The purpose of this study is to gather and describe case studies of 'struggling' teenage boys, focusing on their identities, which are mediated by the discursive practices associated with school mathematics and other activities. The sociocultural model of identity unites an individual’s psychodynamic continuity with the roles and positions that emerge from his/her social interactions. The setting for the investigation is a small single-sex, non-traditional secondary school, in which the sample is seven boys, ages sixteen to eighteen, who have lost interest in the academic mainstream. Qualitative data were collected on individual boys, and then matched in a table to the theoretical framework. The study raised five issues about identity, struggling teenage boys, and school mathematics. To negotiate the dialectic of opposing identity norms, struggling teenage boys employed identities as expressive tools that held desirable positions for them in school mathematics. In the organization of multiple identities, salience depended upon the intrinsic and extrinsic gratification associated with knowledge of mathematics. Positive mathematical identities clustered with compatible social identities that were also supported by these rewards. The sociohistorical availability of identities increased in nontraditional mathematics courses that provided the boys with opportunities to enact positive roles. Many of the boys communicated positive attitudes towards school mathematics in relation to their future career goals. Though they may have struggled, they expected to achieve conventional success in the adult world. The issue of identity and emotions was illustrated by the shame and mistrust that accompanied the loss of a former identity such as a “gifted” level in school mathematics. For some struggling teenage boys, mistrustfulness was evident in their discussions about money. They expressed an affinity for simple arithmetic, which they could easily master with repetitive practice. Implications for teaching include cultivating future-oriented identities, incorporating 'money themes, and offering customized courses.

Students’ mathematics identity has become a more prominent concept in the research literature (Jackson & Wilson, 2012). The experiences of African Americans are still underreported, with African American elementary students receiving the least attention. This dissertation uses a case study method to explore two learners’ experiences. The purpose of this qualitative study was to explore African American third grade students’ classroom interactions with mathematics in order to better understand factors that promote positive mathematics identities. This research study explored the mathematics classroom influences on three third grade African American learners’ mathematics identities in a K-8 school in a north central Midwestern city in the United States. The school was classified as 100% free and reduced lunch and served approximately 900 students, with the vast majority of students classified as African American. The three student participants and their teacher were all African American. The student participants wore glasses that video recorded their perspectives. A stationary camera was also used to capture the wider classroom environment. Each student participant completed three interviews (Seidman, 2013). The teacher participant completed one interview. Additionally, the student participants completed a mathematics interest questionnaire. Findings showed the importance of an explicit focus on the Standards for Mathematical Practice, a growth mindset, and positioning for promoting positive mathematics identities. In one case study, Janae’s experiences in lessons about fractions highlight the relevance of the Standards for Mathematical Practice, specifically attending to precision and making sense of and persevering in solving problems. In both the classroom and in interviews, she shows the importance of making sense of problems and persevering in solving them and of attending to precision. In the second manuscript, I explore Jaane and Kayla’s different experiences. Janae was positioned more positively and faces limited resistance in maintaining a positive mathematics identity. Kayla, on the other hand, regularly rejected and renegotiated the positions offered to her as she aimed for success and a positive mathematics identity. Kayla’s growth mindset and negotiation of positions offered to her in the classroom were critical factors in how she maintained a positive mathematics identity.

