that create a culture fostering student learning. How are these attitudes and behaviors presented by faculty? What do they do specifically to create this environment?
A study by Kuh, Laird and Umbach (2004) looked at both the Faculty Survey of Student Engagement (FSSE) and the National Survey of Student Engagement (NSSE) to compare faculty and student perceptions of their interactions. Their findings support Umback and Wawrynzski

(2005). Effective practices3 on these measures include: coherent and academic challenge, active and collaborative practices that engage learners with their peers, both in and out of the classroom, in common intellectual work, creating opportunities for student-faculty interaction, presenting diverse perspectives in the classroom, opportunities for extracurricular participation in activities on campus and in the community and providing prompt feedback have better student outcomes and increased interactions with students. In Nadler and Nadler’s (2000) study, they found that faculty who engage with students not only in the classroom, but also outside of classroom were more knowledgeable about their students, felt their connections with students were stimulating and their career to be a major satisfaction in their lives. Nadler and Nadler (2000) also discussed that out of classroom interactions would be especially influential for community college students who are least likely to seek out faculty members outside of class, particularly for math courses, where attrition rates are historically higher. Faculty who provide time for discussions and facilitate relationship building in their classroom, including mathematics classrooms, provide students with a sense of belonging and inclusivity, improving student retention rates. Interaction both in and out of the classroom has an impact on both the student and faculty member (Davidson & Wilson, 2016; Nadler & Nadler 2000).
Quaye and Chang (2012) discussed strategies of fostering inclusivity among diverse classrooms, where community was at the core. Students drew from their own experiences, in classrooms built on trust and safety where race can be discussed. This study on facilitated classroom environments where race is openly discussed on a consistent basis labels faculty as a key component to building inclusivity in institution of higher education. Quaye and Chang’s
3From Chickering and Gamson (1987) and the Educational Commission of the States (1995) empirically derived “principles of good practice”

findings are similar to Umback and Wawrynzski’s (2005), where faculty play a vital role in student engagement and learning in college using effective practices (listed above.) Deeply engaged faculty, who are aware of the culture in their classroom, provide students an opportunity for ownership of the learning community created (Mezirow & Taylor, 2009). Quaye and Chang (2012) found that a faculty member’s own understanding and response to racial interactions can influence the classroom culture, but still have a responsibility nonetheless to shape the culture to create inclusivity and encouragement that is inviting of students’ experiences. Effective racial dialogue builds inclusivity, enabling students of color to no longer feel excluded or marginalized in the classroom. Students who participate in these inclusive environments feel that they matter and are part of the higher education community (Astin, 1984, 1993; Quaye & Chang, 2012;
Tinto, 1987, 2012; Umback & Wawrynzski, 2005). This practice influences stronger student-faculty interaction (Myers & Bryant, 2002; Umback & Wawrynzski, 2005).
The Puente Project is an example of inclusive access to college through relationships and connection with both full time and part time instructors (Bryant & Duke-Benfield, 2014; Laden, 1999). It is a long- standing program founded at the University of California Berkeley, implemented in participating California and Texas community colleges and high schools. Engaged faculty partake in intensive professional development, establishing an understanding of themselves and their students beyond the walls of the institution. It is an environment rich with collective efficacy. The program brings together a counselor and an English instructor to coteach courses in a learning community format. The curriculum started with a focus on Latinx culture as context for the courses, though it has shifted more recently to include other cultures (Bryant & Duke-Benfield, 2014; Laden, 1999). Puente works with first generation college students and students in high school preparing for college, many of who need a developmental

English course, which Puente provides. There is a strong focus on the local communities of participating institutions, with one of the goals of the program being that students go back into their communities armed with strong voices and a deeper knowledge of their culture through literature. With wrap around supports, students’ socio-emotional wellbeing is fostered and provided in the classroom (Bryant & Duke-Benfield, 2014; Laden, 1999). Participating faculty and staff go through an intensive professional development summer institute, creating a community of professional learners within the Puente network that then spreads to other faculty in the colleges (Bryant & Duke-Benfield, 2014; Laden, 1999). The Puente Project is an example of a program with culture at the heart, focused on relationships and inclusivity among students and faculty together (Bryant & Duke-Benfield, 2014; Davidson & Wilson, 2016; Jett, 2014; Laden, 1999; Davidson & Wilson, 2016; Jett, 2014; Newman, Wood & Harris, 2015; Quaye & Chang, 2012).
The Practice of Inclusivity and Cultural Responsiveness in the Math Classroom
What does this look like in a mathematics classroom? How is a sense of belonging and academic validation cultivated, and how is cultural responsiveness practiced by mathematics faculty? Christopher Jett (2014, p. 104), discusses his own practices as a mathematics professor in higher education, positing that the mathematics identity of students of color is robbed by assimilation practices and norms in higher education. He promoted a sense of belonging and cultural relevance using the work of Gloria Ladson-Billings (2009) as his framework, coining the term identity thievery in math to describe how schooling practices “subtract from students’ longstanding culturally rich and mathematically robust identities” (p. 104). Identity thievery is a practice Jett describes seeing in action not only in Predominately White Institutions (PWIs) but in Historically Black Colleges and Universities (HBCUs) as well. In Jett’s mathematics courses,

he, like Ladson-Billings, treated all of his Black and Brown students as mathematically culturally competent beings of brilliance, empowering students to internalize positive affirmations about their math abilities. He takes time in his classes to learn about students’ heritage, strengths and interests to design course projects, validating students’ cultural identities in a mathematical space. Student names are intentionally used in the mathematical problems posed for the class. Critical discourse is embraced in his class meetings, as well as ample time to work in collaborative groups. He encourages students to use math as an analytic tool to study systemic issues of social injustice within education and society. Jett’s practice is one example of how the Multi contextual Model for Diverse Learning Environments is applied at the faculty-student interaction level with respect to validating cultural identities. How might community college developmental mathematics students perceive their instructors as culturally responsive faculty who also foster these practices in their classrooms?
A Participatory Action Research (McIntyre, 2007) study in a developmental mathematics classroom at a community college in New Mexico, by a part time instructor and students, is a strong example of how students of color perceive a sense of belonging (Moreno, 2015). Most of the participants were Latinx, sharing similar experiences in school as a marginalized population. Through discussion, the co-researchers found commonalities both in and out of school, “coming together as a collective” (Moreno, 2015, p. 179). The co-researchers discussed differences between “school and life” (p. 187), where school and life have an opportunity to meet. They related with one another’s experiences of feeling disconnected to math curricula in their past as it did not relate to their lived experiences outside of school. The researchers shared commonalities of discrimination, alienation without a strong sense of belonging at school. School culture and their culture outside of school competed. Moreno explains that it was challenging for students to

discuss their experiences in a mathematics classroom. They were not used to engaging in discussions of race and culture in a mathematics course setting. Through the discussions for this study, Moreno, the instructor of the mathematics course, discovered a deeper understanding of his own identity, both as an adjunct instructional faculty member and as a member of his own community. By framing his study as “coming together as a collective,” the co-researchers learned about each other and found commonalities in their mathematics experiences. Becoming involved as co-researchers in an activity on campus gave them purpose, deepening their mathematical identities (Astin, 1984; Freire, 1973).
Mesa, Celis and Lande (2014) looked at teaching approaches of community college mathematics faculty. They identified a gap in the literature on interactions in the classroom based on how content is taught, as it relates to meaning making for students. They categorized three different approaches: traditional, meaning making and student support. They considered the traditional approach content centered and meaning making and student support more student centered. Most of the community college mathematics instructors observed and interviewed for the study, based on recommendations by department chairs, were more flexible in their teaching based on their awareness of students’ needs beyond learning mathematics exclusively. They also found that remedial course instructors exhibited more student-centered approaches, adapting their instruction to fit their context, as they seemed to understand the constraints associated with teaching mathematics in a community college. Some instructors brought student-centered instruction into their classrooms and others committed to support students beyond the learning of mathematics (Mesa, et al., 2014). Findings from this study presented a need to look at instruction in the content areas and within specific environments to better create strategies that involve students and allow instructors to be aware of students’ learning that encompasses lived

experiences (Mesa, et al., 2014). By teaching to the context of the student, faculty learn more about their students. Race and other demographic information were not provided in this study. The work of Mesa, (2014) is influential research for my study, focusing on faculty in particular. How do students perceive these instructors’ attitudes and beliefs (Umback & Wawrynzski, 2005) to play a role in creating a sense of belonging in a mathematics classroom? Sense of Belonging and Self Confidence in Math
Informal student-faculty interactions have positive effects on student understanding and confidence in mathematics (Thompson, 2001). When students perceive higher levels of informal interaction with their instructors, particularly outside of the classroom, it enhances their perceived educational gains and effort put into their mathematics courses, having a direct effect on their confidence in math. Prasad (2014) used student surveys to analyze what classroom experiences predicted a sense of belonging within the class, created by instructors in the community college mathematics classroom. She looked at whether student characteristics, behaviors and experiences in an algebra course predicted student grades and a sense of belonging. Socio-demographic variables, pre-college and environmental pull factors (including, work experience, degree goals and credits taken), psychosocial factors related to math efficacy and classroom experiences such as peer support, validation from faculty and quality of instruction were used to predict sense of belonging and students’ course grades. Math efficacy (p<05), degree of collaboration (p<001), faculty validation (p<001) and peer support (p<001) were found to be the most significant predictors of sense of belonging. Students self- efficacy (p<001) was the most significant predictor of student performance and grades in the course. This finding aligns with faculty validation and collaborative practices with peers. These findings support previous research that a cultivated sense of belonging in the classroom does influence

academic performance and confidence in math. Prasad found more males than females enrolled in the courses, with women feeling a stronger sense of belonging when collaborative peer groups were practiced in the class, and when a female instructor taught the course. This supports Tinto (1975), Pascarella and Terenzini (1979) and Nadler and Nadler (2000) findings that social contact with other women is important for female students as described earlier in this literature review. Prasad completed this study as a dissertation. There are few, if any, studies done on sense of belonging and confidence in community college mathematics courses. Prasad used surveys and quantitative statistics to analyze student perceptions. In my study, I build on her work by surveying students in developmental mathematics courses and then interviewing the faculty identified by students who promote a sense of belonging.
Developmental Mathematics Courses
How do developmental mathematics courses affect students’ ability, confidence and attitude about math? Pre-and post- surveys were used in Benken, Ramirez, Li and Wetendorfs (2015) study to learn about the mathematics backgrounds of students in developmental math and what students’ thoughts were as a result of taking the course. Students in the study were first year students at a large urban university. Findings in this study showed that many of the students took three to four years of math in high school, with at least three fourths taking a higher- level math course than the developmental course in which they were placed. Twenty percent took calculus. Student responses about their placements included: incorrect placement, not taking the placement test seriously and not liking math, even though they thought they were adequate in math. As a result of taking the developmental course, regardless of their previous math experiences, students felt confidence in passing the class, though their overall perceptions were the same- that they thought they were satisfactory in math. Researchers of the study believed that students should

