Philosophiae Doctor - PhD (Education)

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https://hdl.handle.net/10566/10524

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Browsing by Author "Breiteig, Trygve"

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    Contexts preferred for use in mathematics by Swaziland high performing public schools' junior secondary learners
    (University of the Western Cape, 2011) Ngcobo, Minenhle Sthandile Faith; Julie, Cyril M.; Mtetwa, David; Breiteig, Trygve; Torkildsen, Ole Einar; NULL; Faculty of Education
    At primary school learners are excited about mathematics. This may be an indication that learning related to familiar contexts, connected to the learners’ interests, values and goals is necessary for motivation. At secondary school level learners begin to question the applicability of certain topics in the school syllabus and sometimes do not see the necessity of mathematics in their future careers. This is an indication that they are apprehensive regarding the relevance of mathematics in various contexts. However, relevance has a point of reference, what is relevant to a teacher is not necessarily relevant to the learner and what is relevant to a text book writer might not be relevant to the text book reader. As mathematics educators endeavour to encourage learners to appreciate the relevance of mathematics to everyday life, it is important to be aware of their interests. It is crucial to be informed on the subject areas they desire to know about in order to plan classroom activities that will occupy them in purposeful activity.Usually contexts for learning are chosen by adults without conferring with learners at any point. The present study investigated learners' preferences for contexts to use in learning school mathematics. Furthermore the study sought to establish motivations learners have for preferring particular contexts. The problem the study addressed was that of absence of learners' contribution in contexts used to learn mathematics. The aim was to find out the contexts learners preferred and the reasons they gave for their preferences. It is important to be aware of learners' preferences when choosing contexts to use in teaching. Preferences improve motivation and learning. Furthermore, consulting them sends a message that they matter and have an important role to play in their education.
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    Cryptology: A didactical transposition into grade 10 school Mathematics classroom
    (University of the Western Cape, 2007) Whittles, Kalvin; Julie, Cyril; Torkildsen, Ole Einar; Breiteig, Trygve; School of Science and Mathematics Education; Faculty of Education
    This study in an extension of a Master's study, entitled Realistic Mathematics Education and the strategies grade 8 learners develop for the solution of two simultaneous linear equations. the current study investigates how new content could be introduced into a school mathematical curriculum. The new topic under discussion for this study is the topis of Cryptology. Two research cycles were carried out. For the first design research cycle there were three teaching experiments with teachers, grade 10 learners and students as participants. Seven activities weere developed from the second design research cycle which was worked through with gade 10 learners. All sessions for the second design research cycle were video taped. Important to the development of instrutional materials was the development of a hypothetical learning trajetory about the learning and teaching of each activity. the results of the study indicated that the way learners understood the content and the different ways in which they presented solutions augers well for the introduction of a specific new content strand, cryptology, into a new school mathematical curriculum. It is also important for developers of instructional material to have a strong mathematical content knowledge for the design of instructional materials
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    Epistemological obstacles in coming to understand the limit concept at undergraduate level: a case of the National University of Lesotho
    (University of the Western Cape, 2006) Moru, Eunice Kolitsoe; Persens, Jan; Breiteig, Trygve
    The purpose of this study was to investigate the epistemological obstacles that mathematics students at undergraduate level encounter in coming to understand the limit concept. The role played by language and symbolism in understanding the limit concept was also investigated. A group of mathematics students at undergraduate level at the National University of Lesotho (NUL) was used as the sample for the study. Empirical data were collected by using interviews and questionnaires. These data were analysed using both the APOS framework and a semiotic perspective. Within the APOS framework, the pieces of knowledge that have to be constructed in coming to understand the limit concept are actions, processes and objects. Actions are interiorised into processes and processes are encapsulated into objects. The conceptual structure is called a schema. In investigating the idea of limit within the context of a function some main epistemological obstacles that were encountered when actions were interiorised into processes are over-generalising and taking the limit value as the function value. For example, in finding the limit value L for f(x) as x tends to 0, 46 subjects out of 251 subjects said that they would calculate f(0) as the limit value. This method is appropriate for calculating the limit values for continuous functions. However, in this case, the method is generalised to all the functions. When these subjects encounter situations in which the functional value is equal to the limit value, they take the two to be the same. However, the two are different entities conceptually.
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    Land reform in the news: An analysis of how certain South African newspapers covered land reform before and after the 2005 National Land Summit
    (University of the Western Cape, 2006) Genis, Amelia Jasmine; Julie, Cyril; Torkildsen, Ole Einar; Breiteig, Trygve; School of Government; Faculty of Economics and Management Sciences
    This thesis investigates land reform coverage at the time of the land summit through quantitative and qualitative content analysis. Hard news reports, editorials and opinion pieces that appeared in the daily newspapers Beeld, Business day, Sowetan and Sunday newspapers Rapport and Sunday Times between July and September 2005 were analysed in terms of what they reported , issues that received little attention, portrayal of certain issues and sources used. The findings were used to make inference about the degree to which the newspapers in the study fulfill their societal roles.
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    Students' experiences, learning styles and understanding of certain calculus concepts: A case of Distance Learning at the Zimbabwe Open University
    (University of the Western Cape, 2007) Tsvigu, Chipo; Breiteig, Trygve; Persens, Jan; School of Science and Mathematics Education; Faculty of Education
    The study attempts to understand how distance education practices influence the learning of calculus. Understanding student learning in a distance education environment is an important factor to consider in improving the learning experiences of students who for one reason or the other opt not to study in conventional institutional of higher education. On one hand, understanding student learning may illuminate the influences that the learning environment has on student learning and on the other hand, it may inform on how learning experiences can be improved. The aim of this study is to acquire a deeper understanding of the diverse manner in which distance students learn calculus, Specific focus is also placed on the distance education contect of the Zimbabwe Open University (ZOU) influences student learning. The study describes a group of student's experiences of learning calculus in the ZOU distance education environment.