An investigation into learner understanding of the properties of selected quadrilaterals using manipulatives in a grade eight mathematics class.Singh, Rakesh Issardeo. January 2006 (has links)
Benchara Blandford as quoted in Griffiths & Howson (1974) has provided the researcher with the inspiration to seek new methods of trying to improve the teaching and learning of geometry: "To me it appears a radically vicious method, certainly in geometry, if not in other subjects, to supply a child with ready-made definitions, to be subsequently memorized after being more or less carefully explained. To do this is surely to throwaway deliberately one of the most valuable agents of intellectual discipline. The evolving of a workable definition by the child's own activity stimulated by appropriate questions is both interesting and highly educational". Freudenthal (1973), who states that "the child should not be deprived of this privilege", further echoes this thinking. Recent literature on mathematics education, more especially on the teaching and learning of geometry, indicates a dire need for further investigations into the possibility of devising new strategies, or even improving present methods, in order to curb the problems that most learners have in geometry. It would seem that most educators and textbooks eschew the use of concrete manipulatives to teach important geometrical concepts, as they feel it is time-consuming and unnecessary since it creates noisier classrooms. In some cases, the educators have not been trained in the use of these manipulatives. This study intends highlighting the many uses that tangrams (a Chinese puzzle) have in enhancing learners' understanding of the properties of the square and rectangle, including the properties of their diagonals. The researcher also intends showing that the tangram pieces are an important cog in the wheel that keeps the geometry thinking and reasoning process ticking. The days of "kill and drill" are over because the tangram will soon become an interesting and stimulating manipulative that can effectively be used to teach important geometrical concepts and definitions. Not only will learners find it fun to work with, but it will also provide an alternate means of learning since it is not monotonous. It will create an environment which learners will find relaxing and enjoyable to work in, and consequently, promote collaborative learning. The tangram can be used as an important assessment tool; however, this investigation goes beyond the scope and intention of this study. Several useful implications have evolved from this study which may influence both the teaching and learning of geometry in school. Perhaps the suggestions made may be useful not only to educators, but to important stakeholders in policy-making as well. If these ideas can be incorporated in drafting the geometry curriculum, I am sure geometry will not be regarded as the stumbling block for many aspiring mathematics learners who are striving for an "A" symbol in the mathematics examination. The researcher has used action research and a task-based interview process with ten grade 8 learners to show that the use of manipulatives, namely tangrams, has been effective in enhancing learners understanding of the properties of the square and rectangle. In addition, tangrams can go a long way in helping learners achieve van Hiele level 3. The learners interviewed were able to develop a good understanding of the properties of the square and rectangle resulting in remarkable improved pre-test scores. Furthermore, the investigation reaffirmed the practice that learners can be effectively taught from the general to the more specific, enabling them to develop a better understanding of concepts being taught. / Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2006.
A case study of the constraints to the effective teaching of technology in grade 7 experienced by schools of a district in KwaZulu-Natal.Ziqubu, Thokozani Sibonelo Leo. January 2006 (has links)
This study concerned itself with the constraints experienced to the effective teaching of Technology in Grade 7 by schools of a district in KwaZulu-Natal. The study arose out of personal experiences of managing staff who had a responsibility to teach Technology in my school. It was assumed that by highlighting some of the problems encountered by schools in the teaching of this new learning area, future teaching and learning might improve. The main research question was: What constraints are experienced by Grade 7 teachers to effective teaching of Technology? A number of specific research questions were generated which focused on the main issues of the research. These were: Are there relevant physical resources available for the teaching of Technology in schools?; Do teachers possess the required skills to teach Technology?; Are teachers' understandings of the Technology Learning Area similar to official department policy?; What attitudes do teachers have towards the new Technology Learning Area? Approaching from a realist perspective, a descriptive case study was used to gather both qualitative and quantitative data. Schools offering Technology in Grade 7 in a school district of 94 schools were supplied with questionnaires for the principal and technology teachers to complete and return. These questionnaires were followed by classroom observations and teacher interviews in carefully selected schools. Data were coded, captured, analyzed and interpreted. Arising from the data analysis a number of findings were presented. The main findings were: In most cases, schools in the district do not have the specific resources required for the teaching of Technology in Grade 7. While most had general physical school infrastructure this was not always in a good condition. Teachers do not have many of the skills or competencies required to teach Technology. The majority of teachers who had been assigned to teach Technology had not received sufficient training. Where some training had taken place, the majority found it not very useful. Teachers have a common understanding about what Technology as a discipline is but differ on what should be emphasized in technology education at school. Teachers had a positive attitude to the introduction of the Technology Learning Area in the curriculum but suggest that it be combined with Natural Science Learning Area at the senior phase. Arising from these findings two main recommendations were made involving the allocation of resources to rural schools in which it was felt that the Department of Education should take primary responsibility and the continuing professional development of technology teachers in which two complementary models were suggested. Further research was suggested in the area of separate or integrated science and technology learning areas and on the long term impact of the teaching of Technology on technological literacy and its impact on the economy. / Thesis (M.Ed.)-University of KwaZulu-Natal, 2006.