leave developmental courses after completion with stronger skills, beliefs and attitudes, feeling that their math abilities are the same as those in college level courses, though findings in the study show that they did not feel this way. As a response to this finding, the mathematics department at California State University Long Beach (CSULB) used a specially selected small group of instructors to teach these courses, instructors open to annual training and who were more sensitive to accommodating the holistic needs of students. Summer bridge programs were utilized as well for precollege interventions to increase self- efficacy and beliefs of students. The students in this study came from high school. Non-traditional students, based on age in particular, were not included in this study.
The work of the small group of instructors at CSULB support the idea that faculty who engage with each other collectively and work collaboratively on their instructional practices are more likely to have increased interactions with their students (Benken, et al., 2015; Moore, 2005). Moore (2005) describes faculty classroom practices as facilitation where educators are collaborators and co-creators of knowledge instead of experts and non-experts” (p. 80). Many professors are not trained as educators and this is especially true for math instructors. Faculty who work collaboratively show improvement in their practice to better support student needs in the classroom, engaging students and faculty alike, providing more space for student-faculty interaction (Moore, 2005).
Sense of belonging and inclusivity in the higher education classroom are highlighted in this literature review through an historical timeline of the research, focusing on who the students are as represented in the Multi contextual Model for Diverse Learning Environments framework. Research on math confidence and persistence is also emphasized, with two studies focusing on

the developmental mathematics classroom. In the DLE model, academic validation is described within the classroom context to reflect student confidence and persistence, a distinction from sense of belonging that may or may not be perceived in the institutional context. Studies highlighted in this review of the literature used the term sense of belonging broadly, both in the classroom environment and in the institution. In my study, I connected belonging and validation, inclusivity and math self-confidence, based on faculty practices in the developmental mathematics classroom from the perspective of the student. Student and faculty identity and community context are brought into focus in the Multi contextual Model for Diverse Learning Environments to provide a frame for the research questions: 1) How do mathematics faculty cocreate a culturally responsive and inclusive environment with students at community colleges and 2) How does a faculty member’s engagement with students both in and out of the classroom affect the classroom environment, relative to connectedness with students, and student

This study was conducted in two stages. In the first stage, students in 19 introductory math classes were surveyed in spring 2018 to determine their relationship with the instructor, confidence in math, engagement, belonging and validation relative to the actions of their instructor to foster an inclusive learning environment. Data from the survey were analyzed to identify the four math instructors that ranked highest on these combined measures. The second stage of the study, in fall 2018, consisted of interviews and classroom observations conducted with the four instructors to create case studies of their learning environments. Finally, a crosscase analysis identified major themes and variations for the creation of the instructors’ classroom learning environments in introductory math classes perceived by students as fostering belonging and validation, math confidence, engagement and inclusiveness.
Stage 1: Student Survey, Selection of Instructors
Setting and Participants
This urban community college that is the setting for the study is designated a Hispanic Serving Institution (HSI), serving 31% Hispanic students. More than half of the students are first generation college students. The institution is located in a downtown area where many students travel to campus using public transportation. Roughly half of the student population live in the same county and approximately 80% of students live within a 10- mile radius of the campus. The demographics of the general student population at this urban institution include an average age of 24, 74% of students attend part time, and where 52% are minority students, including 31%

Hispanic, 10% Black, 7% undocumented and 12% reporting as more than one race and unknown/unreported ethnicity.
In the mathematics department of this institution, developmental mathematics courses are set up as labs, occurring an hour prior to the introductory college level course. Students who are considered to be below college mathematics levels co-enroll in a one credit lab course connected to the introductory college level course and taught by the same instructor. This structure allows for students to earn mathematics college credits while receiving additional supports related to the content based on their mathematical level. The same instructor is also aware of students requiring additional support provided in the lab, as they evaluate progress in the college level course.
Selection of courses was a two-stage process. Courses considered to be introductory, with the supplemental one credit lab course for students who needed remediation were selected first. These face to face introductory courses included: a course designed for students in health disciplines, a math course for liberal arts majors, an introductory course for students in STEM majors, and an introductory course in statistics. Online courses were not surveyed for this study.
In the second stage of the course selection process, approval from the math department was required. The department allowed me to survey 19 introductory mathematics courses that were taught face to face. Two of these sections had only one student who participated in the survey. As a result, these two courses were excluded from further analysis. Out of the 19 total math courses surveyed, 17 courses were included in stage 1 analysis.

A total of 191 students in the 17 introductory mathematics courses were surveyed. The demographics of the 191 participants somewhat mirrored the race and ethnicity of the college with 60% being minority students, where 35% of the surveyed students identifying as Hispanic, Latinx, Mexican or Chicano4, 10% Black and 26% chose not to identify. Most of the students in the courses were 18 and 19 years old, making up 28% of the total surveyed, with 51% ages at 17-
22. A majority of the students, 59%, reported that this was their first year at the institution. Instrument: Student Survey
The student survey was created in Qualtrix and consisted of 28 items that were arranged into six categories: 1) Relationship with Math Instructor, 2) Confidence and Interest in Math, 3) Class Structure, 4) Belonging and Validation, 5) Math History in Higher Education and 6) Demographics. Criteria for the six categories in the student survey relate to Chickering and Gamson’s (1987) and the Educational Commission of the States (1995) “principles of good practice” as employed by Umback and Wawrynzski (2005) and Myers and Bryant (2002). Some of the survey questions were based on the National Survey of Student Engagement (NSSE), though specific questions about sense of belonging and math were created to fit with the research questions in this particular study. Survey questions are detailed in the Appendix.
Each category is detailed below.
Relationship with the Math Instructor
The first construct, Relationship with Math Instructor (Cronbach’s Alpha .90,) included seven questions about the students’ relationship with their math professor. Questions in this category focused on the time the instructor provided for students outside of class, the frequency
4 The question of race and ethnicity was a fill in the blank for students to self-identify.

with which students shared about their life outside of school including: home life/family, career goals, neighborhood and culture and whether they perceived their instructor to understand their life outside of school. Representative items included “My instructor makes time for students outside of class” and “I share information about my life outside of school with my instructor.” Confidence and Interest in Math
Confidence and Interest in Math (Cronbach’s Alpha .90) had ten questions relating to how students felt about math, describing their confidence level and interest in the subject. Six of the questions referred to the student’s interest in math because of the instructor, asking about how much they like math as a subject, their interest in assignments, how hard they try and their participation. Four of the questions referred to students’ self-confidence including how well they perceive to be doing in the course and in the subject of math. Representative items in this category included “Because of this instructor, I like this math course better than most math courses I have taken in the past” and “Because of this instructor, I participate in class discussions in this math class.”
Class Structure
The Class Structure (Cronbach’s Alpha .70) variable had three questions about the students’ perceptions of the class structure provided by the math instructor. Questions in this category inquired about assignments, large group activity and work with peers in small groups. How much time was allotted in class for discussion about topics perceived to be relevant by the student, time provided to work with their peers and how assignments related to the students’ lives were asked. Representative items included “My math classroom environment provides time for discussion about topics relevant to me” and “My assignments relate to my life and my experiences.”

Belonging and Validation
The Belonging and Validation category (Cronbach’s Alpha .90) included four questions. Students’ perception of the instructor’s understanding of their community and culture and whether the instructor listened to and cared about the students was highlighted. Another question in this section asked if the student looked forward to attending class because of the instructor. In this category, belonging and validation of the student by the instructor was measured based on whether the student felt acknowledged in the academic environment. Representative items included “My instructor listens to me” and “My instructor cares about me.”
Math History in Higher Education
The four questions of the survey referred to students’ history in higher education. Three of the questions were multiple choice. Questions included “How many years have you attended this college” and “Is this your first mathematics course at a higher education institution?” A follow up fill in the blank question was asked if they answered “yes” to “have you taken another a math course at this institution” and to list the course/s they took previously.
Demographic Information
The final four questions asked for the students’ demographic information. Questions were all fill in the blank to self-identify in the way they prefer. There were spaces for students to fill in their: ethnicity, race, gender and age.
Data Collection
Student surveys were administered by the researcher in face to face classrooms in spring 2018, between weeks five and nine in the fifteen-week semester. Students had the choice of filling out the survey online using their personal computer or phone, or a paper copy collected by the researcher. A letter of consent for students was provided, as the survey was voluntary.

Students identified in their survey, based on their own experiences, how faculty created a sense of belonging in their classrooms. Survey results from Qualtrix were exported to SPSS. When exporting the Qualtrix survey results into SPSS, answers associated with Always, Strongly Agree, etc. had the lowest values. The lowest scores possible are what determined which instructors created the strongest sense of belonging according to the students surveyed. The scores for the four scales: Relationship with Instructor, Interest and Confidence in Math, Class Structure and Belonging and Validation were calculated as Z scores, each with an overall mean of zero and standard deviation of 1, so that they would each weigh equally in the composite score used to rank and select instructors for this case study. (Table 1.)