Girls' relationship with mathematics has been an extensive and contested area of investigation during the last 40 years, mainly in developed countries. This contrasts with the small amount of research from developing countries, where the topic has been largely neglected but may present different challenges. In Chile, such lack of empirical evidence is surprising, particularly because of several national reports describing attainment differences in the national assessment test (SIMCE), where girls are consistently outperformed by boys. Currently, there are no studies which systematically explore gender differences in attainment in Chile. In addition, only a small number of studies have tried to explain why these differences, as well as others in engagement, attitudes and enrolment in mathematics, arise in this country. The main goal of this thesis is to critically examine these issues by investigating how girls relate to mathematics during early adolescence in Chile, and how such relationships are influenced/mediated by certain social variables (e.g. social class, classroom cultures and peer group identities).In order to do this, this thesis has adopted a mixed methods approach, thus linking analysis and results from studies that use both quantitative and qualitative methodologies. Firstly, I investigate the size and distribution of the gender attainment gap in Mathematics in Chile using a Multilevel approach to analyse data from the national census of educational quality (SIMCE). Here, I analyse the naturalization of gender differences based on results, and conclude that differences found in attainment between boys and girls are small and dependent on socioeconomic status. I then explore how girls' subjective relationships with mathematics are constructed, and how different social influences mediate this process. Using the concept of Mathematical Identities [MIs] as a main tool I explore the influence of social variables on the construction of girls' MIs in Chilean classrooms and I also consider how teaching practices and peer social relations in the classroom mediate these identities. A key finding here is the positive relationship between students' perceptions of their teaching as student-centred and more positive MI, which is in fact the same for girls and boys. A second key finding is that both representational and enacted aspects of girls' MI are mediated by their relationship with peers and peer groups. This mediation process can be described as a negotiation of different forms of belonging to social groups, which involved also the negotiation of different MIs inside the classroom. The main conclusion of this thesis is that in order to understand the role of gender in mediating girls' relationships with mathematics, we need to acknowledge the profoundly situated nature of this relationship in the cultural practices of the classroom, including mathematical practices, but also peer group practices. This argues against discourses that essentialise and naturalize 'gendered relationships with mathematics' which appear to be pre-dominant in the collation of national assessment data (like SIMCE) where categories such as gender, class, ethnicity etc. are viewed as causal or explanatory rather than produced 'in practice'.

This project used narrative inquiry to examine adolescent experiences that contributed to the development of positive mathematics identities in successful African Americans. Ten African Americans, who had worked in a STEM-related occupation for at least two years, were asked to reflect on in- and out-of-school experiences with mathematics during their middle and high school years. Data collection included individual interviews and one focus group discussion. A combination of internal and external factors emerged as contributors to participants’ adolescent mathematics identities. Internal factors included early career interest, finding enjoyment in the challenges associated with learning mathematics, or facing setbacks they were determined to overcome. External influences included parents/family members, teachers/school staff, and peers who were influential agents in participants’ mathematics socialization. Participants’ stories revealed that mathematics identities were developed in several communities of practice—the mathematics classroom, after-school (or school-affiliated) programs, summer programs, and during unstructured free time. The findings offer three possible applications to practice: 1) Continue developing school-based and out-of-school programs aimed at exposing African American adolescents to STEM and allowing them to apply the knowledge gained in the classrooms in the real world; 2) Increase efforts to educate African American parents about the variety of occupations related to STEM and the foundational knowledge needed to gain access to these occupations; and 3) Continue efforts to recruit African American secondary teachers for STEM-related courses.

Despite the effort of teacher education programs, early childhood, and elementary preservice teachers often fear mathematics, have high mathematics anxiety, hold negative self-perceptions in relation to mathematics, find mathematics irrelevant, and have low mathematics achievement. The aim of this study was to implement and investigate the influence of an identity exploration intervention on preservice teachers’ identities in mathematics during a required mathematics content course of a teacher education program to provide insight into the patterns of change in identity and motivation towards mathematics. Twenty-four preservice teachers focusing on either early childhood education or non-mathematics secondary education were included in this study from a college algebra course specifically designed for education majors. Data collection included surveys, identity-related worksheets, identity exploration tasks, reflective writing assignments, interviews, and observations. Data was analyzed using the Dynamics Systems Model of Role-Identity and the principles for promoting identity exploration (Kaplan, 2014). This model highlights the interaction between self-perceptions, beliefs, purposes and goals, and actions. Analysis led to identification of patterns of change in student role identities and themes across cases that highlight the differences in change between the early childhood participants and secondary education participants, the influence of initial identity, and the impact of perceived relevance on identity exploration. This study contributes to the understanding of identity exploration in a mathematical setting and discusses future directions of research in promotion of identity exploration in preservice teachers. / Math & Science Education

