3. Electronic Theses and Dissertations (ETDs) - All submissions
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Item On identities of Euler type and partitions with initial repetitions(2024) Mugwangwavari, BeaullahIn this research, we explore partition functions related to identities of Euler type and partitions with initial repetitions. On identities of Euler type, we mainly focus on identities due to P. A. MacMahon, G. E. Andrews and M. V. Subbarao. We give new bijections for partition theorems due to MacMahon and Andrews and provide a generalization of Subbarao’s finitization theorem. For the original Euler’s identity which gave rise to identities of Euler type, Andrews and M. Merca found a new combinatorial interpretation for the total number of even parts in all partitions of n into distinct parts. We genaralize their result and establish more variations with connections to some of the work of S. Fu and D. Tang. By conjugating partitions into distinct parts, we obtain partitions without gaps. Andrews extended the notion of partitions without gaps to partitions with initial repetitions. We study partitions with initial repetitions and give several Legendre theorems. These theorems provide partition-theoretic interpretations of some well known q-series identities of Rogers-Ramanujan type. We further deduce parity formulas for partition functions associated with this class of partitions.Item The experiences and challenges of women teachers' lives.(2015-05-19) Nagan, SelmaThis study explores women teachers’ lives to understand their experiences of teaching in South Africa today. Accountability and a culture of performativity have to come to dominate schooling in South Africa. Since then, teachers have decreased discretion and autonomy over their work. This study examines the claim that educational reforms and initiatives have changed the nature of teachers’ work. This is a qualitative study drawing on autobiographies, journal entries and interviews. This study which was conducted with four women teachers from secondary schools, provides a commentary on their past experiences with the intention of exploring their identity formation, and how it frames the enactment of their personal and professional identities. The study analyses the ways in which women teachers experience the new mode of regulation which has changed the nature of professionalism and teacher identity. It examines the expansion of teachers’ roles and responsibilities and their negotiating a balance between work and family. The findings show that the women teachers bring into schools experiences gleaned from their personal history. A prominent feature in the narratives is the women teachers’ struggle to find a balance between the demands of home and school in the light of the new mode of teacher regulation. This thesis contributes to South African research on women teachers and their negotiation of the relationship between work and home.Item Preparing pre-service mathematics teachers to teach in multilingual classrooms : a community of practice perspective.(2013-10-01) Essien, Anthony AnietieThis study takes a particular look at mathematics teacher education communities of practice (CoPs) in order to provide rich descriptions of the CoPs and make claims about its relation/in relation to teacher preparation and particularly the preparation of preservice teachers for teaching mathematics in multilingual classrooms. The three dimensions of communities of practice proposed by Wenger (mutual engagement, shared repertoire and joint enterprise) were used in conjunction with Mortimer and Scott’s notion of meaning making as a dialogic process as a theoretical lens to gain an entry into the nature of communities of practice in pre-service mathematics teacher education classrooms. Data was collected through pre-observation interviews of 12 teacher educators at four Universities in one Province in South Africa in Phase One of the study. A methodological approach based on Wenger’s CoP theory and Mortimer and Scott’s dialogic process was developed and used to analyse classroom observation videos of four of these teacher educators’ classroom communities of practice in two universities in Phase Two of the study. Using the privileged practices in the CoPs as points of departure and how these practices shaped and were shaped by other dynamics in the CoPs, the findings emerging from the study indicate that within the multiply layers of teacher education, there is an overarching emphasis given to the acquisition of mathematical content. Nevertheless, the communicative approaches and patterns of discourse used by the different teacher educators opened up different possibilities as far as preparing preservice teachers for teaching (in multilingual classrooms) is concerned. Wenger’s community of practice theory has found applications in different spheres of life and in different organisational and educational settings. Its use to understand and describe mathematics pre-service classrooms is, however, still largely unexplored. A theoretical contribution that this study makes lies in the extension of Wenger’s CoP theory to include dialogic processes. A methodological contribution lies in the development of an organisational language (based on Wenger’s three dimensions of CoP) to characterise pre-service teacher education classrooms.Item The interactional negotiation of individual and collective identities among married couples.(2012-09-03) Ronge, AngelikaLiterature on identities in marriage has suggested that there is a tension between the interpretation of marriage as a unity between two partners, and the importance of each partner within the marriage maintaining his/her individuality. By drawing on data from seven semistructured qualitative interviews with married couples or couples involved in marriage-like relationships I examine some ways in which these boundaries between individual and collective identities and associated epistemic rights are drawn or become treated as blurred. Specifically, I use a conversation analytic approach to examine two sets of practices that reveal how this tension is made observable and is negotiated: 1) the use of personal and collective pronouns and 2) shifts in gaze direction. In contrast to previous research on this topic, I focus on the exploration of these phenomena in their moment-by-moment construction in talk-in-interaction. Based on my findings, I conclude that these practices serve to demonstrate the oriented-to ways in which marriage involves compromising one’s own individual identity or epistemic rights while becoming a part of a unit and show how and where this is done in interaction.Item Investigating constructions of masculinity in men's talk of male rape.(2010-05-28T10:18:39Z) Field, Shelley AnneThe research investigated how men perceive constructions of masculinity in the talk of male rape. Research on gender relations and masculinities is a growing area of interest. The topic of male rape however, remains underrepresented within this. Male rape draws on discourses of gender, trauma, sex, sexuality and violence. It further offers a controversial topic that participants could engage in to further make sense of the multitude of masculine identities that exist, and how these directly influence responses to gendered phenomena. It is therefore likely to elicit significant constructions of masculinities and hence was used as a vehicle to further add insight into the constructed nature of masculinities. This was achieved through the use of a group of thirteen men who were divided into three focus groups. Each focus group made use of a vignette and a semi-structured interview schedule. Through this method the masculine identities that arose in their talk on male rape were examined. Data were analysed using thematic content analysis in which a social constructionist perspective was applied. It was found that participants strongly adhered to a hegemonic masculine point of reference in discussions. The patriarchal nature of this masculine identity that is subordinating of both women and other masculine identities was consistently used in discussions, thus representing the relatively stable influence of hegemony in gendered relations. Subordinated masculinities emerged more subtly, illustrating a growing acceptance of multiple forms of masculine identities. The results were understood as largely representative of broader society that still elevates the constructed standards of hegemony in conceptualising masculinities. This study thus sheds light on the social constructionist nature evident in society that continually influences the connotations attached to gendered identities within it. The significance in considering the masculine influences in responding to male rape lies in the multiplicity of factors that each involves as these collectively shape society's continued gendered understanding in shaping reality. A topic such as male rape, that directly threatens constructed notions of masculinities, thus allows for a new understanding to emerge in its consideration of the masculine identities that arise in responding to this traumatic experience.