Table 1
Z scores by Each Construct
Math course Instructor n Relationship Interest Structure Belonging Average Instructor Z Score Rank
Math 1 A 16 .30 .78 .41 .45 .48
Math 2 B 9 -1.40 -.50 -.47 -.46 -.70 3
Math 3 B 6 -1.40 -.46 1.18 -.71 -.35 6
Math 4 C 13 .013 .018 -.50 .34 -.03
Math 5 C 21 1.24 .47 .48 1.08 .81
Math 6 D 5 1.46 1.46 1.98 2.49 1.85
Math 7 E 8 2.20 1.32 1.76 1.40 1.67
Math 8 E 9 -.11 .24 .12 .44 .17
Math 9 F 8 .92 1.50 .96 1.01 1.10
Math 10 G 11 -.34 -.20 .33 -.52 -.18
Math 11 H 12 -1.06 -1.27 -.83 -1.01 -1.04 2
Math 12 J 10 .50 -.77 -1.45 -.25 -.49 5
Math 13 J 13 -.93 -.51 -.11 -.73 -.57 4
Math 14 K 17 -.60 .06 -.68 -.75 -.49 5
Math 15 K 12 -.97 -1.12 -1.36 -1.27 -1.18 1
Math 16 L 11 .16 -.11 .04 .01 .02
Math 17 L 8 .02 -.21 .01 -.39 -.14
Note. The lower the Average Z score, the better the instructor scored.
As a result of the averaged Z scores, 4 instructors: 1 female full- time professor, 2 male full- time professors and 1 male adjunct instructor5 where considered to have the overall highest
5 This particular adjunct faculty member was promoted to a full-time faculty member for the 2018-2019 academic year.

scores on the four survey categories based on Spring 2018 student survey data (Table 1.) These four instructors comprised the purposive sample for interviews and observations in Fall 2018.
Three instructors, B, J and K, ranked high in both of their courses, each taught two surveyed courses identified in survey data as creating a strong sense of belonging and validation (Table 1.) Instructor B’s two courses had a lower number of students surveyed, nine and six students respectively, ranking third with a Z score of -70 and sixth with Z score of -35 (Table 1.) Instructor J’s two courses had thirteen and ten students in class who participated in the survey. Instructor J ranked fourth with a Z score of -57 and fifth with a Z score of -49 (Table 1.) Instructor K had twelve and fifteen students in the two surveyed classes. These classes ranked first with a Z score of -1.18 and fifth with a Z score of -49 (Table 1.) Instructor H taught one of the surveyed courses with twelve surveyed students, ranking second with a Z score of -1.04 (Table 1.)
Stage 2: Case Study
A case study methodology (Yin, 2004) was used in stage two to investigate the phenomenon that took place in the context of the instructors’ classrooms over the course of the semester. A case study is a social science method to describe a significant social event (Yin, 2004). Yin (2004) describes the phenomenon as a real-life event and the context as the natural setting in which the event occurs. This study captured student perceptions during their time in the courses of interest, followed by observations and interviews of the identified faculty who engaged in practices that created sense of belonging, inclusion and engagement. The phenomenon and context are integrated, which Yin discusses as a useful strength of the case study method (2004). Key themes are often extrapolated to help predict future trends and bring light practices that can provide a means for understanding an issue with more clarity (Mills,

Durepos & Wiebe, 2010). Due to the high attrition rates in mathematics courses in community colleges, particularly for students of color, inclusive classrooms is an important issue to investigate, as it effects the goals and lives of college going individuals (Bailey 2009; Bailey & Cho, 2010; Bailey, et al., 2015; Hurtado & Carter, 1997). Using the case study method provides a deeper understanding of the phenomenon that is belonging and validation for students, as identified by students and created by faculty through the themes uncovered in faculty observations and interviews.
At the urban institution where this study took place, there were a total of 108 full time faculty and 285 part time faculty. In the math department there were 17 full time faculty, though not all of these faculty members taught introductory courses. It was unknown how many part-time faculty served in the department. For this study, the students in the courses of 11 instructors were surveyed, with some teaching more than one surveyed section. Of these 11 instructors, 3 were adjunct and 8 were full time faculty. Only instructors teaching face to face course sections offered during the weekday were surveyed for this study. Of the instructors surveyed, 4 were white, 3 were Asian, 2 were African and 2 were Hispanic. There were 3 women and 8 men who taught the surveyed courses.
Faculty Interviews and Observations Interviews
Once the four faculty members were identified as employing “principles of good practice” (Chickering & Gamson, 1987; Educational Commission of the States; 1995) from the student survey data, three face-to-face interviews were conducted with each faculty member

individually during the fall 2018 semester. All of the interviews were recorded and then transcribed for analysis. The first interview was a structured format, conducted the week before courses began to understand each instructors’ teaching philosophy and goals for their students and themselves. Each faculty member was asked the same questions: 1) Tell me about your education background, 2) What brought you to the community college to teach mathematics, 3) What is your philosophy and most important practice that you integrate into your pedagogy, 4) How do you plan and start your course off at the beginning of the semester to create community and sense of belonging, 5) What are your goals for your students and for yourself.
The second interview was conducted during weeks five and six of the semester. This interview was unstructured. Questions were asked that specifically pertained to the three classroom observations conducted prior to the second interview. Questions such as, “you sat with the group in the back first. What made you decide to start there?” Or, “How do you use the information on the sticky notes you collected at the end of class?” These questions gave each instructor an opportunity to describe in more detail the reasoning behind their practice, interactions with students and interactions among students.
The final interview was conducted after the last observation. This interview was semi-structured. Some questions were asked of all four faculty: 1) What do you feel proud of this semester, 2) Did you make any changes this semester that you noticed a difference in compared to previous semesters, 3) How is this class with respect to relationships compared to your other classes, 4) How many of your students are passing the course thus far. Other questions asked in this third interview were based specifically on observations made about their course in particular.

Five observations were conducted per course that each faculty member taught. The courses I observed were chosen collaboratively with the instructor, based on the time it was offered and the mathematics level. The most introductory level course each instructor taught was chosen, as these courses statistically have higher attrition rates (Bailey & Cho, 2010). The five observations were conducted on the first day of the course and during the second week of the course (in August), the fourth week (in September), the eighth week (in October), and thirteenth week (just before fall break in November). The five observations were spread across the fifteen-week semester intentionally, as a way to observe attendance and how the community of learners was formed and established. Each observation was conducted during the whole duration of the class meeting time. I took photos of notes on the board and posters created by students. I also collected handouts instructors distributed in class.
A rubric was not used during observations. General practices were highlighted that went beyond the subject of math. Observations focused on the relational aspect and conversation interactions among students and instructors. I observed for a variety of practices the instructors used to engage with students. Observation data collected included: whether faculty asked questions to engage students in conversation and how they did this, if and how often they used student names, how often they engaged students in small group discussions and when these discussions took place, discussion of office hours and their availability for students, what time they came in to the classroom and how late they stayed after class and how often and what topics were discussed beyond math in relation to student identity, culture and community. Observation data was also collected about how the instructor answered and engaged with questions brought up by students about their experiences and whether the instructor shared their own as well. How

the instructors introduced math and how they related it to students’ prior experiences to build confidence and engagement was also observed. All of the observation and interview data related back to the core box of the Multi contextual Model for Diverse Learning Environments (Hurtado, et al., 2012), where student and instructor identity are situated, and how the instructor creates a sense of belonging and provides academic validation in a diverse classroom of students. An observation rubric was not used.
Thematic Analysis
A thematic analysis (Boyatzis, 1998; Braun & Clarke, 2006) was conducted after observation and interview data was collected to find and learn about patterns and overarching themes in the practice of each of the four identified instructors. Themes were created using an inductive analysis. After all interview and observation data was collected and transcribed, I looked for: 1) terms or ideas that signaled belonging and validation, 2) discussion of practices that went beyond the subject of math, such as learning names and how they conversed with students , 3) how they discussed particular students and what they noticed and shared about their knowledge of their students, 4) contemplation of curriculum and their delivery styles, 5) discussion of their personal preferences, what motivated them and issues they grappled with as instructors, 6) how they spent their time while at the institution and 6) their interpretations of the questions asked in the interviews.
Observation data was analyzed based on interactions instructors had with students, and interactions students had with one another, both in their actions and in conversation.
Observations provided the space to see whether what the instructor said in the interviews aligned with their actual practice with students. I was able to clarify and ask questions around practice in the interviews based on observations, giving further insight into themes that were surfacing. As

an inductive process, I identified broad comments made on the part of the instructors that signaled qualities of inclusive practice both in and out of the classroom and then found both similarities and differences among the four instructors. The Multicontextual Model for Diverse Learning Environments (Hurtado, et al., 2012) was used in the analysis to find commonalities in the practices by the instructors in relation to how they viewed students and themselves in diverse learning environments as they created belonging, promoted validation, inclusivity and engagement with and among their students.
To ensure the reliability and validity of my findings, I informed the mathematics department and consent was required to conduct the study before surveys were implemented in Spring 2018. Once consent was established, students were surveyed in their classrooms, where they were monitored by me without their instructor present. Students filled out a consent form to ensure that they understood the study. Student surveys were anonymous and did not include names or identifiable information. Surveys included brief demographic data but were not identified in the study. The intent was to find four faculty members who create a sense of belonging and engagement in their classes.
For faculty interviews, semi-structured interviews for the first meeting helped to eliminate some bias by asking the same questions to all four of the faculty, with the opportunity to clarify as necessary. Recorded interviews were transcribed to keep the interview answers authentic. The observation data of each instructors’ class meeting will be not be kept once the analysis and study are complete. The second and third interviews were purposely unstructured as at this point interview data was gathered for a more in-depth understanding of the individual practice by the instructor. I created a relationship with the instructors, so questioning was more

comfortable and informal as meetings took place throughout the semester (Shenton, 2004). Member checks were conducted once the data was analyzed. The four instructors had the opportunity to review the material in the findings from the thematic analysis that referred to their particular course and practice to make sure what was written reflected them appropriately, and with validity.

