AN EXPLORATION OF STUDENT BELONGINGNESS AND TEACHER EMPATHY IN A COREQUISITE MATH COURSE By Amy Danielle Scheerhorn A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Curriculum, Instruction, and Teacher Education– Doctor of Philosophy 2023 ABSTRACT A lack of belongingness is an area of concern for developmental math students due to negative implications for academic outcomes. Many college students placed into remedial math courses lack a sense of belonging within the math classroom. This study identified evidence of factors of belongingness among freshman college students who participated in a corequisite course for math remediation. The corequisite consisted of a college level math class paired with a math support course. As the instructor for the course, I implemented an intervention to foster students' sense of belonging during the support course. This intervention involved students writing in a weekly reflective journal regarding their feelings and experiences in the math course. In turn, I provided weekly written feedback with the goal of offering an empathetic response to foster each student’s sense of belonging. Findings from this study demonstrated that a teacher can implement a weekly student reflective journal as a medium to provide empathetic feedback and thus foster a student’s feelings of belonging in the classroom. Through the data analysis, I observed that as the semester progressed my written empathetic feedback shifted from sharing my personal or academic stories to acknowledging the student in various ways. Evidence of factors related to a student’s sense of belonging were noted in students’ written responses to my feedback. Other findings of this work demonstrated that student interactions with peers during the math class and support course were essential in fostering belongingness in the math classroom. This study adds to the field through providing concrete ways to portray teacher care through written empathetic feedback. Further research on the use of written empathetic teacher feedback is necessary to refine the practice and better understand its role in fostering a student's sense of belonging. Copyright by AMY DANIELLE SCHEERHORN 2023 This dissertation is dedicated to Emma, Kevin, Mom, Dad, Kara, and Eric. Thank you for your support, time, and encouragement. iv TABLE OF CONTENTS CHAPTER 1: INTRODUCTION…………………………………………………………………. 1 REFERENCES…………………………………………………………………………… 3 CHAPTER 2: WAYS FRESHMAN COLLEGE STUDENTS EXPERIENCE BELONGINGNESS IN A COREQUISITE MATH COURSE…………………………………... 4 REFERENCES………………………………………………………………………….. 60 APPENDIX A: MATH SENSE OF BELONGING SCALE...…………………………..62 APPENDIX B: STATEMENTS FROM MATH SENSE OF BELONGING SCALE … 64 APPENDIX C: STUDENT INTERVIEW QUESTIONS…...……………………..…… 65 APPENDIX D: STUDENT JOURNAL PROMPTS………...……………………..…… 67 CHAPTER 3: THE USE AND DEVELOPMENT OF WRITTEN TEACHER EMPATHETIC FEEDBACK TO FOSTER BELONGINGNESS IN A COREQUISITE MATH COURSE THROUGH A WEEKLY STUDENT REFLECTIVE JOURNAL….………………………….. 71 REFERENCES………………………………………………………………………… 113 APPENDIX………………………………………...………...………………………… 116 CHAPTER 4: HOW TO IMPLEMENT A STUDENT REFLECTIVE JOURNAL AND PROVIDE WRITTEN EMPATHETIC FEEDBACK IN A COREQUISITE MATH COURSE……………………………………………………………………………………….. 120 REFERENCES………………………………………………………………………… 138 v CHAPTER 1: INTRODUCTION I am a math instructor at a private university in Grand Rapids, Michigan. During Fall 2021, I was given the opportunity to teach a pilot section of a corequisite math course. A corequisite course is an alternative to a traditional developmental math class. I have taught developmental math courses for almost ten years and through this experience I have encountered many students who described hardships in their past math experiences. In addition, research has shown many students placed into developmental mathematics feel they do not belong within the math class (Silva & White, 2013). With the goal of fostering belongingness in the corequisite math classroom, I implemented a weekly student reflective journal with written empathetic feedback. I hypothesized that written teacher empathetic feedback provided a way to show teacher care and in turn foster belongingness in the math corequisite classroom. This dissertation takes the form of three separate articles, each written for a different scholarly audience. The following articles include a study on the ways students experience a sense of belonging, a study on the use and development of written teacher empathetic feedback, and a practitioner piece on how to implement a weekly student reflective journal with written teacher empathetic feedback in a corequisite math course. First, Article 1 is focused on the ways students experience a sense of belonging. In this study, I looked for aspects of belongingness reflected in student weekly journals, end of semester student interviews, and student responses to teacher feedback. I also used a pre and post math sense of belonging scale to support the qualitative findings. The findings provide a window into ways students experience math sense of belonging through writing in a weekly reflective journal, receiving written empathetic feedback and interacting with peers. I chose the journal PRIMUS for this article, as this study speaks to the problem of students’ lack of belonging in the context 1 of a math classroom. Next, Article 2 is focused on the use and development of written teacher feedback. In this study, I explored the potential of providing written empathetic feedback as a means of showing teacher care by investigating the ways in which I incorporated empathetic feedback, and the sense of belongingness expressed by students in response to my feedback. Data for the study included my written empathetic feedback, student journal entries, student responses to my feedback, and my reflective teacher journal. Using a thematic approach, I looked at how and in what ways my practice of providing empathetic feedback changed over the course of the semester. I also looked for evidence of aspects of belonging in student responses to my feedback. The findings suggest my practice of providing written empathetic feedback shifted over the course of the semester. In addition, the findings indicate that student responses to different types of empathetic feedback reflect different aspects of belongingness. I chose the journal College Teaching for this article as this study provides an innovative teaching practice to portray empathy and foster belongingness. In addition, these ideas are important across various disciplines and implementing a student reflective journal may be applicable to other content areas. Finally, Article 3 is a practitioner piece focused on how to implement a weekly student reflective journal with teacher feedback in a corequisite math course. In this chapter, I provided logistics, suggestions for instructors to provide empathetic written feedback, and examples of actual feedback I provided. I chose the journal MathAMATYC Educator as developmental math is one of the areas of interest for this publication. 2 REFERENCES Silva, E., & White, T. (2013). Pathways to Improvement: Using Psychological Strategies to Help College Students Master Developmental Math. Carnegie Foundation for the Advancement of Teaching. 3 CHAPTER 2: WAYS FRESHMAN COLLEGE STUDENTS EXPERIENCE BELONGINGNESS IN A COREQUISITE MATH COURSE Introduction Many college students placed into developmental mathematics sense they do not belong within the math class or in college overall (Silva & White, 2013). When students do not feel they belong, this poses potential negative implications for student outcomes including persistence in completing developmental math courses (Byrk et al., 2013) and continued pursuit of STEM degrees (Good et al., 2012). Walton and Cohen (2007) stated, “one of the most important questions that people ask themselves in deciding to enter, continue, or abandon a pursuit is ‘Do I belong?’” (p. 94). Historically, developmental math courses are a common point of exit from college for students (Royer & Baker, 2018). Therefore, a focus on fostering a student’s sense of belonging to the academic domain of mathematics is crucial for a student’s success in completing introductory math courses and in turn the continued pursuit the of their degree. Corequisite math courses, an approach to remediation for college students placed in developmental math, potentially provides a unique opportunity to foster a student’s sense of belonging. Corequisites are implemented and structured in various ways (Dana Center, 2018). Therefore, with typically small class sizes and class time available for “soft skills” to help students succeed in math, this provides an opportunity to implement course design around fostering a student’s sense of belonging within the math classroom. In addition, studies show the need for continued improvement in helping developmental math students succeed in the corequisite model (e.g. Childers et al., 2021; Matz & Tunstall, 2019). This study aims to extend prior research on sense of belonging in classroom settings through identifying ways students 4 experience a sense of belonging to the academic domain of mathematics. The study was conducted in a math corequisite course, in which freshman college students wrote in weekly reflective journals and received written empathetic feedback from their teacher. Prior research with college freshman indicates the need for more research on contextual characteristics that promote a student’s sense of belonging (Freeman et al., 2007). Therefore, understanding the ways developmental math students experience feelings of belonging is important for promoting belongingness in these classroom settings. Literature Review Given the aim of this study, I will discuss prior work on academic outcomes associated with a student’s sense of belonging to highlight the importance of feelings of belonging for learning. I will also discuss prior work on belongingness in classroom settings through student experiences with peers and teachers to provide a foundation for contextual characteristics that are known to promote a student’s sense of belonging. This review will help provide context for understanding the need for identifying the ways students experience a sense of belonging to the academic domain of mathematics. This study was conducted in a developmental math course that included a weekly student reflective journal with teacher written empathetic feedback. The Importance of Belongingness for Learning The need to belong, to form connections with others, is an important part of human motivation (Baumesiter & Leary, 1995). Relatedness is one of three basic needs for motivation; the other two needs are competence and autonomy (Osterman, 2010). When students feel connected to others and see themselves as worthy of respect and love, their sense of belonging indicates their need for relatedness has been met (Osterman). Belongingness is known to affect individuals both emotionally and cognitively (Baumesiter & Leary) and therefore provides 5 implications for education and learning. Prior research provides the foundation for the importance of studying belongingness. Research connects belongingness to important academic outcomes (Osterman, 2000). These outcomes include: the development of certain psychological processes crucial for student success, attitudes (academic, social, and personal), motivation, participation, engagement, and achievement (Osterman, 2000, p. 327). Regarding psychological processes crucial for student success, relatedness has been described as one of three basic needs for the development of, “intrinsic motivation, internalization, and emotional integration” (Ryan, 1995, p. 397). Pertaining to academic attitudes, studies show students who felt accepted related positively to school, course work, and their teacher and showed interest and joy related to their schooling (Osterman, 2000). Therefore, the link between a student’s sense of belonging and various important academic outcomes suggests strong reason to continue to study and gain understanding of belongingness. When students do not feel they belong, this poses potential negative implications for students. A lack of belonging has been linked to various negative effects ranging from health to adjustment to general wellbeing (Baumesiter & Leary, 1995). A lack of belonging has been identified as playing a role in racial disparities with regards to achievement (Walton & Cohen, 2007). This lack of belonging, which has been called belonging uncertainty, is connected to an increased uncertainty of the strength of social bonds in both academic and professional settings for members of socially stigmatized groups (Walton & Cohen, 2007). In addition, belongingness is an indicator of student participation (Osterman, 2000). If students feel their sense of belonging is at risk, participation decreases; when students feel they belong their perceived risk decreases, and participation increases (Osterman, 2000). Consequently, prior research suggests 6 negative implications for student learning when students do not feel they belong. Therefore, the current literature provides a foundation for the importance of belongingness for learning as it is connected to important academic outcomes and a lack of belonging has negative implications for student success. To understand more about how to foster belongingness in classroom settings it is important to review the literature on the influence of teachers and peers. This will help to provide an understanding of the contextual characteristics shown to support feelings of belonging in classroom settings. The Role of Teachers and Peers in Supporting Sense of Belonging A student’s sense of belonging is supported in classroom settings through experiences with both peers and teachers (Osterman, 2010). Prior research on how peers and teachers affect a student’s sense of belonging provides a picture of influences on belongingness in academic settings. Teachers can enhance a student’s sense of belonging in a classroom setting through both personal and academic support (Osterman, 2010). Additionally, teachers that provide opportunities for interacting with peers through collaboration in itself can support a student’s feelings of belonging; however, particular aspects of peer interactions have also been connected with belongingness. The following sections I discuss some of these aspects in further detail. Peers Prior research indicates interactions with peers in a classroom setting can influence a student's sense of belonging (e.g. Soloman et al., 1996; Kiefer et al., 2015; Hamm & Faircloth, 2005; Keyes, 2019). Peers can influence a student’s sense of belonging through peer emotional support and peer academic support (Kiefer et al., 2015). Peer emotional support, through friendships, has been shown to make students feel like they fit in, were accepted, secure, and happy, which in turn supported students’ sense of belonging (Kiefer et al., 2015). Peer academic 7 support, both being able to help others (Hamm & Faircloth, 2005), as well as receiving help from peers (Hamm & Faircloth, 2005; Kiefer et al., 2015; Keyes, 2019) has been shown to support a student’s sense of belonging. Therefore, providing class time for students to collaborate and interact seems to be a crucial component of students’ feelings of belonging. In one study, being a strong math tutor was identified as a predictor of early adolescent students’ sense of classroom belonging (Hamm & Faircloth, 2005). In that, the way students are viewed by their peers, the reputation that they have among peers, was related to students seeing themselves as being able to bring value to the community (classroom) by being able to help others with their math assignments (Hamm & Faircloth). Furthermore, prior research in math classes provides evidence that a student’s sense of belonging is supported when students feel valued and accepted by peers, feel their ideas will be taken seriously, and feel that they can make mistakes without being shamed (Hamm & Faircloth). In addition, talking with peers outside of class regarding course work correlated with a sense of belonging for students through feelings of membership or affiliation to the college community (Hurtado & Carter, 1997). Teachers Although experiences with peers have an important impact on a student’s sense of belonging, research has identified the teacher as having the greatest impact on belongingness for students (e.g. Osterman, 2010; Kiefer et al., 2015). The ways students experience a sense of belonging is influenced by teacher practices. Practices that empower students to be successful and independent learners, have been connected to supporting a student’s sense of belonging (Osterman, 2010; Kirby &Thomas, 2022). Teachers can positively influence a student’s sense of belonging through both personal and academic support (Osterman, 2010; Keyes, 2019). First, personal support includes relating to students (Osterman, 2010; Keyes, 2019), building positive 8 relationships through getting to know students on a personal level (both in and out of the classroom) (Kiefer et al., 2015; Osterman, 2010), empathizing with students to understand feelings and needs (Osterman, 2010), being open with students (Freeman et al., 2007), and being understanding, welcoming, and caring (Solomon et al., 1996; Kirby &Thomas, 2022; Kiefer et al., 2015; Freeman et al., 2007; Booker & Lim, 2018). Second, prior research on teacher academic support connected to a student’s sense of belonging includes teacher practices such as: helping students learn (Osterman, 2010; Keyes, 2019), supporting student confidence and competence (Osterman, 2010), building trust through listening to students and providing honest academic feedback (Keyes, 2019), providing opportunities for group work and cooperation (Solomon et al., 1996; Keyes, 2019; Osterman, 2010), and supporting student learning in that they feel valued (Keyes, 2019; Zumbrunn et al., 2014). Keyes (2019) conducted an interview study with high school students to explore classroom factors that support classroom belonging and engagement. Interviews consisted of asking students about their favorite and least favorite class to understand instructional practices used by teachers to foster belongingness and engagement. Keyes provided evidence of the ways high school students experience belongingness through teacher practices. For example, teacher- student trust was one way to foster classroom relationships and engagement. Students described three ways that teacher developed trust with students. First, teachers took time to build positive relationships with students. Next, teachers actively listened to students and used their ideas. Lastly, teachers built trust through supporting and respecting students, which in turn helped them to feel valued. In addition to teacher student trust, Keyes also identified classroom management, structured and organized class time, and support for learning as ways that teacher could foster belongingness and promote engagement. The present study adds to this work through studying a 9 different student population, undergraduate math students. In addition, the present work used interviews as well as a student weekly reflective journal to explore the ways students experience belongingness. In addition, the majority of the literature on teacher practices that support a student sense of belonging are correlational comparing teacher practices with classroom belonging (e.g. Kirby &Thomas, 2022; Freeman et al., 2007). Qualitative research using student interviews have been conducted to better understand classroom factors that influence classroom belonging and engagement (Keyes, 2019) and the ways teachers (and peers) encourage belonging, engagement, and motivation. Consequently, the majority of qualitative research on a student’s sense of belonging has been studied together with motivation and/or engagement. The present work focuses only on a student’s sense of belonging. Although we know teachers can influence a student’s sense of belonging through personal and academic support; less is known about aspects of a student’s sense of belonging that are influenced through these teacher practices. Belongingness in Mathematics Classrooms Studying a student’s sense of belonging in a developmental math class is important for student success. Prior research has shown the predictive utility of sense of belonging to math regarding achievement (Barbieri & Miller-Cotto, 2021). In that, when comparing other well- established motivation and belief measures (e.g. math self-concept) research indicates math sense of belonging was the sole significant predictor of algebra learning (Barbieri & Miller- Cotto). This provides important implications for student learning in developmental math courses as algebra is a common topic. Regarding developmental math, research has shown that belonging uncertainty was the greatest predictor of persistence through the course; in that if a student’s belonging uncertainty is 10 low then their persistence would be high (Bryk et al., 2013). In addition, of those who stayed in the developmental course it was also an indicator of readiness for upcoming math courses (Bryk et al., 2013). To add to this, when one’s sense of belonging is low, one tends to leave a given domain, even if they show high achievement. (e.g. women in mathematics) (Good et al., 2012). It has been argued that negative stereotypes in mathematics for women (Good et al.) and underrepresented racial and ethnic minorities (Barbieri & Miller-Cotto, 2021) play a role in a student’s lack of a sense of belonging to the academic domain of mathematics. Consequently, students that sense they do not belong may not persist to successfully complete math courses. Therefore, it is imperative to understand ways students experience belongingness to be able to foster belongingness in the math classroom settings. This is crucial in a developmental math course, as these courses are known to be a common point of exit from college (Royer & Baker, 2018). Booker and Lim, (2018) studied the ways a math teacher fostered the belongingness in the math classroom. The study used interviews with middle school African American girls to understand student belongingness through student and teacher relationships. All of the student participants discussed the impact of teacher support on their feelings of membership within the mathematics classroom. These feelings of membership were recognized in participants that felt connected to their teacher and in turn felt a sense of membership within the math classroom. The participants feelings of membership were also influenced by their teacher’s caring and helpful behaviors along with a high regard for each student on a personal level. Overall, they found the importance of a positive interpersonal relationship between the students and their math teacher enhanced the students’ sense of belonging. These findings highlight the importance of teacher care in fostering students’ sense of belonging in the math classroom (Booker & Lim). The 11 present work adds to Booker and Lim’s research through studying a broader student population of undergraduate developmental math students. The present work is important as the ways college students experience belongingness through interactions with their teacher may be different than adolescents. Summary and Research Question In summary, prior research provides strong reason for continuing to study belongingness; as a student’s sense of belonging has been connected to positive academic outcomes (Osterman, 2000). In addition, a lack of belonging puts college math students at risk of failure (Bryk et al., 2013) and the continued pursuit of their degree (Royer & Baker, 2018; Good et al., 2012). Education-based literature provides various teacher practices to support a student’s sense of belonging; however, less is known regarding the ways students experience belongingness through these practices. Keyes (2019) and Booker and Lim (2018) provided evidence on ways high school students and adolescents respectively experienced belongingness; however, this study aims to understand ways undergraduate math students experience belongingness. The literature also provides evidence on the influence of peer emotional and academic support on students’ feelings of belonging (Kiefer et al., 2015). However, less is known about the specific aspects of a student’s sense of belonging that are influenced by peer support. Previous work on belongingness has mainly focused on a student’s sense of belonging as a whole (e.g. Freeman et al., 2007); however, theoretically, various aspects of belongingness come together to make students feel they belong. In addition, most research on a student’s sense of belonging has been correlational; comparing a sense of belonging with motivation (e.g. Freeman et al, 2007) or engagement (e.g. Wilson et al., 2015), or connecting teacher practices with classroom belonging (e.g. Solomon et al., 1996; Kirby & Thomas, 2022). More qualitative 12 research is needed to understand specific aspects of a student’s sense of belonging that are influenced by experiences with teachers and peers. For example, the literature has identified that helping peers with assignments supports a students’ sense of belonging (e.g. Hamm & Faircloth, 2005). However, I wanted to know more about the specific aspects of a student’s sense of belonging that are influenced by helping peers. Good et al. (2012) breaks down math sense of belonging into five factors and in this study, I looked for evidence of these factors in the data. Specifically, I looked for evidence of factors of Good’s et al. (2012) math sense of belonging as student participants wrote and talked about experiences in the corequisite course. These experiences included writing in their weekly reflective journal, receiving written feedback, and interacting with peers. This work is important as, theoretically, various aspects of belonging come together to influence a student’s sense of belonging overall. Therefore, a variety of classroom experiences may be needed to fully address feelings of belonging for individual students. In addition, each student is different and therefore may need different approaches to influence their feelings of belonging. Consequently, knowing about aspects of belonging that students experience, through interactions with teachers and peers, is important to better address belongingness in the classroom overall. This study aims to extend prior research on sense of belonging in classroom settings through identifying ways freshman college students experience a sense of belonging to the academic domain of mathematics. This study occurred in the context of a math corequisite course in which students wrote in weekly reflective journals and received written empathetic feedback from me, their teacher. This study is informed through the research discussed previously and guided by the following research question: 13 In what ways do students experience a sense of belonging to the academic domain of mathematics while participating in a math corequisite course? Theoretical Framework In this study, my choice to investigate the ways that students’ experience belongingness in a corequisite course, specifically, was guided by prior work that assumes a student’s sense of belonging is influenced by teacher practices and peer support. In addition, as the teacher I utilized journals and provided empathetic written feedback as a means to enact practices known to impact a student’s sense of belonging. I hypothesized that responding to the students weekly reflective journal with a focus on empathetic feedback would provide a concrete way to portray care and communicate understanding (Solomon et al., 1996; Kirby &Thomas, 2022; Kiefer et al., 2015; Freeman et al., 2007; Booker & Lim, 2018), empathize with student feelings and needs (Osterman, 2010), and to be open and honest with students (Freeman et al., 2007), which are all known teacher practices that impact student belongingness. Therefore, I assumed teacher feedback with a focus on empathy would be a concrete way to foster belongingness. Finally, to determine the ways in which students’ experienced belongingness in this setting I applied Good et al. (2012) model of belongingness. Specifically, to conceptualize math sense of belonging, they stated, “sense of belonging, as we conceptualize it, involves one’s personal feelings of membership and acceptance in an academic community in which positive affect, trust levels, and willingness to engage remain high” (Good et al., p. 702). Good’s et al. definition was chosen as it defines a student’s sense of belonging in the academic domain of mathematics. In addition, their definition allows for the exploration of the ways students experience a sense of belonging through identifying factors of math sense of belonging in the data. 14 Good et al. (2012) define factors of math sense of belonging and provide an example of each to conceptualize the meaning. Examples are provided in Table 1. Table 1 Good et al. Factors of Math Sense of Belonging Factor Example Membership “I feel like I belong to the math community” Acceptance “I feel accepted” Affect “I feel comfortable” Trust “I trust my instructors to be committed to helping me learn” Desire to Fade “I wish I could fade into the background and not be noticed” (Good et al., p. 705) These five factors as a whole comprise sense of belonging to the academic domain of mathematics. These factors of math sense of belonging allowed me to address the research question through identifying the ways students experienced belonging. In other words, I used the factors of math sense of belonging to describe aspects of belonging that were supported through writing in a weekly student reflective journal, receiving written empathetic feedback, and interacting with peers. The factors of math sense of belonging address the research question as these factors provide evidence of the ways students experience a sense of belonging to the academic domain of mathematics. Throughout this paper, “sense of belonging” will be used to represent “sense of belonging to the academic domain of mathematics.” Method Context Participants in this study were enrolled in a corequisite math course which included a college level math class (Math120 College Math) and a paired math support course. This design for corequisite remediation is called a blended model. Childers et al. (2021) defined blended model as when students who are identified as needing remediation enroll in a traditional gateway 15 math course along with other students who are not identified as needing remediation. In addition, the students identified as needing remediation also enroll in a support course during the same semester. The blended model has also been defined as co-mingling; defined as a class with a mix of college ready students and students needing remediation in the same class (Dana Center, 2018). Although the pairing of the college level math course and the support course comprise the corequisite model used in this study, when “corequisite” is referenced in this study I am referring to the support class. In