This is an evaluative case study to determine what science problem-solving skills learners have developed at the end of the Intermediate Phase. Grade six learners were used in this study as they represented the last grade within the Intermediate Phase. The main question that framed this study: How successful are learners with science problem-solving tasks at the end of the Intermediate Phase? An attempt has also been made to answer the key research questions relating to learners' success at solving problems, the types of problem tasks they can solve, any relationship between their ability at solving problems and their normal science achievement, any differences between groups such as male and female or across different classes, and the opportunities that enabled them to develop problem-solving skills? Operating in a post-positivist/realist paradigm, qualitative as well as quantitative data were gathered through participant observation. The quantitative data was obtained by administering "paper and pencil" and group problem tasks to 116 learners in grade six. Learners' responses to the problem tasks provided the answers to questions relating to their success with science problems as well as the problem-solving skills used. The qualitative data was obtained from questionnaires based on the task and from semi-structured and focus group interviews with learners to attain a deeper understanding on how they responded to the problem tasks and thus determining their success. Documents were analysed from grades four, five and six in an attempt to view the type of problem-solving skills learners had experienced in their science lessons within the Intermediate Phase. An interrogation of the documents provided answers to the research questions dealing with the opportunities learners were given to develop these problem-solving skills. The grade six learner's final Natural Science marks as well as the problem-solving tasks were analysed quantitatively as well as qualitatively to see if there was a relationship between the two. From this study, it was found that in general learners' success was uneven. Learners had more success when problems were closed, inside type requiring one step simple reasoning and were presented as tables rather than as diagrams. They also seemed to have more success when answering the multiple-choice component of the question but had little success explaining their choice of answers. There was not a strong relationship between learners doing well at their normal school tests and being able to solve problems. Learners appeared to be unable to use reasoning to explain their answers. They were unable to work with more than one variable simultaneously. Group differences within the case revealed that Black and Coloured learners had different levels of success with the problem tasks. There was no difference in the marks for boys and girls scores for the problem tasks but there was a difference in their scores for the Natural Science test. In general, learners within the 11 year age group had greater success with the problem tasks. The findings of this study indicate that learners at the Intermediate Phase level are not taught to solve problems and therefore have very limited success with solving problem tasks. However, learners' uneven success also implies that although some learners were unable to solve problems there are others that do have the ability to use problem-solving skills even if they were not formally taught these skills within their science lessons. Learner's inherent ability to solve problems by constructing their own knowledge from their experiences forms the core of this study. Teachers need to build on these in the science classroom, which will result in learners becoming expert problem solvers. This study suggests that providing learners with experiences relating to solving science problems can only assist in developing learners' problem-solving ability and thus benefiting society. The intention of this study is to open up the possibility of a more detailed research into science problem-solving in the primary school within the new reforms of our South African education system. / Thesis (M.Ed.)-University of KwaZulu-Natal, 2006.