Many mathematics students experience dissonance between their sense of who they are and their perception of who they are expected to be in mathematics classrooms. Such students lack a sense of belonging while in mathematics class, believe that learning mathematics requires a natural ability they do not possess, experience classroom mathematical practices as being monotonous and devoid of meaning, or view mathematics as irrelevant to their present and future lives outside of the mathematics classroom. Together, these perceptions form students’ views of themselves in relation to the study of mathematics—their mathematics identities. However, whereas students’ mathematics identities are known to impact their academic motivation and achievement, the mathematics education literature lacks insight into how to promote positive mathematics identities in students. Flum and Kaplan (2006) identified the Eriksonian concept of exploration—the seeking out and processing of self-relevant information—as a key process in adaptive identity formation and one that may be harnessed as a motivational force in academic settings. The current study investigates the effects of a school-based program that is being implemented with the goal of promoting Algebra 2 students’ motivation and achievement by facilitating mathematics identity exploration. The data are based on pedagogical materials and student artifacts administered by three teachers as part of a classroom-based program that included reflective writing assignments that applied principles for promoting identity exploration around the curriculum. The research involves analyses of the data collected during this project undertaken in Algebra 2 classrooms in a suburban high school throughout one semester. Students were randomly assigned to either participate in the innovative pedagogical program or to one of two control groups. I found the mathematics identity exploration program to promote hints of exploration for some students but not others. Additionally, students who perceived the course as triggering mathematics identity exploration, whether assigned to the exploration program or to a control group, were found to have more adaptive motivational profiles at the end of the semester. The findings point to the benefits of identity exploration within the mathematics classroom to students’ mathematics identities and motivation in mathematics, and they provide directions for further research and the design of effective interventions that promote students’ identity exploration around the mathematics curriculum across student groups and contexts. / Teaching & Learning

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<p> </p> <p>Issues of social justice continue to permeate all aspects of life in the United States. Acknowledging recent calls for racial justice, as well as efforts to restrict what is taught in mathematics classrooms, researchers and practitioners are increasingly exploring the promises of teaching mathematics for social justice in secondary mathematics classrooms. This dissertation contributes to research about how a social justice mathematics course can be utilized in teacher education programs to support prospective mathematics teachers’ (PMTs’) development of their mathematics identities, as well as how PMTs translate social justice mathematics theory into</p> <p>practice with their secondary mathematics students. This research complexifies the role of primarily white mathematics teachers and teacher educators working toward teaching</p> <p>mathematics for social justice by foregrounding some of the ways in which social justice mathematics curricula and instruction may continue to center whiteness. </p> <p><br></p> <p>This dissertation includes three studies focused on the design and delivery of a social justice mathematics course offered to undergraduate students, as well as the learning outcomes</p> <p>for 11 PMTs enrolled in the first iteration. As such, each study is formatted for submission to a research journal and contains its own questions, methods, findings, discussion, and conclusion. </p> <p><br></p> <p>The first and second studies detail the experiences of PMTs in a social justice mathematics course. In the first study, I explored how engaging in such a course contributed to PMTs’ mathematics identities. Findings in this case study suggest that sustained engagement with social justice mathematics can contribute to PMTs’ conceptions of mathematics and encourage them to address issues of social justice in their mathematics classrooms. Building on this, three of the PMTs enrolled in the course and I engaged in a critical participatory action research study to investigate their experiences working toward teaching mathematics for social justice in their secondary mathematics field placements. Prior to engaging their students with social justice mathematics tasks, the PMTs focused on developing relationships and trust with students and also maintained a commitment to engaging students with dominant mathematics. </p> <p><br></p> <p>Informed by a finding in the first study (i.e., PMTs continued to view mathematics as objective and neutral), in the third study, I investigated the prominence of whiteness in the development and facilitation of the course. Using action research and critical whiteness studies, I detail areas in which I perpetuated whiteness, as well as areas in which I began to make progress.</p>