context, the students and I called the support course the “Math Lab”. I chose to call the support course, “Math Lab”, because the English Department at this university uses the term “English Lab” when talking about their corequisite support course. So, “Math Lab” is the term used by students when they are taking about the corequisite support course. The corequisite course was provided at a small, private non-profit university in Michigan. The university has multiple campus locations throughout Michigan, and a global campus online; however, all participants took the course in-person at a campus location in western Michigan. The college level math course, Math120, included a focus on functions with algebra topics, and a collection of other topics such as set theory and dimensional analysis. The math course included weekly in-depth application problems titled Course Enrichment Projects (CEPs). The math course also included online weekly homework through Pearson’s MyLab Math. There were two required department tests that were multiple choice and only a calculator was allowed. There were 8 students in the corequisite support course. Seven of the students were in the paired Math120 class that met prior to the support course, and one student was enrolled in another section of Math120 with the same instructor. The paired Math120 class that met prior to the support class had 18 total students. The math support course was set at a maximum of 15 16 students, 12 students were enrolled at the start of the semester, 9 students started the class, 8 students remained in the course. The corequisite support course was non-credit-bearing and students were charged a $300 course fee. Some of the students in the support class also needed remediation in English and were enrolled in the corequisite for remediation in English. The corequisite math support class met 10 minutes after the paired Math120 course and met twice a week for 80 minutes. One day a week students worked in groups of three or four. Active learning was emphasized on these class meetings through small group collaborative learning. Students discussed ideas, supported each other in learning, and presented their thought processes on various problems to the class. The other class meeting during the week, students met in a computer lab. Students wrote in their weekly reflective journal, worked on their online homework through Pearson’s MyLab Math, read the textbook sections for the week, and took notes on their reading. Although students were allowed to collaborate in the computer lab, and some did, many students sat on their own and worked at their computer. On those class days, I gave students space and time to write in their journals, about 20 minutes total each week to respond to my written feedback and write a reflection on the weekly journal prompt. My instructional approach included supporting student learning through sitting with each small group, asking questions to understand student thinking, and supporting further understanding of ideas. I also provided opportunities for students to share their thinking and understanding of math problems through presentations in both the math class and support course. I put problems from the daily assignment on the whiteboard and students were able to decide on their own if they would like to write up their work. Students wrote up their work on the board as they were working on assignments during class. I reviewed presented work and at times I would 17 talk through potential mistakes with students prior to when they presented to the class. Towards the end of class each student would come to the board and explain their thinking and thought process for the problem they chose to present on. During the math class and the support course, I sat with students, asked questions regarding what they were working on, and guided students through questioning to help them complete problems. On the days students were in the computer lab during the support course, I sat with students to review current grades, asked students about missing work or progress on current work, and asked students to tell me about what they were working on and if they needed additional support. Although most of the class time spent in the support course was focused on providing time to work on course requirements for Math120, there were a few other aspects to the curriculum for the corequisite support course. First, as mentioned before, students wrote and responded to teacher feedback in a weekly reflective journal. Next, about once a week students worked on “basic math skills” such as fractions, operations, solving equations, and graphing. These activities were chosen by me, the instructor, who used these activities when teaching the developmental math class that the corequisite replaced. I also decided when to work on various basic skills through knowledge of the upcoming requirements in the Math120 class. I participated in a training for teaching math corequisite courses that also influenced the delivery of the corequisite support course. Specifically, the training impacted the way grades were determined and provided resources for articles and videos to show students how to employ study habits that could positively impact their math learning. These videos were only shown to students during the first week or two of class. As the semester progressed there was a greater need to provide time to work on assignments. Students always had requirements from the Math120 class to work on and therefore there was not time for additional topics on study skills. 18 Student grades in the corequisite support course were credit or no-credit. Letter grades were assigned; however, these grades did not impact student GPA. Students needed a C (73%) or higher to receive credit for the support course. Grades were determined using weighted percentages. Part of the grade for the support class was based on assignments from the college level math class (Math120). Specifically, 20% of the support class grade was the student’s grade on their online homework (Pearson’s MyLabMath) from Math120 and 20% of the support class grade was the student’s grade on their weekly assignments from Math120 (CEPs- Course Enrichment Projects). The rest of the student’s grade in the support class was based on aspects tied directly to the math support class. Specifically, 10% for in class presentations (at least 3 presentations for full credit), 20% for weekly journal entries/responses to teacher feedback, and 30% for in class assignments based on basic math skills and continuation of practice problems from topics from the college level math course (Math120). Participants There were eight freshman math students in the corequisite course and five of those students participated in this study. Pseudonyms were assigned to each participant and the pseudonyms are: Wyomia, Luan, Hondo, Caleb, and Anna. These students were all coded by the university as “New First Time Freshman”. The students in the corequisite were identified by their advisor as needing math remediation. The standards for remediation were set by the math department at the university, using the following guidelines, lower than 2.5 high school GPA and/or lower than a C in high school Algebra 2. If students had ACT score greater than or equal to 18 and a SAT score greater than or equal to 500 they would not be advised into math remediation. Students were not required to take a remedial math course. Therefore, the placement tools were a guideline for advisors to help students make an informed choice. 19 Data Collection Math Sense of Belonging Scale The present study furthers the use of the Math Sense of Belonging Scale (Good et al.) to explore use with a different math student population, specifically students who are identified as needing math remediation. Good’s et al. (2012) scale was chosen over other scales developed to understand student’s feelings of belonging, such as Goodenow’s (1993) Class Belonging and Support Scale, due to the fact Good’s et al. scale was developed for college students and used in math courses at the college level. On the other hand, Goodenow’s scale was developed originally for use with early adolescents. A pre and post Math Sense of Belonging Scale (Good et al., 2012) was used to capture students’ feelings of belongingness through the course. Good’s et al. (2012) Math Sense of Belonging scale was originally developed to understand differences in males’ and females’ sense of belonging to the academic domain of mathematics and their pursuit of future math courses at the college level. This scale is composed of five factors: Membership, Acceptance, Affect, Desire to Fade, and Trust. The factor Desire to Fade is reverse coded and there are reverse coded factors for Acceptance and Affect. The scale is composed of 28 statements. There are 4 statements on the scale related to Membership, 8 statements related to Acceptance (4 of which are reverse coded), 8 statements related to Affect (4 of which are reverse coded), 4 statements related to Trust, and 3 statements related to Desire to Fade (reverse coded), and 1 for Active Participant (Good et al., 2012). An 8-point Likert Scale is used from 1, strongly disagree, to 8, strongly agree. Good’s et al. (2012) study showed through a confirmatory factor analysis that the five factors are first order factors for Sense of Belonging to Math (Good et al., 2012). These five factors have been validated and therefore as a whole comprise Math Sense of Belonging 20 Scale. See Appendix A for the scale and Appendix B for a breakdown of factors with statements. The scale was emailed two times during the semester, once at the beginning and once at the end. The scale was completed on a Google Form. Students completed the scale in a computer lab, during class time. Absent students completed the scale on their own time. Student Weekly Journals Students’ weekly journals were used to better understand the student experience in the math course, Math120, and in the paired corequisite course. These journal entries provided one of the data sources used to investigate the ways students experience a sense of belonging through identifying text connected to Good’s et al. (2012) factors of math sense of belonging. During the corequisite course each week students were given about 10 minutes to write a journal entry given a journal prompt. Students created a Google Doc and shared it with me, their teacher. I suggested to students to write freely and without worrying about grammar, sentence structure, and spelling. I wrote the weekly journal prompts with a focus on getting students to share their feelings and experiences in the math course, corequisite course, or on math in general. See Appendix D for the specific journal prompts. Student Responses to Teacher Feedback During the corequisite class each week students were asked to read and respond to my written empathetic feedback. This feedback included an emotional and cognitive response. Specifically, Warren’s (2018) conceptualization of empathy as perspective taking and empathetic concern along with Wiseman’s (1996) attributes of empathy provided a structure for my empathetic feedback. Students were given about 10 minutes each week in class to read the feedback and then write a response in their journal. Students were asked to write a response to the feedback through stating what it was like to read the feedback and how it made them feel. I 21 used these student responses to understand the ways students experienced belongingness. There were 42 student responses to teacher feedback from the five participants. This is a mean of 8.4 student responses to teacher feedback per participant with a standard deviation of 0.894. Student Interviews On the last day of class, I asked students to volunteer for a 30-minute interview. The five participants in this study, as mentioned previously, completed the student interview, and the interviews were recorded over a Zoom video call. These semi-structured interviews were conducted individually. The audio from each video call was used to transcribe the interviews. The interview protocol guided the interviewer and can be found in Appendix C. Students received a $25 Amazon gift card for their participation. The interviewer was a graduate student who was not connected to the course in anyway, students did not know the interviewer. Data Analysis Qualitative Data I started data analysis by operationalizing the factors (Membership, Acceptance, Affect, Trust, Desire to Fade) from Good’s et al. (2012) Math Sense of Belonging Scale, which is described in detail in the next section. After operationalizing the factors, I then coded the qualitative data (student weekly journal entries, student responses to written teacher empathetic feedback, and end of semester student interviews) using the factors of sense of belonging to the academic domain of mathematics defined by Good et al (2012). After reading through the data many times, writing memos, and looking for themes for the participants individually and across the data, the main themes began to emerge. I settled on organizing the coded data by the five factors of math sense of belonging and then by participant. I noted which data source each quote was from which included in-process (student weekly journal entries and student responses to 22 teacher feedback) and retrospective data (end of semester interviews). Using a thematic approach, I read through quotes pertaining to each factor of math sense of belonging and I looked for themes across the participants. I noted the themes that showed up across all, almost all (4 out 5), or most (3 out 5) participants. The themes were pertaining feelings and experiences connected to the factors of math sense of belonging. These themes, student feelings and experiences, provided evidence for various factors of math sense of belonging in the data. Operationalizing the Factors. I used Good and colleagues’ (2012) sense of belonging scale by operationalizing codes from statements in the scale to be used to code interview and written data from student participants. Good et al. (2012) identified key words or phrases from the statements in their scale connected to each factor of sense of belonging to the academic domain of mathematics. I operationalized these key words or phrases (see below) to develop a coding scheme for the interview and written data from my study. In the following subsections I will share Good et al. (2012) key words or phrases for each factor they identified for sense of belonging to the academic domain of mathematics. Then, I will share how I operationalized the key words or phrases from each factor to code the interview and written data in this study. Lastly, I will share quotes from the interview or written data connected to each factor. Membership. Good et al. (2012) identified the key words or phrases from their scale related to the sense of belonging factor Membership. These key words or phrases are, “belong, member, a part of, and connected” (p. 703). To operationalize these key words or phrases as codes for the interview and written data in this study I expanded on the meaning for each of these key words or phrases. First, I recognized “belong” as belonging with peers in the math class or corequisite course by creating a community feeling. Next, I identified “member” as a member of the math community. “A part of” I recognized as a student feeling they were a part of their 23 collaborative small group, a part of the math class or corequisite or a part of the math community in general. Finally, I identified “connected” as connection to their teacher or other students in the math class or corequisite course. See Table 2 below for details. Table 2 Membership Phrase or key Operationalized phrase or Quotes from student interview or written data word from key word for analysis of Good et al. interview and written data (2012) Belong Belonging with peers in “I feel like I kind of created a bond with the the math class or people in our math lab.” corequisite course by creating a community feeling Member A member of the math “She gave personal feedback, and it made you community relate, as she's a math teacher, so it made you relatable to her as in like a math community and everything. So, that was good” A part of A part of their “She put us in groups in the math class. It's kind collaborative small group, of like a competition. I don’t want to say a part of the math class or competition, but it's kind of like proving to corequisite, a part of the myself that, yeah, I really know this. Like I took math community in time to practice this, so I should know this. That general really helped me feel like I'm in the math community and everything.” Connected Connection to their “I feel as if we are the same in some ways…I teacher or other students also think it’s cool that we have some things in in the math class common like being scared to ask questions.” Acceptance. Good et al. (2012) identified the key words from their scale related to the sense of belonging factor Acceptance. These key words are, “accepted, respected, valued, and appreciated” (p. 703). Regarding Acceptance (reverse coded) the key words are, “disregarded, neglected, excluded, and insignificant.” To operationalize these key words as codes for the interview and written data in this study I expanded on the meaning for each of these key words. I recognized students expressing feelings of being accepted, respected, valued, and appreciated 24 by their peers in the math class or corequisite course or by their teacher. Next, regarding the key words for the factor Acceptance that were reverse coded I identified statements in the interview or written data where students expressed feeling disregarded, neglected, excluded, or insignificant with regards to peers in the math class or corequisite class, their teacher, or in their previous math experiences related to their teacher, peers, or the math community in general. See Table 3 and 4 below for details. Table 3 Acceptance Phrase or key Operationalized phrase or Quotes from student interview or written data word from key word for analysis of Good et al. interview and written data (2012) Accepted, Feelings of being “I definitely felt like she never judged me or Respected, accepted, respected, anything, and I feel like she welcomed me with Valued, and valued, and appreciated by open arms.” Appreciated their peers in the math class or corequisite course or by their teacher Table 4 Acceptance (Reverse Coded) Phrase or key Operationalized phrase or Quotes from student interview or written data word from key word for analysis of Good et al. interview and written data (2012) Disregarded, Feeling disregarded, “I do like keeping to myself in classrooms Neglected, neglected, excluded, or because I do not want to seem like an outsider, Excluded, and insignificant with regards which I know sometimes isn't a bad thing, but Insignificant to peers in the math class no one wants to be blatantly wrong in front of or corequisite class, their an entire class.” teacher, or in their previous math experiences related to their teacher, peers, or the math community in general 25 Affect. Good et al. (2012) identified the key words or phrases from their scale related to the sense of belonging factor Affect. These key words or phrases are, “at ease, comfortable, content, and calm” (p. 703). To operationalize these key words or phrases as codes for the interview and written data in this study I expanded on the meaning for each of these key words. First, I recognized “at ease” as students expressing feeling at ease during the math class or corequisite course, students feeling at ease while completing math course work, or students feeling at ease while working with their peers or teacher. Next, I acknowledged the key word “comfortable” as students expressing feelings of comfort with regards to math class or the corequisite course, expressing feelings of comfort regarding interactions with their teacher or peers, or communicating feelings of comfort regarding participating in class or completing math course work (including writing in their journal). Next, I recognized students feeling “content” when they expressed joy, happiness, appreciation, or stated that they liked the math class or the corequisite course or stated math class or the corequisite was fun. Lastly, I recognized participants expressing feeling “calm” through participating in the math class or corequisite course or completing course work (including writing in their journal or assessments). Regarding Affect (reverse coded) the key words are, “anxious, tense, nervous, and inadequate” (Good et al., 2012, p. 703). To operationalize these key words as codes for the interview and written data in this study I expanded on the meaning for each of these key words. I recognized students feeling anxious, tense, nervous, or inadequate with regards to course work (including writing in their journal or assessments), participation in class or with their small group, or their grade. See Table 5 and 6 below for details. 26 Table 5 Affect Phrase or key Operationalized phrase or Quotes from student interview or written data word from key word for analysis of Good et al. interview and written data (2012) At ease Feeling at ease during the “But I thought it was cool that you had us write math class or corequisite in our journals about how we feel about class course, students feeling at and the math homework we get. Especially ease while completing about the last tests. Writing about it actually got math course work, or some tension off of my chest. It was helpful in students feeling at ease many ways. while working with their peers or teacher, or writing in their weekly journal/receiving feedback Comfortable Feelings of comfort with “Basically just putting all the information on regards to math class or the journal, and she looks at it, and she the corequisite course, basically knows what you're going through. It expressing feelings of made me feel more comfortable…I feel like it comfort regarding made me even more comfortable to talk interactions with their basically because I knew she knew what teacher or peers, or situation I was in mentally.” communicating feelings of comfort regarding participating in class or completing math course work (including writing in their journal/receiving feedback). Content Feeling content when “I feel like Math lab is pretty great I enjoy the students expressed joy, class.” happiness, appreciation, or stated that they liked the math class, the corequisite course, or their weekly journal/feedback or stated math class, the corequisite, the weekly journal was fun 27 Table 5 (cont’d) Calm Feeling calm with regards “Writing the journal made me feel calm…felt to participating in the like a way of relieving stress and just speak my math class or corequisite mind.” course, or completing course work (including writing in their journal or assessments) Table 6 Affect (Reverse Coded) Phrase or key Operationalized phrase or Quotes from student interview or written data word from key word for analysis of Good et al. interview and written data (2012) Anxious, Feeling anxious, tense, “Whenever I hear you say the word test I just Tense, nervous, or inadequate get anxiety and I feel nauseous.” Nervous, or with regards to course Inadequate work (including assessments), participation in class or with their small group, or their grade. Trust. Good et al. (2012) identified the phrases from their scale related to the sense of belonging factor Trust. These phrases are, “test is unbiased, don’t have to prove worth, help me learn, and faith in potential” (p. 703). To operationalize these phrases as codes for the interview and written data in this study I expanded on the meaning for each of these phrases. First, regarding the phrase, “test is unbiased”, I recognized this when a student described feeling the assessments were reflective of the course material. Next, I identified, “don’t have to prove worth”, when a student expressed not feeling the need to prove their worth to anyone but themselves. Next, I identified, “help me learn”, when a student referenced feeling their teacher was there to support them in their learning and help them succeed in the math course. Lastly, I recognized the phrase “faith in potential” when a student expressed feeling their teacher had faith 28 in their potential or the student themselves had faith in their potential to be successful in math class. See Table 7 below for details. Table 7 Trust Phrase or key Operationalized phrase or Quotes from student interview or written data word from key word for analysis of Good et al. interview and written data (2012) Test is Feeling the assessments “I did, because we also had my Math Lab unbiased were reflective of the assignments in the computer, and it was course material actually material she actually taught us in class, so you wouldn’t be surprised and be like, uh, we didn't learn this. It was actually something you knew that she probably made, like she took time and made it, because we didn't get any surprise equations or anything because she taught us already.” Don’t have to Not feeling the need to “She always made you feel like you're doing prove worth prove their worth to your best. So, for me, I didn't have to really anyone but themselves prove anything, but she pushed us, not that I had to prove anyone right or wrong or something, but she definitely motivated us though, but I didn't feel like I had to prove myself to anyone, only myself.” Help me learn Feeling their teacher was “I really do appreciate you always helping not there to support them in only me but the whole class. It’s actually their learning and help helpful when you come up to each table and them succeed in the math help us figure some things out. I think it’s also course helpful when you put so much pressure on me (joking) but it actually helps with the one on one talks too. Like you point out the mistakes I made and you help me figure it out.” Faith in Feeling their teacher had “I am happy that you as my professor are potential faith in their potential or confident in me” the student themselves had faith in their potential to be successful in math class Desire to Fade/Active Participant. Good et al. (2012) identified the key words or phrases 29 from their scale related to the sense of belonging factor Desire to Fade and Active Participant. These key words or phrases for Desire to Fade (reverse coded) are, “fade, say little, and wish I was invisible” and for Active Participant the key word is “active participant” (p. 703). To operationalize these key words or phrases as codes for the interview and written data in this study I expanded on the meaning for each of these key words or phrases. First, I recognized a student’s “desire to fade” when a student expressed wanting to fade into the background during math class or previous math classes and not participate during class discussions or disconnected from participating in the course requirements. Next, I acknowledged the phrase “say little” when a student expressed not wanting to raise their hand or ask questions during math class or previous math classes or if they expressed not wanting to talk during small group work. Lastly, I recognized a student expressing that they wished they were invisible when they discussed not wanting to be seen or noticed in math class or in classes during their previous math experiences. Regarding the phrase “active participant” I acknowledged this phrase when a student signified participating in math class or during the corequisite course through asking questions, presenting math thinking, working on math course materials, or collaborating with their small group. See Table 8 and 9 below for details. Table 8 Desire to Fade Phrase or key Operationalized phrase or Quotes from student interview or written data word from key word for analysis of Good et al. interview and written data (2012) 30 Table 8 (cont’d) Fade Wanting to fade into the “I hopefully can get a good grip on math from background during math this year and not shy away from it anymore.” class or previous math classes and not participate or disconnected from participating in the course requirements Say little Not wanting to raise their No examples found hand or ask questions during math class or previous math classes or if they expressed not wanting to talk during small group work Wish I was Not wanting to be seen or No examples found invisible noticed in math class or in classes during their previous math experiences Table 9 Active Participant Phrase or key Operationalized phrase or Quotes from student interview or written data word from key word for analysis of Good et al. interview and written data (2012) Active Participating in math class “I love having the group discussions, I feel as if participant or during the corequisite they help tremendously. I do have a large desire course through asking to understand math” questions, presenting math thinking, working on math course materials, or collaborating with their small group Quantitative Data I organized the statements on the Math Sense of Belonging Scale by each factor of math sense of belonging as defined by Good et al. (2012). The scale uses an 8 point Likert Scale with two anchor points from 1 “Strongly Disagree” to 8 “Strongly Agree.” Next, I calculated the 31 average Likert Scale response for each factor of math sense of belonging for each participant’s pre and post scale responses. I created a spaghetti plot for each participant to show their average pre and post scale responses connected to each factor of math sense of belonging as defined by Good et al. (2012). This provides a visual of any change in each student’s average response from pre to post scale. Findings Quantitative Results Math Sense of Belonging Pre and Post Scale Good et al (2012) Math Sense of Belonging Scale was given to students at the beginning and end of the semester. Most of the student responses to statements from the scale started above the midpoint. There were not many low responses to statements from the participants at the beginning of the semester. This suggests that there was not much change recognized in each student’s responses to the statements on the scale from the beginning of the semester to the end of the semester. There was a slight increase in agreement for many of the responses to statements connected to several factors of belonging for each participant. Please see the figures below to visualize the change noted from pre to post scale for each participant and each factor of belongingness. 32 Figure 1 Wyomia Pre/Post Scale Factor Average 8 7 Membership Acceptance 6 Acceptance (reverse coded) 5 Affect 4 Affect (reverse coded) 3 Trust 2 Desire to Fade (reverse coded) 1 Active Participant 0 1 2 As seen in Figure 1 above, a positive change from pre to post scale for Wyomia’s average response to statements connected to the following sense of belonging factors Membership, Acceptance, Affect, Affect (reverse coded), Trust, and Desire to Fade (reverse coded). No change was noted from pre to post scale for Wyomia’s response to the Active Participant statement from the scale. A negative change from pre to post scale was noted for Wyomia’s average response to statements connected to the negative statements regarding the factor Acceptance (reverse coded). 