Authentic Caring: A Student-Centered Practice
There was a wide gap between the four highest ranked instructors compared to other instructors in the study (see Table 1, Chapter III, p. 35). This gap provided evidence that the four selected instructors approach to teaching introductory mathematics was qualitatively different from most other instructors as perceived by surveyed students. Student comments during my observations in the classrooms signaled their perceptions of this difference. One student said, “I like how you teach” to Instructor B. I observed another student in Instructor B’s class tell a classmate that he took math courses from other instructors and likes Instructor B most, “I really like the way this teacher explains. I finally like math.” In Instructor J’s class, a student turned to me and whispered, “this is my third time taking this course. [Instructor J] is a great math teacher.
I am passing and feel like I can do math.” Students described their feelings about their instructors’ practices as related to their enjoyment of math and passing the course.
Thematic analysis across the four cases resulted in four themes, 1) Advocacy: Students First, Education as a Right, Shared Accountability, 2) Partnership: Reciprocity and Interdependence, 3) Reflection and 4) Expression of Difference, that suggest why the classes of theses instructors were perceived as spaces that were inclusive and created a sense of belonging for students. The themes were found based on the interactions instructors had with students, the interactions students had with each other in the classes, behaviors exhibited by the instructor and alignment between what was discussed in the interviews and then presented and practiced in the classroom. Foundational to each of these four themes was the authentic caring and student-centered approach of the instructors, with cultural responsiveness ingrained in almost every

aspect of the instructors’ practices. The themes were present in the observed classrooms; however, their practices were expressed differently, their teaching styles quite different from one another.
Advocacy: Students First, Going Above and Beyond, Shared Accountability
“ ...they have a right to all of the support. Lack of support is unjustifiable. ” Instructor H
All four of the instructors believed that all students have a right to learn and that learning math is something of which everyone is capable. For these instructors, their students came first, and their energy was derived from their work with students. The instructors were advocates for their students by going above and beyond with students, sometimes bending the department and institution rules to meet student learning needs. They had high expectations, scaffolding the content to make sure that each student was within their zone of proximal development (Vygotsky, 1987) as shared accountability.
Students First
All four of the instructors discussed the one credit labs for developmental education students associated with the courses they teach. One of the instructors did not have a lab with their course in the fall semester as it was considered a higher-level math course, not an introductory course. Even though this instructor did not teach a lab, in our interviews, the lab was brought up from the introductory courses taught in prior semesters. The instructors conducted their lab courses differently. Some had additional activities and assignments, some used it as time to go deeper into the content delivered in the main course. However, they all saw this lab as time to work more closely with students in an informal way. To reach all of their students, instructors shared that students who had not signed up for the lab could attend it nevertheless, and many did. They described this as “a secret” or “bending the rules” because it

was not protocol at the college. They believed that all students have a right to learn and they did not want to create barriers, so every student was welcome. In our second interview, Instructor J said, “I don’t even know who is signed up for lab and who isn’t anymore. All of my students have been there at some point.” Instructor H said that everyone comes to both the lab and the main math course, so it is treated as one in the same. When I came a little early to observe in Instructor H’s class one day, I thought I had come at the wrong time as I could not tell when the transition took place between lab and the content course. When I asked Instructor H about this in our interview it was shared that the lab and the course are like one in the same. Instructor K said, “if someone not in the lab wants to come, I ask the lab group if they are ok with it. I keep it secret, they aren’t supposed to come.”
In addition to the labs, instructors described themselves as deviating from the institutional
rules in other ways. Instructor B believed that “it’s best to slow down and cover something well
so at least they get this part correctly” deviating from the course curriculum by skipping over a
lot of what was thought to be of review to focus on and expose students to the new material only.
By doing this, Instructor B felt that a more comfortable rhythm was created in the classroom.
I know the syllabus is some type of contract but I still it’s like I inherited this syllabus. And that person inherited it and then it comes from the board of education] who outlines what I need to be addressing in this class in this amount of time, well you know- then somebody show me how to do that.
Taking time and going deeper into a few key concepts rather than glossing over many minor concepts was very important to Instructor B. This belief was a result of seeing too many students struggle with the volume of material to review. As a math course leader within the department, Instructor B made the assessments flexible for the class and for other faculty teaching the course, meaning that questions on the assessments could be deleted or revised as needed for what was

covered in the courses. As a student-centered instructor, adjusting the syllabus and in essence,
bending the rules, was very worth it, to meet students’ needs.
Education as a Right: Going Above and Beyond
Instructor J not only made the labs accessible for students in the college level course but
found that students go to office hours more when they are offered in classrooms, so this
instructor would find classroom to host office hours.
I’m approachable. Outside of class and course inside of class too but that just happens. But I think you do have to convince them a little bit to come see you outside of class but you gotta do just a little bit more... When I hold office hours in an empty classroom, more students come, lots of students regularly. Eventually I weasel my way into a classroom for office hours.
Instructor J would make this happen by going above and beyond to reach students, attempting to meet them where they are, literally, because, “it can be the difference between passing and not passing.” In the course I observed, Instructor J learned that the classroom was not occupied for the hour following the class meeting time. Students would go the lab an hour before the course started, attend class and because Instructor J stayed an hour after in the same room, some students would stay in the classroom with Instructor J for a total of three to four hours working on math.
Instructor J also volunteers in the tutoring center sharing in our first interview that,
I care more about this [volunteering in the tutoring center] than committee work for the college. My commitment in this job is to them [students] first, not necessarily to committees. I want to get to know other students and how they are taught by their instructors. I don’t put hours [that I am] in the tutoring center on my syllabi anymore for this reason, and my students still find me.

There was a sense of deep commitment to students, making them the priority of Instructor J’s practice. It was often hard to schedule time to meet and interview Instructor J as they6 talked with students in the halls, up in the tutoring center or coming back from a meeting with the students.
Instructor K goes above and beyond when meeting students outside of the classroom as well. This instructor said,
In the classroom I have to be equal to everyone. Outside of the classroom however, a different story.. .If you come to my office I will spend time with you, I will explain everything to you and I will have students come to me at 6am because they are working all day.. .if you can’t make it to office hours, I will be here at 6, 6:30, 7 [am].
When I came to Instructor K’s office for the third interview, students were in the office. I waited
twenty minutes while Instructor K worked with the students, making sure they understood the
material before they left. The instructor just shrugged their shoulders and said, “They didn’t get
it. Sorry, I had to help them until they got it.” Instructor K apologized, unapologetically. The
students came first.
Instructor H had an open-door policy for office hours; “I am in my office. Students can come. Sometimes they come and sit in [here] and camp.” In our second interview a story was shared about a student who came to the office and would just sit and work. This student did not often ask for help, the student just wanted to sit in the office alongside Instructor H to get work done. As Instructor H said, “The students keep me here, they pay me, they have a right to all of the support. Lack of support is unjustifiable. They need support. I hope that will carry in their life and [they will] reciprocate it.”
6 To keep instructor identities and genders anonymous, the pronouns “they, their and them” are used.

Instructor B held office hours both in their office and in the tutoring center, “students go to the tutoring center more because it is less intimidating, but they will talk more personally in my office.” It is not encouraged by administration to hold office hours in the tutoring center, though Instructor B saw it as an opportunity to reach more students, bending the rules for the needs of the students.
Shared Accountability
The instructors saw office hours as a responsibility of the students, though they made efforts to reach students and bend the rules to make being accountable for their learning a little easier. They wanted to gradually release responsibility to the student so that they own their understanding of the content. One of the questions asked in the first interview was their goals for themselves professionally and their goals for students. The goals mentioned included students building confidence in their own math abilities by showing evidence of taking responsibility for their learning and understanding. Each instructor described this in their own way, building on the idea of education as a right, as each one of them genuinely believed that every student was capable of learning the mathematical concepts and relating these concepts to their lives. They saw themselves as providing a service that each of their students has a right to and wanted them to own their learning. Instructor B described it as filling a bucket, “They fill it, I sort it. The students are the employer.” Instructor H said, “I respond to need, and I fill in what they need help with.” Instructor K explained, “I adapted math to American students. I needed to understand how they learned math in order to help them.”
When it came to building skills and math confidence, each instructor saw this as an opportunity for the classroom community to learn from one another and work together. Instructor

H encouraged students to work together, to see the course as more than math, but as a place
where students walk out of the class as critical thinkers and manage their lives.
I like to teach something that is not totally math. Math is a tool, they have to learn how to use that tool Math is logic. If you use that tool, you solve a problem logically and hopefully you use that logic in law school and biology. It’s like a lock, you twist it this way and then that way. Learning how to use the tool. We use different tools every day.
Instructor H also included students in planning the use of their time in the classroom as a way to
develop time management skills for their use outside of the classroom. Instructor B described
math as a way to train a person in a way of thinking, similar to Instructor H’s description of math
as a tool and use of time for students in the classroom.
Our hours in class are your [student’s] class hours, but I’m up there for the whole thing. You know that expectation if I can just get them to do math during the class time, I think. Once they get out of the class, their motivations, duties, responsibilities. I want them to self-gauge, I think them doing math while they are there is good...
During my first observation, Instructor B told students, “this is your class,” encouraging students
to catch mistakes made on the board and to feel comfortable asking for clarification.
Instructor B described a different level of accountability in the higher-level courses.
These courses do not include the lab component, so there is more accountability on the student to
ask questions and be more open about how they are doing in the course.7
For classes with labs, even though they are technically for students who are remedial, but it does help create relationships and slow things down, so you get to know the students. I knew more about where they were with homework and could probe more. Without the lab, I only get information about them from quizzes and tests. I cannot see their homework, how they do it and what they did.
The curriculum for this course, among others in the math department, uses MyMathLab, an online textbook and homework program. For Instructor B, when teaching courses with lab
7 Instructor B did not teach an introductory course in the fall semester. As a result, I observed one of the higher-level courses taught by this instructor that did not include a lab course.

sections, homework was done in the lab. When students turned in assignments in MyMathLab for the course I observed in the fall, the instructor explained that the students’ processes could not be seen. It was easy for the student to use the help tab and get the answer without computation or explanation. Therefore, Instructor B saw office hours as essential for student accountability to help them further their understanding of the material, explaining, “I’m willing to work with them, but it is on them.” Instructor K and J also shared that they saw accountability as students helping one another and coming to office hours.
Instructor B and H both shared in their first interview that math was not something that came easy for them. Instructor B shared:
I am a regular person with math and now I make a living off of it. I never thought I was going to be a math major. I tell them that for a while it is like banging your fists against a wall, but once you see the general, the basic idea, then there is a satisfaction and beauty to these numbers and stuff and when you get deeper into it you realize that things connect.. .it’s based on the same thing, then it becomes interesting. Anybody can do it. I want to instill that type of confidence.
To support the idea that mathematical concepts connect, Instructor B introduced students to the foundational concepts in the course by incorporating some of the Roman and Greek history of math into the lesson on the first day of class.
Instructor H shared with students in the first class I observed, “I still struggle with math” and in our interview shared a story with me of their mother doing their homework for them because math was not enjoyable when learning it, so there were gaps in understanding. As a result, these two instructors saw confidence building in math as essential.
Instructor K told the students on the first day of class, “I have another lover, my other lover is math. I have a terrible memory, so math doesn’t always come easy. I have to use logic,” similar to what Instructor H described. Instructor K described math as something that is enjoyable, but a challenge, similar to relationships in life. Instructor K saw the barrier to math

