Thesis (M.A.)--Chinese University of Hong Kong. / Bibliography: leaves 56-59.

published_or_final_version / Education / Master / Master of Education

This dissertation reports case studies conducted at two secondary schools in Durban. With the introduction of the Further Education and Training (FET) curriculum in 2006, learners who terminate their study of Mathematics at the end of grade nine will have to study Mathematical Literacy, an applications-based mathematics course. In South Africa the Mathematics results at the grade twelve exit examination are generally poor and learners are known to underachieve in the field of geometry. This study was aimed at determining the readiness of learners in studying geometry under the Learning Outcome, Space, Shape and Measurement in the Mathematical Literacy curriculum. Questionnaires were administered to grade nine learners who had elected not to study, or were excluded from studying, Mathematics from grade ten onwards. Data was sought to determine what factors influence the decision to discontinue mathematics, and to gauge attitudes to the study of mathematics. Learners were given a test to measure geometry skills and knowledge that they ought to have acquired by the end of the senior phase in geometry. Data was also obtained from focus group interviews with both of learners and educators. This study indicates that learners do not continue mathematics because of the difficulties they experience. Furthermore they do not have the requisite skills and knowledge in Space, Shape and Measurement to cope with the Mathematical Literacy curriculum. Nevertheless, the attitudes of learners to the study of this new subject are positive. It is suggested that educators need to conduct baseline assessments to determine learners' abilities so as to plan appropriate revision measures before continuing with the teaching of Mathematical Literacy. / Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2006.

This research considers specific strategies that would enhance teaching and learning of fractional concepts in mathematics at a secondary school. The notion of the Zone of Proximal Development (ZPD) ~ Vygotskian view, is invoked as one of the fundamental frameworks for explaining fractional knowledge. This view is contested on the bases of that "human thinking is inherently social in its origin" (Goos, 2004: 259). Another theory that bears testimony to mathematics education especially abstract concepts like fractions is that of constructivism, drawn from the works of, Lave (1996), Steffe (1990) and others. Learners' informal knowledge is investigated for the purposes of highlighting what learners know and can do. Therefore, the study examined the development of learners' understanding of fractions during instruction with respect to the ways their prior knowledge of whole numbers influenced the meanings and representations they construct for fractions as they build on their informal knowledge. There were 30 participants (15 School A and 15 from School B) that were engaged in worksheets. Thereafter, 6 cases of the participants were carefully selected for clinical interview purposes. The overall methodology of this study is participatory action research (Kemmis & Mctaggart, 2000). / Thesis (M.Ed.)-University of KwaZulu-Natal, 2006.

The integration of technology into teaching and learning has come as new in education. It is a shifting of paradigm from one way of educational thinking to the other. Before entering their classrooms for the first time students already have been using technology devices and educators’ cannot ignore this facts. The South African Ministry of Education has responded to this issue by designing implementation strategies and has mandated all schools in the country to have integrated Technology in the curriculum by 2013. The study anticipated to understand how Educational Video (EV) is used to facilitate learning of mathematics in two Secondary schools in Durban, KwaZulu-Natal Province. The underlying principle was to ascertain the challenges educators encounter in facilitating teaching and learning of mathematics, using EV in two secondary schools in Durban, KwaZulu-Natal Province. A qualitative research approach and case methodology were used to explore these experiences of educators in mathematics instruction. Semi-structured interviews, classroom observations and documents review methods were used to collect data that were analysed and discussed, using the principles of Engagement and Activity theories. Four purposively selected educators and ten grade ten students were interviewed and their mathematics lessons observed. The findings indicated that the integration of video in teaching and learning appears to assist both learners and educators in two schools, and the educators from the two Secondary Schools in Durban, KwaZulu-Natal Province have shown to be comfortable with its use in facilitating mathematics instruction for it enables authentic and higher order thinking in learners by engaging them in complex tasks within collaborative learning contexts. Issues of professional empowerment financial support, and lack of materials, delay the integration of EV in two schools. This would be solved easier if all stakeholders in the education sector were effective in their individual roles for the betterment of education in the whole country. / Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2008.

This study explores the phenomenon of mathematics anxiety with respect to a group of matric students at a secondary school in KwaZulu-Natal. The contextual factors associated with mathematics anxiety were examined from the perspective of ten mathematics students and three teachers of mathematics. In this study, qualitative research methodology was used. The data was gathered through semi-structured interviews and questionnaires. Various factors, such as the belief in mathematical myths and negative experiences during the early school years, interact to contribute to the phenomenon of mathematics anxiety. The study revealed the need to dispel mathematical myths, to create supportive learning environments for students, and to provide support for mathematics teachers in the form of on-going professional development. / Thesis (M.Ed.)-University of Natal, Durban, 2000.

M.Ed. (Subject Didactics) / The ideal in education is that the curriculum provided (by the teacher) and the curriculum received (by the pupil), as originally drafted by the designers, should agree. However, there are indications that this ideal is often not achieved in the teaching of Mathematics, the reason being, inter alia, the backlog in the subject arising from inadequate knowledge as a result of misconceptions in regard to certain basic concepts. Misconceptions among pupils indicate that the shaping of understanding and mastering the concepts have been inadequate. It should be kept in mind that frame of reference and world view are peculiar to each pupil and will be utilized by him for interpreting and processing new concepts. It is therefore essential that the world view of the pupil should be investigated as being the factor which is probably basic to the problem of misconception. The point of departure is therefore that pupils have divergent world views, which invariably affect their understanding of Mathematics. Throughout the ages misconceptions were inextricably part of natural science in general and Mathematics in particular. During modern times, since the 1960s, Boyd has paved the way for reflection regarding misconceptions in natural scientific teaching by using the term "unfounded beliefs", and the attention was actively drawn to the problems surrounding misconceptions. Terms now mostly used as synonyms for misconceptions are conceptual framework, alternative frameworks, and alternative conceptions...