33 Figure 2 Luan Pre/Post Scale Factor Average 9 8 Membership 7 Acceptance 6 Acceptance (reverse coded) 5 Affect 4 Affect (reverse coded) 3 Trust 2 Desire to Fade (reverse coded) 1 Active Participant 0 1 2 As seen in Figure 2 above, a positive change from pre to post scale for Luan’s average response to statements connected to the factors Membership, Acceptance (reverse coded), Desire to Fade (reverse coded), and Active Participant. No change was noted from pre to post scale for Luan’s average response to statements connected to the factor Acceptance. A negative change from pre to post scale was noted for Luan’s average response to statements connected to the factors Affect, Affect (reverse coded), and Trust. 34 Figure 3 Hondo Pre/Post Scale Factor Average 9 8 Membership 7 Acceptance 6 Acceptance (reverse coded) 5 Affect 4 Affect (reverse coded) 3 Trust 2 Desire to Fade (reverse coded) 1 Active Participant 0 1 2 As seen in Figure 3 above, a positive change from pre to post scale for Hondo’s average response to statements connected to the factors Membership and Trust. No change was noted from pre to post scale for Hondo’s average response to statements connected to the factors Acceptance (reverse coded) and Active Participant. A negative change from pre to post scale was noted for Hondo’s average response to statements connected to the factors Acceptance, Affect, Affect (reverse coded), and Desire to Fade (reverse coded). 35 Figure 4 Caleb Pre/Post Scale Factor Average 8 7 Membership Acceptance 6 Acceptance (reverse coded) 5 Affect 4 Affect (reverse coded) 3 Trust 2 Desire to Fade (reverse coded) 1 Active Participant 0 1 2 As seen in Figure 4 above, a positive change from pre to post scale for Caleb’s average response to statements connected to the factors Membership, Acceptance, Acceptance (reverse coded), Affect, Trust, and Active Participant. A negative change from pre to post scale was noted for Caleb’s average response to statements connected to the factors Affect (reverse coded) and Desire to Fade (reverse coded). 36 Figure 5 Anna Pre/Post Scale Factor Average 8 7 Membership Acceptance 6 Acceptance (reverse coded) 5 Affect 4 Affect (reverse coded) 3 Trust 2 Desire to Fade (reverse coded) 1 Active Participant 0 1 2 As seen in Figure 5 above, a positive change from pre to post scale for Anna’s average response to statements connected to the factors Membership, Acceptance (reverse coded), Affect, Affect (reverse coded), Trust, and Desire to Fade (reverse coded). No change was noted from pre to post scale for Anna’s response to the Active Participant statement from the scale. A negative change from pre to post scale was noted for Anna’s average response to statements connected to the factor Acceptance. Qualitative Findings Student comments, from both in-process and retrospective data, suggest that specific aspects of a student’s sense of belonging were supported through writing in a weekly journal, receiving written teacher feedback, and interacting with peers. Participants described these experiences, that occurred while participating in corequisite math course, with examples that support factors of Math Sense of Belonging as defined by Good and colleagues (2012). Consequently, to address the research question, evidence of factors of math sense of belonging indicate ways students experience belongingness. First, student comments reflect that receiving 37 empathetic written feedback from me, their teacher, supported four factors of belongingness: Membership, Acceptance, Affect, and Trust. Next, student comments suggest that the act of writing in a student weekly reflective journal supported three factors of belongingness: Membership, Acceptance, and Affect. Lastly, student comments suggest that interactions with peers supported two factors of belongingness: Membership and Acceptance. There were also comments made by participants that suggested assessments in the math course did not support feelings of belongingness. Receiving Teacher Feedback Supported Four Factors of Students’ Sense of Belonging: Membership, Acceptance, Affect, and Trust All participants discussed receiving written feedback from me, their teacher, with examples that suggest particular factors of Good et al. (2012) math sense of belonging were supported. The evidence suggests that receiving written empathetic feedback supported belongingness factors of Membership, Acceptance, Affect, and Trust. In the following subsections I will describe the evidence that these factors were supported, as suggested by the participants. Membership. Student comments suggests that receiving written feedback from me, their teacher, in their weekly journal supported the belongingness factor Membership for all participants. Evidence of statements that reflect the aspects of membership surfaced through student statements that suggest a connection to their teacher and/or the math community. For example, one student, Luan, reflected on receiving teacher written feedback through the semester. He wrote, “I really liked the responses, they were really motivating. The stories and how we as math people have similar stories is very interesting.” His statement, “we as math people” reflects being a member or a part of the math community. Relating to his teacher is 38 noticed here with the “we” part of his reflection. It seems he sees himself and his teacher as “math people”; which suggests he sees himself as similar to me, his teacher, a member of the math community. This response also reflects a sense of membership through “similar stories”; in that, he suggested that he has math stories similar to me, his teacher. Connecting with me, his teacher, also surfaced in statements made by Luan in his post- semester individual interview. In response to the interview question, “Did writing in your weekly journal and getting teacher feedback make you feel like you belonged as a member of a math community?”, Luan responded: She gave personal feedback, and her personal relations to math. Yeah, she gave personal feedback, and it made you relate, as she's a math teacher, so it made you relatable to her as in like a math community and everything. So, that was good. This response from Luan suggests a connection to his teacher through relating to his teacher’s personal feedback/stories regarding her math experience. His response suggests that he could relate to his teacher’s math stories. Also, since his teacher is a member of the math community his response also reflects connection to the math community. Acceptance. Student comments on receiving written feedback from me, their teacher, reflect aspects of the belongingness factor Acceptance for almost all the participants. The student comments suggest the belongingness factor Acceptance through statements that indicate being understood, valued, respected, or appreciated. For example, in response to reading feedback from me, her teacher, Wyomia wrote in her journal: After reading your response it made me feel better about myself. Especially after I read about your experience. It made me realize that I’m really not the only one who struggles with this problem. I would also like to say thank you. Thank you for sharing your 39 experience with me. Wyomia stated that she was not the only person to struggle with a particular problem. This reflects the belongingness factor Acceptance through the aspect of being understood. Another student, Anna described receiving feedback in that it, “made me feel like I was actually a person and a student and that I mattered.” This suggests the belongingness factor Acceptance as Anna reflected that receiving feedback from her teacher made her feel like an actual person and that she mattered. To add to this, Anna also stated, “I definitely felt like she never judged me or anything, and I feel like she welcomed me with open arms.” Anna stated that she did not feel judged by her teacher. This statement indicates respect which in turn connects to aspects of the belongingness factor Acceptance. Also, she stated that her teacher welcomed with open arms. This statement reflects the belongingness factor Acceptance as being welcomed with open arms suggests a person could feel valued, respected, or appreciated. Next, when students talked about their teacher noticing their participation in class, their comments suggest aspects of the factor Acceptance through value and respect. First, during his interview, Hondo stated: Sometimes she would actually even notice something I didn't know, like how maybe I will be helping other people in class. She would tell me, that’s actually a great thing and she appreciates it. And that made me also feel valued and respected too in some sense. Hondo reflected on reading feedback from his teacher, specifically feedback where his teacher noticed his participation in class through helping other students. In turn, he suggested that he felt valued and respected through feedback in which I, his teacher, noticed that he was helping other students. His comment reflects the belongingness factor Acceptance as being valued and respected are aspects of the factor Acceptance. 40 Affect. Most of the participants provided comments that suggest the belongingness factor Affect regarding receiving written feedback from their teacher. These statements from students connect to the belongingness factor Affect as this factor relates to feeling comfortable, at ease, or content. First, Wyomia wrote and spoke about how receiving feedback from her teacher brought about feelings of comfort. In response to feedback from her teacher in her journal Wyomia wrote, “Like I read what you say and it makes me feel a little more comfortable in class.” Wyomia’s comment suggests that reading feedback from her teacher in her weekly journal influenced the way she felt in class and brought about feelings of comfort. To add to this, during her interview she was asked how the feedback influenced her feelings of comfort and she stated, “The more I got to know about her, it made me feel more comfortable.” This provides more context to Wyomia’s statements about feeling of comfortable. Her comment indicates that the journal provided a way for Wyomia to get to know her teacher and as she got to know her teacher in turn she stated that it made her feel more comfortable. Next, Caleb discussed receiving feedback in his journal. He stated, “it definitely made me feel a lot more at ease going into things that were big throughout the semester…She really seemed to take into account how we felt throughout our journals.” This comment reflects that the feedback Caleb received in his journal helped him feel at ease throughout the semester. This included course tasks such as assessments and assignments. Feeling at ease is an aspect of the belongingness factor Affect. Lastly, Anna wrote about receiving feedback from her teacher. She responded to feedback from her teacher in her journal writing, “It makes me happy that you take time to read what we say and answer back.” This statement regarding happiness reflects an aspect of the belongingness factor Affect. Trust. Finally, all participants made statements that reflect the belongingness factor 41 Trust as they mentioned receiving written feedback from their teacher. Aspects of the belongingness factor Trust are suggested through statements about confidence, a sense of their teacher’s faith in their potential, and their perception of the teacher’s desire to help them learn. Almost all of the participants provided statements in response to feedback from their teacher that reflected confidence in themselves or acknowledged the confidence their teacher had in their success. For instance, in response to feedback from his teacher in his journal Hondo wrote, “Thank you for your feedback. What you said makes me feel confident in myself and my abilities. Now I feel confident enough to take on the test.” This written reflection signifies that feedback from his teacher supported his confidence in himself and his abilities. In turn, he felt confident to take the upcoming test. This suggests that the feedback from his teacher provided a way for Hondo to know that his teacher had faith in his potential and in this case his potential to do well on an assessment. This statement from Hondo reflects aspects of the sense of belonging factor Trust through suggesting a sense that I had faith in his potential. Additionally, Hondo provided context in his interview on how feedback from his teacher influenced his confidence. He stated, When I was talking about how I was mentally…when I was ready for an exam, I was feeling I was nervous, and I thought like I didn't know what to do, but then she told me all the progress I have been doing. She basically gave me reassurance. And in the final exam, when I told you, okay, it feels like another day in the office, I'm not even nervous this time around. And she's like, yes, all the preparation you've been doing and all the work you're doing in class is paying off. And I go, yeah, and I confident, so I was like yeah. Hondo wrote in his journal how he was feeling nervous for an upcoming exam. After reading 42 feedback from his teacher, his comments reflect confidence regarding taking the exam. He stated that I noticed the work he did to prepare for the test which reflects that I had faith in his potential. This reflects the belongingness factor Trust through the aspect of a teacher having faith in the student’s potential. Luan also talked about confidence connected to feedback from his teacher in his journal. During his interview he stated, As time went, I started being confident, actually answering class questions, like when she asked questions in class, I'd be able to raise my hand and answer the question. The journal really helped me. Her reflection for that really helped boost my confidence, I guess. This statement reflects that receiving feedback from his teacher in his journal helped Luan gradually gain confidence over the course of the semester. This signifies a sense of belonging related to the factor Trust as feedback from his teacher seemed to support his confidence to participate in class. All participants made statements regarding the experience of receiving feedback from me, their teacher, in their journal. These statements suggest that the participants felt that their teacher wanted to support them and help them learn. For example, in response to reading feedback from their teacher Wyomia wrote, “The feedback I received was very comforting. I like the fact that you actually want to help” and Anna wrote, “Reading this feedback, it gives me a sense of relief that you are looking out for us, your students. I see that you are fighting for us and that makes me very happy, and glad I am in your class.” These statements from Wyomia and Anna reflect the belongingness factor Trust through the aspect that the teacher is there to help students learn. To add to this, during his interview, Luan stated, “She really also put her personal feedback. She'd reflect on your journal with her personal stories, so it really made you 43 feel like she was really trying.” This statement reflects the belongingness factor Trust through teacher support recognized through my feedback in his journal. Caleb also discussed support from me, his teacher, through receiving feedback in his journal. He stated, I'll tell you; professors sometimes don’t really make the effort to hear how you feel or get to know what you're struggling or what you're excelling at. I think that was a good one, because she was always very detailed in her responses with what you said. This statement reflects the belongingness factor Trust as an aspect of Trust is a sense that the teacher is there to help students learn. Lastly, Anna also talked about help from her teacher. She stated, It wasn't like a little sentence that she was writing back either. Sometimes it was two or three paragraphs, and it was like vital information and just like great overall feedback. She was like just so helpful and supportive with anything that I ever said. This statement suggests the feedback that Anna received from me supported the belongingness factor Trust. This is because the aspects of the factor Trust include help and support from the teacher. Overall, all participants provided comments that about reading feedback from their teacher. The comments suggest that the feedback gave them a sense that their teacher was there to support them and help them learn. These comments relate to the belongingness factor Trust through the aspects of teacher support to help students learn. Writing in a Weekly Reflective Journal Supported Three Factors of Students’ Sense of Belonging: Membership, Acceptance, and Affect Almost all of the participants discussed the act of writing in a weekly journal through examples that suggest it supported their sense of belonging. Statements from the participants suggest the sense of belonging factors that were supported through writing in a weekly journal 44 include Membership, Acceptance, and Affect. In the following subsections I will provide examples that support these factors. Membership. Student comments about the act of writing in a weekly journal provide examples that connect to aspects of the belongingness factor Membership. Almost all the participants made comments about connecting to their teacher and/or the math community through writing in their journal. For instance, during her interview, Anna talked about writing in her journal. She stated, I connected to my Professor, Amy, kind of on a different level than I can in front of other people… I told her things that I was struggling on, and she sent me videos to my own personal email. We went over things in class that I had questions on. We talked about my family life. We talked about her family life. Just cool stuff like that, that you really don’t talk to professors about sometimes. This statement suggests that writing in a weekly journal provided a way for Anna to connect with her teacher. This connection signified a sense of belonging related to the belongingness factor Membership. She was able to share personal and academic experiences and suggested this provided a level of communication that isn’t typical with most professors. Additionally, she stated, “I just felt like I was heard, and I was talking to another person in the math community, you know, my professor, who is great at math and teaches math and stuff like that.” This comment about writing in her journals relates to the belongingness factor Membership. This is because the journal provided a way for Anna to be heard by her teacher who is a part of the math community. Acceptance. The act of writing in a weekly journal provided a way for students to share their feelings and open up to their teacher. Participant comments on the acting of writing in a 45 weekly journal reflect the belongingness factor Acceptance through examples that suggest feeling valued, respected, understood, and not judged. Students noted that writing in a weekly journal helped them to share their feelings or open up to their teacher. For example, Anna wrote in her journal, “I really like having a private conversation and being able to list how I feel. I feel valued and respected.” This comment indicates that sharing her feelings in her weekly journal connects to the belongingness factor Acceptance through statements about being valued and respected. To add to this, during her interview Anna also described being able to share her feelings with her teacher. She stated, “It's almost like a diary. You get to write this little diary and this journal and tell her exactly how you feel without any bias on her end and stuff like that.” Writing in her journal provided a way for Anna to express her feelings. Her statement reflects that she did not feel judged by her teacher which relates to the belongingness factor Acceptance. In addition, students commented that writing in a weekly journal also allowed them to “open up” to their teacher. For instance, Wyomia talked about writing in her journal during her interview stating, “It's kind of like just texting, so it made me…I don't know…it just made me more open to her.” This statement suggests that writing in her weekly journal provided a way for Wyomia to open up to her teacher. This signifies the belongingness factor Acceptance as the act of opening up suggests vulnerability. Vulnerability relates to the belongingness factor Acceptance through the aspects of feeling valued, respected, appreciated, or not judged. To add to this, Hondo also discussed being able to open up to his teacher through writing in his journal. He stated, “It felt like I'm putting everything out there, and basically she would understand me in some situations.” This comment indicates that through writing in his weekly journal Hondo was able to share with me, his teacher, by “putting everything out there.” In turn, this relates to the 46 belongingness factor Acceptance as this factor connects to feeling understood. Affect. Finally, almost all participants made comments that reflect the belongingness factor Affect through the experience of writing in their weekly journal. As suggested by student comments, the act of writing in a weekly journal reduced tension or stress and provided comfort with learning, participating, or interacting with me, their teacher. Statements from the participants also reflected being calm through the act of writing in a weekly journal. Almost all of the participants provided comments that reflect comfort through the act of writing in a weekly journal. Participants described that writing in their journal provided comfort with learning, participating in class, or a sense of comfort with their teacher. For example, during his interview Hondo stated, Basically just putting all the information on the journal, and she looks at it, and she basically knows what you're going through. It made me feel more comfortable… I feel like it made me even more comfortable to talk basically because I knew she knew what situation I was in mentally. In this quote, we see Hondo stating that writing in his journal made him feel “more comfortable” to participate in class because he had a sense that I, his teacher, knew the things he was going through. Another student, Luan also talked about the act of writing in his journal. During his interview he stated, “It made me feel more comfortable, because I also wrote my flaws in the math class. So, it made me feel more comfortable.” This statement suggests that writing in his journal gave Luan a space where he could write about his “flaws” and his comment suggests that this provided a sense of comfort. Comments from the participants also indicate that writing in a weekly journal provided a way for students to reduce tension and stress. One student, Wyomia, wrote about her experience 47 writing in her journal over the course of the semester. She wrote, Well to be honest I wasn’t really expecting to have a little journal type of thing in college. But I thought it was cool that you had us write in our journals about how we feel about class and the math homework we get. Especially about the last tests. Writing about it actually got some tension off of my chest. It was helpful in many ways. This comment suggests that writing in her journal throughout the semester about how she felt about math homework and tests was a way for Wyomia to decrease tension. This reflects the belongingness factor Affect through the aspects of feeling calm and at ease. Hondo also wrote about his experience writing in his journal over the course of the semester. He wrote, Writing the journal made me feel calm and heard it felt natural and felt like a way of relieving stress. Mathlab was amazing throughout the semester. I liked the journal part the most and I would recommend to other students. This statement indicates that writing in a weekly journal provided a way for Hondo to reduce stress during the semester and the act of writing also provided a sense of calm. Additionally, Hondo reiterated these experiences during his interview stating, “I was pretty comfortable all around…. The journals, writing in the journals kind of helped me put my mind to rest.” This statement reinforced that writing in his journal provided a way to reduce stress and in turn supported the factor Affect through indicating ease and comfort. Interactions with Peers Supported Two Factors of Students’ Sense of Belonging: Membership and Acceptance All participant provided comments suggesting that interactions with peers supported the belongingness factors Membership and Acceptance. In the following subsections I will describe examples of these factors, Membership and Acceptance, through examples of participants 48 interacting with peers. Membership. All of the participants discussed collaborating with peers in a small group setting both in the math class and in the corequisite course. Student comments about collaborating with peers suggest a math community through giving and receiving help as well as building positive working relationships with peers. First, almost all of the participants discussed giving and receiving help to and from their peers. For example, Anna stated, “My table group is really nice and we all collectively help each other out with problems when we don’t understand them.” Similarly, Wyomia stated, “Everyone helps each other, and they seem pretty cool. Everyone at my table is pretty cool too.” Both statements reflect being a part of a math community through collaborating with peers. This math community is recognized as there is a sense of teamwork in helping others out, as well as receiving math help from others. In addition to giving and receiving help from peers, most of the participants described a positive working relationship with their peers as they learned new math concepts and completed assignments. For instance, Luan talked about the working relationship he had with his small group during his interview. He stated, She put us in groups in the math class. It's kind of like a competition. I don’t want to say competition, but it's kind of like proving to myself that, yeah, I really know this. Like I took time to practice this, so I should know this. That really helped me feel like I'm in the math community and everything. The dynamics of working collaboratively with his small group to learn concepts and complete assignments indicates the belongingness factor Membership. This is because the factor Membership relates to the aspect of being a part of a math community. Anna also reflected on a positive working relationship with her group. She wrote, 49 I have enjoyed working with my group. I like collaborating with them, because we all kind of have pieces of a puzzle and we bring it together to make one whole puzzle. I want to keep pushing ahead and learning more and more. I appreciate that we get to explain our thinking and have that included in our answers. It’s fun to see that everyone thinks differently. Anna described a positive working relationship with her small group. She noted how each person contributed something different and they all worked together to learn the material. This collaboration in learning math concepts suggests being a part of a math community. Acceptance. All of the participants discussed interacting with peers in the math class or the corequisite course through providing examples that relate to the belongingness factor Acceptance. Students commented on forming friendships with classmates, having a sense that they fit in, and suggested a willingness to participate with peers in learning. First, most participants provided comments on friendship, fitting in, or getting to know classmates. For example, Wyomia wrote in her journal about interactions with peers in the corequisite class. She wrote, It is cool that I’m finally opening up. And I feel like I’m slowly starting to open up to people in class. It also started from the math lab. I feel like everyone in that class is helping me open up. Like I start to talk to them and become friends. Wyomia formed friendships with her peers in the corequisite course. Friendship signifies the belongingness factor Acceptance. She also mentioned that “everyone in that class is helping me open up” which indicates the belongingness factor Acceptance as well. Hondo also mentioned interacting with peers in the corequisite course. He stated the corequisite class was, “just like a comfortable place, a place I could be myself basically, and help other people, get help from other 50 people too.” A place that he could be himself indicates the belongingness factor Acceptance as Hondo stated he was able to be himself. Finally, Anna also wrote about interactions with peers. She wrote, I also love my group. It seems that if someone doesn't understand something, 9 out of 10 times at least one other person in our group will. We also do get along on an interpersonal level as well and that makes me happy because I can trust them and they don’t make me feel dumb for not understanding something. Normally in groups I get down on myself if I don’t understand something but they do not make me feel like that in the slightest and I am very appreciative of that. Anna mentioned getting along with her peers on an interpersonal level which signifies friendship and fitting in. These interactions with peers indicate the belongingness factor Acceptance as this statement suggests that she could trust her group members. Anna also indicated that she appreciated being able to express difficulties with understanding topics with the peers in her small group. This relationship with her group members reflects the belongingness factor Acceptance; in that her group did not make her feel inadequate. Assessments Did Not Support a Sense of Belonging All participants provided comments that indicate negative feelings regarding assessments in their Math120 course. Participant statements provide examples that reflect being nervous, anxious, scared, or inadequate regarding assessments. For example, students were asked to reflect on an upcoming test in their journal. Wyomia wrote, “I feel like everything I learned is gonna just vanish as soon as the test is passed out. Whenever I hear you say the word test I just get anxiety and I feel nauseous.” Wyomia described feeling anxious whenever she heard me say the word test and it also influenced a negative physical response within her as well. This 51 suggests negative feelings connected to the factor Affect (reverse coded). In turn, this suggests that assessments did not support belongingness for Wyomia. Next, when reflecting on an upcoming test Anna wrote, “I am feeling very nervous, because I dislike tests very much.” Anna felt nervous regarding an upcoming test which connects the belongingness factor Affect (reverse coded). This provides another example suggesting assessments in the Math120 class negatively influenced students’ sense of belonging through the factor Affect (reverse coded). Discussion & Implications The findings of this study add to prior research on belongingness through providing details on the ways students experience a sense of belonging. First, student