confidence as not understanding the language, that reading a problem and translating the problem was the bigger issue. To build confidence and encourage accountability for their learning of the concepts using logic as the tool, Instructor K used real life examples with charts on the best place to live as a woman, asthma and smoking, buying a car, etc. The instructors were honest about their relationship with math, while making an effort to relate the concepts to the students’ lives. This made math more tangible and less daunting, while also fostering stronger relationships with the students to show them that they can “do math.”
Instructor J used a flipped classroom model, describing it as a strategy for accountability. Students learn the material as homework and then do the work in class. Instructor J created a library of over 56 videos along with the textbook readings to guide students through a concept. When students came to class, Instructor J reviewed a few concepts based on questions that arose from students. They worked on the assignments in groups during class. Students were accountable for watching the videos and readings as preparation for groupwork in the course and accountable for working together to help one another. As a result of this practice, Instructor J told students that they might not remember the details from the course but wanted them to know and remember how working with classmates contributed to understanding the core concepts. Students also had a project in this course of which they got to choose the topic. The concepts of the course were integrated into the project to reinforce the key concepts.
The four instructors showed strong commitment to their students. The students were at the core and heart of their practice. They believed education was a right, valuing the students and the assets they brought to the classroom space. There was an intuitive sense of working with adult learners because they saw themselves as learners too. There was a reciprocity in their practice with students as it was steeped in who they were authentically as instructors. They were

humble and open with students, carving space for interdependence with a genuine sense of “we” as a community of learners in their classroom space.
Partnership: Reciprocity and Interdependence
“Once you open up, they see you as a partner rather than as a teacher. ” Instructor H
The instructors described teaching as a practice that went hand in hand with learning, as if they were one in the same. They saw themselves as learners alongside their students. The teaching and learning process was reciprocal. When they described a lesson or activity the term “we” was used. The classroom was a community of partners, and they saw themselves as one of the partners. Instructor K said that “Respect is the most important part as a teacher... we have to find the common ground.”
Relationships: Cultural Responsiveness, Valuing Individuals
When I asked, “How do you plan and start your course off at the beginning of the semester to create community and sense of belonging” in the first interview, each instructor discussed how they introduce themselves. There was an intention to build a mutual respect and approachability with the students, to show that they are people with identities other than “instructor,” evidence of being culturally responsive with their students. Instructor B said, “I introduce myself thoroughly. I like people to know who I am. I am an immigrant, I identify with [student] immigrants, it is easy to make that connection. I want to be a role model in more than just math. I want to make a good impression.” In the first observation of Instructor B’s class, Instructor B spelled out their name and pronounced it a few times to share how the name is authentically pronounced and then shared what “everyone else calls me.” Instructor B included in the introduction to the class that English was not their native language and welcomed discussion in their native language for students more comfortable communicating in this

language. Instructor K provided a power point on the first day of class with photos of their native country to give visual context. Instructor K also shared that English was not their native language or their second language. After the visual introduction, Instructor K insisted that students call them by their first name, without titles. This instructor shared in the interview, “I want them to have a short distance, if they don’t have this distance, it’s easier to ask questions.” Instructor J told students their name, then said another name explaining, “This is what everyone calls me except for my mother,” with humor infused in their introduction. For introductions in Instructor H’s class, students paired up to introduce each other. Instructor H participated in the activity, so a student does the introduction for them, “sometimes it’s easier when someone else introduces us. It is less intimidating.” Instructor H did not mention the word “math” at all on the first day. The goal for Instructor H was to create community first.
The instructors made sure, within the first 10 minutes of the first class that the students knew a little about their background and what to call them. However, their focus for the rest of the semester was on the students and knowing about them. The instructors knew all of their students’ names by the second week and used students’ names on a regular basis. Instructor K assigned each student to create a video about themselves that was posted on Desire to Learn8. Instructor K used these videos to learn names and practice how to pronounce them, “I can watch 1000 times to learn names from video.” Instructor B took time to make sure every name was pronounced correctly during the first week. In the first two observations, I observed Instructor B whispering the students’ names to practice as they worked on a math problem. Instructor H greeted every student by name as they entered the classroom, occurring in all five observations.
Desire to Learn (D2L) is the online platform used for course management.

If a student was missed, or came in late, Instructor H went to where they were sitting to greet
them. Instructor J emphasized knowing names as a cornerstone of their practice.
I do a really good job of memorizing names within the first week. I just practice at it and what I do is I just stand in the back and when class is over, I stand at the door and as they leave, I say goodbye to each one of them. I think that’s kind of a big thing because they really seem to like that.
I observed this at the end of every observation in Instructor J’s classroom. Like Instructor H, Instructor J made a point to greet every student individually at the start of class. In my second observation, Instructor J walked by each student and said their name to make sure pronunciation was correct.
After learning the names of students, each instructor would address their students by name whenever a question was asked or a was comment made. As a result, I learned students’ names and could refer to them by name in the instructor interviews. For instance, Instructor B would acknowledge a student’s idea during class by using their name, “Yes! Let’s use (student’s name) idea!” or, “Yes, yes, what (student’s name) said!” This particular practice seemed to be validating for students.
The instructors made an effort to know more about their students, often discussing where the balance was of helping and probing students in their understanding and learning. Instructor H explained, “There is a lot more than math in a classroom. I want to know them so that I can help them better so if something happens, I know what to ask about.” Instructor H stood behind this idea, particularly when discussing success and persistence rates in the third interview. Instructor H mentioned that four students stopped coming to class. While discussing these students, there was concern and sadness, “I feel like a failure.” Instructor H worked with advisors to reach out, and for all four students, Instructor H gave background on why they stopped coming to class, knowing enough about the students to understand the root cause and their math capability.

Instructor B mentioned that “you gotta probe and get to know them but at the same time you gotta be like, ‘hey I’m still going to keep you honest.’” Speaking a language other than English opened up opportunities for students who spoke the same language to come to office hours, however, Instructor B said that some students take advantage of this so boundaries have to be created. Instructor K shared in the third interview, “I know them all a little bit. They show me pictures, boyfriends, looking for apartments. I don’t know a lot, but I try.”
For Instructors H and K, there was a student in each of their classes who would interrupt and respond to the instructors in a way that was defensive. I took note of these interactions and asked about this in our second and third interviews. The student in Instructor H’s class dropped early on in the semester as the course was not needed. I shared my observation of the interaction and behavior the student exhibited. Instructor H responded, “when students are defensive, I want to find the root cause. I always go back to remembering who the students are first.” According to Instructor H, this particular student was defensive because they had just graduated high school and never had homework before. Instructor H was accepting and understanding, even though this student interrupted often and interacted with an impatient tone. In my first two observations in Instructor K’s class, the student questioned their practice, interrupted and would talk to other students loudly while Instructor K was in the middle of an explanation. I noticed a change in this student in my fourth and fifth observations. The student no longer shouted out, smiled when Instructor K came to work at that table and said goodbye to Instructor K when leaving. I asked about this student in our third interview. Instructor K said that they had a conversation in the middle of the semester, initiated by the student. According to Instructor K, the student described feeling angry about personal issues at the beginning of the semester and admitted using Instructor K as a “punching bag.” Instructor K asked the student, “Why? What did I do to you?”

The student replied, “Nothing, you actually just held it very well, thank you for that.” Instructor K told me during the interview, “I am no punching bag! But the student was struggling, and it is part of my job to help students, no matter what.” Instructors H and K looked beyond the behavior, responding with an understanding and compassion.
Reciprocity: Learning Together
Beyond knowing students, these four instructors go deeper. There is a belief of reciprocity with their students. Instructor K said, “People don’t respect you if you don’t respect them. It’s not about me, it’s about your classmate, it’s about your coworker...” This instructor wanted a strong working relationship with the students describing that if this was not present, learning could not take place. Instructor B said, “My ideal as a teacher is to instill confidence. You get to know your students and work from there.” Though Instructor B felt a sense of urgency with the curriculum, there was a sense of calmness. Each lesson was a conversation with the students.
If we are going to do some math, we are going to do some math [referring to getting into the “nitty gritty” on the board together.] I do the harder problems on the board with them so if you are going to sweat it out, I’m going to sweat it out with you.
Instructor H included students in the planning of the course, letting students decide on the time
allotted for “lecture, groupwork and question/answer,” giving students a voice and ownership of
the class as well as learn how to manage time. Reciprocity was deeply rooted in Instructor H’s
practice and philosophy.
I see my role as a partner with my students. It’s a team, and the image of that is the rowing team. And I just sit there and say, ‘left right one two!’ But they have to do the work and I am there to kind of guide them but they have to do all of the work.. .1 don’t think I can do it alone. It’s a relationship I have with my students for that 3.5 months that I build over time. At least that is what I want to see.

Similar to Instructor H, Instructor J explained the partnership dynamic in the classroom as “an equal sharing kind of thing” with the goal “that students get to know each other and for you to grow you need to learn how to work with other people.” Instructor J embedded questions in assignments as a way to get to know students. For example, in the first week of class, a data collection activity was assigned as a way to learn about students and for students to learn about one another. The data was also used in subsequent lessons.
One practice the four instructors engaged in when forming partnerships was sitting down with students when answering questions, checking in and/or working through math equations and problems. There was an authenticity in the way they interacted, as they each had their own way of doing this. It was of mutual respect, a deep want for the students to understand and feel successful. It was explained by the instructors as an example of showing responsibility to the student, but when I observed, it was a care that emanated as authentically them as an instructor. There was a sense of commitment and compassion that students respected based on the way the students looked at and spoke with the instructor.
Instructor J specifically said that more attention was given to students working in groups to encourage them to work together. During my observations, I noticed that just as much time was spent with students not in groups than those in groups. The same diagrams were drawn on the white board in different areas of the room explaining a concept to small groups of students, personalizing the explanations for each group. I shared this observation with Instructor J in our second interview. It did not occur to Instructor J that this was happening, as this instructor was truly in the moment with students while in class. There was no more attention to groups than to those sitting by themselves. Instructor J described their structure with pride, but during my

observations, this instructor was attentive to everyone, being authentic to the deep care shown for students whether they were in groups or not.
Instructor K also found a deep sense of pride in groupwork during each class meeting. Instructor K sat down with each group, asking questions about their processes in solving equations, checking their work and having small conversations. There was a connection made with every single student during this time in the class. Instructor K felt comfortable sitting close to the students and would look at each student directly in the eye. There was a sense of calmness and appreciation in each group when Instructor K would sit with them.
Instructor H strongly encouraged students to work in groups but was understanding if students preferred to work on their own. This class was not structured with specific routines like Instructor J and K’s courses. Every day was structured based on the students’ daily feedback from the prior class meeting. There was a natural flow in this class that went back and forth between groupwork and whole class questions and answers. When students were working on equations in class, Instructor H sat with groups of students and with those working on their own, engaging in dialogue with every student at some point during the class time.
Instructor B structured class as one large group. Students were encouraged to ask one another questions and interact informally as Instructor B lectured. Occasionally a student would shout out a question or comment. These interruptions were welcomed by the instructor.
Instructor B shared that in the courses taught with the lab component, walking around the room and engaging in informal conversations happened more naturally. In the class I observed, this was done most during the breaks. Instructor B mentioned that not having a lab changes the dynamic of the class, explaining that students in the higher-level courses tend to have more confidence, and work on their own. Instructor B had the most students engage one on one after