The introduction of an Outcomes Based approach to education in South Africa has drawn attention to the nature of assessment. This research study investigated learners' perceptions of educator feedback and aimed at investigating and understanding: learners' meanings of educator feedback, forms of feedback that learners consider effective, and why do they consider these feedback forms as effective? In this case study, journal writing and group interviewing were used as data collection instruments. The five participants were Grade: 9 learners from a secondary school in Phoenix, Durban. The participants engaged in seven units of journal entries each. Having read these journal entries, these five learners comprised the group that was interviewed. The group interviewing provided depth in the five case studies. The findings of this study revealed that learners have significant perceptions of 'educator feedback'. Their definitions of feedback conveyed a broader concept of educator feedback than I had expected. Through their definitions of feedback, learners' outlined their expectations of educator feedback. Learners also disclosed their preferences for some forms of feedback over others. Furthermore, they provided reasons for valuing certain forms of feedback. Their views on the significance of feedback related mostly to: enhancement of learning; correction of errors and avoiding the same errors in subsequent tasks Moreover, learners divulged their positive and negative experiences of educator feedback. Learners' positive experiences of feedback resulted from feedback that promoted learning through remediation of errors and feedback that was motivating. Learners' negative experiences were linked to forms of feedback that they considered as inadequate. These forms of feedback were as inadequate in that learners did not understand where they had gone wrong or why they were wrong. Feedback that had a negative effect on their emotions caused them embarrassment. Forms of feedback that encouraged competition were not valued. Learners raised concerns over the language of feedback (verbal and written) and also the use of red ink in written feedback. A further matter raised was that feedback should relate directly to the mathematics, rather than being personal. / Thesis (M.Ed.)-University of KwaZulu-Natal, 2007.
Teacher assessment practices : case study of three grade 9 mathematics teachers in the Northern region of KwaZulu-Natal province.Thabethe, Michael Msawenkosi. January 2009 (has links)
The research project explored the Grade 9 mathematics teachers' assessment practices in the context of the National Policy on Assessment and Qualifications for Schools in the General Education and Training Band in South African Schools. The research project also explored the mathematics teachers' understanding of the assessment policy in Mathematics and the impact of teachers' understanding of assessment on their assessment practices. The research project was a case study of three Grade 9 Mathematics teachers from three schools in Obonjeni District in the Northern Zululand Region in KwaZulu-Natal Province. The data was collected through observations of teachers teaching Grade 9 Mathematics lessons, analysis of teachers' planning and assessment documents and teacher interviews. Each teacher was observed teaching his/ her lessons five times. Based on the results obtained it was concluded that: (a) teachers have different understandings of the same assessment policy and this resulted in teachers implementing the assessment policy differently. (b) teachers are using some of the assessment practices that are recommended in the assessment policy. and (c) teachers' understanding of assessment does not influence their assessment practices. Finally, recommendations made concerning assessment practices, could lead to teachers' better understanding of assessment. / Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2009.
An investigation into learner perceptions of mathematics : a means to understanding the challenges of learning mathematicsMoodley, Mogasuri. January 2007 (has links)
The purpose of this study was to investigate the experiences and perceptions that learners have in the maths class with the aim of determining learners’ attitude to maths. It also intended to identify and understand the challenges that maths learners face in the maths class. The findings from this investigation would be used in the development of strategies to (a) improve the attitude of learners in the maths class, (b) develop healthier self-efficacy beliefs in learners and (c) create a positive learning environment for maths learners. To this end, a poster activity and group interview were used as the data collection instruments for the qualitative part of the research. The poster activity entailed the development of a poster by learners in which they recorded information on their experiences and perceptions of maths. This highlighted emerging themes that were further explored in the group interview and used in the development of the questionnaire. A group interview was conducted with a select group of learners with the intention of confirming the themes that had emerged from the poster activity. The quantitative phase of the study included a questionnaire, the design of which was based on the findings from the poster activity and was administered to all grade eleven learners of maths in order to determine whether the findings from the poster activity were representative of all the grade eleven maths learners. These data collection instruments generated data that was used to answer the main research questions. Analysis and interpretation of the findings lead to the following conclusions being reached: (a) Learner attitude to maths is in part a product of the accumulated experiences and perceptions of learners in the maths class, (b) The teacher, peers and learners’ self-efficacy beliefs affect maths learning and (c) The learning environment is an important factor in maths learning. The final part of the write-up includes the implications that this research has for the practising maths teacher with suggestions for further research in the area of affect. / Thesis (M.Ed.)-University of Kwazulu-Natal, 2007.