comments reflect that receiving empathetic written feedback from me, their teacher, supported four factors of belongingness: Membership, Acceptance, Affect, and Trust. Next, student comments suggest that the act of writing in a student weekly reflective journal supported three factors of belongingness: Membership, Acceptance, and Affect. Lastly, student comments suggest that interactions with peers supported two factors of belongingness: Membership and Acceptance. There were also comments made by participants that suggested assessments in the math course did not support feelings of belongingness. These findings provide implications for fostering belongingness in classroom setting through acknowledging that different class experiences support various aspects of a student’s sense of belonging. These findings are important as, theoretically, various aspects of belonging come together to influence a student’s sense of belonging overall. Therefore, these findings imply that various aspects of the corequisite course, not only writing in a weekly journal and receiving teacher empathetic feedback, may impact a student’s sense of belonging. Multiple classroom approaches, such as providing opportunities to collaborate with peers, may be needed to foster each student’s sense of belonging. Other aspects 52 of the corequisite course not identified through the findings in this study may also have contributed to each student’s sense of belonging. In addition, each student is different and therefore may need different approaches to influence their feelings of belonging. Consequently, knowing about aspects of belonging that students experience, through writing in a student weekly reflective journal, receiving written empathetic teacher feedback, and interacting with peers, is important to better address belongingness in the classroom overall. In the following paragraphs I will discuss the connections between these findings and the current literature. First, the findings of this study suggest that receiving written feedback from a teacher can provide a concrete way via a weekly reflective journal for teachers to relate to students, build trust, and foster feelings of acceptance and positive affect. First, receiving written teacher feedback provided a way for students to connect and relate to their teacher, which indicates the belongingness factor Membership. Prior research shows that a teacher’s personal support, which includes students relating to their teacher (Osterman, 2010; Keyes, 2019), supports a student’s sense of belonging. Additionally, prior research with college students has established a connection between a student’s sense of class-level belonging and the student’s perception of their instructor’s “warmth and openness” (Freeman et al., 2007, p. 210). The “warmth and openness” of the instructor includes a desire to help students learn and share personal experiences relevant to the course content (Freeman et al., 2007, p. 212). The findings suggest that receiving written feedback from me, their teacher, provided a way for me to portray warmth, openness, and a desire to help students learn as well as share my own personal stories. Next, the findings of this study indicate that written teacher feedback supported the belonginess factor Trust through examples that I, the teacher had faith in student potential, a desire to help students learn, and confidence in student success. Prior research with high school 53 students indicated building trust between students and teachers impacts a student’s sense of classroom belonging; specifically building trust through teacher actions such as providing honest feedback and listening (Keyes, 2019). Prior research also indicates teacher practices such as supporting student confidence and competence (Osterman, 2010), as well as helping students learn (Osterman, 2010; Keyes, 2019), are connected to a student’s sense of belonging. Additionally, findings of this study indicate that receiving teacher feedback supported the belongingness factor Acceptance through examples of students indicating feeling understood, valued, respected, or appreciated. Prior research shows the influence of a teacher on a student’s sense of belonging through practices such as: fostering respect (Kiefer et al., 2015; Osterman, 2010; Keyes, 2019), supporting student learning in ways that make students feel valued (Keyes, 2019), and empathizing with students to understand feelings and needs (Osterman, 2010). Lastly, findings from this study indicate receiving written teacher feedback supported the belongingness factor Affect through examples reflecting comfort, ease, or feeling content. Implications of these findings regarding receiving empathetic written feedback from me, their teacher, suggest strong reason to implement this teacher practice in developmental math courses. The only factor of belongingness, as defined by Good et al. (2012), that was not recognized through receiving written teacher feedback was Desire to Fade. I argue that this did not show up overwhelmingly in the data because student participation may be identified more easily through observation, not necessarily discussed directly by students. The qualitative data, student journals and interviews, may not have fully captured student lack of participation. Next, the findings from this study suggest the act of writing in a weekly journal supports the belongingness factors of Membership, Acceptance, and Affect. First, the act of writing in a weekly journal suggested evidence of the belongingness factor Membership through examples of 54 connecting with me, their teacher, and/or the math community. Prior research indicates teachers can enhance a student's sense of belonging through getting to know students on a personal level and building positive relationship (Kiefer et al., 2015; Osterman, 2010). Writing in a weekly journal provided a way for students to share about themselves and have an opportunity to connect with me, their teacher. Next, the process of writing in a weekly journal allowed students to share their feelings and open up to their teacher. Student comments on the act of writing in a weekly journal related to the belongingness factor Acceptance through examples that reflect feeling valued, respected, understood, and not judged. Prior research has shown teachers can enhance a student sense of belonging through understanding student feelings (Osterman, 2010) and student journal entries can provide a way for students to share their feelings. Additionally, the findings suggest the act of writing in a weekly journal reduced tension and provided stress relief for students. In turn, this stress relief reflects the belongingness factor Affect through comments that suggested comfort in learning, participating, and interacting with their teacher. Prior research has indicated that a student’s sense of belonging may contribute to a decrease in psychological distress and reduced mental health concerns (Kirby & Thomas, 2022). Findings from this study provide evidence that the act of writing in a weekly reflective journal can help to foster a student’s sense of belonging through stress relief and consequently provides indication to implement in the developmental math classroom. Finally, the findings suggest that the experience of interacting with peers in the math class and corequisite support course supported the belongingness factors of Membership and Acceptance. First, student comments reflected support for the belongingness factor Membership. Thist was identified through student comments regarding collaborating with peers, specifically 55 by giving and receiving help and creating positive working relationships with peers. Prior research, such as Solomon et al. (1996) has emphasized the importance of incorporating cooperative learning as an essential mechanism for encouraging sense of community within the classroom. In addition, prior research with sixth grade math students indicated a student’s sense of belonging was greater when other students perceived them as being able to help them with their math assignments (Hamm & Faircloth, 2005). In addition, Kiefer’s et al. (2015) research with early adolescent students also indicated helping behaviors of peers supported students’ sense of school belonging. This aligns with the findings of this study as student comments about helping peers with their math assignments reflect the belongingness factor Membership through connecting with peers. Additionally, participants described examples that supported the belongingness factor Acceptance through examples of interacting with peers to form friendships and fit in. Prior research has shown peer emotional support, which included fitting in, forming friendships, and feeling accepted supported a sense of school belonging for early adolescent students (Kiefer et al., 2015). Findings from this study, also showed students had a willingness to participate in learning with peers which provides evidence connected to the belongingness factor Acceptance. This aligns with prior research with college students that indicates students with higher feelings of belonging felt respected and valued by their peers (Zumbrunn et al., 2014). Findings from this study support prior work on the importance of collaboration with peers in a classroom setting in fostering a student’s sense of belonging. The findings from the Math Sense of Belonging Scale also indicate support for students’ math sense of belonging when comparing beginning and end of semester results. A slight increase in student agreement was noted overall, from the pre to post scale. However, many of 56 the student responses from the pre-scale were above the midpoint of the scale and therefore did not provide much room for growth from the beginning to end of the semester. Pre-scale responses from students may have been influenced by knowledge the I was going to review their responses and students may have wanted to provide a good first impression. Implications of this work suggest that several class experiences known to support a student’s sense of belonging may need to be employed to address various aspects of belongingness. The Math Sense of Belonging Scale may be used in the future to determine factors of belonging that may be lacking for a student. In turn, various class experiences may be able to cater to individual student needs for belongingness. Limitations There are various limitations to the findings of this study. First, one of the data sources for this study was student journals which included weekly journal entries and student written responses to my feedback. Since students knew that I would be reading and responding to their written responses this likely influenced what they wrote in their journal. Students may have chosen not to share pieces of their experience since I was their instructor, and I was required to provide students with course grade. Next, the math sense of belonging framework from Good et al. (2012) has limitations in that there may be aspects of belongingness not considered. Good et al. Math Sense of Belonging Scale was created and verified to recognize college students’ intent to pursue math courses in the future. Good et al. used the Math Sense of Belonging Scale to recognize differences in males and females continued pursuit of math courses. Acknowledging differences in aspects of math sense of belonging for males and females may be different than belongingness factors that pertain to math students placed into a developmental math course. For example, students placed 57 in a developmental math course may feel they do not belong at the university as they were not able to be directly placed into a college level math course. In addition, the Good et al. scale did not specifically account for factors of belonging related to race or ethnicity. Consequently, the findings of this study are limited by using Good et al. (2012) Math Sense of Belonging scale as various aspects of belonging (such as sense of belonging in college or belongingness factors influenced by race or ethnicity) were not specifically recognized. Lastly, there are limitations regarding the quantitative findings from the Math Sense of Belonging Scale as the sample size was small, only five participants. In addition, the Math Sense of Belonging Scale was given to students in “construct” form, in that all questions pertaining to a factor of belongingness were presented consecutively, instead of staggered throughout the survey. I did not find any reason provided by Good et al. for the scale questions to be written in construct form. Therefore, student responses to the statements in the scale may have been influenced by grouping all statements connected to each factor in order. Conclusion The aim of this study was to contribute to prior research on belongingness through studying ways college freshman experience a sense of belonging to the academic domain of mathematics. The findings of this study provide evidence for ways students experience a sense of belonging through the class experiences of writing in a weekly reflective journal, receiving written teacher empathetic feedback, and interacting with peers. Specifically, the findings suggest that writing in a weekly reflective journal supported the belongingness factors of Membership, Acceptance, and positive Affect. Next, the findings suggest that receiving teacher written empathetic feedback supported the belongingness factors of Membership, Acceptance, Trust, and positive Affect. Lastly, the findings provide evidence for ways students experience 58 belongingness through interactions with peers through evidence of the belongingness factors of Membership and Acceptance. Evidence of these belongingness factors provides a window into ways students experience math sense of belonging through the experiences of writing in a weekly reflective journal, receiving written empathetic feedback, and interacting with peers. The findings provide evidence that implementing a student reflective journal, providing written empathetic feedback, and ensuring class time to work and interact with peers may be essential in fostering belongingness in the corequisite math classroom. This study helps the field to understand ways in which students experience a sense of belonging through using evidence of Good’s et al. (2012) factors of math sense of belonging. These findings are important as lack of belonging is a risk factor for the success of developmental math students (Bryk et al., 2013). 59 REFERENCES Barbieri, C. A., & Miller-Cotto, D. (2021). The importance of adolescents' sense of belonging to mathematics for algebra learning. Learning and Individual Differences, 87, 101993. Baumeister, R. F., & Leary, M. R. (1995). The need to belong: desire for interpersonal attachments as a fundamental human motivation. Psychological Bulletin, 117(3), 497. Booker, K. C., & Lim, J. H. (2018). Belongingness and pedagogy: Engaging African American girls in middle school mathematics. Youth & Society, 50(8), 1037-1055. Bryk, A. S., Yeager, D. S., Hausman, H., Muhich, J., Dolle, J. R., Grunow, A., & Gomez, L. (2013, June). Improvement research carried out through networked communities: Accelerating learning about practices that support more productive student mindsets. In A White Paper prepared for the White House meeting on “Excellence in Education: The Importance of Academic Mindsets. Childers, A. B., Lu, L., Hairston, J., & Squires, T. (2021). Impact and Effects of Co-Requisite Mathematics Remediation. PRIMUS, 31(2), 167-183. Dana Center. (2018). Co-requisite Courses: Narrowing the Gap between Instruction and Supports. Dana Center Math Pathways. Freeman, T. M., Anderman, L. H., & Jensen, J. M. (2007). Sense of belonging in college freshmen at the classroom and campus levels. The Journal of Experimental Education, 75(3), 203-220. Good, C., Rattan, A., & Dweck, C. S. (2012). Why do women opt out? Sense of belonging and women's representation in mathematics. Journal of Personality and Social Psychology, 102(4), 700. Goodenow, C. (1993). Classroom belonging among early adolescent students: Relationships to motivation and achievement. The Journal of Early Adolescence, 13(1), 21-43. Hamm, J. V., & Faircloth, B. S. (2005). Peer context of mathematics classroom belonging in early adolescence. The Journal of Early Adolescence, 25(3), 345-366. Hurtado, S., & Carter, D. F. (1997). Effects of college transition and perceptions of the campus racial climate on Latino college students' sense of belonging. Sociology of Education, 324-345. Keyes, T. S. (2019). A qualitative inquiry: Factors that promote classroom belonging and engagement among high school students. School Community Journal, 29(1), 171-200. Kiefer, S. M., Alley, K. M., & Ellerbrock, C. R. (2015). Teacher and peer support for young adolescents’ motivation, engagement, and school belonging. RMLE Online, 38(8), 1-18. 60 Kirby, L. A., & Thomas, C. L. (2022). High-impact teaching practices foster a greater sense of belonging in the college classroom. Journal of Further and Higher Education, 46(3), 368-381. Matz, R. L., & Tunstall, S. L. (2019). Embedded Remediation Is Not Necessarily a Pathway for Equitable Access to Quantitative Literacy and College Algebra: Results from a Pilot Study. Numeracy: Advancing Education in Quantitative Literacy, 12(2). Osterman, K. F. (2000). Students' need for belonging in the school community. Review of Educational Research, 70(3), 323-367. Osterman, K. F. (2010). Teacher practice and students’ sense of belonging. In International research handbook on values education and student wellbeing (pp. 239-260). Springer, Dordrecht. Royer, D. W., & Baker, R. D. (2018). Student success in developmental math education: Connecting the content at Ivy Tech Community College. New Directions for Community Colleges, 2018(182), 31-38. Ryan, R. M. (1995). Psychological needs and the facilitation of integrative processes. Journal of Personality, 63(3), 397-427. Silva, E., & White, T. (2013). Pathways to Improvement: Using Psychological Strategies to Help College Students Master Developmental Math. Carnegie Foundation for the Advancement of Teaching. Solomon, D., Battistich, V., Kim, D. I., & Watson, M. (1996). Teacher practices associated with students' sense of the classroom as a community. Social Psychology of Education, 1(3), 235-267. Walton, G. M., & Cohen, G. L. (2007). A question of belonging: race, social fit, and achievement. Journal of Personality and Social Psychology, 92(1), 82. Warren, C. A. (2018). Empathy, teacher dispositions, and preparation for culturally responsive pedagogy. Journal of Teacher Education, 69(2), 169-183. Wilson, D., Jones, D., Bocell, F., Crawford, J., Kim, M. J., Veilleux, N., ... & Plett, M. (2015). Belonging and academic engagement among undergraduate STEM students: A multi- institutional study. Research in Higher Education, 56(7), 750-776. Wiseman, T. (1996). A concept analysis of empathy. Journal of advanced nursing, 23(6), 1162- 1167. Zumbrunn, S., McKim, C., Buhs, E., & Hawley, L. R. (2014). Support, belonging, motivation, and engagement in the college classroom: A mixed method study. Instructional Science, 42(5), 661-684. 61 APPENDIX A: MATH SENSE OF BELONGING SCALE (Adapted from Good et al., 2012) Today I have some questions I would like you to answer about your experience with math courses and in the math academic community. When I mention the math academic community, I am referring to the broad group of people involved in that field, including the students in a math course. I would like you to consider your membership in the math community. By virtue of having taken many math courses through your schooling experience, you could consider yourself a member of the mathematics community. Given this broad definition of belonging to the math community, please respond to the following statements based on how you feel about that group and your membership in it. There are no right or wrong answers to any of these statements; I am interested in your honest reactions and opinions. Please read each statement carefully, and indicate the number that reflects your degree of agreement. The scale is 1 to 8. 1 is strongly disagree and 8 is strongly agree. All the questions start with, "When I am in a math setting..." The following 28 statements ask for you to reflect when in a math setting. 1. I feel that I belong to the math community. 2. I consider myself a member of the math world. 3. I feel like I am part of the math community. 4. I feel a connection with the math community. 5. I feel accepted. 6. I feel respected. 7. I feel disregarded. 8. I feel valued. 9. I feel neglected. 10. I feel appreciated. 11. I feel excluded. 12. I feel insignificant. 13. I feel at ease. 14. I feel anxious. 15. I feel comfortable. 16. I feel tense. 17. I feel nervous. 18. I feel content. 19. I feel calm. 20. I feel inadequate. 21. I wish I could fade into the background and not be noticed. 22. I try to say as little as possible. 23. I enjoy being an active participant. 62 24. I wish I were invisible. 25. I trust the testing material to be unbiased. 26. I have trust that I do not have to constantly prove myself. 27. I trust my instructors to be committed to helping me learn. 28. Even when I do poorly, I trust my instructors to have faith in my potential. 63 APPENDIX B: STATEMENTS FROM MATH SENSE OF BELONGING SCALE Categorized by Factors of Math Sense of Belonging (Good et al., 2012) Factors of Math Sense of Statements from Math Sense of Belonging Scale Belonging Membership • I feel that I belong to the math community. • I consider myself a member of the math world. • I feel like I am part of the math community. • I feel a connection with the math community. Acceptance (positive) • I feel accepted. • I feel respected. • I feel valued. • I feel appreciated. Acceptance (reverse coded) • I feel disregarded. • I feel neglected. • I feel excluded. • I feel insignificant. Affect (positive) • I feel at ease. • I feel comfortable. • I feel content. • I feel calm. Affect (reverse coded) • I feel anxious. • I feel tense. • I feel nervous. • I feel inadequate. Trust • I trust the testing material to be unbiased. • I have trust that I do not have to constantly prove myself. • I trust my instructors to be committed to helping me learn. • Even when I do poorly, I trust my instructors to have faith in my potential. Desire to Fade/Active • I wish I could fade into the background and not be Participant noticed. • I try to say as little as possible. • I enjoy being an active participant. • I wish I were invisible. (Good et al.) 64 APPENDIX C: STUDENT INTERVIEW QUESTIONS ● Would you tell me about your experience in the math lab (corequisite course) this semester? ● Would you tell me about your experience writing in your weekly journal? ● What was it like reading the teacher feedback each week in your student journal? ● Would you recommend the student journal for other math labs in the future? Why or why not? ● What are the things you liked or did not like about the math lab class? ● Did writing in your weekly journal and getting teacher feedback make you feel that you belong, are a member of, are part of, or are connected to the math community? Why or why not? ● Are there times when you felt you didn’t belong during the semester? If so, provide an example. ● Did writing in your weekly journal and getting teacher feedback influence feelings of being accepted, respected, valued, or appreciated? Why or why not? ● Did writing in your weekly journal and getting teacher feedback influence feelings of being at ease, comfortable, content, or calm? Why or why not? ● Are there times when you felt anxious, tense, nervous, or inadequate during the semester? If so, provide an example. ● Did writing in your weekly journal and getting teacher feedback influence feelings of trust regarding your instructor and their desire to help you learn or that your instructor had faith in your potential? Why or why not? 65 ● Are there times when you felt you needed to prove yourself during the semester? If so, provide an example. ● Did you trust the math testing materials? Why or why not? ● Did writing in your weekly journal and getting teacher feedback influence your participation in class? Why or why not? ● Would you say writing in your weekly journal and getting teacher feedback influenced your sense of belonging to the math community? Why or why not? ● Would you like to share anything else about your experience writing in your weekly journal and getting teacher feedback this semester? ● Would you like to share anything else about your experience in the math lab this semester? 66 APPENDIX D: STUDENT JOURNAL PROMPTS ● Journal #1: This is your chance to tell me about your past experiences in math classes and your feelings about math in general. Reflect on your experiences in elementary school, middle school, high school, and college, etc. Describe what your experiences were, how you felt about math at those times, and how you feel about math today. o The goal of this prompt was to learn about the student’s experiences with math in the past as well as provide a way for the student to express prior feelings about math. ● Journal #2: Reflect on your experiences in math this past week. Tell me about your experiences in math this week. How are you feeling about math this week? o The goal of this prompt was to learn about what experiences stood out for the student that week. This prompt was intended to address any issues students may have or to see what aspects of the course the students choose to discuss. ● Journal #3: Tell me about something that happened in math class this week and how it made you feel. o This prompt was a more focused version of the previous week, intended to get students to write more about something specific that happened in math class, instead of general thoughts or feelings. ● Journal #4: Reflect on your experience in math this week. Tell me something that happened in math this week. What was that experience like... thoughts, feelings? o Once again, this prompt was intended to elicit students feelings regarding an experience in math class. 67 ● Journal #5: We have reflected on math class the last few weeks. Today I would like you to reflect on your experience in the math lab class. Tell me about your experience in the math lab class so far. Thoughts? Feelings? Comments? o As the previous weeks were focused specifically on learning how students were feeling about the math class, this prompt provided a way for the teacher to learn more about students experience in the math lab class (corequisite). It was also the goal to determine if there was evidence of students’ feelings of belonging. ● Journal #6: We have our first test coming up in a week and a half. Reflect on how you are feeling about the upcoming test. Why are you feeling this way? Provide examples. o Math tests seem to evoke strong feelings for students. This prompt provided a way to learn about how students were feeling about the upcoming test and support students through teacher feedback. It also provided a way to learn what aspects of class potentially supported their feelings regarding the upcoming test. ● Journal #7: How are you feeling about the school subject of math in general? Provide reasons why. Have you noticed any changes in the way you feel about the subject of math this semester? o This prompt was intended to see if there was evidence of a change in students’ feelings regarding math in contrast to their initial journal entry regarding their prior math experiences. ● Journal #8: Today I would like you to reflect on your test. How are you feeling about your test? What are the study habits that worked well for you to prepare for the test? What could you do moving forward to improve study habits as you prepare for the next test? 68 o There was a wide range of test scores from the students in the corequisite course. This prompt provided a way to express how they were feeling about the test, as well as reflect on how to improve or reflect on what they felt was working well for them. ● Journal #9: Free write... tell me something that is going on with you, could be about math, could be about something else. o At this point in the semester the students had reflected a lot on their experience in math and there was some sense this was getting tiring. This prompt provided a way for the teacher to learn more about the student, potentially on a personal level, and provide another way to connect and empathize with the student. ● Journal #10: We have our second test next week Thursday. Reflect on how you are feeling about the upcoming test. Why are you feeling this way? Provide examples. o Once again, students typically have strong feelings about tests, especially now that this was the second test for students. In addition to providing a way to support the student through feedback, this entry also provided a way for the students to communicate if additional math support was needed. ● Journal #11: Tell me about your experience writing in a journal this semester. What was it like writing and receiving feedback from your instructor through the journal? Would you recommend the journal for future math students in the math lab? Why or why not? o This prompt provided a way for students to communicate their experience with writing in a journal and receiving feedback. ● Journal #12: Describe your experience in the math lab class this semester. Reflect on the beginning. middle, and end of the semester. What did you like or dislike about the math 69 lab class? Would you recommend the course to other students? Have your feelings about math changed at all this semester or stayed the same? o This prompt was used as the “final exam” for the corequisite course. It was a way for the teacher to learn about the experiences of students in the corequisite course. 