class than any of the other instructors, with some following the instructor to their office. In one observation, 12 students came up after class to ask questions and engage, two of whom spoke in the instructor’s native language. There was a sense of wanting time individually with the instructor and Instructor B made time for this. In my second observation, Instructor B came seven minutes late to class with a student, explaining to the students waiting that they needed more time with the student. This explanation may have created an opportunity for other students to take note of the importance of office hours with this instructor.
Informal Interactions With Students
The informal interactions and presence of the instructors with and among students in the classroom exhibited a level of respect and genuine enjoyment of the students. I observed joking, laughter and storytelling in each classroom. Building relationships and being honest with students was a vital part of their practice, that came from a place of authenticity. Students were at the center of their work. In order for students to be themselves, the instructors had to be themselves too. Instructor B showed this by engaging in conversation with students about an equation while casually tossing the white board marker in the air and in another observation jokingly told the class they were attempting to make a perfect circle, with sound effects and exaggerated movement, based on a video they saw of someone making a perfect circle with ease. When students asked to take another course with Instructor H the following semester, Instructor H encouraged them to take a course with another math instructor to learn from different perspectives saying, “I will have ran out of all of the jokes! You’ll get bored of me!” Instructor K replied to a student with a question in class, “I LOVE your question! I am absolutely in love with your question!” Instructor J uses sarcasm, tone and subtle humor to joke with students. There is

a casualness about each instructor that made them approachable. According to each instructor in our interviews, this was intentional, though in my observations, they seemed quite natural, evidence of them just being themselves with their class.
In our interviews, instructors brought up a variety of individual students in their classes, sharing about student work commitments, goals and aspirations, children, past education experiences, cultural backgrounds and identities. There was genuine informal conversation to know the students and build relationships. Instructor H discussed football with two students, Instructor B shared stories of driving through snow, a student engaged in discussion with Instructor J about music and Instructor K shared stories of children and family. Each instructor made an effort to talk with students about topics besides math. They did this with intention, in their own way. Instructor J would subtly eavesdrop while walking by groups and then enter the discussion students had about music, sports, work, etc. This instructor made an effort in every space, whether it be in the classroom, lab, tutoring center or even the hallway to get to know students and build relationships. It also meant that students were more likely to visit Instructor J in office hours (that usually took place in a classroom,) an important component of success for this instructor.
Among Students
Relationships among students was also evident, however these developed more slowly and over time. In my fourth observation, I noticed student groups sitting together more naturally and the conversations over the semester shifted from math to personal events. It was this fourth observation in October, weeks eight to ten in the semester, where permanent groups were formed of the students’ accord. In the first three observations, students collaborated with classmates who

sat nearby out of convenience. By the fourth observation, some students moved to a different seat in the classroom, partnering with students they intentionally chose.
Instructor J said in our second interview, “I see potential for some real friendships in this class.” During my fifth observation, two women were deep in conversation about an event that transpired the night before for one of them. One of the women put her arm around the student talking. At the end of class, they left together, making plans to talk later that evening. I also noticed another group of three students talking about personal stories unrelated to class. They stayed after class to finish their work and left together when they were done.
In Instructor H’s class, I observed two students who started off working together earlier in the lab hour. Then three more students came into the classroom and sat near the two students. They all immediately engaged together enthusiastically, where one of the students updated the rest of the group on a situation she was dealing with outside of class. As the student shared, another group member took candy out of his backpack and put it on the table for the group. This group laughed together and seemed to enjoy each other’s company. They knew each other on a personal level as a result of meeting in class. In our third interview, Instructor H shared that two women who met in the class were discussing plans of starting a business in Houston together as they both planned on moving there after they earned their degree. Working in groups allowed these two women to get to know one another and their strengths in the field.9
I noticed that students moved around most in instructor K’s class, landing with a consistent group by the fourth observation. One student in particular moved from group to group during my observations. In the fourth observation, I noticed she settled into a group of three.
This group of three talked about their math assignments as well as personal topics. Another
9 Many of the students in this particular class were business majors.

group in the class moved their chairs to the window to sit and talk casually over the allotted class break. There was one group of older students who sat together, sharing pictures of children, often talking about work with one another.
Instructor B intentionally started conversations unrelated to math topics during scheduled breaks. In my second observation, a discussion about cats ensued. Students shared about their pets, with some showing photos to students sitting nearby. In another observation, the topic of cars came up. As a result of this conversation, two students would get together during the break and discuss cars in my subsequent observations. These students spoke fairly loudly, which encouraged other students in the class to carry conversations with one another. One concern Instructor B shared was that this particular course was part of a pathway that attracted a higher percentage of international students, who did not interact as much with other students. These students tended to visit Instructor B during office hours more regularly, making connections with the instructor rather than with students. Instructor B said that a lot of students will go to office hours before the final exam, “students sit at the tables outside my office, in my office, they are everywhere.” In this case students had additional opportunity to talk and work together, even though it was late in the semester.
Among Other Faculty
Partnerships among department faculty members was observed and discussed in the interviews with the four instructors. The instructors shared their practices and saw opportunities for learning from and with their colleagues. In my first interview with Instructor K, on the day faculty were back on campus after summer break, three faculty members came in to say hello and one gave Instructor K a gift. Instructor K invited each faculty member into the office, even

though we were in the middle of the interview. Relationships with colleagues were important to Instructor K. Other instructors visited Instructor K in the second interview as well.
Instructor B engaged in informal discussions with department faculty “over beers.” They planned and discussed instructional strategies for improvement. For Instructor B, there was a strong sense of comradery among faculty. This instructor engaged in recreational activities with other faculty, mentioning these outings in all three interviews. Instructor B was also open about discussions with faculty with their class, “I was not satisfied with this [one of the problems used for an example], I had to talk with other instructors about it. We had a hard time coming to a consensus about it.” Instructor B let students know there are times faculty struggle with math and that partnerships are important so they can work through these challenges together.
Instructor H utilized a support faculty member for community activities in the classroom. The instructor did this on the first day of class and at another time in the semester (not during one of my observations.) Instructor H modeled collaboration with a fellow faculty member on a class activity to encourage community building and partnership.
Instructor J spoke about learning and collaborating with faculty in a variety of different ways, with the most influential being in the tutoring center. In all three interviews, the tutoring center was a focus. Instructor J saw the tutoring center as an opportunity to learn what tutors and other instructors were doing, explaining that the tutoring center “teaches my teaching.” The tutoring center was such a positive component of pedagogy and teaching practice for Instructor J that this instructor encouraged other instructors to participate. Instructor B discussed the tutoring center as well, using this space as a way to build stronger relationships with students and learn more about what students were doing in other courses.

“Talking about my practice really helped my own understanding of what I do more. ” Instructor J.
One key element of the over-arching theme, Authenticity of Practice, was the natural ability of the instructors to reflect. All of the instructors mentioned in the second and third interviews that they enjoyed discussing their practices and learning from our conversations. They also found feedback from students helpful to better their practice. Instructor H described feedback as vital to practice,
I need feedback, that is how I learn. It brings an awareness of what I can do differently so that I don’t bring in a bad attitude into class or else I should quit. Work and life overlap. I want to be a better human being, so that I can be a better teacher.
At the end of every class, Instructor H gave students a sticky note to provide feedback in the
form of a comment or question to stick on the door as they left. The feedback informed how the
lessons and activities were planned for the next class meeting. If a student had a request,
Instructor H accommodated. Posters about goal setting and what students wanted out of the
course were created as a first day class activity. After the first test, Instructor H revisited the
posters with the class, asking students to reflect on the posters, making adjustments as necessary,
modeling reflection and incorporating this practice into the course content. Instructor J used a
similar practice where course expectations were co-planned with students. The co-created
expectations were displayed at the end of occasional class sessions for everyone, including
Instructor J, to reflect on how they were doing with respect to the expectations they set together.
Instructor K reflected often on how students used logic to solve problems and how they
interacted in groups. There was a structure to how logic was introduced to students, yet students
could use another strategy if they chose. Instructor K discussed how students reflected on their

use of logic, sharing a comment from a student, “I realize you teach us how to think versus how to remember.” Groupwork was another topic of reflection for Instructor K, particularly in how the introductory videos were used, tying this activity into how students helped one another. Students working together was an essential practice. How groups interacted over the course of the semester was what Instructors K and J discussed most.
Instructor J shared their own observations of how groups formed, morphed and then settled, paying careful attention to group processes and patterns. Interviews with Instructor J were streams of reflection. There was an energy about Instructor J when discussing practice, from the flipped classroom model that was continually revised, expanding the contextual project based on student feedback, volunteering in the tutoring center and learning from other instructors and tutors, to setting up office hours in classrooms and learning how each student interacted with peers. At the end of our last interview, Instructor J said, “I really enjoyed being part of this study. Talking about my practice really helped my own understanding of what I do more.”
Instructor B reflected often in our interviews of the challenges regarding boundaries of responsibility between student and instructor, explaining that students should be responsible but felt torn about how much help they should receive in order to be successful. There were two students in particular whom spoke the same native languages as Instructor B, visiting in office hours regularly. Instructor B felt that the more the students opened up in their conversations, they would also try to ask for more extensions and get out of assignments. This caused Instructor B to feel torn about what is most helpful for these students. In addition to reflection about the student and instructor relationship during office hours, Instructor B also reflected on concerns about whether it is intrusive to walk around and look at students’ work as they are solving problems in class. Instructor B treated students as equals, respecting their space and decisions, so the student

and instructor relationship was a place of deep reflection. When reflecting on practice, Instructor
B shared, “I tried unconventional approaches, like flipped classrooms, but for me I just do
traditional, more like lecture. I try to prepare them for what they will be working on.” In
Instructor B’s practice, there was a natural process of reflection with students when working
through problems on the board, often asking the class what function would be best, using their
suggestions. During one observation, Instructor B told the class,
I’m not a native English speaker... If I read this [a problem that involved finding the slope of a ski run] a long time ago, even if I was a native English speaker, I would need to make this into a picture. Might make it easier to understand because I don’t know anything about skiing, or about terminals.
Instructor B then continued to create a drawing for the problem, showing vulnerability in processing with students about a topic that was unfamiliar.
Reflection challenged the instructors’ practice. It kept the student and faculty relationship at the center, supporting the Multicontextual Model for Diverse Learning Environments and Culturally Responsive Teaching (Hurtado, et al., 2012). Reflection was at the heart of their authenticity to better their own individual practice.
An Expression of Difference “Do YOU.” Instructor J
The instructors showed similarities in that they were reflective about their practice, advocates for and partners with their students, with shared accountability that reflected expectations of completion and success. However, their student centered, culturally responsive approaches to these were quite different. Their styles of practice were wholly their own in a way that felt natural. I would describe the four styles as: the casual lecturer, the insistent collaborator, the energetic partner and the structurer.