Curriculum, context and identity : an investigation of the curriculum practices of grade 9 teachers in three contrasting socio-economic school contexts.Naidoo, Devika. January 2006 (has links)
This study investigates variations in actual curricular practices across three diverse socio-economic status (SES) urban schools in the province of KwaZulu-Natal, at the end of the first decade of democracy. The aim of the study was to derive a theoretically informed understanding of the contribution of curriculum practices to social stratification. An eclectic theoretical approach, with an emphasis on Bernsteinian structural interactionist approach involving the micro situation reflecting macro level power relations, informed the study. A qualitative research design was used. The findings of the study showed that there were significant variations in the internal structuring of pedagogic discourse across the three contrasting socio-economic school contexts. Deep-seated inequalities in access to diverse forms of knowledge and to intellectual enhancement of students were being reproduced across the three schools. The students in the elite, independent SES school, and top stream of the middle SES school, were being inducted into a variety of strongly classified and framed distinct disciplinary-based subjects and weakly classified and framed integrated projects and had far better chances of entry to fields of study in higher education than students at the lower socio-economic status school. Utilitarian ideology, simple everyday and community knowledge discourses, and incoherent pedagogy dominated classroom practices at the lower SES school. The consequence was that students were being positioned in segmental horizontal discourses. At the elite and lower SES schools the variations in knowledge and intellectual skills taught are attributed to teachers' differential grasp of subject content arising from their own stratified educational experiences and to the persisting extreme inequalities in distribution of resources. This situation indicates continuities with apartheid-structured inequalities. The assimilationist approach followed by the middle SES school, a former White school that had become racially and socio-economically diverse, was clearly being challenged by many students, with adverse student outcomes. The different curriculum practices across the three schools have implications for the reproduction of social stratification. The study suggests that South Africa's historical legacy context is an extremely powerful force in influencing and constraining actual outcomes in South African schools. The lack of attention to contextual realities by the 'one size fits all' policy functions to undermine transformative impulses. The non-interventionist policy of the post-Apartheid government with reference to school development and improvement, namely the policy of decentralisation and the devolution of power and governance to local schools, benefited the advantaged schools that possess the necessary economic and social capital to compete and exercise choice and manipulate the system to their advantage. For the disadvantaged school that lacked the material and intellectual resources the policy became the means for the entrenching of inequalities in access to diverse forms of knowledge and thus to the reproduction of social inequalities. / Thesis (Ph.D.)-University of KwaZulu-Natal, 2006.
Ramklass, Serela Samita.
This study focuses on physiotherapy professional development and professional education and the multitude of theoretical, practical and political forces that shape and influence physiotherapy education. It does so by addressing the questions: how is an undergraduate physiotherapy curriculum within a historically disadvantaged university responding to post apartheid societal transformation in South Africa; and why is the curriculum responding in the way that it is within the current social, economic, political, cultural and historical context of South Africa. The study is theoretically and methodically located within critical, feminist and post-modern framings that disturb and disrupt the dominant medical model of health sciences practice. Employing narrative inquiry as the selected methodology, data was produced through multiple methods to obtain multiple perspectives and orientations. This multi-sectoral data production approach involving student physiotherapists, physiotherapy academics and practicing physiotherapists included in-depth focus group interviews, individual interviews, life-history biographies and open-ended questionnaires. The data is analysed firstly separately for each group of research participants - physiotherapy students, practitioners and academics, and then followed by a cross-sector analysis. The analysis illustrated current disciplinary trends and shortcomings of the physiotherapy undergraduate curriculum, whilst highlighting that which is considered valuable and progressive in physiotherapy and health care. The dominant themes that emerged included issues relating to physiotherapy theory and practice, and issues that influenced the construction of relationships in the curriculum. The main thesis presented is that for physiotherapy in the South African context, the notion of caring is identified as the link between transformation and professional development. The model proposed is: A Caring-Transformative Physiotherapy Practitioner Model for physiotherapy professional development advancing a view of what it could mean to be an agent of transformation in South Africa within the health care system. This model is located within multiple framings of caring that re-casts the physiotherapy professional previously located primarily within a medical model ideology, into a practitioner with a broadened view of practice and professional accountability within a critical-feminist framing. / Thesis (Ph.D.) - University of KwaZulu-Natal, 2006.
