Yes / Considerations of rigour and relevance rarely acknowledge students, learning, or the textbooks many of the academic community use to frame education. Here we explore the construction of meaning around rigour and relevance in four leadership studies textbooks – the two most globally popular leadership textbooks and two recent additions to the field – to explore how these ideas are represented. We read the four texts narratively for structure, purpose, style, and application. We further embed the analysis by considering the cultural positioning of the textbook-as-genre within leadership studies as a field more generally. This exploration of the textbook raises critical questions about rigour, relevance and the relationship constructed between them. From this, we argue for a re-commitment to the genuine ‘text-book’ written to engage students in understanding leadership as a continuing conversation between practices, theories, and contexts, rather than as a repository of rigorous and/or relevant content that lays claim to represent an objective science of leadership studies.

The purpose of the study was to investigate the rigour and relevance of IS research; as researchers and practitioners are divided and living in a different world of aspiration m conducting research. This division is as a result of many reasons. The gap between researchers and practitioners has promulgated debate and argument among the two that has lasted for years. Many believed that IS research is effective and others opposed it. Others within or outside the discipline consider whether IS research output affects and impacts decision making in the industry. Meanwhile, the debate on rigour and relevance has lasted for decades but, in reality, the differences gap still persists, in spite of efforts by researchers. Their efforts and hard-work seem not to be very effective. This study seeks to determine whether practitioners meet their needs and expectations and whether they address them through the rigour and relevance of IS/academic research. It is also to determine whether this debate which has lingered over the years is worth it. The growing problems and needs in the practitioners' world call for an investigation into this rigour and relevance. There is an on-going criticism that IS research lacks rigour, relevance. effective communication and acceptance in the field as noted in the literature. The identified problem under investigation now is lack of rigour, relevance and other issues such as consistency, transparency, communication and inaccessibi lity in IS research. The population for the study comprised academic lecturers attending the South African Institute for Computer Scientists and Information Technologists (SAICSIT 2012) conference and North-West University IS and Computer Science (Mafikeng Campus) academics. The population was 90 lecturers/academics and the sample size of 73 answered the questionnaires. / Thesis (M.Com.(Information Systems) North-West University, Mafikeng Campus, 2013

This thesis is about the nature of proofs in mathematics as it is practiced, contrasting the informal proofs found in practice with formal proofs in formal systems. In the first chapter I present a new argument against the Formalist-Reductionist view that informal proofs are justified as rigorous and correct by corresponding to formal counterparts. The second chapter builds on this to reject arguments from Gödel's paradox and incompleteness theorems to the claim that mathematics is inherently inconsistent, basing my objections on the complexities of the process of formalisation. Chapter 3 looks into the relationship between proofs and the development of the mathematical concepts that feature in them. I deploy Waismann's notion of open texture in the case of mathematical concepts, and discuss both Lakatos and Kneebone's dialectical philosophies of mathematics. I then argue that we can apply work from conceptual engineering to the relationship between formal and informal mathematics. The fourth chapter argues for the importance of mathematical knowledge-how and emphasises the primary role of the activity of proving in securing mathematical knowledge. In the final chapter I develop an account of mathematical knowledge based on virtue epistemology, which I argue provides a better view of proofs and mathematical rigour.

Tomando como punto de partida el proceso revisión de los fundamentos matemáticos llevado a cabo durante el siglo XIX, este estudio se centra en uno de los conceptos matemáticos más importantes: el infinito. Es innegable la importancia de este concepto en el avance de las Matemáticas y es fácil encontrar ejemplos matemáticos en los que interviene (definición de límite, definición de derivada, definición de integral de Riemann, entre otras). Debido a que algunas de las paradojas y contradicciones originadas por la falta de rigor en las Matemáticas están relacionadas con este concepto, se comienza con el estudio epistemológico del concepto matemático del infinito revisando la bipolaridad que presentan algunos conceptos semánticos, definidos de forma inseparable y conjunta, constituyendo un único concepto como si representaran los polos de un imán. En este estudio se concluye que la bipolaridad revela que una lógica conceptual que puede asumir la comprensión de la negación, debe ser una lógica dialéctica, es decir que admite como verdaderas algunas contradicciones. En el caso del concepto matemático de lo finito-infinito, nos encontramos de nuevo con una bipolaridad lógica. Por todo lo expuesto se presenta una teoría no cantoriana para el infinito potencial y actual, basada en la imprecisión lingüística del concepto de infinito, y utilizando el concepto de conjunto homógono, formado por una sucesión convergente y su límite, previamente introducido por Leibniz, que permite aunar los dos polos del concepto de infinito en un único conjunto. Esta nueva teoría de conjuntos permitirá presentar en lenguaje homogónico, algunos de los conceptos fundamentales del análisis tales como, la diferencial y la integral, así como algunas aplicaciones a la Óptica y a la Mecánica Cuántica. Posteriormente se presenta la categoría lógica de la oposición cualitativa a través de diferentes ejemplos de diversas áreas de la ciencia, y se define, a través de tres reglas o normas básicas, el paso de la lógica aristotélica o analítica a la lógica sintética, que incluye al neutro como parte de la oposición cualitativa. Con la aplicación de estas normas a la oposición cualitativa y, en particular, a su neutro, se demuestra que la lógica sintética permite la verdad de algunas contradicciones. Esta lógica sintética es dialéctica y multivaluada y da a cada proposición un valor de verdad en el intervalo [0,1], que coincide con el cuadrado del módulo de un número complejo. Esto marca una notable novedad respecto de la lógica aristotélica o analítica que otorga valores de verdad reales, o incluso a la lógica difusa que, a pesar de ser una lógica multivaluada otorga valores de verdad reales en el intervalo [0,1]. En esta lógica dialéctica, las contradicciones del neutro de una oposición pueden ser verdaderas. Finalmente se plantea la aplicación de la lógica dialéctica, a la Mecánica Cuántica, cuyo carácter es no determinista y en la que es posible encontrar ejemplos de situaciones contradictorias debido a la dualidad onda-corpúsculo. Para ello se establece un isomorfismo entre la lógica dialéctica y la teoría de la probabilidad, a la que se añade el concepto de fortuidad, precisamente para reflejar el carácter no determinista.