Instructor B had a conventional approach, standing at the whiteboard while talking through and modeling examples, in a casual, conversational style. Students sat in rows and took notes. They would occasionally shout out an idea, ask a question or whisper thoughts to someone seated nearby. Students occasionally worked in pairs. The atmosphere was relaxed and informal, and throughout my five observations I observed every student contribute to the large group discussion at some point.
Instructor H taught the course based on daily student feedback. Students worked in groups, partners and one or two worked alone. I observed what Instructor H called “question and answer” where most everyone in the room engaged in a large group discussion, as well as students working problems out on the board with the instructor and a student or two, and some lecture. Not one of my five observations in this classroom looked the same.
In Instructor J’s classroom, there was a buzzing energy that was present in all five observations. Students talked with one another throughout the class meeting time. There was a lot of laughter. The instructor would occasionally pause students to make a point or go over a concept quickly and the students would add input, similar to a casual give and take at a dinner table with friends. The energetic instructor moved around the room often, yet it felt casual and relaxed. At the end of the class meeting, Instructor J always stood in the back of the room to say goodbye as students left, though most students stayed well after the course time ended to continue working together during “office hours.”
Instructor K had a very structured style. Students had sets of notes they printed out on their own prior to class that they used to follow along and fill in as the instructor modeled the concepts. The instructor often encouraged input from students and paused to ask students for clarification to check for basic understanding. Sometimes a tangential conversation would ensue

as the problems incorporated social justice issues. After roughly 15 minutes, students would get into groups to work on example problems while the instructor sat with each group. Instructor K had a direct, stem approach, balanced with humor that softened the strict exterior. The students often laughed to themselves well beyond a joke that was told in passing because this instructor was really quite funny. I often laughed as well.
Persistence and Passing Rates
The four instructors had higher student persistence and passing rates in their courses compared to the national average. The national average for students referred to a developmental math course who complete and pass an introductory college mathematics course is 32 percent (Bailey, Jeong & Cho, 2015). In this study, an average of 82 percent of students persisted and an average of 71 percent passed the introductory mathematics course. Students in the four classes observed attended the course throughout the entire semester as reported by the instructors. A higher number of students in these courses continued to attend whether they were passing at the time or not. The instructors encouraged students to persist by modeling and believing that everyone in the class was capable of learning math. A higher number of students also passed the introductory math course as compared to the national average. This also meant that students coenrolled in the introductory course and lab course passed at a higher rate in a shorter amount of time than having to take the developmental mathematics course as a stand-alone course.

The purpose of this study was to learn how instructors who teach introductory mathematics courses in community colleges address attrition through their practices in creating inclusive, culturally responsive environments that promote a perceived sense of belonging for their classrooms of diverse learners using the Multi contextual Model for Diverse Learning Environments (DLE model, Hurtado, et al., 2012) as the conceptual framework. Community colleges are critical for many of the country’s underrepresented populations pursuing higher education, yet a large proportion leave before obtaining a degree. A particular obstacle to graduation is the requirement that students demonstrate college readiness in mathematics by passing introductory courses- known for high rates of student attrition. Research in higher education, and community colleges in particular, has repeatedly found that perceptions of inclusion and belonging are associated with students’ persistence to graduation.
Previous research has identified observable characteristics of higher education environments that are correlated with student perceptions of inclusion, belonging and validation, described in detail in Chapter II. Observable characteristics include faculty-student interactions outside the classroom, including frequency of contact (Nadler & Nadler, 2000; Pascarella & Terenzini, 1978; 1979), and evidence of cultural responsiveness and faculty commitment to an inclusive environment of diverse learners (Alicea, et al, 2016; Astin, 1993; Cole, 2007; Gutierrez et al, 2009; Hurtado, et al., 2011, 2012; Jett, 2014; Ladson-Billings, 1995, 2009; Quaye &
Chang, 2012). These characteristics are an essential component to higher student persistence in college (Davidson & Wilson, 2016; Nora, et al., 2005; Tinto, 1987, 1997, 2012) and in developmental math (Bailey, et al, 2015; Mesa, et al., 2014; Moreno, 2015; Prasad, 2014).

The cross-case analysis of the four instructors involved in this study provided support for each of the characteristics of inclusive higher education environments as described above. The details of those cases have been provided in Chapter IV, but will be summarized here, with attention to how their practices provided a more refined understanding of what these actions entail specific to introductory mathematics courses. Very few studies have researched what instructors do inside the classroom, from week to week, that create student perceptions in introductory or developmental math courses at the community college, where attrition rates are highest.
The four instructors provided insight into what they did behind and beyond the curriculum, that students described as creating an environment perceived to be inclusive, culturally, and that fostered a sense of belonging. The partnerships and mutual respect the faculty provided in the learning environment, both in and out of the classroom, supported and extended the central component of the DLE Model. The practices of the four instructors in this study led to higher student persistence and passing rates than the national average for students referred to developmental mathematics courses who complete an introductory college level mathematics course.
Authentic Caring, Student Centered
One of the most noteworthy findings of this study was the authenticity of the instructors’ teaching practice. The instructors were authentically themselves in sharing about their cultural identities first and mathematical identities second. This provided opportunities for students to share about themselves as well. The instructors owned their identities, often reflecting upon these in class throughout the semester with their students, allowing a space for students to do the same.

They encouraged inclusiveness and promoted a perceived sense of belonging for students, though not as intentionally designed discussion topics (Quaye & Chang, 2012), pre-planned lessons or environmental elements (Gutierrez, et al., 2009), the instructors did this by being themselves, using practices that felt natural to who they were as instructors. The four instructors believed that in order to be effective, they had to be themselves and use the practices that worked best for them. As described in Chapter IV, each instructor’s teaching style was quite different, in structure, content delivery and practice; it was an expression of difference. One instructor lectured, another used a flipped classroom model, one used student feedback to plan every day and another was extremely structured and strict. It was less about a certain presentation style; creating community and serving students first was most important to them.
Mesa, et al. (2014) categorized three different approaches of teaching in their study: traditional, meaning making and student support, suggesting that the most effective instructors who taught developmental mathematics courses were more student centered and flexible in nature. The four instructors in this study were student centered and made meaning of the mathematical content for students, it the foundation of their practice. However, their delivery of content differed greatly.
Surveyed students in this study stated that the four instructors created inclusive environments where they perceived a sense of belonging because their instructor cared about them. Based on observations and interviews, instructors did show that they cared, and went above and beyond to advocate for their students at the institution, but they all did this in their own way. It was not about using a particular method, it was about teaching in a manner that fit who they were as people, so that they could genuinely show up, advocate and care for their students. They had to be authentically themselves as practitioners in the field if they were to be

effective instructors, because being effective and meeting students’ needs is what mattered most to these instructors.
Inclusion, Cultural Responsiveness, Belonging and Validation as the Responsibility of the Instructor
Each instructor believed that all of their students were capable of learning the content. Understanding of the material was deeply important to the instructor, embodying the belief that if students felt respected and valued first, that learning the material happened as a result, the foundation of inclusivity and culturally responsive classrooms. Yosso, et al. (2009) discussed that minority students feel responsible for integrating in with the college environment and in their classes, and Demcho (2011) described this responsibility as that of the institution. However, these four instructors saw the responsibility as theirs, further supporting the DLE model where “climate for diversity,” at the center of the model that includes instructor, student and pedagogical methods, is a key foundation where climate and inclusivity on campus is created (Hurtado, et al., 2012).
The instructors took this responsibility on not as a commitment to the institution, but as a commitment to the students. Quaye and Chang (2012) findings support this claim, showing a commitment to students by making their voices heard in the classroom, and Moreno (2015) further supports this belief by including students in developmental mathematics classrooms. The mathematics instructors in this study believed in shared accountability and making the students voice heard in the classroom as well, and then going beyond by advocating for students in the institution, outside of the classroom. Instructor H said they “work for the student, that the students are employer.” By looking at their job through this lens, the instructors were focused on their role in creating a climate of inclusion, where students felt validated by the instructor and

could achieve their goals. The instructors served and supported students first, as in the climate for diversity box in the DLE model; the institutional and policy contexts were secondary. In the interviews conducted with the instructors, the institution was rarely discussed. Discussion of the institution by the four instructors involved how they would bend the rules of the institution out of necessity to advocate for students’ needs. This was evidenced in how they opened the supplemental lab course to all of their students and how and when they held office hours, even if it was not favored by the institution.
Persistence and Passing Rates
The instructors’ belief in their students’ capability of learning the content through their authenticity and partnerships with students contributed to higher persistence and completion rates in their introductory mathematics courses compared to the national average. The national average for students referred to a developmental math course who complete and pass an introductory college mathematics course is 32% (Bailey et al., 2015). In this study, students persisted at a higher rate with over 71% of the students in the four classrooms passing the course. The instructors showed evidence of student persistence in their courses as very few (two to three) students stopped attending their courses by week 11. Due to the relationships created among the instructors and students, instructors could explain what happened to the students who stopped coming. Not one instructor said, “I don’t know what happened to [student].” The students liked the instructors, and both through spring survey results and fall observations, was evidenced in their persistence in continuing to attend the class meetings even if they might not be passing. The instructors worked with the students as partners. All of them mentioned that there was opportunity to pass throughout the semester. They never gave up on their students and this kept persistence higher.