Greenbaum, Lesley Anne.
This study reviews the curriculum of the four-year undergraduate Baccalaureus Legum (LLB) degree, introduced in 1998 as part of the transformation agenda in post-apartheid South Africa. Ten years since its inception, the question is whether the vision of the originators has translated into curricula that are producing a representative supply of appropriately-educated graduates for practice as legal professionals. The demand for the transformation of legal education resulted in the introduction of an undergraduate LLB as a single, affordable qualification for entry to legal practice. Law faculties were permitted to develop their own curricula, although there was agreement on core content. Three key principles were to inform curriculum design: (i) South African law exists in and applies to a diverse or pluralistic society; (ii) skills appropriate to the practice of law must be integrated into the degree; and (iii) faculties must strive to inculcate ethical values in students. A decade later, stakeholders are expressing dissatisfaction with the quality of graduates. Few graduates complete the LLB within four years, and a significant proportion of African students, already under-represented in law faculties, do not complete their studies. The attorneys’ profession is still predominantly white-owned. In the first part of the study, phenomenological interviews were conducted with three members of the 1996 Task Group of Law Deans who drafted the proposals for the new degree. The data elicited described the lived experience of curriculum change. Five current Law Deans were also interviewed to develop an understanding of their experience of implementing the law curriculum. The second component of the study was a phenomenographic analysis, in which six graduates, who are now attorneys, were interviewed, to identify their experiences of the law curriculum at one Law faculty. The graduates’ employers were interviewed to ascertain their perceptions of the graduates’ preparedness for professional practice. The study suggests that reactive conservatism on the part of legal academics resulted in law curricula that replicate a cycle of disadvantage, and fail to achieve transformative learning which integrates knowledge, skills and ethical values. A focus on incorporating an ontological component in law curricula, to develop high quality legal professionals is recommended. / Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2009.
A consideration of some aspects of general education in the universities of the United States of America.Williams, Aston Rowland. January 1963 (has links)
The three major fields of human knowledge are the humanities, the social sciences, and the natural sciences. An undergraduate, whose special interests lie in one of these fields, should be able to understand his own field in the context of the whole of human knowledge. This necessitates some knowledge of the other two fields. This practice is followed in American colleges, and is called in these pages ' general education '. Formal study is required of undergraduates in each of these fields? and the passing of examinations in them is a condition of graduation . The purposes of general education are discussed in the first chapter for the student as undergraduate , and for the man as scholar, for the man in his profession, for the man in the community, and for the man, and the woman, during leisure hours. This analysis raises the question as to what should be the aims of university education? and this is considered briefly in the first chapter, and more fully in the last. The first chapter concludes with an outline, which also is elaborated in the last chapter, of the widest purposes of general studies. These are, in the words of the authors of the Harvard report, to enable students 'to think effectively, to communicate thought, to make relevant judgments, and to discriminate among values ' . A ' liberal education' is defined in the last chapter as one which provides both the values of depth, which arise from specialist studies, and the values of breadth, which are to be found in general 'studies. Specialist studies liberate a man from ignorance and prejudice in his own field. General studies put a man on the road to freedom from ignorance and prejudice in all other fields . In point of fact, in the earlier chapters, the terms ' liberal education ' , 'liberal studies', 'general education', and 'general studies' are used almost as synonyms . This is inevitable, as the many writers quoted on this subject use these terms to mean much the same thing. The content of general education. programs is traced in chapter 2 . The major headings are: 2. 2, Harvard College; 2. 3, the Massachusetts Institute of Technology; 2.4, Yale College; and 2.5, Columbia College . In each casethe contributions to curricula of the humanities, the social sciences, the natural sciences, and 'communication' are given. In chapter 3, however, the major headings are: 3.1, the humanities; 3.2, the social sciences; 3.3, the natural sciences; and 3.4, communication. Here, in each case, the uses made of these fields of knowledge in undergraduate curricula are compared with respect to two very different university colleges -- the College of the University of Chicago, and University College in Michigan State University. Communication in general education is such an important subject that a separate chapter (5) is devoted to it; this forms the one component of general studies which is invariably present. Chapter 6 deals with similarities and differences in general education programs in the United States of America. In the General College of the University of Minnesota, the emphasis is as much on social