Students’ performances in mathematics in an Open Distant Learning setting have not always been impressive. An exploratory study into the problem solving skills of the University of South Africa students in the Calculus module MAT112 is being conducted using past examinations scripts between 2006 and 2009. The study re-assesses the work done in the end-of-year Calculus examinations, by both looking at the distribution of marks awarded and assigning new scores based on an assessment rubric adapted for the problem at hand. Further assessment of qualitative dimensions that is important for problem solving in Calculus is developed from the data obtained from the assessment rubric. Using factor analysis, a hesitation factor, transfer-of-knowledge factor as well as ingenuity factor, are identified in successful Calculus problem solving. The study proposes two conceptual models; the first is to guide students in solving Calculus problems while the second one is meant to assist lecturers in the assessment of students of Calculus. / Science and Technology Education / M. Ed. (Technology Education)

This thesis argues that truth-telling in high level (nursing home) aged care is a undamentally important aspect of care that ought to reside equally alongside instrumental care. The health of the resident in a nursing home, as with individuals in other care contexts, is directly linked to care provision that allows the resident to be self determining about their care and thus allows them to make reasonable choices and decisions. This qualitative study explores the meaning of truth-telling in the care providerresident dyad in high level (nursing home) aged care. Grounded within the epistemology of social constructionism and the theoretical stance of symbolic interactionism, this study relied on oral and written text from care providers (personal care assistants and registered nurses) and residents. Thematic analysis of data relied on practices within grounded theory to determine their understanding and the conditions and consequences of their understanding about truth-telling in the nursing home. Through an understanding of the relationship-role-residency trinity, truth-telling in high level (nursing home) care comes to be understood. It has been determined that the link between truth-telling and the nature of the care provider-resident (and residents' families) relationship is that both personal carers and nurses in this study premise their understanding of truth disclosure on knowing a resident's (and resident's family's) capacity for coping with the truth and therefore catering for the resident's or family's best interests. The breadth and depth of this knowing and how the relationship is perceived and described determine what care providers will or will not tell. That is, the perceptions both personal carers and nurses have about the relationship - how they describe themselves as 'family like', 'friend' and 'stranger', has implications for the way disclosure operates and is described. Additionally, how care providers perceive and understand their role determines what care providers will or will not tell. That is, the perceptions both carers and nurses have about their own and each other's role - how they describe themselves for example as 'hands-on' carer and 'happy good nurse' has implications for the way disclosure operates and is described. Furthermore, care providers' meaning and understanding of truth-telling in aged care is not possible in the absence of an appreciation of how the care providers give meaning to and come to understand the care circumstance - residency, the aged care facility, the nursing home. That is, the perceptions both personal carers and nurses have about the aged care facility - how they describe residency as 'Home away from Home' (and what this means), as a place of little time and a plethora of situations have implications for the operation of truth-telling as a whole. Recommendations from the study include the implementation of a telling audit to better serve the truth-telling preferences of residents and the reorientation of care practices to emphasise affective care (talk rather than tasks). Furthermore, it is recommended that changes occur to the care provider roles, that care providers define themselves as facilitators rather than protectors, and education be ongoing to improve communication with and care of residents with dementia and those dying. Finally, the language of residency as 'home' needs to capture an alternate philosophy and attendant practices for improved open communication.