Research on the importance of interactions between students and instructors outside of the classroom as a factor of persistence is undecided in the literature. Pascarella and Terenzini (1978, 1979, 1980) found that that student- faculty interaction and involvement is important for student persistence in their first year of college and beyond, and Cole (2007) found this particularly important for students of color to feel a sense of belonging. Umbach and Wawrzynski (2005), however, claimed that interaction outside of the classroom was not a significant practice to increase student engagement and learning.
Instructors of this study exhibited that interactions outside of the classroom were a key to student persistence through their flexibility of where and when they met with students and how much time was spent with them. Nadler and Nadler (2000) found that female faculty spent more time with students outside of class and that female students were more likely to share more personal information with their instructors. In this study, three of the four cases were men, only one was a woman, gender did not appear to influence how much time students spent with their instructor outside of class hours. As described in Chapter IV, some students would work in their instructors’ offices, some would stay for an hour after class in the office hours offered in the classroom and in one instance an instructor came to class late because they were meeting with a student.
The surveyed classes in this study not only had a diverse population of students, the faculty who taught the courses were also diverse, including the four instructors who ranked highest, a unique aspect of this study. Cole (2007), Hurtado & Carter (1997), Laird, (2005) and Nora, et al. (1996) all claimed that race and prior academic experiences had more influence in how much time was spent with instructors, and Pascarella (1980) reported that students seek out and spend more time with faculty who they feel they have similar interests and aspirations. This

study supported these findings, showing that what mattered to students was the cultural responsiveness of the instructor, a key component in Hurtado, et al.’s DLE model.
Not only did the instructors share that visits outside of the class hours were important for students, it was important to the instructors as well, a finding not currently found in previous studies. As supported by the DLE model, the valuing of both student and faculty identities is at the foundation of the campus climate. When students met with instructors outside of class hours, the instructors considered this act on the part of the student as feedback and validation of their pedagogical practice. They felt value and worth by their students, which was more important to them than any institutional rules that they felt went against student learning. It was reflective of students making an effort to build a relationship with the instructor and care for their own success in math; a two-way street. Both parties benefitted from this type of interaction. These practices provided significance in creating a climate of learning and partnership beyond the classroom.
The four instructors, as participants in this study, discovered a deeper understanding of their professional identities, through discussion and reflection of their practices and the dynamics in their classrooms, similar to those in the Moreno (2015) study. As a result of this study, recommendations for academic departments and institutions to consider are to focus on validating faculty identities, provide professional development opportunities on practices that make a difference for students based on the findings in this study, and to consider flexibility in the one credit supplemental mathematics course.

Validating Faculty Identity and Reflection
Validating student identity was the first, vital component in creating an inclusive environment where a sense of belonging and understanding was perceived in the classroom among students. In this particular study, not only were the students of diverse backgrounds, the instructors were as well. Acknowledgment and validation of faculty identity would be an addition to consider in the Multi contextual Model for Diverse Learning Environments (Hurtado, et al., 2012). The instructors brought their identity to the forefront in the beginning of the semester, on the first day of class, a culturally responsive practice. They were open about who they were with their students. Discussion of their backgrounds came first, then their mathematics background followed. Students had the opportunity to do the same as a large group, in small groups and individually with the instructor throughout the semester. This study suggests that this strategy of validating student and instructor identity is an important contribution to student persistence, as informed by the student perception survey. Additional suggestions of elements of practice to create inclusive culturally responsive environments that promote belonging and
validation are included in Table 2.

Table 2
Elements of Inclusive Environments
Culturally Inclusive Practice Actions of Practice
Know student names Students create a video to share online - Listen to student names and rehearse to self Greet every student by name and say goodbye to every student by name as they leave - Use names of students when acknowledging their ideas
Share background and culture Instructors present their background with class on first day Students partner to introduce one another to the class Students have opportunity to share their background in small groups, in office hours
Describe math background Instructors share their own math history with students Students have time to share their own math history
Provide scaffolding of material Sit with students to engage with them individually when they are working on problems Observe groups
Create shared set of expectations Ask for feedback regularly - What they want from their instructor - Revisit expectations every few weeks
Offer time for students to work together in class - Encourage time for students to work together - Build in breaks or allow time for conversations that may stray from the subject to encourage relationship building
Create opportunities to meet outside of class Tutoring center - Meet in classrooms for office hours Common student meeting areas
Community college faculty are evaluated on an annual basis. Evaluation tools that include a measure on inclusive environments reflecting student and instructor partnership may encourage this practice. An emergent rubric from the observations of the classrooms focusing on the quality and substance of the interactions among students and among faculty and students would benefit the engagement of students in community colleges. A rubric such as this would

further inform math departments on perceived student sense of belonging would further inform department and individual instructor practices.
Flexibility in Supplemental Developmental Lab Courses
Another component that contributed to increased student persistence for these instructors was their use of the supplemental lab course for students at the developmental education level who were required to enroll in this one credit course. The supplemental lab is intended for only those who enroll, though these four instructors let any student come to the lab hour prior to the college content course starting. They saw it as helpful for every student, encouraging more interaction with math, their peers and the instructor. The instructors said that they would not want to turn down anyone who asked for additional supports, so they let anyone who expressed interest attend. Out of respect, they asked the enrolled students if it was acceptable for the other students to attend. The students enrolled in the lab course welcomed them, as they saw it as more support and collaboration with classmates. The supplemental lab course is an accelerated developmental practice to shorten time for students in the developmental sequence as well as a way for them to earn college credit in their first semester of college (Bailey, et al., 2015). However, an additional hour is spent with the same instructor, which provides an opportunity to build stronger relationships among students and with the instructor. Due to the success of this one credit supplemental course and the use of the course by college level students there may be more options to consider in how this course can be accessed by more students to accelerate learning and provide more equity in college level coursework.
Limitations and Future Research
Due to this study having only four cases, generalizable conclusions could not be drawn.
A larger sample would be necessary for two main reasons. First, the persistence rates and passing

rates in the courses were higher than the national average. The national average is based mostly off of traditional developmental education course offerings. The one credit supplemental lab course could have possibly created a selection effect in operation for student enrollment and not necessarily due to instructor effectiveness entirely. Additionally, one of the courses was not considered an introductory course. Second, part of the data collection involved instructors’ own descriptions of their practice, without confirmation of being able to observe all of their actions in the classroom directly or triangulate them with student accounts. However, observations were conducted that confirmed what was shared in interviews, and in some cases, confirming comments were shared by students during classroom observations.
Students were surveyed in spring courses to determine which instructors would be observed and interviewed in the fall. The instructors were selected by a different group of students than who were in the observed classes. Therefore, the students in the observed fall courses should have been surveyed as well during the final observation to analyze whether they ranked the instructors similarly to the previous semester’s students. For example, Instructor B felt that the dynamic in the observed fall class was different than the spring classes and other classes taught before. One student said while completing the survey in the spring class, “my answers to this survey make it sound like I have a crush on [Instructor B] ” In the observed fall semester course, Instructor B did lose approximately six students by week 11, more than the two to three in the other observed courses. According to Instructor B this was more than any other course they taught, including their other sections in the fall semester. In the observed class, about half of the students were not passing, whereas most were passing in Instructor B’s other sections. This was a source of deep reflection and concern by Instructor B, discussed in the third interview and after the fourth and fifth observations. However, Instructor B did share that the students who

were not passing did continue to persist, meeting with them to work hard on passing the course. Students felt a connection with the instructor and continued attending, regardless of the grade. Instructor B also shared that there was a chance of passing the course and did not let go of this vision for their students. Surveying the students in this fall course may have provided insight about the dynamic of this class compared to the others.
Another limitation was that by the fall semester, when observation data collection occurred, all of the selected instructors were full time faculty members in the mathematics department. This is not a representation of all of the mathematics instructors in the department, considering the larger ratio of adjunct to full time instructors. However, the survey results indicated these four instructors ranked highest in the findings according to the students by a large margin. Further study on adjunct instructors using the conceptual framework and findings in this study would add to the literature on adjunct faculty in community colleges. The DLE model describes the climate of diversity for faculty, students and staff. Perceptions of campus climate may be different for full time faculty than for adjunct faculty. This area of study may provide more insight in how the DLE model is framed as well.
Reflectiveness was a crucial component in how these instructors created relationships with their students, colleagues and even with me, as the researcher. Studies, including this one, show the impact relationships have on students. This particular study also gave some insight into the impact these relationships have on faculty, an important component in the DLE framework. Further research on faculty validation and how they benefit from relationships with students would be a strong addition to the existing literature and how these relationships influence curricular and co-curricular practices in the DLE framework.

Questions that often came up during data collection was the relationship between student understanding of the content and whether this affected their feelings about their instructor. Did students like their math instructors simply as a result of understanding math? If the students understood the content, did they automatically feel a stronger connection to their instructor, and did this translate in other subject areas with other instructors? These questions may warrant further research on factors that influence why a student likes their instructor. In addition, this study showed evidence of students persisting at a higher rate because they liked their instructor even though they may not have been passing the course at the time (though they still had confidence that they might.) This practice on the effort of the student not only kept them attending class, it also kept them coming to the college, as these courses were face to face. Further research on how a student’s validation in the classroom translates to how they feel about the institution and other areas of the college may give more insight into the DLE model and how the components are connected as perceived by students.
To draw more light on how inclusive and culturally responsive environments are created in mathematics courses, it is important to bring attention to mathematics instructors’ practice, rather than focusing solely on mathematics curriculum. This study showed that mathematics instructors perceived by students as promoting academic validation and creating a sense of belonging in the classroom has direct influence on persistence rates. The mathematics content was not necessarily the reason for increased persistence according to surveyed students, what mattered was how the instructor showed up for their students, and the belief that all students were capable. They were genuinely valued by the instructor just for being an individual who was part of the classroom community. As the DLE framework suggests, all members of the

institution need to feel valued. These instructors are evidence of this at the core of the model, as they believe that students are ultimately their employer, and just like their students, they need to feel of value as well.

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Relationship with Math Professor
1. My instructor makes time for students outside of class.
Always Sometimes Rarely Never I don’t know
2. Because of my instructor, I feel comfortable going to office hours.
Strongly Agree Agree Disagree Strongly Disagree
3. My instructor is available to me outside of class AND outside of scheduled office hours.
Strongly Agree Agree Disagree Strongly Disagree
4. I share information about my life outside of school with my instructor:
Often Rarely Never
Home life/Family Career goals Neighborhood Culture Life events
5. My Instructor understands my:
Strongly Agree Agree Disagree Strongly Disagree
Home life/Family Career goals Neighborhood Culture Life events
6. My instructor is: (check all that apply)
____ Positive
____ Supportive
____ Understanding
Self-confidence and interest in math

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