70 CHAPTER 3: THE USE AND DEVELOPMENT OF WRITTEN TEACHER EMPATHETIC FEEDBACK TO FOSTER BELONGINGNESS IN A COREQUISITE MATH COURSE THROUGH A WEEKLY STUDENT REFLECTIVE JOURNAL Introduction Students placed in developmental math often feel they do not belong in the math classroom (Silva & White, 2013). These feelings put developmental math students at risk of failure and continued pursuit of their degree (Bryk et al., 2013). Research has shown that teacher care is a way to foster belongingness in the classroom (Solomon et al., 1996; Kirby & Thomas, 2022; Kiefer et al., 2015; Freeman et al., 2007; Booker & Lim, 2018). Yet, portraying empathy to students is a challenge for educators (Meyers et al., 2019). Empathy is hard work (Cameron et al., 2019) and although teacher empathy is connected to positive learning outcomes for students (Cornelius-White, 2007), finding the time and a way for teachers to convey empathy to students is difficult. During Fall 2021, I taught a pilot section of a corequisite math course. Corequisite math courses, an approach to remediation for college students placed in developmental math, provide a unique opportunity to potentially foster belongingness in the math classroom. Corequisite math courses typically have flexibility on how to use class time and therefore provide an opportunity to implement activities other than math content. I hypothesized that implementing a student weekly reflective journal would be a way to foster each student’s sense of belonging through providing written empathetic feedback. I argue that written teacher empathetic feedback provided a way to show teacher care and in turn foster belongingness in the math classroom. This study sought to explore the potential of providing empathetic feedback as a means of showing teacher care by investigating the ways in which I incorporated empathetic feedback, and 71 the sense of belongingness expressed by students in response to my feedback. This work is important as both teacher empathy and a student’s sense of belonging have been linked to positive student outcomes (Osterman, 2000). Teacher empathy and a student’s sense of belonging have mainly been studied separately (Cai et al., 2022). Consequently, this work aims to add to the conversation on connections between teacher empathy and a student’s sense of belonging. Ultimately, there is limited research on how teachers apply empathy through their practice (Warren, 2018). This study adds to research on the development of teacher empathetic practices through analyzing the development of teacher written empathetic feedback over the course of a semester. In turn, this study extends prior research on teacher practices that support a student’s sense of belonging. Literature Review Given the aim of this study, I will discuss prior work on empathetic teacher practices and known ways to portray empathy. To provide context for the importance of this study I will review positive student outcomes associated with teacher empathy and a student’s sense of belonging separately. In addition, I will look at literature that connects teacher empathy and a student’s sense of belonging. I will also discuss prior work on the use of student journals in the field of mathematics or mathematics education. This review will help to highlight the need for research on empathetic teacher practices, such as the use of written empathetic feedback, to support students’ belongingness in the math classroom via a student weekly journal. The Importance of Belongingness for Student Learning Prior research indicates the importance of studying belongingness. Research connects belongingness to important academic outcomes for students (Osterman, 2000). These outcomes include: the development of certain psychological processes crucial for student success, attitudes 72 (academic, social, and personal), motivation, participation, engagement, and achievement (Osterman, 2000, p. 327). Regarding psychological processes crucial for student success, relatedness has been described as one of three basic needs for the development of, “intrinsic motivation, internalization, and emotional integration” (Ryan, 1995, p. 397). Pertaining to academic attitudes, studies show students who felt accepted related positively to school, course work, and their teacher and showed interest and joy related to their schooling (Osterman, 2000). Therefore, the link between a student’s sense of belonging and various important academic outcomes suggests strong reason to continue to study and gain understanding of belongingness. Teachers can positively influence a student’s sense of belonging through personal support (Osterman, 2010; Keyes, 2019). Personal support can include relating to students (Osterman, 2010; Keyes, 2019), building positive relationships through getting to know students on a personal level (both in and out of the classroom) (Kiefer et al., 2015; Osterman, 2010), empathizing with students to understand feelings and needs (Osterman, 2010), being open with students (Freeman et al., 2007), and being understanding, welcoming, and caring (Solomon et al., 1996; Kirby &Thomas, 2022; Kiefer et al., 2015; Freeman et al., 2007; Booker & Lim, 2018). This study aligns with prior research that suggest a teacher’s personal support for students can foster belongingness. The Importance of Teacher Empathy for Student Learning Prior research also indicates the importance of studying teacher empathy for positive student outcomes. Specifically, teacher empathy positively correlates with positive student outcomes such as student participation, critical thinking, and achievement in math (Cornelius- White, 2007). Bozkurt and Ozden (2010) studied student perceptions of their teacher’s empathetic behaviors and attitudes. They found empathetic behaviors more greatly contributed 73 to student success when compared to the competence of their teacher, as self-reported by students. These results suggest the importance of studying teacher empathetic practices. Empathetic Teacher Practices There is limited research on how teachers apply empathy through their practice (Warren, 2018). There is even less literature on teacher empathetic practices with college students. Meyers et al. (2019) is one study that provided research on empathetic teacher practices with college students. They have three recommendations for bringing empathy into one’s teaching practice. First, they recommend learning about a student’s personal life to better understand reasons for potential student struggles. For example, a student who misses class may have various responsibilities outside of class that are pulling their time and attention. Understanding this about a student helps teachers to respond and make decisions with empathy. Next, Meyers et al. suggest structuring time to be able to learn about students in their personal lives. They suggest that learning about students’ personal lives could be done through a student survey. Finally, they urge teachers to develop empathetic teaching practices through course design and course polices that reflect an awareness of students’ personal lives. For example, allowing for late work on request instead of having a no late work policy. A retake or redo policy also communicates teacher empathy (Meyers et al.). The present work adds to research on the empathetic teaching practices with undergraduate math students. In a review of empirical research on teacher empathy in K-12 settings, Berkovish (2020) identified 28 articles. Berkovish (2020) categorized the articles on teacher empathy into four categories, “empathy as a trait, empathy as a state, empathy as communication, and empathy as a relationship” (p. 1). Although the present work does not take place in the K-12 setting, the present work aligns with the category of empathy as communication. This category of empathy 74 is recognized as conversational in which the teacher uses verbal or nonverbal communication to convey an empathetic message which is transmitted to the student to process. Within this category of teacher empathy, Berkovish (2020) identified 7 studies in the literature; three of these studies investigated the development teacher skills to communicate empathetically (Boyer, 2010; Montataianu, 2014; Black & Phillips, 1982). This is where the present work fits in the literature as this study sought to investigate the development of teacher empathetic communication through written empathetic feedback. Most of the prior work on the development of teacher’s communication of empathy was with pre-service teachers (Boyer, 2010; Black & Phillips, 1982). Portraying Empathy through Similar Experiences Research in psychology points to a potential way to portray empathy to others through sharing prior similar experiences. Eklund et al. (2009) found positive correlation between empathy and previous similar experiences. They describe that, in order to truly empathize with another, you need to have had a similar experience and this similar experience can occur at different levels. Therefore, the empathizer does not have to experience the exact same experience as another. Instead, “the other’s experience can be generalized to a level at which it resembles something the empathizer has previously experienced and can thereby be felt and understood” (Eklund et al., 2009, p.68). This research offers implications for teacher practice as a student weekly journal provides a means to share similar experiences with students to portray teacher empathy. Connections Between Teacher Empathy and a Student’s Sense of Belonging Education-based research has just started to recognize connections between teacher empathy and a student’s sense of belonging. For example, Cai et al. (2022) studied connections 75 between teacher empathy and student belongingness in school. They found that together teacher empathy and a student’s sense of school belonging positively impact student achievement (Cai et al., 2022). Specifically, they found, “students taught by more empathetic teachers had a higher sense of school belonging, which was again associated with higher reading achievement” (Cai et al., 2022, p. 10). Although prior research identifies a link between teacher empathy and belongingness to promote positive student outcomes, more research is needed on teacher practices to portray empathy. Student Journals in Math and Math Education A weekly student reflective journal may provide a way to portray empathy to developmental math students. The use of a reflective journal with math students, especially undergraduates, is largely missing from the math education literature. Math journaling found in the literature is primarily focused on math thinking and understanding (Benson-O'Connor et al., 2019; Gordon & Macinnis, 1993; Rogers, 2014; Hamdan, 2017). Research on journaling with college students has been conducted in a capstone course with preservice secondary math teachers and in a Discrete Mathematics course with the purpose of writing to develop a deeper understanding of math content (Rogers, 2014; Hamdan, 2017). Math journals have been used as a way for teachers to learn about student understanding of math concepts and in turn adjust teaching practice (Gordon & Macinnis). In prior research with math journaling, reflection has been a feature of students’ math journals (e.g. Gordon & Macinnis); however, learning about students’ feelings and experiences was not the primary focus. This study adds to research on the use of math journals with undergraduates to learn about students’ feeling and experiences, not focused on math content. In addition, specific types of teacher feedback in math journals have largely been 76 overlooked. Although their research was not focused on the development of written teacher feedback, Gordon and Macinnis (1993) provided details on components of the feedback provided by the teachers in their study. The teachers’ responses to the early adolescent students’ math journals, “consisted of comments, questions, notes of encouragement, and/or assurance” (Gordon and Macinnis, 1993, p. 42). The teacher responses showed the teachers were paying attention to students and the responses displayed teacher care. The overall intent of the teacher journal response was to provide a positive response and share the teacher’s own thoughts and experiences. Through their yearlong math journal writing experience the teachers in Gordon and Macinnis’s (1993) study noticed, “one of the driving forces for the students’ writing appeared to be their keen interest in the teacher’s response and the need to maintain that communicative bond” (Gordon & Macinnis, p. 38). These findings suggest that students are paying attention to the written responses they receive from their teacher. Consequently, this study acknowledged the importance of learning more about how to utilize teacher written feedback to specifically foster student belonging in the math classroom. Summary and Research Questions In summary, teacher empathy and a student’s sense of belonging have both been identified in the literature as important for student learning. However, they have mainly been studied separately (Cai et al., 2022). The literature provides evidence that teachers can foster belongingness in the classroom through teacher support (e.g. Osterman, 2010; Keyes, 2019). Teacher support includes building positive relationships with students, showing teacher care, being open with students, empathizing with student feelings, and relating to students. In addition, prior research shows teacher empathy connects with positive student outcomes such as student participation, critical thinking, and achievement in math (Cornelius-White, 2007). 77 I hypothesized that written teacher empathetic feedback provided a way to show teacher care and in turn foster belongingness in the math classroom. This study will add to research connecting teacher empathy and a student’s sense of belonging. This work is important as there is limited research on how teachers apply empathy through their practice (Warren, 2018). Additionally, prior research using journals in math or math education has mainly focused on using journals to strengthen the understanding of math concepts (e.g. Benson-O'Connor et al., 2019). Using reflective journaling with math students to learn about student experiences and feelings is largely missing from the math education literature. I argued for the use of a student weekly reflective journal in a developmental math course as a way to foster belongingness which would theoretically support positive student outcomes. This study adds to research on the development of teacher empathetic practices through analyzing the development of teacher written empathetic feedback over the course of a semester. The present work aims to continue the conversation in the literature regarding the connections between teacher empathy and a student’s sense of belonging. Specifically, this study argues for the use of teacher written empathetic feedback to foster a student’s sense of belonging to the academic domain of mathematics. This study also adds to research on the use of student journals in mathematics as the written feedback from me, the teacher, was provided in a student weekly reflective journal. This study is informed through the research discussed previously and guided by the following research questions: In what ways does an undergraduate mathematics instructor utilize empathetic feedback with the goal of enhancing belongingness to the academic domain of mathematics? a) How and in what ways does the teacher’s practice of providing written empathetic feedback change over the course of the semester? 78 b) In what ways do student responses to teacher written empathetic feedback reflect evidence of sense of belonging to the academic domain of mathematics? Theoretical Framework In this study, my choice to explore the use and development of written empathetic feedback over the course of a semester in a corequisite math course was guided by Warren (2014, 2018) and Meyers et al. (2019) conceptualizations of empathy. Empathy is conceptualized by scholars as emotional (empathetic concern) and cognitive (perspective taking) (Warren, 2018). Teacher empathy has been defined as, “the degree to which an instructor works to deeply understand students personal and social situations, to feel care and concern in response to students’ positive and negative emotions, and to respond compassionately without losing the focus on student learning” (Meyers et al., 2019, p. 160). Similar to Warren’s (2018) conceptualization of empathy, Meyers et al. (2019) definition of teacher empathy encompasses cognitive and affective pieces and adds in a behavioral component as well. Regarding the cognitive component of empathy, Warren (2014) described perspective taking in the modality of “imagine other” to think about what the other person is feeling in that moment. From the teacher perspective, what is the student feeling in this moment? The cognitive part of Meyers’ et al. (2019) definition also includes perspective taking to develop an understanding of students’ personal and social circumstances. The affective piece of teacher empathy as described by Meyers et al., centers on feelings, similar to Warren’s empathetic concern. Meyers et al. definition includes responding to both positive and negative emotions, whereas Warren’s view of empathetic concern focuses more on negative emotions. Warren (2014) described empathetic concern as represented by the feelings of “sympathy, personal closeness, grief, and/or the emotional human connection of the observer 79 to the target” (p. 398). In addition, Meyers et al. described how they conceptualized the affective part of teacher empathy through explaining that empathy typically entails feeling the same emotions of another, but with teacher empathy it involves feeling comparable emotions. Lastly, Meyers et al. described the behavioral component of teacher empathy as setting boundaries and making student learning a priority. Portraying empathy in math classes requires teachers to develop an understanding of a student’s experiences and portray an emotional response. The design of the intervention I used in this study is informed by both Warren’s (2014, 2018) and Meyers et al.’s (2019) work on empathy. First, drawing from Warren’s (2018) definition in that perspective taking is the “anchoring dimension” of expressing empathy to others. I provided written empathetic feedback through perspective taking by restating the experience of the student as well as providing reasons why I, the teacher, may understand the student’s circumstances and/or emotions. I drew on Meyers et al. (2019) description of the affective or emotional response to encompass empathetic responses that respond to both positive and negative emotions. For example, a student might feel anxious (negative) or ecstatic (positive). I also borrowed from Meyers et al. (2019) in that teacher empathy involves feeling similar but not always the same emotions. As I responded to students’ weekly journal entries, empathetic concern as well as perspective taking were a guide in writing empathetic feedback. Also, guiding my written empathetic feedback were the defining attributes of empathy, borrowed from research in the field of nursing. These defining attributes of empathy as defined by Wiseman (1996) are: “see the world as others see it, non-judgmental, understanding another’s feelings, communicate the understanding” (p. 1165). In addition, I utilized journals and provided empathetic feedback as a means to display 80 teacher care. Teacher care supports a student’s sense of belonging (Solomon et al., 1996; Kirby &Thomas, 2022; Kiefer et al., 2015; Freeman et al., 2007; Booker & Lim, 2018). Therefore, teacher empathy, in theory, supports a student’s sense of belonging. To be able to respond empathetically to students, teachers need to gain an understanding of students’ personal and social situations (Meyers et al., 2019). Student journaling can be used by educators to understand students’ personal and social situations or in other words the student’s perspective. Gordon and Macinnis (1993) reflected on the experience of learning about students through students’ math journals. They stated: Through the journal, we as teachers began to understand better what was happening in the classroom by ‘listening’ and observing in a more focused way. As a result of this watching and listening, teachers and students became a community of learners. (p. 37) This quote speaks to student journals as a way for teachers to understand a student’s perspective, a key component of teacher empathy. In addition, Gordon and Macinnis (1993) described that reading and responding to student journal entries created a feeling of community, which is related to fostering belongingness in the classroom. Finally, to identify student responses to teacher written empathetic feedback that reflect evidence of sense of belonging I applied Good’s et al. (2012) factors of math sense of belonging. I also used their definition of math sense of belonging. They stated, “sense of belonging, as we conceptualize it, involves one’s personal feelings of membership and acceptance in an academic community in which positive affect, trust levels, and willingness to engage remain high” (Good et al., p. 702). Good’s definition was chosen as it defines a student’s sense of belonging in the academic domain of mathematics. Throughout this paper, “sense of belonging” will be used to represent “sense of belonging to the academic domain of mathematics.” Good et al. define 81 factors of math sense of belonging and provide an example of each to conceptualize the meaning. Examples are provided in Table 10. Table 10 Good et al. Factors of Math Sense of Belonging Factor Example Membership “I feel like I belong to the math community” Acceptance “I feel accepted” Affect “I feel comfortable” Trust “I trust my instructors to be committed to helping me learn” Desire to Fade “I wish I could fade into the background and not be noticed” (Good et al., p. 705) These five factors as a whole comprise sense of belonging to the academic domain of mathematics. These factors were used to help to recognize a student’s sense belonging to the academic domain of mathematics in the data. Method Context This study is a part of a larger study on the ways students experience belongingness while participating in a math corequisite course. Prior work focused on student experiences in the course overall; however, this research focused on the student journals and the “prompt – feedback – response” cycle. Specifically, the second part of the research question for this study focused on evidence of factors of belongingness in student written responses to my empathetic feedback in their weekly reflective journal. Participants in this study were enrolled in a corequisite math course which included a college level math class (Math120 College Math) and a paired math support course. This design for corequisite remediation is called a blended model. Childers et al. (2021) defined blended model as when students who are identified as needing remediation enroll in a traditional gateway 82 math course along with other students who are not identified as needing remediation. In addition, the students identified as needing remediation also enroll in a support course during the same semester. The blended model has also been defined as co-mingling; defined as a class with a mix of college ready students and students needing remediation in the same class (Dana Center, 2018). Although the pairing of the college level math course and the support course comprise the corequisite model used in this study, when “corequisite” is referenced in this study I am referring to the support class. In context, the students and I called the support course the “Math Lab”. I chose to call the support course, “Math Lab”, because the English Department at this university uses the term “English Lab” when talking about their corequisite support course. So, “Math Lab” is the term used by students when they are taking about the corequisite support course. The corequisite course was provided at a small, private non-profit university in Michigan. The university has multiple campus locations throughout Michigan, and a global campus online; however, all participants took the course in-person at a campus location in western Michigan. The college level math course, Math120, included a focus on functions with algebra topics, and a collection of other topics such as set theory and dimensional analysis. The math course included weekly in-depth application problems titled Course Enrichment Projects (CEPs). The math course also included online weekly homework through Pearson’s MyLab Math. There were two required department tests that were multiple choice and only a calculator was allowed. There were 8 students in the corequisite support course. Seven of the students were in the paired Math120 class that met prior to the support course, and one student was enrolled in another section of Math120 with the same instructor. The paired Math120 class that met prior to the support class had 18 total students. The math support course was set at a maximum of 15 83 students, 12 students were enrolled at the start of the semester, 9 students started the class, 8 students remained in the course. The corequisite support course was non-credit-bearing and students were charged a $300 course fee. Some of the students in the support class also needed remediation in English and were enrolled in the corequisite for remediation in English. The corequisite math support class met 10 minutes after the paired Math120 course and met twice a week for 80 minutes. One day a week students worked in groups of three or four. Active learning was emphasized on these class meetings through small group collaborative learning. Students discussed ideas, supported each other in learning, and presented their thought processes on various problems to the class. The other class meeting during the week, students met in a computer lab. Students wrote in their weekly reflective journal, worked on their online homework through Pearson’s MyLab Math, read the textbook sections for the week, and took notes on their reading. Although students were allowed to collaborate in the computer lab, and some did, many students sat on their own and worked at their computer. On those class days, I gave students space and time to write in their journals, about 20 minutes total each week to respond to my written feedback and write a reflection on the weekly journal prompt. My instructional approach included supporting student learning through sitting with each small group, asking questions to understand student thinking, and supporting further understanding of ideas. I also provided opportunities for students to share their thinking and understanding of math problems through presentations in both the math class and support course. I put problems from the daily assignment on the whiteboard and students were able to decide on their own if they would like to write up their work. Students wrote up their work on the board as they were working on assignments during class. I reviewed presented work and at times I would 84 talk through potential mistakes with students prior to when they presented to the class. Towards the end of class each student would come to the board and explain their thinking and thought process for the problem they chose to present on. During the math class and the support course, I sat with students, asked questions regarding what they were working on, and guided students through questioning to help them complete problems. On the days students were in the computer lab during the support course, I sat with students to review current grades, asked students about missing work or progress on current work, and asked students to tell me about what they were working on and if they needed additional support. Although most of the class time spent in the support course was focused on providing time to work on course requirements for Math120, there were a few other aspects to the curriculum for the corequisite support course. First, as mentioned before, students wrote and responded to teacher feedback in a weekly reflective journal. Next, about once a week students worked on “basic math skills” such as fractions, operations, solving equations, and graphing. These activities were chosen by me, the instructor, who used these activities when teaching the developmental math class that the corequisite replaced. I also decided when to work on various basic skills through knowledge of the upcoming requirements in the Math120 class. I participated in a training for teaching math corequisite courses that also influenced the delivery of the corequisite support course. Specifically, the training impacted the way grades were determined and provided resources for articles and videos to show students how to employ study habits that could positively impact their math learning. These videos were only shown to students during the first week or two of class. As the semester progressed there was a greater need to provide time to work on assignments. Students always had requirements from the Math120 class to work on and therefore there was not time for additional topics on study skills. 85 Student grades in the corequisite support course were credit or no-credit. Letter grades were assigned; however, these grades did not impact student GPA. Students needed a C (73%) or higher to receive credit for the support course. Grades were determined using weighted percentages. Part of the grade for the support class was based on assignments from the college level math class (Math120). Specifically, 20% of the support class grade was the student’s grade on their online homework (Pearson’s MyLabMath) from Math120 and 20% of the support class grade was the student’s grade on their weekly assignments from Math120 (CEPs- Course Enrichment Projects). The rest of the student’s grade in the support class was based on aspects tied directly to the math support class. Specifically, 10% for in class presentations (at least 3 presentations for full credit), 20% for weekly journal entries/responses to teacher feedback, and 30% for in class assignments based on basic math skills and continuation of practice problems from topics from the college level math course (Math120). Participants There were eight freshman math students in the corequisite course and six of those students participated in this study. Pseudonyms were assigned to each participant and the pseudonyms are: Jasmine, Wyomia, Luan, Hondo, Caleb, and Anna. These students were all coded by the university as “New First Time Freshman”. The students in the corequisite were identified by their advisor as needing math remediation by the standards set by the math department at the university, using the following guidelines, lower than 2.5 high school GPA and/or lower than a C in high school Algebra 2. If students had ACT score greater than or equal to 18 and a SAT score greater than or equal to 500 they would not be advised into math remediation. Students were not required to take a remedial math course. Therefore, the placement tools were a guideline for advisors to help students make an informed choice. 