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)

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)

Research has shown that academic under-performance in higher education can be attributed inter alia to psychosocial difficulties arising from students’ under-preparedness for the rigours of university life, the struggle to accommodate diverse cultural worldviews and poor proficiency in the language of learning and teaching (Chang 1999). As internationalisation of higher education institutions has became more common worldwide, the need for support systems to deal with problems of a multicultural student body has become essential if students are to have equitable opportunities for success. In this regard, Monash South Africa (MSA), an international multicultural higher education institution, introduced a tutor-mentor programme to improve academic outcomes among mathematics students in the Foundation Programme (FP). The impact of this programme was investigated by means of an empirical investigation and framed by a bricolage of learning theories which served as a conceptual framework for the study under the metaphors of acquisition and participation. The literature study showed that tutoring and mentoring programmes tend to be successful pedagogical supports. The empirical inquiry took the form of a mixed-method case study which explored the impact of participation in the tutor-mentor programme on mathematical performance among FP mathematics students at MSA. The participants in the study, which was carried out in two phases, were mathematics students, tutor-mentors and lecturers in the FP. Phase 1 quantitatively explored the extent of effectiveness of the tutor-mentor intervention, using a quasi-experimental non-equivalent control group design. Two formal tests were used to gather data, which were analysed by an analysis of covariance and the Johnson-Neyman technique. Quantitative findings supported the initial assumption of the study: that participation in the tutor-mentor programme as an intervention strategy improved the mathematics scores of FP students at MSA. Phase 2, a qualitative study, used purposive sampling. Data was gathered through focus group and individual interviews, observation, spontaneous conversations and photographs. Interpretation of the quantitative and qualitative data was presented according to the phases and thereafter integrated. Qualitative findings provided information about the dynamics of the tutor-mentor programme in providing academic and psychosocial support to students. Finally, a situation-producing theory was developed from the integrated findings, and recommendations made for improvement of practice. / Educational Studies / D. Ed. (Comparative Education)

The study was undertaken to identify the factors that influence standard seven pupils when they choose whether to continue with mathematics at senior secondary level or not. The relative importance of the factors was also determined. The literature study identified the following factors: attitude towards mathematics, utility of mathematics, family members' influence, mathematics teacher's influence, peer group influence, achievement and gender. The empirical study dealt with the following: * A 77 item questionnaire was completed by 201 standard seven pupils. * The statistical analysis revealed significant differences between pupils who chose mathematics and those who did not, with regard to all variables except gender. * A regression analysis identified the most influential factors as achievement, family members' influence, attitude and the mathematics teacher. * The overall implications were: - Pupils be made to experience success so that their attitudes may change. - Parents must be involved in their children's education. / Psychology of Education / M. Ed. (Psychology of Education)

Research has shown that academic under-performance in higher education can be attributed inter alia to psychosocial difficulties arising from students’ under-preparedness for the rigours of university life, the struggle to accommodate diverse cultural worldviews and poor proficiency in the language of learning and teaching (Chang 1999). As internationalisation of higher education institutions has became more common worldwide, the need for support systems to deal with problems of a multicultural student body has become essential if students are to have equitable opportunities for success. In this regard, Monash South Africa (MSA), an international multicultural higher education institution, introduced a tutor-mentor programme to improve academic outcomes among mathematics students in the Foundation Programme (FP). The impact of this programme was investigated by means of an empirical investigation and framed by a bricolage of learning theories which served as a conceptual framework for the study under the metaphors of acquisition and participation. The literature study showed that tutoring and mentoring programmes tend to be successful pedagogical supports. The empirical inquiry took the form of a mixed-method case study which explored the impact of participation in the tutor-mentor programme on mathematical performance among FP mathematics students at MSA. The participants in the study, which was carried out in two phases, were mathematics students, tutor-mentors and lecturers in the FP. Phase 1 quantitatively explored the extent of effectiveness of the tutor-mentor intervention, using a quasi-experimental non-equivalent control group design. Two formal tests were used to gather data, which were analysed by an analysis of covariance and the Johnson-Neyman technique. Quantitative findings supported the initial assumption of the study: that participation in the tutor-mentor programme as an intervention strategy improved the mathematics scores of FP students at MSA. Phase 2, a qualitative study, used purposive sampling. Data was gathered through focus group and individual interviews, observation, spontaneous conversations and photographs. Interpretation of the quantitative and qualitative data was presented according to the phases and thereafter integrated. Qualitative findings provided information about the dynamics of the tutor-mentor programme in providing academic and psychosocial support to students. Finally, a situation-producing theory was developed from the integrated findings, and recommendations made for improvement of practice. / Educational Studies / D. Ed. (Comparative Education)

The study was undertaken to identify the factors that influence standard seven pupils when they choose whether to continue with mathematics at senior secondary level or not. The relative importance of the factors was also determined. The literature study identified the following factors: attitude towards mathematics, utility of mathematics, family members' influence, mathematics teacher's influence, peer group influence, achievement and gender. The empirical study dealt with the following: * A 77 item questionnaire was completed by 201 standard seven pupils. * The statistical analysis revealed significant differences between pupils who chose mathematics and those who did not, with regard to all variables except gender. * A regression analysis identified the most influential factors as achievement, family members' influence, attitude and the mathematics teacher. * The overall implications were: - Pupils be made to experience success so that their attitudes may change. - Parents must be involved in their children's education. / Psychology of Education / M. Ed. (Psychology of Education)