Close to a decade ago Hong Kong completed the implementation of a New three-year Senior Secondary (NSS) curriculum by introducing the Hong Kong Diploma of Secondary Education (HKDSE) examination. Because mathematics is one of the core subjects intricately involved in this education reform, it is necessary to evaluate the connection between the Hong Kong S1 – S6 mathematics curriculum and the mathematics compulsory portion of the HKDSE examination. A curricular alignment study can provide insight to policymakers, students, teachers, and schools concerning agreement between the intended curriculum and the assessed curriculum. This research study adopted a combination of criteria from the Achieve’s alignment protocol and Webb’s alignment method to determine the alignment between the Hong Kong S1 – S6 mathematics curriculum and the mathematics compulsory part of the 2018 HKDSE examination. A panel of three mathematics educators identified the assessment item/learning objective match, classified the content centrality value of each match, and identified the Depth of Knowledge of each assessment item. The alignment results indicate a wide range from no to strong indication of alignment between the Hong Kong S1 – S6 mathematics curriculum standards and the 2018 HKDSE examination. Areas of misalignment were found within the Measures, Shape and Space strand and the Data Handling strand of the Hong Kong S1 – S6 mathematics curriculum, where both show deficiencies in meeting the minimum benchmark for the categorical concurrence and the range of knowledge correspondence.

published_or_final_version / Education / Master / Master of Education

Text in Afrikaans / 'n Leerling se wiskunde-selfkonsep wys heen na die konsep wat hy van homself op wiskundige vakgebied het. Die kwaliteit van hierdie konsep word bepaal deur die kwaliteit van sy eie betrokkenheid by, belewing van en sin- en betekenisgewing aan wiskundige vakinhoud. Wanneer die kwaliteit van 'n leerling se wiskunde-selfkonsep ontoereikend is, word sy onvermoe om op daardie tydstip sukses op wiskundige vakgebied te behaal, geopenbaar. Dit plaas die opvoeder voor die opgawe om bemoeienis met die leerling te maak en hom ten aansien van sy probleem te help. In die lig hiervan is 'n hulpverleningsprogram ter bevordering van die wiskunde-selfkonsep ontwerp. Aangesien leerlinge in Suid-Afrikaanse skole tans gedurende die st.7-skooljaar die besluit neem om die studie van wiskunde te staak of daarmee voort te gaan, is die inhoud van die program derhalwe op die st.7-leerling van toepassing gemaak. Spesifieke doelsteilings wat in die ontwerp van die program nagestreef is, is die volgende: Om die leerling te begelei tot insig in en die begryp van die kwaliteit van sy eie wiskunde-selfkonsep en grondliggende oorsake vir die vorming daarvan, ten einde hom in staat te stel om sy eie situasie in perspektief te plaas. Om die leerling te begelei tot die ontwikkeling van spesifieke vaardighede aan die hand waarvan hy homself op 'n meer selfstandige wyse kan handhaaf ten aansien van die begripmatige bemeestering van wiskunde as vak. By wyse van 'n loodsondersoek is die toepasbaarheid van die onderhawige program ondersoek. Uit die terugvoergesprekke met die leerlinge tydens die groepsessies en die inligtingstukke wat hulle voltooi het, blyk dit dat hulle baat gevind het by hulle deelname aan die program. Met die oog op moontlike toekomstige navorsing is spesifieke leemtes ten opsigte van die onderhawige studie uitgelig en aanbevelings gedoen wat as verdere riglyne geimplementeer kan word. / A pupil's mathematical self-concept is the concept a pupil has of himself in the sphere of Mathematics as a subject. The quality of this concept is determined by the quality of his own involvement in, live-experiencing of, and significance attribution in respect of mathematical subject content. When the quality of a pupil's mathematical self-concept is inadequate, his inability is manifested in his failure to master Mathematics as a subject. This confronts the educator with the task of becoming involved with the pupil and helping him with his problem. In view of this, an aid programme was designed to improve the mathematical self-concept. Owing to the fact that, at present, pupils in South African schools have to decide during their Std 7 school year whether they are going to continue with their study of Mathematics or discontinue these studies, the content of the programme was aimed at the Std 7 age group. The following are the specific aims that were pursued in the designing of the programme: To guide the pupil to insight in and understanding of the quality of his own mathematical self-concept and its underlying causes, in order to enable him to place his own situation in perspective. To guide the pupil in the development of specific skills to help him cope more independently with the successful mastery of Mathematics as a subject. The possibility of implementing such a programme in practice was established by means of a pilot investigation. From feedback discussions with the sample group during group sessions and from questionnaires they filled in, it appears that they benefited from their participation in the programme. With a view to possible future research, specific shortcomings with respect to the investigation were highlighted and recommendations made which can be implemented as further guidelines. / Psychology of Education / M. Ed. (Sielkundige Opvoedkunde)