86 Data Collection Student Weekly Journal Entries Student weekly journal entries were used to allow students to express their feelings and experiences. These journal entries provided the source for me, the teacher to respond with written empathetic feedback. During the corequisite course each week students were given about 10 minutes to write a journal entry given a journal prompt. Students created a Google Doc and shared it with me, their teacher. I suggested to students to write freely and without worrying about grammar, sentence structure, and spelling. I wrote the weekly journal prompts with a focus on getting students to share their feelings and experiences in the math course, corequisite course, or on math in general. See the Appendix for specific journal prompts. Teacher Written Empathetic Feedback Each week I provided a written empathetic response to each student through their weekly journal entry. The empathetic feedback was guided by Warren’s (2014, 2018) and Meyers et al. (2019) definitions of empathy and Wiseman’s (1996) defining attributes of empathy. I used this teacher empathetic feedback to document development and changes of my approach to empathetic written feedback through the semester. Table 11 below provides the mean and standard deviation of the amount of feedback I provided per student journal entry (word count): Table 11 Word Count, Mean and Standard Deviation, for Teacher Feedback per Student Journal Entry Participant Mean Word Count Standard Deviation for Teacher Feedback Jasmine 146.5 48.8 Wyomia 190.2 76.7 Luan 182.5 57.8 Hondo 115.7 57.2 Caleb 151.7 91.1 Anna 230.2 103.0 87 Student Responses to Teacher Feedback During the corequisite class each week students were asked to read and respond to my written empathetic feedback. Students were given about 10 minutes each week in class to read the feedback and then write a response in their journal. Students were asked to write a response to the feedback through stating what it was like to read the feedback and how it made them feel. I used these student responses to look for evidence of Good et al. (2012) belongingness factors. Over the course of the semester, there were 52 student responses to my teacher feedback from the six participants. This is a mean of 8.67 student responses to teacher feedback per participant with a standard deviation of 1.03. Teacher Reflective Journal Each week I reflected on my teaching practice in the corequisite course, which included the practice of writing empathetic feedback. The teacher reflective journal provided a source to note any changes or developments in my teaching practice regarding the use of empathetic written feedback. This data source is an explanatory role for the findings from the analysis of the teacher written empathetic feedback. Data Analysis First, I will describe my process for the analysis of my empathetic written feedback. I will also include the ways I used my teacher reflective journal as an explanatory role for the analysis of my written empathetic feedback. This analysis provided evidence for the development of my written empathetic feedback over the course of the semester (RQ1a). Next, I will describe the process I used to analyze the student responses to teacher feedback using Good et al. (2012) factors of math sense of belonging. This analysis provided evidence for student responses to teacher feedback that reflected evidence of factors of belongingness (RQ1b). 88 Data Analysis for Research Question 1a First, I coded my written empathetic feedback using Warren’s (2014, 2018) terms perspective taking and empathetic concern. After noticing the existence of evidence of empathetic written responses, through perspective taking and empathetic concern, I then used a thematic approach to understand the ways I utilized empathetic written feedback. The following themes emerged: 1) restating what the student wrote in their journal, 2) teacher personal or academic story, and 3) acknowledging a student’s understanding of math concepts, participation, work ethic, confidence, or feelings. Next, to understand the development of my written empathetic feedback over the course of the semester I organized the teacher feedback by date and then by participant. This organization helped me to recognize a potential shift in the ways I utilized empathetic feedback over the course of the semester. As I reviewed the chronological data, I noted shifts in my written feedback. When a shift was noted, I then referenced the dates in my teacher reflective journal to provide more context and detail regarding any changes in my written empathetic feedback practice. Consequently, I used both the thematic analysis of my written empathetic feedback as well as my reflective journal to understand development of my feedback over the course of the semester. Finally, to understand the ways I utilized empathetic feedback I used the student weekly journal entries. These journal entries provided a source to identify the parts of the student’s journal entry that I was responding to in my written feedback. This helped me to gain an understanding of the use of my written empathetic feedback. 89 Data Analysis for Research Question 1b I used Good et al. (2012) factors of math sense of belonging to identify aspects of belongingness in the student responses to my empathetic feedback. In order to use the factors from Good et al. I operationalized the factors (Membership, Acceptance, Affect, Trust, Desire to Fade) and this process is described in detail in the next section. After operationalizing the factors, I then coded the student responses to written teacher empathetic feedback using the factors of math sense of belonging. Next, I looked for student responses that showed evidence of Good’s et al (2012) factors of math sense of belonging. I created a table in a Word document with three columns to contain the student journal entries, teacher written empathetic responses, and student responses to empathetic feedback. I removed any data that did not include all three parts because if students did not respond to my empathetic feedback, then I would not be able to look for evidence of statements reflecting belonging. When I recognized a factor of belongingness in a student response to my feedback, I then followed the pattern of conversation backwards. Therefore, I followed the conversation from the student response to my feedback, back to the feedback I provided, and then back to the student journal entry. This process allowed me to see a flow of conversation through the data. In turn, this allowed me to recognize data that reflected aspects of belongingness in the student responses to my empathetic feedback. It also allowed me to see what parts of the student journal entries I was responding to. Operationalizing the Factors. In their study, Good and colleagues developed a scale titled “Math Sense of Belonging Scale.” I used Good and colleagues’ sense of belonging scale by operationalizing codes from statements in the scale to be used to code the student responses to my empathetic feedback. Good et al. (2012) identified key words or phrases from the statements 90 in their scale connected to each factor of sense of belonging to the academic domain of mathematics. I operationalized these key words or phrases (see below) to develop a coding scheme for the student responses to teacher feedback. In the following subsections I will share Good et al. (2012) key words or phrases for each factor they identified for sense of belonging to the academic domain of mathematics. Then, I will share how I operationalized the key words or phrases from each factor to code the student responses to teacher feedback. Lastly, I will share quotes from student written journal entries or student responses to teacher feedback connected to each factor. Membership. Good et al. (2012) identified the key words or phrases from their scale related to the sense of belonging factor Membership. These key words or phrases are, “belong, member, a part of, and connected” (p. 703). To operationalize these key words or phrases as codes for the written data in this study I expanded on the meaning for each of these key words or phrases. First, I recognized “belong” as belonging with peers in the math class or corequisite course by creating a community feeling. Next, I identified “member” as a member of the math community. “A part of” I recognized as a student feeling they were a part of their collaborative small group, a part of the math class or corequisite or a part of the math community in general. Finally, I identified “connected” as connection to their teacher or other students in the math class or corequisite course. See Table 12 below for details. Table 12 Membership Phrase or key Operationalized phrase or Quotes from student written data word from key word for analysis of Good et al. student written data (2012) 91 Table 12 (cont’d) Belong Belonging with peers in “I feel like I kind of created a bond with the the math class or people in our math lab.” corequisite course by creating a community feeling Member A member of the math “I really liked the responses, they were really community motivating. The stories and how we as math people have similar stories is very interesting.” A part of A part of their ““I have enjoyed working with my group. I like collaborative small group, collaborating with them, because we all kind of a part of the math class or have pieces of a puzzle and we bring it together corequisite, a part of the to make one whole puzzle.” math community in general Connected Connection to their “I feel as if we are the same in some ways…I teacher or other students also think it’s cool that we have some things in in the math class common like being scared to ask questions.” Acceptance. Good et al. (2012) identified the key words from their scale related to the sense of belonging factor Acceptance. These key words are, “accepted, respected, valued, and appreciated” (p. 703). Regarding Acceptance (reverse coded) the key words are, “disregarded, neglected, excluded, and insignificant.” To operationalize these key words as codes for the student written data in this study I expanded on the meaning for each of these key words. I recognized students expressing feelings of being accepted, respected, valued, and appreciated by their peers in the math class or corequisite course or by their teacher. Next, regarding the key words for the factor Acceptance that were reverse coded I identified statements in the student written data where students expressed feeling disregarded, neglected, excluded, or insignificant with regards to peers in the math class or corequisite class, their teacher, or in their previous math experiences related to their teacher, peers, or the math community in general. See Table 13 and 14 below for details. 92 Table 13 Acceptance Phrase or key Operationalized phrase or Quotes from student written data word from key word for analysis of Good et al. student written data (2012) Accepted, Feelings of being “I felt truly seen, and heard by you and that is a Respected, accepted, respected, great feeling to get from professors.” Valued, and valued, and appreciated by Appreciated their peers in the math class or corequisite course or by their teacher Table 14 Acceptance (Reverse Coded) Phrase or key Operationalized phrase or Quotes from student written data word from key word for analysis of Good et al. student written data (2012) Disregarded, Feeling disregarded, “If i’m being honest I really didn’t like math Neglected, neglected, excluded, or mainly because I didn’t understand or didn’t Excluded, and insignificant with regards know when to use a formula. I was scared of Insignificant to peers in the math class being called on because I was scared that I or corequisite class, their might not know the answer. Math was always a teacher, or in their struggle for me. I thought that I was too dumb previous math experiences to be in the class or I was not smart enough to related to their teacher, fit in with everyone else in classes.” peers, or the math community in general Affect. Good et al. (2012) identified the key words or phrases from their scale related to the sense of belonging factor Affect. These key words or phrases are, “at ease, comfortable, content, and calm” (p. 703). To operationalize these key words or phrases as codes for the student written data in this study I expanded on the meaning for each of these key words. First, I recognized “at ease” as students expressing feeling at ease during the math class or corequisite course, students feeling at ease while completing math course work, or students feeling at ease 93 while working with their peers or teacher. Next, I acknowledged the key word “comfortable” as students expressing feelings of comfort with regards to math class or the corequisite course, expressing feelings of comfort regarding interactions with their teacher or peers, or communicating feelings of comfort regarding participating in class or completing math course work (including writing in their journal). Next, I recognized students feeling “content” when they expressed joy, happiness, appreciation, or stated that they liked the math class or the corequisite course or stated math class or the corequisite was fun. Lastly, I recognized participants expressing feeling “calm” through participating in the math class or corequisite course or completing course work (including writing in their journal or assessments). Regarding Affect (reverse coded) the key words are, “anxious, tense, nervous, and inadequate” (Good et al., 2012, p. 703). To operationalize these key words as codes for the student written data in this study I expanded on the meaning for each of these key words. I recognized students feeling anxious, tense, nervous, or inadequate with regards to course work (including writing in their journal or assessments), participation in class or with their small group, or their grade. See Table 15 and 16 below for details. Table 15 Affect Phrase or key Operationalized phrase or Quotes from student written data word from key word for analysis of Good et al. student written data (2012) 94 Table 15 (cont’d) At ease Feeling at ease during the “But I thought it was cool that you had us write math class or corequisite in our journals about how we feel about class course, students feeling at and the math homework we get. Especially ease while completing about the last tests. Writing about it actually got math course work, or some tension off of my chest. It was helpful in students feeling at ease many ways.” while working with their peers or teacher, or writing in their weekly journal/receiving feedback Comfortable Feelings of comfort with “Thank you for sharing your experience with me. regards to math class or You don’t know this but it actually brought me a the corequisite course, little comfort.” expressing feelings of comfort regarding interactions with their teacher or peers, or communicating feelings of comfort regarding participating in class or completing math course work (including writing in their journal/receiving feedback). Content Feeling content when “I really like feedback, and these journals.” students expressed joy, happiness, appreciation, or stated that they liked the math class, the corequisite course, or their weekly journal/feedback or stated math class, the corequisite, the weekly journal was fun Calm Feeling calm with regards “Writing the journal made me feel calm and to participating in the heard it felt natural and felt like a way of math class or corequisite relieving stress Mathlab was amazing through course, or completing out the semester. I liked the journal part the course work (including most and I would recommend the to other writing in their journal or students.” assessments) 95 Table 16 Affect (Reverse Coded) Phrase or key Operationalized phrase or Quotes from student written data word from key word for analysis of Good et al. student written data (2012) Anxious, Feeling anxious, tense, “Whenever I hear you say the word test I just Tense, nervous, or inadequate get anxiety and I feel nauseous.” Nervous, or with regards to course Inadequate work (including assessments), participation in class or with their small group, or their grade. Trust. Good et al. (2012) identified the phrases from their scale related to the sense of belonging factor Trust. These phrases are, “test is unbiased, don’t have to prove worth, help me learn, and faith in potential” (p. 703). To operationalize these phrases as codes for the student written data in this study I expanded on the meaning for each of these phrases. First, regarding the phrase, “test is unbiased”, I recognized this when a student described feeling the assessments were reflective of the course material. Next, I identified, “don’t have to prove worth”, when a student expressed not feeling the need to prove their worth to anyone but themselves. Next, I identified, “help me learn”, when a student referenced feeling their teacher was there to support them in their learning and help them succeed in the math course. Lastly, I recognized the phrase “faith in potential” when a student expressed feeling their teacher had faith in their potential or the student themselves had faith in their potential to be successful in math class. See Table 17 below for details. 96 Table 17 Trust Phrase or key Operationalized phrase or Quotes from student written data word from key word for analysis of Good et al. student written data (2012) Test is Feeling the assessments “I am feeling pretty confident, I just have to unbiased were reflective of the touch upon a few chapters and I think Ill do course material good. I am feeling this way because i have understood what the CEP’s were about and I did pretty good on the practice test. I have done linear and exponential functions before so I am a bit confident.” Don’t have to Not feeling the need to No examples found prove worth prove their worth to anyone but themselves Help me learn Feeling their teacher was “I really do appreciate you always helping not there to support them in only me but the whole class. It’s actually their learning and help helpful when you come up to each table and them succeed in the math help us figure some things out. I think it’s also course helpful when you put so much pressure on me (joking) but it actually helps with the one on one talks too. Like you point out the mistakes I made and you help me figure it out.” Faith in Feeling their teacher had “I am happy that you as my professor are potential faith in their potential or confident in me” the student themselves had faith in their potential to be successful in math class Desire to Fade/Active Participant. Good et al. (2012) identified the key words or phrases from their scale related to the sense of belonging factor Desire to Fade and Active Participant. These key words or phrases for Desire to Fade (reverse coded) are, “fade, say little, and wish I was invisible” and for active participant the key word is “active participant” (p. 703). To operationalize these key words or phrases as codes for the student written data in this study I expanded on the meaning for each of these key words or phrases. First, I recognized a student’s “desire to fade” when a student expressed wanting to fade into the background during math class 97 or previous math classes and not participate during class discussions or disconnected from participating in the course requirements. Next, I acknowledged the phrase “say little” when a student expressed not wanting to raise their hand or ask questions during math class or previous math classes or if they expressed not wanting to talk during small group work. Lastly, I recognized a student expressing that they wished they were invisible when they discussed not wanting to be seen or noticed in math class or in classes during their previous math experiences. Regarding the phrase “active participant” I acknowledged this phrase when a student signified participating in math class or during the corequisite course through asking questions, presenting math thinking, working on math course materials, or collaborating with their small group. See Table 18 and 19 below for details. Table 18 Desire to Fade Phrase or key Operationalized phrase or Quotes from student written data word from key word for analysis of Good et al. student written data (2012) Fade Wanting to fade into the “I hopefully can get a good grip on math from background during math this year and not shy away from it anymore.” class or previous math classes and not participate or disconnected from participating in the course requirements Say little Not wanting to raise their No examples found hand or ask questions during math class or previous math classes or if they expressed not wanting to talk during small group work 98 Table 18 (cont’d) Wish I was Not wanting to be seen or No examples found invisible noticed in math class or in classes during their previous math experiences Table 19 Active Participant Phrase or key Operationalized phrase or Quotes from student written data word from key word for analysis of Good et al. student written data (2012) Active Participating in math class “I love having the group discussions, I feel as if participant or during the corequisite they help tremendously. I do have a large desire course through asking to understand math” questions, presenting math thinking, working on math course materials, or collaborating with their small group Findings Through the data analysis I observed that as the semester progressed, my teacher practice of providing written empathetic feedback shifted from sharing personal or academic stories to acknowledging the student through their understanding of math concepts, participation, work ethic, confidence, or feelings. Evidence of factors related to a student’s sense of belonging were noted in students’ written responses to teacher feedback. This evidence was noted through written responses that reflected the belongingness factors of Membership, Acceptance, and positive Affect in response to my personal or academic stories and evidence of the belongingness factor of Trust in response to my feedback that acknowledged the student. 99 Written Empathetic Feedback Provided by the Teacher Shifts over the Course of the Semester from Sharing Stories to Acknowledging the Student (RQ1a) My goal in providing written feedback to students through a weekly journal was to portray an empathetic response and in turn foster students’ sense of belonging. Throughout the semester, evidence of responding to student’s emotions (empathetic concern) and aiming to understand the student’s perspective (perspective taking) were recognized. First, in response to student emotions I responded with phrases such as: “I understand”, “ I can see”, “I know”, and “I can relate”. After recognizing the student’s emotion, I often restated the experience the student explained in their journal entry. This feedback was intended to recognize the student’s feelings by aiming to provide empathetic concern, as well as perspective taking by restating the student’s experience. Next, I felt my empathetic feedback needed context and reason to convey my understanding of student emotions as well as the student’s perspective. At the beginning of the semester, I shared a personal or academic story from my past or current life to provide context and reason for understanding student emotions. Early in the Semester: Teacher Written Empathetic Feedback through Personal and Academic Stories (RQ1a) Early in the semester, to portray context and reasoning for understanding student emotions, I shared stories from my own life. I wanted students to know that I have faced similar experiences and have experienced similar emotions. These stories were both academic and personal in context and were from my past or current experiences. I wanted students to know that even though I’m their math teacher, I too have had academic and personal struggles. As I read student journal entries each week, I reflected on my own life experiences and thought about 100 times I felt similar emotions and shared my stories with students through written feedback. Teacher Academic Story from a Past Experience. An example of a time I wrote empathetic feedback with an academic story from my past was in response a student named Anna. She wrote in her first journal entry, “I struggle with math truly, and it is something I am beyond anxious about in college...I still want to work hard and get my classes taken care of with a good GPA.” To provide empathetic feedback to this part of Anna’s journal entry I reflected on a time I felt anxious in college and felt pressure to have a good GPA. My feedback stated, “I understand the anxious college feeling and wanting to do well.” I portrayed empathetic concern and perspective taking through stating I understood her emotions and provided perspective taking through restating her feelings and her desire to do well. Next, to provide context and reasoning for understanding Anna’s emotions I shared an academic story from my past. I wrote, “I had a scholarship in college that I needed to keep a certain GPA and I was always worried about doing well enough.” This story provided an empathetic response through sharing a similar experience where I felt anxious and pressured to do well in college and earn a certain GPA. Teacher Personal Story from a Current Experience. Next, an example of a time I wrote empathetic feedback with a current personal story was in response to a student, Wyomia. During the fourth week of the semester, Wyomia wrote: Well I missed class on Tuesday because I felt sick and it was a bummer but I ended up feeling better the next day. But I missed a lot of work that I was supposed to do that day. So I'm kinda behind. So my plan this week is to finish all the homework I missed and to turn it all in by Friday. And on top of it all I forgot to do my math lab homework. So I'm feeling really stressed right now. To provide feedback to Wyomia feeling stressed and behind, I reflected on a time that I also felt 101 those emotions. In response to Wyomia’s journal entry I wrote, “I know that feeling of being behind and feeling stressed.” This statement reflects empathetic concern and perspective taking through recognizing Wyomia’s emotions and restating what she wrote. Next, to portray reasoning and context for my understanding I shared a personal story. I wrote: I actually have felt that way this week too. Not because I was sick, but last weekend I worked on a landscaping project with my husband and parents all weekend. I didn’t get to any of the things I needed to work on for school over the weekend and so I started off the week behind. All week I’ve felt stressed trying to get caught up. This personal story was from my current life experiences. This story reflects a time where I also felt stressed and behind. I wrote this story from my own life to empathize with Wyomia also feeling stressed and behind. Student Responses to Teacher Empathetic Feedback Indicate the Belongingness Factors of Membership, Acceptance, and Affect (RQ1b). Each week students responded to the feedback I provided in a reflective journal where they shared what it was like to read the feedback and how it made them feel. Student responses to my personal and academic stories provide evidence of feelings of belongingness connected to the factors Membership, Acceptance, and positive Affect. Four out of six of the student participants responded to my personal or academic stories with statements reflecting the belongingness factors of Membership through connecting or relating to me, their teacher. Three out of the six of the participants provided responses to my personal or academic stories that reflect the belongingness factor of Acceptance through seeing they aren’t the only one, they are appreciated, and they are not judged. Lastly, four out of the six participants responded to my personal or academic stories with statements connected to positive Affect reflecting comfort, ease, or contentment. 