For many people music is an important aspect of their daily life. Music preference is a complex subject tied to social identity, personality, leisure activities, religion, family and friends, and so forth. Music is also a form of expression, which is communicated to the public over various mediums and formats. The themes depicted in music media (music in the form of television, radio, and internet sources, both auditory and visually presented) are vast owing to the array of different artists and their individual worldviews that they put on offer for the public. The lyrical content and/or imagery put forward by musicians depicts an array of different themes, which are contextualised by individuals in their personal conception of their favourite music. The meaning that listeners/viewers attach to their music is equally related to their own background and life experience, including their belief system (religion). There has been a controversial increase in the sexualisation and explicitness of music media; however, there is a gap in the intersection between music, sex, and religiosity as a field of study. Understanding the influence of music media requires an understanding of the people who are experiencing this content. Taking a cybernetic approach and the position of the listener who determines the meaning of an utterance, as put forward by cyberneticist Heinz von Foerster, this study is a reflexive contextual enquiry into how people are experiencing and interpreting their music media and whether this media challenges their view on religion (if they consider themselves aligned to a religion). To address this broad research question, a two-part study was conducted. The first part consisted of a quantitative study of 459 students from the University of Johannesburg to obtain a snapshot of a young adult demographic in terms of their music media, sexuality, and religiosity choices. Thereafter, using the results from this first part of the study, a qualitative interview-based study was conducted. Together the quantitative and qualitative studies provide a basis for answering the main research question. The results show that the young adults in the study are thinking beings, not just manipulated by mainstream music media; rather, they decide what is right for them often motivated by their views on religion. Methodologies used in religious studies have been subject to criticism. One specific aspect is the lack of acknowledgment of epistemology within research designs. In addressing this critique, a second- order cybernetic study was conducted. By introducing a cybernetic approach to qualitative religious study, a new approach is thus also presented which is called A Reflexive Recursive Learning Approach to Religious Studies. / Religious Studies and Arabic / D. Litt. et Phil. (Religious Studies)

Students’ performances in mathematics in an Open Distant Learning setting have not always been impressive. An exploratory study into the problem solving skills of the University of South Africa students in the Calculus module MAT112 is being conducted using past examinations scripts between 2006 and 2009. The study re-assesses the work done in the end-of-year Calculus examinations, by both looking at the distribution of marks awarded and assigning new scores based on an assessment rubric adapted for the problem at hand. Further assessment of qualitative dimensions that is important for problem solving in Calculus is developed from the data obtained from the assessment rubric. Using factor analysis, a hesitation factor, transfer-of-knowledge factor as well as ingenuity factor, are identified in successful Calculus problem solving. The study proposes two conceptual models; the first is to guide students in solving Calculus problems while the second one is meant to assist lecturers in the assessment of students of Calculus. / Science and Technology Education / M. Ed. (Technology Education)

Researchers conceptually recommend inquiry-based learning as a necessary means to alleviate the problems of learning but this study has embarked on practical implementation of inquiry-based facilitation and learning in Euclidean Geometry. Inquiry-based learning is student-centred. Therefore, the teaching or monitoring of inquiry-based learning in this study is referred to as inquiry-based facilitation. The null hypothesis discarded in this study explains that there is no difference between inquiry-based facilitation and traditional axiomatic approach in teaching Euclidean Geometry, that is, H0: μinquiry-based facilitation = μtraditional axiomatic approach. This study emphasises a pragmatist view that constructivism is fundamental to realism, that is, inductive inquiry supplements deductive inquiry in teaching and learning. Participants in this study comprise schools in Tshwane North district that served as experimental group and Tshwane West district schools classified as comparison group. The two districts are in the Gauteng Province of South Africa. The total number of students who participated is 166, that is, 97 students in the experimental group and 69 students in the comparison group. Convenient sampling applied and three experimental and three comparison group schools were sampled. Embedded mixed-method methodology was employed. Quantitative and qualitative methodologies are integrated in collecting data; analysis and interpretation of data. Inquiry-based-facilitation occurred in experimental group when the facilitator probed asking students to research, weigh evidence, explore, share discoveries, allow students to display authentic knowledge and skills and guiding students to apply knowledge and skills to solve problems for the classroom and for the world out of the classroom. In response to inquiry-based facilitation, students engaged in cooperative learning, exploration, self-centred and self-regulated learning in order to acquire knowledge and skills. In the comparison group, teaching progressed as usual. Quantitative data revealed that on average, participant that received intervention through inquiry-based facilitation acquired inquiry-based learning skills and improved (M= -7.773, SE= 0.7146) than those who did not receive intervention (M= -0.221, SE = 0.4429). This difference (-7.547), 95% CI (-8.08, 5.69), was significant at t (10.88), p = 0.0001, p<0.05 and represented a large effect size of 0.55. The large effect size emphasises that inquiry-based facilitation contributed significantly towards improvement in inquiry-based learning and that the framework contributed by this study can be considered as a framework of inquiry-based facilitation in Euclidean Geometry. This study has shown that the traditional axiomatic approach promotes rote learning; passive, deductive and algorithmic learning that obstructs application of knowledge in problem-solving. Therefore, this study asserts that the application of Inquiry-based facilitation to implement inquiry-based learning promotes deeper, authentic, non-algorithmic, self-regulated learning that enhances problem-solving skills in Euclidean Geometry. / Mathematics Education / Ph. D. (Mathematics, Science and Technology Education)