The purpose of the study was to explore the relationship between mathematics teachers’ subject matter knowledge and their teaching effectiveness. A convenient sample of 19 grade 11 mathematics teachers and 418 students were initially selected for the study and took part in some stages of the study. Of this lot, only 11 teachers and 246 students participated in all the stages of the study. Explanatory Mixed methods research design which entails the use of a co-relational study and a descriptive survey design were employed in the study. Data was collected from the teachers using a self report questionnaire, Teacher Subject Matter Knowledge of Trigonometric Functions Scale (TSMKTFS) and peer evaluation questionnaire, and from students using teacher evaluation questionnaire and Student Trigonometric Functions Performance Scale (STFPS). All the instruments had their validity and reliability accordingly determined. Quantitative data gathered was analysed using descriptive and inferential statistics while qualitative data gathered from teachers’ and students’ tests were analysed using task performance analysis. It was found that a positive, statistically significant relationship existed between teachers’ subject matter knowledge and the composite measure of their teaching effectiveness. The relationships between teachers’ subject matter knowledge and students’ achievement and also between teachers’ subject matter knowledge and students’ rating of the teachers’ teaching effectiveness were found to be positive and statistically significant. However, the relationships between teachers’ subject matter knowledge and teachers’ self rating as well as teachers’ subject matter knowledge and peers’ rating of teachers’ teaching effectiveness were not found to be statistically significant though they were positive. Further data analysis showed that there was a difference between the subject matter knowledge of effective and ineffective teachers and also between the students taught by effective teachers and the students taught by the ineffective teachers. / Institute of Science and Technology Education / PhD (Mathematics Education)

The purpose of the study was to explore the relationship between mathematics teachers’ subject matter knowledge and their teaching effectiveness. A convenient sample of 19 grade 11 mathematics teachers and 418 students were initially selected for the study and took part in some stages of the study. Of this lot, only 11 teachers and 246 students participated in all the stages of the study. Explanatory Mixed methods research design which entails the use of a co-relational study and a descriptive survey design were employed in the study. Data was collected from the teachers using a self report questionnaire, Teacher Subject Matter Knowledge of Trigonometric Functions Scale (TSMKTFS) and peer evaluation questionnaire, and from students using teacher evaluation questionnaire and Student Trigonometric Functions Performance Scale (STFPS). All the instruments had their validity and reliability accordingly determined. Quantitative data gathered was analysed using descriptive and inferential statistics while qualitative data gathered from teachers’ and students’ tests were analysed using task performance analysis. It was found that a positive, statistically significant relationship existed between teachers’ subject matter knowledge and the composite measure of their teaching effectiveness. The relationships between teachers’ subject matter knowledge and students’ achievement and also between teachers’ subject matter knowledge and students’ rating of the teachers’ teaching effectiveness were found to be positive and statistically significant. However, the relationships between teachers’ subject matter knowledge and teachers’ self rating as well as teachers’ subject matter knowledge and peers’ rating of teachers’ teaching effectiveness were not found to be statistically significant though they were positive. Further data analysis showed that there was a difference between the subject matter knowledge of effective and ineffective teachers and also between the students taught by effective teachers and the students taught by the ineffective teachers. / Institute of Science and Technology Education / PhD (Mathematics Education)

The purpose of this study is to formulate guidelines upon which Technology Education can be put into operation in the South African schools with specific reference to standard eight students. The objective is to formulate Technology Education guidelines suitable for and within the broad framework of the South African curricula. In attempting to translate Technology Education curriculum to South Africa, the author explores the state of advancement in Technology Education in various developed and developing countries. The status, principles and theoretical assumptions of Technology Education are also explored. The role of the teacher in the Technology Education programme is also discussed. Guidelines for Technology Education, including Technology Education teaching strategies, guidelines for Technology Education assessment standards and guidelines for integrating Technology Education, Science and Mathematics are also formulated. The author qualifies the significance of Technology Education in South Africa through a pilot study over a year. The subjects of this (pilot) empirical study consisted of a total of 175 standard eight students, 77 of who were in a control group, who had received no tuition in Technology Education. A group of 98 received tuition in Technology Education for a year. The normal end of the year examination in 1994 measured academic performance of the two groups. Performance in 1993 is also used in the statistical analysis. The Univariate Analysis of Variance (ANOVA) is applied in the analysis of data. Statistically significant differences are found between the academic performance of these two groups in relation to the overall Examination marks, English, Science and Mathematics marks. Statistically significant differences are also found between the 1993 and 1994 performance of the experimental group after receiving Technology Education tuition in standard eight in terms of the overall Examination, marks, English, Science and Mathematics marks. In the control group, no statistically significant differences were evidenced in Mathematics, English and Science when comparing marks in 1993 and in 1994. It is only applicable in the average Examination mark. These results confirm the role that Technology Education plays in enhancing performance in Science and Mathematics including English. / Curriculum and Institutional Studies / D. Ed. (Didactics)

The study intends to investigate the nature and cognitive demands of contextual word-problems posed in the FET mathematics examinations of IEB and NSC. The analysis of the mathematization of real-life situations to form contextual word-problems is based on the theory of authentic task situations. The theoretical basis for analyzing mathematics teaching and learning is the Realistic Mathematics Education (RME) theory. Data was obtained using the schedule of mathematization of real-life situations and the schedule of total marks of contextual word-problems and national performance. All contextual word-problems included in the 2008-2013 question papers of IEB and NSC mathematics examinations were analysed. The research revealed that 509 marks out of 1800 marks were allocated to contextual word-problems in IEB examinations; whereas 473 marks out of 1800 marks were allocated to contextual word-problems in NSC examinations. / Mathematics Education / M. Sc. (Mathematical Education)