102 For example, in response to my personal story from my current life (shared above) regarding a time I felt stressed and behind Wyomia wrote, “Once again your feedback was comforting. It’s actually pretty nice knowing that I’m not the only one that feels this way. I feel as if we are the same in some ways.” This response from Wyomia to my personal story about feeling stressed and behind, reflects the belongingness factors Membership, Acceptance, and positive Affect. First, her statement, “I feel as if we are the same in some ways” reflects connecting or relating to me, her teacher, which signifies the belongingness factor Membership. Next, she stated, “I’m not the only one that feels this way” and this reflects the belongingness factor Acceptance. Lastly, she remarked that the feedback was comforting which reflects the belongingness factor positive Affect. Although participants provided evidence of the belongingness factors of Membership, Acceptance, and positive Affect in response to my personal and academic stories; this type of feedback did not always elicit feelings of belongingness. Student responses to my feedback that did not reflect any factors of belongingness can be categorized as sharing something new, a positive response not connected to a factor of math sense of belonging, restating something from their original journal entry, showing appreciation, or talking about feelings in past tense. Four Weeks into the Semester: Teacher Written Empathetic Feedback through Acknowledging the Student (RQ1a) As the semester progressed students started to write about more positive experiences and emotions. Due to this change in the content of student journal entries, I had difficulty responding empathetically to positive experiences and emotions using a personal or academic story. In my teacher reflective journal, I wrote, “It seems I may have a harder time finding the words to respond with empathy for positive student reflections.” As I was grappling with how to best 103 provide written empathetic feedback to students, I reflected on the difficulties of always providing feedback focused on empathy. In Week 6 of the 15 week semester I wrote, “Sometimes I’ve gotten the feeling the empathy feedback focuses too much on the struggles, tough times, commiserating. I need something to support the positive things that are happening for students.” At this time, I found an article by Carol Steckl, Ph.D. titled, “Empathy: It’s About Happiness, Too” that helped me to re-center my empathetic feedback. In Week 8 of the 15 week semester, I reflected writing: I feel as I’ve shared more of myself and experiences, I’m having less “stories to tell” about my struggles and I’ve shifted more to noticing students in class...As the student journal responses have turned more positive in general, I feel less of a need to tell them about something that happened similar to me. It doesn’t feel the same as sharing about a struggle I’ve had. Instead, it feels more authentic to show I am seeing and experiencing those positive moments with students in class. During Week 6 of the semester, in my teacher reflective journal I wrote, “I wondered how I might continue to provide empathetic feedback that is genuine and different from what I’ve already said.” To help me determine how to add more ways to provide written empathetic feedback I looked to the responses from my students. In my reflective journal during Week 6 of the semester I discussed implications from student responses to my written feedback. I stated: I’ve also noticed at least 3 times where I have provided journal feedback that I mention noticing something students did in class or how their participation changed when they have mentioned the change in their reflection or that they are doing well with something. It seems to elicit a positive response from students. I plan to try to include this more in my feedback and see if I continue to get these positive responses. Only providing this 104 type of feedback when students actually mention it first, not just bringing it up out of the blue. Therefore, I started to shift my practice of providing written empathetic feedback from sharing personal or academic stories to acknowledging the student through their participation. Due to the positive response from students, I began to provide written empathetic feedback through acknowledging student participation or accomplishment. In summary during Week 8, I wrote: It seems, to respond to negative experiences with empathy, I use my personal experience to provide perspective taking. However, with positive experience to respond empathetically, it seems I am starting to use “noticing” of students and then the reasons why I notice such and such positive experience for the student. So, the negative I use my own experiences to provide perspective and understanding and for positive experiences I use noticing students in class and their actions/emotions to rely the perspective taking. As the semester progressed, I provided empathetic feedback by acknowledging the student’s understanding of math concepts, participation, work ethic, confidence, or feelings. Understanding of Math Concepts. One way I provided empathetic feedback was through acknowledging students’ understanding of math concepts. For example, Anna wrote in a journal entry, “When I do understand something like exponential growth and decay, that makes me feel good inside because I like understanding things we are learning about.” To respond to this statement in Anna’s journal entry I wrote, “I’ve noticed your understanding with exponential functions! That is a great feeling when you understand how something works.” This feedback acknowledged Anna’s understanding of a math concept, exponential functions. This response provided an emotional response through acknowledging Anna’s positive feelings and provided perspective taking through restating and acknowledging that I also noticed that she understood 105 exponential functions. Participation. Another way I provided empathetic feedback was through acknowledging students’ participation. For example, Caleb wrote in his journal: Its nice to go through some of the questions on worksheets/Hw assignments because its the questions that I actually struggled with that we are going over and everybody can help each other out and give insight on what helped them or if they had another way that helped them solve the question. I responded to Caleb’s journal entry stating, “I notice that you work well with the other students in math lab class and I can see that you appreciate the help and support as well as learning about how others understand the math problems.” My feedback reflected acknowledging Caleb through his participation in class. This feedback provided perspective taking through restating and acknowledging Caleb’s participation. Work Ethic. Providing feedback through acknowledging students’ work ethic was another way I responded to students with empathy. Jasmine wrote in her journal, “I've been studying more so I can get myself prepared for the test.” In response to Jasmine writing about studying to prepare for the test, I wrote, “I can also see you have been studying hard, you really have improved your grade on my lab math and you are working through and doing well on the CEPs.” This feedback reflects perspective taking through acknowledging Jasmine’s work ethic and providing examples of ways I have seen the accomplishments of her hard work. Confidence. Another way I provided empathetic feedback was through acknowledging students’ confidence. For example, Wyomia wrote about her confidence regarding an upcoming test, she wrote, “If I’m being honest I feel confident.” To acknowledge Wyomia’s confidence I wrote back stating, “I can see your confidence grow every class, as you chime in answers with 106 small groups and with the whole class.” My feedback provided perspective taking through acknowledging Wyomia’s confidence and providing examples of how I recognized her confidence through her participation. Feelings. I also provided empathetic feedback through acknowledging positive and negative student emotions. An example of acknowledging positive feelings is seen in Luan’s journal entry. He wrote, “I felt very good before the test.” I also observed Luan’s positive energy on the day of the test, and I provided feedback stating, “I could sense you had good energy going into the test. You were there early, studying and you have worked hard on assignments and to truly understand math topics. All the things to set yourself up for success.” This feedback provided an emotional response through recognizing Luan’s positive energy. In addition, my feedback provided perspective taking through restating, acknowledging, and providing reasons for Luan’s positive feelings prior to the test. An example of acknowledging negative feelings is seen in Anna’s journal entry regarding her test experience. She wrote, “I am a little upset looking at my score from the test. I am not surprised because I usually bomb tests so this is usual for me, but still upsetting because no one likes to fail.” In response to Anna feeling upset about her test I wrote, “I can sense your upset feelings with regards to your test.” This feedback from me reflects empathetic concern through recognizing Anna’s upset feelings. In addition, this provided perspective taking through restating and acknowledging that I sensed that she was feeling upset. Student Responses to Teacher Empathetic Feedback Indicate the Belongingness Factor Trust (RQ1b). Each week students responded to the feedback I provided by sharing what it was like to read the feedback and how it made them feel. These responses were written by the students in their reflective journal each week. Student responses to feedback where I 107 acknowledged the student’s understanding of math concepts, participation, work ethic, confidence, or feelings provide evidence of the belongingness factor Trust. Five out of six of the student participants responded to feedback where I acknowledged the student with statements reflecting the belongingness factor Trust. Aspects of the belongingness factor Trust were recognized through student statements that their teacher had faith in their potential/confidence in them or that their teacher was there to help them learn. For example, Anna reflected on thoughts about math. She wrote: I am feeling a lot better about math than what I originally did coming into college. Though I still struggle with some topics, I enjoy it way more than I would have ever thought. I thought I was going to come in, and hate math and everything about it. As a whole, math is not a negative thought. It is in the middle because I know I have so much more to learn, but for now I like how I am progressing. I responded to Anna through acknowledging her positive feelings about math. I wrote: I can see you enjoying math this semester, taking time to really understand topics, and use a learning process through notes and discussion with others. You are really an active participant in all of the learning processes. And I can see you enjoying each of those processes of learning in different ways… learning with your group, creating useful notes, understanding the “help me solve” etc. My feedback reflects acknowledging Anna’s positive feelings. I provided an emotional response through recognizing that she was enjoying math. In addition, I provided perspective taking through restating and acknowledging Anna’s positive feelings. I also offered examples of reasons why I saw that she was enjoying math. Anna responded to my feedback stating, “I appreciate you recognizing me being involved 108 and trying my best to hopefully understand math this year.” This reflects evidence of belongingness connected to the factor Trust. In that, Anna’s response suggests that she saw that I had faith in her potential, which reflects the sense of belonging factor Trust. This response from Anna came from feedback where I acknowledged that Anna was enjoying math this semester through seeing her participation in class. Five out of the six participants provided evidence of the belongingness factor Trust in response to feedback where I acknowledged the student’s understanding of math concepts, participation, work ethic, confidence, or feelings. However, feedback where I acknowledged the student did not always elicit statements connected to the belongingness factor Trust. Student responses that did not reflect evidence of belongingness can be categorized as a positive response not connected to a factor of math sense of belonging, sharing something new, restating something from their original journal entry, showing appreciation, or talking about feelings in past tense. There were also two students that responded with statements that reflect comfort or contentment; however, there was not enough evidence to generalize this as a response to the students receiving feedback with acknowledgement. Discussion and Implications The findings of this study demonstrate the development of a teacher practice to portray empathy. Specifically, I provided evidence on the development of my written empathetic teacher feedback over the course of a semester. Through the data analysis I recognized that my written empathetic feedback shifted from portraying empathy through my personal or academic stories to acknowledging the student through their understanding of math concepts, participation, work ethic, confidence, or feelings. Prior research in psychology indicated a connection between empathy and prior similar experiences (Eklund et al., 2009). The present work aligns with prior 109 research as I used my personal or academic stories to convey an empathetic written response. It also puts findings from the field of psychology into practice in the field of education. This study provides preliminary evidence on the use of written feedback to a weekly reflective journal as a teacher practice to portray empathy. These finding are important as there is not much research on how teachers apply empathy through their practice (Warren, 2018). Meyers et al. (2019) recommended learning about each student’s personal life as a way to understand potential student struggles. This study furthers the use of this strategy by using a student weekly reflective journal to learn about student feelings and experiences. The student journal entries provided a source for me, the teacher, to learn about my students’ academic and personal experiences. I learned things about my students that I never would have known without the weekly journal. The journal helped me to understand my students and it also directed my teaching practices. Next, this study provides preliminary findings on connections between teacher empathy and a student’s sense of belonging. These findings are important as there is limited research on the connection between these constructs that are important for student learning. The student written responses to my empathetic feedback provide evidence of factors of math sense of belonging. In response to my personal or academic stories the findings indicate evidence, through student written statements, of the belongingness factors Membership, Acceptance, and positive Affect. On the other hand, student written responses to feedback where I acknowledged the student through their understanding of math concepts, participation, work ethic, confidence, or feelings provide examples that reflect the belongingness factor Trust. Finally, the findings of this study provide implications for the use of a reflective student journal in a math setting. Prior research on journaling in math or math education has focused on 110 the student developing a deeper understanding of math concepts through writing. The preliminary finding of this study suggests my written empathetic feedback supported aspects of Good et al. (2012) factors of math sense of belonging. This is important as students that are placed into developmental math courses commonly lack feelings of belonging (Silva & White, 2013). Consequently, implementing a student weekly reflective journal in a developmental math course, specifically a corequisite course, may provide a concrete way for teachers to portray empathy through written feedback and in turn foster belongingness in the math classroom. Conclusion In conclusion, this study provided evidence on the use and development of my written empathetic feedback over the course of the semester. The findings indicate that my practice of providing written empathetic feedback shifted over the course of a semester. The shift was noted as I went from sharing personal or academic stories early in the semester to acknowledging students through their understanding of math concepts, participation, work ethic, confidence, or feelings as the semester progressed. Evidence of factors of Good’s et al. (2012) math sense of belonging are reflected in student responses to my written empathetic feedback. Examples that reflect the belongingness factors Membership, Acceptance, and positive Affect are noted in student responses to my academic or personal stories. Examples that reflect the belongingness factor Trust are noted in student responses to acknowledgement through their understanding of math concepts, participation, confidence, work ethic, or feelings. These findings are important as research is limited on the application of empathy through teacher practice (Warren, 2018). These preliminary findings suggest that written empathetic feedback via a student reflective journal may provide a way for teachers to foster belongingness in the developmental math classroom. These findings are important as there is limited research 111 on the connections between teacher empath and a student’s sense of belonging (Cai et al., 2022). In addition, developmental math students often feel they do not belong in the math classroom (Silva & White, 2013) and this puts these math students at risk of failure and continued pursuit of their degree (Bryk et al., 2013). Corequisite math courses provide a potential structure to implement a weekly student reflective journal as class time is flexible and class sizes are typically small. Future research on the teacher empathetic written feedback via a student reflective journal is suggested with other vulnerable student populations and potentially in disciplines other than mathematics. 112 REFERENCES Bryk, A. S., Yeager, D. S., Hausman, H., Muhich, J., Dolle, J. R., Grunow, A., & Gomez, L. (2013, June). Improvement research carried out through networked communities: Accelerating learning about practices that support more productive student mindsets. In A White Paper prepared for the White House meeting on “Excellence in Education: The Importance of Academic Mindsets. Benson-O'Connor, C. D., McDaniel, C., & Carr, J. (2019). Bringing math to life: Provide students opportunities to connect their lives to math. Networks: An Online Journal for Teacher Research, 21(2), 3. Berkovich, I. (2020). Conceptualisations of empathy in K-12 teaching: A review of empirical research. Educational Review, 72(5), 547-566. Black, H., & Phillips, S. (1982). An intervention program for the development of empathy in student teachers. The Journal of Psychology, 112(2), 159-168. Booker, K. C., & Lim, J. H. (2018). Belongingness and pedagogy: Engaging African American girls in middle school mathematics. Youth & Society, 50(8), 1037-1055. Boyer, W. (2010). Empathy development in teacher candidates. Early Childhood Education Journal, 38(4), 313-321. Bozkurt, T., & Ozden, M. S. (2010). The relationship between empathetic classroom climate and students’ success. Procedia-Social and Behavioral Sciences, 5, 231-234. Cai, Y., Yang, Y., Ge, Q., & Weng, H. (2022). The interplay between teacher empathy, students’ sense of school belonging, and learning achievement. European Journal of Psychology of Education, 1-17. Cameron, C. D., Hutcherson, C. A., Ferguson, A. M., Scheffer, J. A., Hadjiandreou, E., & Inzlicht, M. (2019). Empathy is hard work: People choose to avoid empathy because of its cognitive costs. Journal of Experimental Psychology: General, 148(6), 962. Childers, A. B., Lu, L., Hairston, J., & Squires, T. (2021). Impact and Effects of Co-Requisite Mathematics Remediation. Primus, 31(2), 167-183. Dana Center. (2018). Co-requisite Courses: Narrowing the Gap between Instruction and Supports. Dana Center Math Pathways. Cornelius-White, J. (2007). Learner-centered teacher-student relationships are effective: A meta- analysis. Review of Educational Research, 77(1), 113-143. Eklund, J., Andersson-Straberg, T. & Hansen, E. M. (2009). “I've also experienced loss and fear”: Effects of prior similar experience on empathy. Scandinavian Journal of 113 Psychology, 50(1), 65-69. Freeman, T. M., Anderman, L. H., & Jensen, J. M. (2007). Sense of belonging in college freshmen at the classroom and campus levels. The Journal of Experimental Education, 75(3), 203-220. Good, C., Rattan, A., & Dweck, C. S. (2012). Why do women opt out? Sense of belonging and women's representation in mathematics. Journal of Personality and Social Psychology, 102(4), 700. Gordon, C. J., & Macinnis, D. (1993). Using journals as a window on students' thinking in mathematics. Language Arts, 70(1), 37-43. Hamdan, M. (2017). Beyond the Given: Stretching Mathematical Thinking Through Journaling. PRIMUS, 27(10), 916-925. Keyes, T. S. (2019). A qualitative inquiry: Factors that promote classroom belonging and engagement among high school students. School Community Journal, 29(1), 171-200. Kiefer, S. M., Alley, K. M., & Ellerbrock, C. R. (2015). Teacher and peer support for young adolescents’ motivation, engagement, and school belonging. RMLE Online, 38(8), 1-18. Kirby, L. A., & Thomas, C. L. (2022). High-impact teaching practices foster a greater sense of belonging in the college classroom. Journal of Further and Higher Education, 46(3), 368-381. Meyers, S., Rowell, K., Wells, M., & Smith, B. C. (2019). Teacher empathy: A model of empathy for teaching for student success. College Teaching, 67(3), 160-168. Motataianu, I. T. (2014). The empathy and communication–pride personality's dimensions of the teacher. Procedia-Social and Behavioral Sciences, 142, 708-711. Osterman, K. F. (2000). Students' need for belonging in the school community. Review of Educational Research, 70(3), 323-367. Osterman, K. F. (2010). Teacher practice and students’ sense of belonging. In International research handbook on values education and student wellbeing (pp. 239-260). Springer, Dordrecht. Rogers, K. C. (2014). Journal Writing in a Mathematics Capstone Course for Prospective Secondary Teachers: Future Teachers Making Connections. PRIMUS, 24(6), 465-479. Ryan, R. M. (1995). Psychological needs and the facilitation of integrative processes. Journal of Personality, 63(3), 397-427. Silva, E., & White, T. (2013). Pathways to Improvement: Using Psychological Strategies to Help 114 College Students Master Developmental Math. Carnegie Foundation for the Advancement of Teaching. Solomon, D., Battistich, V., Kim, D. I., & Watson, M. (1996). Teacher practices associated with students' sense of the classroom as a community. Social Psychology of Education, 1(3), 235-267. Steckl, C. (n.d.). Empathy: It’s about happiness, too. Centersite, LLC. https://www.mentalhelp.net/blogs/empathy-it-s-about-happiness-too/ Warren, C. A. (2014). Towards a pedagogy for the application of empathy in culturally diverse classrooms. The Urban Review, 46(3), 395-419. Warren, C. A. (2018). Empathy, teacher dispositions, and preparation for culturally responsive pedagogy. Journal of Teacher Education, 69(2), 169-183. Wiseman, T. (1996). A concept analysis of empathy. Journal of Advanced Nursing, 23(6), 1162- 1167. 115 APPENDIX ● Journal #1: This is your chance to tell me about your past experiences in math classes and your feelings about math in general. Reflect on your experiences in elementary school, middle school, high school, and college, etc. Describe what your experiences were, how you felt about math at those times, and how you feel about math today. o The goal of this prompt was to learn about the student’s experiences with math in the past as well as provide a way for the student to express prior feelings about math. ● Journal #2: Reflect on your experiences in math this past week. Tell me about your experiences in math this week. How are you feeling about math this week? o The goal of this prompt was to learn about what experiences stood out for the student that week. This prompt was intended to address any issues students may have or to see what aspects of the course the students choose to discuss. ● Journal #3: Tell me about something that happened in math class this week and how it made you feel. o This prompt was a more focused version of the previous week, intended to get students to write more about something specific that happened in math class, instead of general thoughts or feelings. ● Journal #4: Reflect on your experience in math this week. Tell me something that happened in math this week. What was that experience like... thoughts, feelings? o Once again, this prompt was intended to elicit students feelings regarding an experience in math class. 116 ● Journal #5: We have reflected on math class the last few weeks. Today I would like you to reflect on your experience in the math lab class. Tell me about your experience in the math lab class so far. Thoughts? Feelings? Comments? o As the previous weeks were focused specifically on learning how students were feeling about the math class, this prompt provided a way for the teacher to learn more about students experience in the math lab class (corequisite). It was also the goal to determine if there was evidence of students’ feelings of belonging. ● Journal #6: We have our first test coming up in a week and a half. Reflect on how you are feeling about the upcoming test. Why are you feeling this way? Provide examples. o Math tests seem to evoke strong feelings for students. This prompt provided a way to learn about how students were feeling about the upcoming test and support students through teacher feedback. It also provided a way to learn what aspects of class potentially supported their feelings regarding the upcoming test. ● Journal #7: How are you feeling about the school subject of math in general? Provide reasons why. Have you noticed any changes in the way you feel about the subject of math this semester? o This prompt was intended to see if there was evidence of a change in students’ feelings regarding math in contrast to their initial journal entry regarding their prior math experiences. ● Journal #8: Today I would like you to reflect on your test. How are you feeling about your test? What are the study habits that worked well for you to prepare for the test? What could you do moving forward to improve study habits as you prepare for the next test? 117 o There was a wide range of test scores from the students in the corequisite course. This prompt provided a way to express how they were feeling about the test, as well as reflect on how to improve or reflect on what they felt was working well for them. ● Journal #9: Free write... tell me something that is going on with you, could be about math, could be about something else. o At this point in the semester the students had reflected a lot on their experience in math and there was some sense this was getting tiring. This prompt provided a way for the teacher to learn more about the student, potentially on a personal level, and provide another way to connect and empathize with the student. ● Journal #10: We have our second test next week Thursday. Reflect on how you are feeling about the upcoming test. Why are you feeling this way? Provide examples. o Once again, students typically have strong feelings about tests, especially now that this was the second test for students. In addition to providing a way to support the student through feedback, this entry also provided a way for the students to communicate if additional math support was needed. ● Journal #11: Tell me about your experience writing in a journal this semester. What was it like writing and receiving feedback from your instructor through the journal? Would you recommend the journal for future math students in the math lab? Why or why not? o This prompt provided a way for students to communicate their experience with writing in a journal and receiving feedback. ● Journal #12: Describe your experience in the math lab class this semester. Reflect on the beginning. middle, and end of the semester. What did you like or dislike about the math 118 lab class? Would you recommend the course to other students? Have your feelings about math changed at all this semester or stayed the same? o This prompt was used as the “final exam” for the corequisite course. It was a way for the teacher to learn about the experiences of students in the corequisite course. 119 CHAPTER 4: HOW TO IMPLEMENT A STUDENT REFLECTIVE JOURNAL AND PROVIDE WRITTEN EMPATHETIC FEEDBACK IN A COREQUISITE MATH COURSE Introduction Through teaching developmental math courses for almost ten years, I encountered many students who described hardships in their past math experiences. Over the years, I developed assumptions that students placed into developmental math typically do not like the subject, have struggled with math in their prior schooling, or have had negative experiences connected to math. In part, this view contributed to a feeling that students in developmental math classes lack a sense of belonging to academic mathematics. And in fact, my anecdotal belief is backed up by research as many students placed into developmental mathematics feel they do not belong within the math class (Silva & White, 2013). I am a math instructor at a private university in Michigan. During Fall 2021, I was given the opportunity to teach a pilot section of a corequisite math course. Students were enrolled in a college level math course, Math120 College Math, paired with a corequisite math support class. A corequisite course is an alternative to a traditional developmental math class. Corequisites are implemented and structured in various ways (Dana Center, 2018). The corequisite I taught was structured using a blended model (Childers et al., 2021). This design has students who are identified as needing remediation enroll in a traditional gateway math course along with other students who are not identified as needing remediation. In addition, the students identified as needing remediation also enroll in a support course during the same semester (Childers et al.). Prior to the start of the semester, I participated in a webinar training titled “Corequisite Solutions” provided through Almy Education. As I prepared to teach the corequisite, I reflected on the curriculum for the course. My anecdotal evidence, that students placed into 120 developmental math have faced hardships through their past math experiences, was a key influence in my reflections about the course. I decided to implement a weekly student reflective journal. A student weekly journal provided a way for students to share their feelings and experiences over the course of the semester. I hypothesized this would allow students to tell me about their prior difficulties with math. In turn, I would write empathetic feedback to convey understanding with a goal of fostering belongingness in the math classroom. To provide support for the importance of my endeavor, I looked to the research literature. Research has shown that teacher care is way to foster belongingness in the classroom (Solomon et al., 1996; Kirby & Thomas, 2022; Kiefer et al., 2015; Freeman et al., 2007; Booker & Lim, 2018). In addition, teacher empathy (Cornelius-White, 2007) and a student’s sense of belonging (Osterman, 2000) have both been identified as important for positive student outcomes. For example, belongingness has been connected to the development of certain psychological processes crucial for student success, attitudes (academic, social, and personal), motivation, participation, engagement, and achievement (Osterman, 2000, p. 327). Prior research also indicates that teacher empathy positively correlates with student outcomes such as student participation, critical thinking, and achievement in math (Cornelius-White, 2007). This article is written with the practitioner in mind. Specifically, this article is intended for math teachers, in particular those teaching a corequisite math course with undergraduate freshman math students. Teachers in other disciplines or with other student populations could also use this article and adapt for individual needs. In the following sections, I will share logistics on how I implemented a weekly student reflective journal during the Fall 2021 semester in my corequisite support class. Next, I will provide background literature on empathy that guided my written empathetic feedback as well as how I identified belongingness in student 121 responses to my feedback. In addition, I will share findings from my research to provide examples of student statements that reflect belongingness in response to my written empathetic feedback. These examples provide evidence for the use of written teacher empathetic feedback to foster belongingness in the corequisite math classroom. Finally, I will offer strategies on how to provide written teacher empathetic feedback along with actual examples from student journal entries and my written feedback. These strategies for providing written empathetic feedback are informed through both my own teaching experience as well as findings from my research on the ways a teacher utilizes empathetic feedback with the goal of fostering belongingness in the math classroom. Logistics I will start by describing how I setup a student weekly reflective journal in my corequisite support course during the Fall 2021 semester. • Each student created their own Google Doc and shared it with me o Students set the Google Doc with editing rights for me • Students named the Google Doc using their first and last name (Ex. Jasmine Smith’s Math Journal) • Students wrote the date and the journal prompt for each journal entry • I picked a font color (blue) to use for all of my feedback During the Fall 2021 semester, there were 8 students enrolled in the corequisite course. Over the course of the 15 week semester there were twelve journal prompts that the students responded to. Students wrote in their journal once a week, unless there was an assessment scheduled in the math class. Each week during class time students spent about 20 minutes total reading, writing, and responding in their journal. There was about 10 minutes allotted to write a 122 response to the journal prompt and about 10 minutes allotted to reading and responding to the feedback I provided. I wrote my own journal prompts with a focus on eliciting student feelings as this is an important aspect to be able to provide an empathetic written response. For the initial journal prompt, at the beginning of the semester, students wrote their own “Math Story” regarding past feelings and experiences in elementary through high school. For the rest of the semester, I wrote journal prompts with a focus on learning about student feelings and experiences. I repeated some of the journal prompts a couple times over the course of the semester. Here are a few journal prompts that I used: o “Tell me about something that happened in math class this week and how it made you feel.” o “We have our first test coming up in a week and a half. Reflect on how you are feeling about the upcoming test. Why are you feeling this way? Provide examples.” o “We have reflected on math class the last few weeks. Today I would like you to reflect on your experience in the math lab class. Tell me about