objectives as on academic aims. Next, the curricula of four new colleges are sketched -- and all have strong general studies programs: Michigan State University, Oakland; Monteith College in Wayne State University, Detroit; the University of South Florida; and Harvey Mudd College in California. This leads on to a consideration of the State prescriptions in California, with three examples: the State College of San Francisco, Stanford University, and the California Institute of Technology. A description of two well-known, but atypical liberal arts colleges follows: Amherst and Antioch. Berea College, like Antioch College, has a work-study plan, but of a different kind. Finally the programs of St. John's College, and Sarah Lawrence College are given, and they illustrate the concluding section of this dissertation in chapter 9 on the philosophical foundations of general education. One stands to one side of the Harvard pattern, and the second to the other side. The division of the fields of human knowledge into the humanities, the social sciences, and the natural sciences is obviously an over-simplification. An analysis by Cassidy of Yale at the start of chapter 7 shows the relationship of the liberal arts and sciences to their professional applications on the one hand, and to their philosophical bases on the other. This leads on to details of the requirements of the professions in America in respect of general education in undergraduate studies: engineering, architecture, law, medicine, dentistry, pharmacy, nursing, business administration, journalism, music, and teaching. The opportunity is taken of tracing various methods of arrangement of general studies in section 7.23 on engineering education. Chapter 8 raises the problem of finding time for all the studies which should be included in undergraduate curricula. Should an extra year be provided? Indeed, is one year less a possibility? Opponents of the practice of general education usually avoid its challenge by stressing the time problem, or by saying that its values can be attained at the secondary school level, or after graduation through adult education. A study of examination papers from M.I.T. (page 111), Columbia (page 114), and Keele in England (page 232) will show that work at this level demands a maturity beyond that of the school- boy or school-girl, and requires far more time than the adult, burdened with employment and domestic responsibilities, could find. Other ways of escaping the challenge of general education are to look to possible alternatives~ living in residence, student activities, lecture series, the cultural background of a good home. It is contended in these pages that although these are valuable supplements, they are nevertheless inadequate alternatives. Chapter 4 separates the first three and the last five chapters through comparisons of Great Britain, Canada, and the United States of America. There is much incisive writing in Britain on the value of liberal education, of which, with certain exceptions, there occurs relatively little in practice. The Colleges of Advanced Technology have good programs of liberal studies. The University of North Staffordshire at Keele has a foundation year of general education, and what would be called in America 'distribution requirements', in the following three years. Beyond this, univerSity undergraduate curricula and British sixth form courses are highly specialized, but less so in Scotland than in England. Chapter 4 contains a full portrayal of British practice with respect to special and general studies. This has been given because a statement of British reactions to the challenge of general education, it is hoped, will serve to sharpen thinking on the subject. For the Same purpose Canadian views and practice are described; Canadian universities . in this respect are closer to those of Britain and France than to those of the United States of America. Reference is made also to Germany, Holland, Australia, and India, to show the geographic spread of discussion on these matters. It is hoped that this dissertation may be of value to South African university authorities, who are considering at the moment (1963) the possibility of an extra year at the beginning of the university Bachelor's course, and this point is mentioned in section 8.24 . The extent to which a country can reject the challenge of general education i s outlined in section 4.81; the South African prescripti on for subjects outside the field of specialization is usually framed in terms of not more than rather than not less than . The difficulties of implementing a general education program can be understood best with respe ct to universities where general studies are largely absent; here too South African practice providesin section 8.52 a useful basis for discussion. Finally, South Africa is referred to again in section 9.22 in an attempt to define general education, and to show what, at the very least, a program of general education must include to be worthy of the name. This study was made possible by a Leader Program award of the State Department of the United States of America in 1955, and by a Carnegie Corporation of New York travel grant in 1960. Two stimulating and memorable visits resulted. This analysis of general education has been undertaken in the conviction that 'thinking on this subject, and fundamental thinking, was never more necessary than it is today ' , to use the words of the University Grants Committee of Great Britain. It is hoped that these pages will indicate that the world has a great deal to learn about this matter from the United States of America. / Thesis (Ph.D.)-University of Natal, 1963.
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