your experience in the math lab class so far. Thoughts? Feelings? Comments?” o “How are you feeling about the school subject of math in general? Provide reasons why. Have you noticed any changes in the way you feel about the subject of math this semester?” I provided written feedback to student journal entries each week. I aimed to offer feedback that portrayed an emotional (empathetic concern) and cognitive (perspective taking) response (Warren, 2018). I read through each student journal entry, and I reflected on how I 123 could relate to the student through the feelings and experiences they described. I thought about what experiences I might share from my own life that were similar to the experiences the student described. In the next section, I will describe the principles that guided my written empathetic feedback each week as well as how I identified aspects of belongingness in student responses to my feedback. Guiding Principles of Teacher Empathy and Aspects of Belongingness My practice of providing written empathetic feedback was guided by conceptualizations of empathy from the literature. I used Warren (2014, 2018) and Meyers et al. (2019) conceptualizations of empathy as a foundation for my written feedback each week. First, Warren (2018) stated that empathy is defined by scholars as emotional (empathetic concern) and cognitive (perspective taking). Next, Meyers et al. (2019) defined teacher empathy as, “the degree to which an instructor works to deeply understand students personal and social situations, to feel care and concern in response to students’ positive and negative emotions, and to respond compassionately without losing the focus on student learning” (Meyers et al., 2019, p. 160). As I provided written feedback to students, I thought about how Warren (2014) described perspective taking as imagining another. From the teacher perspective, I thought about what the student was thinking or feeling in the moment they described in their journal. The weekly student journal entries helped me to develop an understanding of students’ personal and social circumstances, which is a crucial component of empathy according to Meyers et al. (2019). Also, guiding my written empathetic feedback were the defining attributes of empathy, borrowed from research in the field of nursing. These defining attributes of empathy are defined by Wiseman (1996) as: “see the world as others see it, non-judgmental, understanding another’s feelings, communicate the understanding” (p. 1165). As I wrote feedback to students each week, 124 I thought through the attributes and asked myself if my feedback aligned. One way I provided context and reasoning for understanding a student’s feelings or experiences was by writing about a similar experience. Research in psychology found a positive correlation between empathy and previous similar experiences. They described that in order to truly empathize with another, you need to have had a similar experience and this similar experience can occur at different levels. Therefore, the empathizer does not have to experience the exact same experience as another. Instead, “the other’s experience can be generalized to a level at which it resembles something the empathizer has previously experienced and can thereby be felt and understood” (Eklund et al., 2009, p.68). Similarly, Meyers et al. (2019) explained that empathy typically entails feeling the same emotions of another, but with teacher empathy it involves feeling comparable emotions. Over the course of the semester, I collected my written feedback and student responses to my feedback to learn more about the effects my empathetic feedback might have on students’ sense of belonging in the math course. I used Good et al. (2012) factors of math sense of belonging to recognize aspects of belongingness in student responses to my feedback. Good et al. (2012) conceptualized math sense of belonging as, “one’s personal feelings of membership and acceptance in an academic community in which positive affect, trust levels, and willingness to engage remain high” (p. 702). Thus, Good’s et al. (2012) five factors of belongingness are: Membership, Acceptance, Affect, Trust, and Desire to Fade. In the next section, I will share what I learned regarding how students responded to different types of my empathetic feedback, and aspects of belongingness that surfaced in those responses. Findings on Student Belongingness After analyzing students’ journal responses to my empathetic feedback, I discovered 125 patterns in how aspects of belongingness were evident in students' responses based on the type of empathetic feedback I offered. First, student responses to similar experiences through my personal and academic stories provided examples that reflect a student’s sense of membership and acceptance as well eliciting positive feelings (Good et al., 2012). For example, one student wrote in her journal, “The first week of school was hard for me because I didn't know how to do anything and I felt so behind.” Below I share my written response to this student. I provided written feedback by restating the student’s experience, sharing an academic story from my past, and providing an emotional response. I wrote: I know the stress and worry [emotional response] that can come with feeling behind the first week of school [restating-perspective taking]. When I started my master’s program, the first math class I took was really difficult. It seemed the other students in the class understood what was going on, but I felt very behind. As the semester went on, I had breakthroughs in my learning and I felt so accomplished in the end for learning something that was really difficult for me. But, during the semester I can remember the feeling of not being sure if I could do it or if I would make it through the class [similar experience-my academic story]. The student responded to this feedback writing, “It feels nice to know that we both had hardships with math but we continue to get better each day.” This student seemed to recognize that we both had hardships in math and despite this we both have pushed forward and improved. This suggests an aspect of belonging through membership (Good et al., 2012) as the student described connecting or relating to me, her teacher. Next, a student wrote in her journal about a math experience in elementary school. She wrote, “I’ve also had a bad experience in elementary. I asked my teacher one question and all the 126 kids laughed at me. I felt so small in the room.” Below I share my written response to this student. I provided written feedback by restating the student’s experience, sharing a personal story from my past, and providing an emotional response. I wrote back to this student stating: I am sorry to hear about your experience in elementary school where other students laughed after you asked a question [restating-perspective taking]; I’ve had experiences where I’ve felt small [emotional response] as well through classmates’ reactions [restating-perspective taking]. I remember in 5th grade I asked my locker partner if she wanted to trade school pictures with me and she said, why would I want to do that? That definitely made me feel small and I can still remember that feeling today [similar experience-my personal story]. In response to this feedback from me the student wrote: After reading your response it made me feel better about myself. Especially after I read about your experience. It made me realize that I’m really not the only one who struggles with this problem. I would also like to say thank you. Thank you for sharing your experience with me. You don’t know this but it actually brought me a little comfort. It seems that when this student read my personal story it made her realize that she was not the one with this type of experience in her past. She recognized she is not the only one and this reflects acceptance, an aspect of belongingness (Good et al., 2012). In addition, it seems that reading my personal story brought her some comfort. Positive feelings, such as comfort, reflect an aspect of belonging through positive affect (Good et al., 2012). On the other hand, an aspect of belonging through trust (Good et al., 2012) was recognized in student responses to instances where I acknowledged the student through their understanding of math concepts, participation, work ethic, confidence, or feelings. Trust was 127 recognized through student statements that I had faith in their potential or that I was there to help them learn. For example, one student wrote in their journal, “I feel like I’m ready to take on the upcoming math test even though I feel like I have a lot of work to cover before I can say I’m ready. I’m pretty confident ill do well.” Below I share my written response to this student. I provided written feedback by restating the student’s experience and by acknowledging the student’s understanding of math concepts and participation. In response to this student’s journal entry, I wrote: I can see you will be ready to take the test next week [restating-perspective taking]. You have been an active participant [acknowledging the student-participation], shown a desire to understand topics, and you take ownership of your thinking and provide us with new ways of understanding through your perspective [acknowledging the student- understanding math concepts]. In response to this feedback the student wrote: Thank you for your feedback. What you said makes me feel confident in myself and my abilities. Now I feel confident enough to take on the test. I just realized how I was thinking of the negatives only and forgetting to also look at the positive side including the time and effort I put in to understand the topics. This student response suggests that my feedback provided a sense of confidence in his abilities, and he was assured that he was prepared to take the test. This suggests that the student recognized that I had faith in his potential to succeed on the upcoming test and that the feedback helped him to feel confident in his abilities. Recognizing that I had faith in his potential and his confidence in his abilities reflect the belongingness factor trust (Good et al., 2012). In summary, my findings suggest that student responses to written empathetic feedback 128 reflected different aspects of belongingness depending on the type of feedback that was provided. First, student responses to similar experiences through my personal and academic stories provided examples that reflect aspects of belongingness through a student’s sense of membership and acceptance as well eliciting positive feelings (Good et al., 2012). Next, an aspect of belonging through trust (Good et al., 2012), was recognized in student responses to instances where I acknowledged the student through their understanding of math concepts, participation, work ethic, confidence, or feelings. These findings are important as they suggest that these types of empathetic feedback have the potential to foster aspects of students’ feelings of belonging in the math classroom. In the next section, I will provide specifics on how to implement written empathetic feedback through a student weekly journal. These guidelines on how to provide empathetic feedback are informed through my own experience implementing this in a corequisite support class that I taught during the Fall 2021 semester as well as findings from my research on the ways I utilized empathetic feedback with the goal of fostering belongingness in a math corequisite course. How to Provide Written Empathetic Feedback I suggest providing written feedback to student journal entries each week. Aim to provide written feedback that portrays an emotional (empathetic concern) and cognitive (perspective taking) response (Warren, 2018). Then, to provide context and reasoning for your understanding you can share a personal or academic story, or you can acknowledge the student through their understanding of math concepts, participation, work ethic, confidence, or feelings. In the following subsections, I will provide suggestions for writing an emotional and cognitive response. Then, I will provide details on how to portray context and reasoning for your understanding of student emotions through your personal or academic stories or through 129 acknowledging the student. Emotional and Cognitive Response First, read through the student journal entry and look for parts of the journal entry where the student talks about emotions. This will help to point you to an opportunity to respond with empathy through an emotional response. There are various phrases to use to begin an empathetic written response. Table 20 provides some common phrases along with examples of actual feedback I wrote in response to student journal entries. These examples are provided to give instructors a starting point to respond empathetically. Table 20 Phrases for Written Empathetic Feedback through an Emotional Response Phrase Examples I understand • I can understand feeling insecure about getting extra help with math. • I understand how not liking math makes it harder to engage/motivate. • I understand those feeling well, being overwhelmed with balancing work, school, family, athletics is not an easy task. • I understand feeling nervous about tests. • I understand feeling lost, confused, and behind. I can see • I can see your confidence grow every class. • I can see where those feelings can make you feel unprepared. • I can see you enjoying math this semester. • I can see how those fears of being called on and not feeling smart enough would make you decide that you didn’t like math, both of those are pretty strong reasons for feeling that way. I can relate • I can relate to feeling nervous about a test. • I can relate to that feeling of accomplishment when you figure out the right answer. • I can relate to those fears of being called on and not feeling smart enough. Next, look for experiences the student is describing as this will help you to provide a cognitive response through perspective taking. To respond to the student’s experience, I suggest 130 to first restate the experience the student wrote about in their journal. Restating the student’s experience helps to provide a response that includes perspective taking as it conveys understanding. Table 21 provides examples of “restating” through my actual written feedback along with the actual student journal entry. These examples are provided to help instructors think through what they might write in response to common experiences students may write about in their journal. Table 21 Examples of Student Journal Entries and Teacher Feedback with Restating Student Journal Entry Teacher Written Feedback with Restating School is a bit overwhelming a I understand those feeling well, being overwhelmed with bit. Its hard to manage time and balancing work, school, family, athletics is not an easy work makes you sleep late and it task. Especially when you are tired, then everything gets super hard to wake up in the seems all the more difficult. morning. Soccer on the other side too. I am trying my best though. Maybe i just had a hard 2 weeks. I’m still struggling on the Quadratics are one of the toughest functions, so that quadratic functions because it's a makes sense you are feeling confused. There are so many little confusing to me. pieces to quadratics and that adds a lot of formulas to learn and understand. I am feeling very nervous because I can relate to feeling nervous about a test. I know what I feel as though I have everything you mean regarding that fear that you won’t know what to down packed but the moment the do when the time comes to take the test. All those test comes I feel unsure about it. feelings are normal. At first I didn’t like the feeling of I can understand feeling insecure about getting extra help being apart of a math lab, because with math. I too know acknowledging the need for help it made me a little insecure about in any situation can bring up feelings of insecurity. receiving extra help. 131 Table 21 (cont’d) This past week in math had me I have that experience too, when I think I understand how confused. I can't lie. When we to do something, and then when I actually go to do it, I get were going over things during stuck somewhere. class I was understanding it just fine, But then I would go work on it by myself and think that I got through it just fine and then I somehow missed a step. I feel like I can ask any questions I understand how important it is to be in a classroom and not feel judged or environment where you are able to ask questions freely embarrassed. without feeling judged or embarrassed. I too have appreciated classes I’ve taken and teachers I’ve had that create a classroom environment that makes me feel safe to ask questions. Teacher Stories and Acknowledging the Student To provide additional context and reasoning for your statements of understanding, I have a few options to suggest. One way to provide context and reasoning for understanding student feelings or experiences is to write about a similar experience from your life. You can write about personal or academic stories from your past or current life. Table 22 provides examples of my personal or academic stories along with the student journal entry that I responded to. Once again, these examples are provided to help instructors get started with responding to student journal entries, as writing empathetic feedback is not an easy task. Table 22 Examples of Student Journal Entries and Teacher Feedback with Personal or Academic Stories Student Journal Entry Teacher Written Feedback 132 Table 22 (cont’d) I’ve also had a bad experience in I am sorry to hear about your experience in elementary elementary. I asked my teacher school where other students laughed after you asked a one question and all the kids question; I’ve had experiences where I’ve felt small as laughed at me. I felt so small in well through classmates reactions. I remember in 5th the room. grade I asked my locker partner if she wanted to trade school pictures with me and she said, why would I want to do that? That definitely made me feel small and I can still remember that feeling today. I started to struggle a bit because I understand that pressure to remember steps, equations, I find myself to not be the best formulas and how that can really be amplified when you with remembering a lot of the are taking a test. I’ve never felt that test taking has been a steps or equations, It was fine for strong suit for me, it is always something I had to work me to get assignments and other hard at and sometimes didn’t get the results I wanted. things done because I was able to take my time and get the help I needed but as soon as it came to test times I had the biggest issues. A classmate and I worked on it I also can see that working with others in class can be together and a lot of it made sense helpful. For many of the math classes I took in college I to me and i had very few question had a couple “math friends” that we would work on things with the math portion of it together. It was great to have someone to get help, especially when I didn’t know where to start. The people at my group gets the I understand the feeling of being in a group where concept easily and i be in total everyone else seems to understand and you are like, how shock cause its like how do you do you know this?! I’ve felt that way in math classes in know how to do that the past. My first math class at Grand Valley for my masters degree was really tough. I had another student in class that I would work with on assignments, and he was very helpful but he always had more understanding than me. As the semester progresses you might feel the need to shift from sharing personal or academic stories to writing about experiences occurring in the class. I found that another way to respond empathically is to acknowledge the student through their understanding of math concepts, participation, work ethic, confidence, or feelings. Table 23 provides examples of my actual written feedback, along with the student journal entry. These examples are provided to 133 offer ideas for ways to respond to common student journal entries. Table 23 Examples of Student Journal Entries and Teacher Feedback with Acknowledging the Student Student Journal Entry Teacher Written Feedback I felt very good before the test. I could sense you had good energy going into the test. You were there early, studying and you have worked hard on assignments and to truly understand math topics. All the things to set yourself up for success. My table group is really nice and I have noticed your group seems to really work well we all collectively help each other together! I’ve noticed a good balance with everyone out with problems when we don’t helping each other out, and good discussions too! It is so understand them. nice to have others to work with in math. When I do understand something Also, I’ve noticed your understanding with exponential like exponential growth and functions! That is a great feeling when you understand decay, that makes me feel good how something works. inside because I like understanding things we are learning about. Honestly for my test im very I could feel your disappointment before I even knew your disappointed, i went through this score on the test, I felt it as you left class after taking the test so confidently thinking that i test. I could tell by your facial expression and energy. I was going to be able to pass and i know those feelings of disappointment too, not doing as didnt, i felt like i blanked out on well as you hoped on a test. Especially when it is the test which made it harder for something that you put time into and worked hard. I often me cause all i thought about was feel those “could of” studied more, worked harder, etc. trying to be able to pass the test, but a lot of times I am just being too hard on myself. Not but i take full accountability for that I don’t have room for improvement but in the my study habits, i could’ve moment I did the best I could with the time, energy, and studied harder and more resources I had. effectively I really have enjoyed the lab I can see you enjoy the math lab class through your active class. participation and desire to develop a strong understanding of the concepts. Then the math lab class also helps I can see you use your math lab class time very well. You out a lot because it gives you time are always focused on your work and you I can tell you you could focus only on math really want to gain a solid understanding of the topics. homeworks and assignments. 134 Conclusion In conclusion, writing empathetic feedback to students through a weekly reflective journal is not an easy task. Empathy is hard work and research has identified that people try to avoid empathy due to the effort it requires (Cameron et al., 2019). However, my analysis of students’ responses to my empathetic feedback suggests that writing empathetic feedback to students through a weekly reflective journal is promising for supporting students’ sense of belonging in mathematics courses. This is especially important as many students who are placed into developmental mathematics sense they do not belong within the math classroom (Silva & White, 2013). In turn, when students do not feel they belong, this poses potential negative implications for student outcomes including persistence in completing developmental math courses (Bryk et al., 2013). Also, historically, developmental math courses are a common point of exit from college for students (Royer & Baker, 2018). Consequently, finding ways to attend to a student’s sense of belonging, especially in the developmental math classroom is imperative. Through my experience, as the semester progressed, writing feedback got easier; however, it still took time and energy. Since the corequisite course did not require much additional grading, I thought of my time spent responding to student journal entries as time I would have spent grading if I was teaching another math class. In a traditional math class with thirty or more students, I’m not sure that implementing a weekly student journal with empathetic feedback would be feasible. However, a corequisite course, with typically a smaller class size (less than 15 students), I argue is the ideal scenario for implementing a student weekly reflective journal. Through reading student journal entries each week, I felt more connected to my students and able to respond to their learning needs on a personal level. It felt like each student and I had 135 a secret way to communicate. I knew things about them, and they knew things about me. Even though we did not typically talk about things written in the journal, I felt we had a deep level of understanding for each other. For example, in an end of semester interview one student talked about his experience writing in a weekly journal over the course of the semester. He said: Basically, just putting all the information on the journal, and she looks at it, and she basically knows what you're going through. It made me feel more comfortable, even if I was to ask a question, or even I was to say the wrong thing in the class, like give the wrong answer, she would understand that, okay, he's probably, like he says in the journal, he's probably going through mental tiredness, or he's actually tired. I feel like it made me even more comfortable to talk basically because I knew she knew what situation I was in mentally. This statement reflects a strong level of communication and understanding between the student and I through the weekly journal. Another student, when asked about her experience writing in her journal through the semester stated, I connected to my Professor, Amy, kind of on a different level than I can in front of other people. It's almost like a diary. You get to write this little diary and this journal and tell her exactly how you feel without any bias on her end and stuff like that. This statement reflects that the journal provided communication between the student and I that would not be possible through only in class interactions. Lastly, when asked about her experience writing in a weekly journal over the course of the semester another student wrote: Well to be honest I wasn’t really expecting to have a little journal type of thing in college. But I thought it was cool that you had us write in our journals about how we feel about 136 class and the math homework we get. Especially about the last tests. Writing about it actually got some tension off of my chest. It was helpful in many ways. I know I say this a lot but your feedback actually helped me feel more comfortable and confident in myself. If I were you maybe I would have other classes do it but I know most people would think it’s like a waste of time and that it’s dumb or something. But I like it. I think you should have other math labs do it. It’s fun and you get to just talk about how you feel. This statement reflects that the weekly journal, along with my written feedback provided comfort, confidence, and ease for this student. She was skeptical initially about writing in a journal; however, this statement reflects that in the end the experience was worthwhile, and she recommends it for future students. For me, these student statements, along with my experience teaching the corequisite course provide adequate reasoning for continuing to implement and learn more about the practice of providing written empathetic feedback. I would also urge other instructors to implement a weekly reflective journal with students in corequisite math courses and share their experiences as well. This work is important, because implementing a weekly student reflective journal with written empathetic feedback provides the potential to foster belongingness in the developmental math classroom. 137 REFERENCES Booker, K. C., & Lim, J. H. (2018). Belongingness and pedagogy: Engaging African American girls in middle school mathematics. Youth & Society, 50(8), 1037-1055. Bryk, A. S., Yeager, D. S., Hausman, H., Muhich, J., Dolle, J. R., Grunow, A., & Gomez, L. (2013, June). Improvement research carried out through networked communities: Accelerating learning about practices that support more productive student mindsets. In A White Paper prepared for the White House meeting on “Excellence in Education: The Importance of Academic Mindsets. Cameron, C. D., Hutcherson, C. A., Ferguson, A. M., Scheffer, J. A., Hadjiandreou, E., & Inzlicht, M. (2019). Empathy is hard work: People choose to avoid empathy because of its cognitive costs. Journal of Experimental Psychology: General, 148(6), 962. Childers, A. B., Lu, L., Hairston, J., & Squires, T. (2021). Impact and Effects of Co-Requisite Mathematics Remediation. Primus, 31(2), 167-183. Cornelius-White, J. (2007). Learner-centered teacher-student relationships are effective: A meta- analysis. Review of Educational Research, 77(1), 113-143. Dana Center. (2018). Co-requisite Courses: Narrowing the Gap between Instruction and Supports. Dana Center Math Pathways. Eklund, J., Andersson-Straberg, T. & Hansen, E. M. (2009). “I've also experienced loss and fear”: Effects of prior similar experience on empathy. Scandinavian Journal of Psychology, 50(1), 65-69. Freeman, T. M., Anderman, L. H., & Jensen, J. M. (2007). Sense of belonging in college freshmen at the classroom and campus levels. The Journal of Experimental Education, 75(3), 203-220. Good, C., Rattan, A., & Dweck, C. S. (2012). Why do women opt out? Sense of belonging and women's representation in mathematics. Journal of Personality and Social Psychology, 102(4), 700. Kiefer, S. M., Alley, K. M., & Ellerbrock, C. R. (2015). Teacher and peer support for young adolescents’ motivation, engagement, and school belonging. RMLE Online, 38(8), 1-18. Kirby, L. A., & Thomas, C. L. (2022). High-impact teaching practices foster a greater sense of belonging in the college classroom. Journal of Further and Higher Education, 46(3), 368-381. Meyers, S., Rowell, K., Wells, M., & Smith, B. C. (2019). Teacher empathy: A model of empathy for teaching for student success. College Teaching, 67(3), 160-168. 138 Osterman, K. F. (2000). Students' need for belonging in the school community. Review of Educational Research, 70(3), 323-367. Royer, D. W., & Baker, R. D. (2018). Student success in developmental math education: Connecting the content at Ivy Tech Community College. New Directions for Community Colleges, 2018(182), 31-38. Silva, E., & White, T. (2013). Pathways to Improvement: Using Psychological Strategies to Help College Students Master Developmental Math. Carnegie Foundation for the Advancement of Teaching. Solomon, D., Battistich, V., Kim, D. I., & Watson, M. (1996). Teacher practices associated with students' sense of the classroom as a community. Social Psychology of Education, 1(3), 235-267. Warren, C. A. (2014). Towards a pedagogy for the application of empathy in culturally diverse classrooms. The Urban Review, 46(3), 395-419. Warren, C. A. (2018). Empathy, teacher dispositions, and preparation for culturally responsive pedagogy. Journal of Teacher Education, 69(2), 169-183. Wiseman, T. (1996). A concept analysis of empathy. Journal of Advanced Nursing, 23(6), 1162- 1167. 139