Wiskunde as taal van die wetenskap en tegnologie is een van die weinige vakke wat spesifiek as voorvereiste vir die bestudering van sekere studierigtings gestel word. Leerlinge met Wiskunde-angs word verhoed om hul ware potensiaal in Wiskunde te verwesenlik en word sodoende gediskwalifiseer om hul regmatige plek in die beroepswereld in te neem. Die doel van hierdie studie was om te bepaal of hipnoterapie aangewend kan word om Wiskunde-angs tot werkbare vlakke te beperk sodat leerlinge optimaal in Wiskunde kan presteer. Die aard, oorsake, aanvang, herkenning, verklaring, gevolge, voorkoms en meting van Wiskunde-angs, die verband daarvan met Wiskundeprestasie en die hulp wat onderwysers en hulpprogramme kan lewer, is nagegaan. Daarna is hipnose en hipnoterapie beskou om te bepaal of dit as terapeutiese hulpmiddel pedagogies verantwoordbaar is. 'n Hipnoterapieprogram is in werking gestel en daar is bevind dat die proefpersone almal tot 'n mindere of meerdere mate daarby gebaat het. / Mathematics as the language of science and technology is one of few subjects used as entrance requirement to certain fields of study. Mathematics anxiety prohibits certain pupils to reach their full potential in Mathematics and thus to obtain their rightful place in the world of work. The aim of this study was to determine whether hypnotherapy can be used to lower Mathematics anxiety levels to such an extend that pupils can optimally achieve in Mathematics. The nature, causes, extent, recognition, explanation, consequences, incidence and measurement of Mathematics anxiety, its relationship to achievement in Mathematics, as well as the help that can be rendered by teachers and treatment programmes were studied. Hypnotherapy was then examined to determine whether its use was pedagogically justifiable. A hypnotherapy treatment programme was introduced which was found to be to some extent beneficial to all the subjects used. / Psychology of Education / M. Ed. (Voorligting)

This study explored the influence of irrational beliefs on adolescent secondary school learners’ Mathematics achievement in Zimbabwe. Learner, home and school factors which influence secondary school learners’ Mathematics achievement were discussed and relevant studies were scrutinised. The theoretical views of Albert Ellis regarding the characteristics, effects, acquisition and maintenance of irrational beliefs were discussed together with the major irrational beliefs and their possible relationship with learners’ Mathematics achievement. A sample of 306 randomly selected adolescent Mathematics learners comprising 182 girls and 124 boys in the 14 to 18 year age range participated in the study. A composite questionnaire with subscales on learners’ irrational beliefs, socio-affective variables and perceptions was used during the empirical investigation. Six major hypotheses were tested. The study established that learners’ irrational thoughts about Mathematics correlate negatively with their Mathematics achievement. Learners’ irrational thoughts about Mathematics correlated negatively with motivation, self-concept, parental involvement, and teacher-learner relationships and positively with stress, anxiety and faulty perceptions. Regression analysis proved that learners’ irrational beliefs, socio-affective variables and perceptions jointly explain a greater proportion of the variance in Mathematics achievement than any one of these factors on its own. Therefore, learners’ Mathematics achievement is affected by irrational beliefs together with their socio-affective variables and perceptions. Practical recommendations were given to Mathematics education stakeholders such as teachers, school counsellors, parents and learners to minimise poor Mathematics achievement attributable to irrational beliefs and the allied variables explored in this study. / Psychology of Education / D. Ed. (Psychology of Education)

This study explored the link between teachers’ inputs and process and students’ academic achievement in Junior Secondary Certificate (JSC) Mathematics for the period 2006 to 2010.The outcome (teacher effectiveness) was obtained by means of value added measures (students’ aggregate JSC Mathematics scores for 2006 to 2010 by school). One hundred and fifty JSC schools out of a total of 573 constituted the units of analysis for the study. The data regarding teachers were obtained by means of self-administered questionnaires, and JSC Mathematics results from 2006 to 2010 were obtained from the Directorate of National Examinations and Assessment (DNEA). Multi-correlation and regression techniques at alpha =0.001; 0.05 and 0.10 were used to analyse the link between teachers’ inputs and processes, and students’ academic achievement in JSC Mathematics. The null hypotheses formulated for the study were tested at the 0.05 (5%) level of significance. In summary, it appears that the various aspects of teachers’ inputs (teachers’ educational qualifications, teaching experience, subject specialisation etc.), processes (standards-based professional development, standards-based classroom activities, and classroom management beliefs) are related to students’ academic achievement in JSC Mathematics. In particular, a linear combination of the following variables had a significant and positive association with students’ academic achievement in JSC Mathematics: teachers’ major in Mathematics (teachers’ inputs); teachers’ usage of whole class discussion (standards-based classroom activities); perceived knowledge of algebra; teachers’ professional development in interdisciplinary instruction; teachers’ review of students’ homework/assignments; and students talking to other students about how to solve mathematics problems. Teachers’ pedagogical content knowledge (PCK) in general, and some classroom practices were not significantly related to students’ academic achievements. This study, therefore, recommends that teachers’ professional development should focus on the subject matter that the teachers will be teaching, as well as alignment of teachers’ learning opportunities with real work experience using actual curriculum materials and assessment. / Educational Studies / D. Ed. (Didactics)

Text in English, Zulu and Afrikaans / The study investigated assistive technology for the deaf, specifically applied to the teaching and learning of mathematics at a rural Namibian special primary school. The problem was the lack of prior research about the effects of Constructivist assistive technology for guiding Namibian special schools and educators. The objective was to conduct an experiment with deaf learners and interviews with the teachers involved. The study was a mixed methods study, involving quantitative academic achievement data and qualitative interview data. The findings suggest that there was a statistically significant effect on the multiplication and division achievement of the learners, but not their addition and subtraction achievement. The emergent Constructivist-related categories were collaborating, cooperating, exploring, selfassessing, learning from errors, seeking knowledge independently, self-regulating, selfreflecting, metacognitive thinking and being self-aware. These scientific insights contribute to the field and stem from a useful method for reviewing and selecting an appropriate learning theory and assistive technology. / Isifundo socwaningo siphenya ngobuchwepheshe obuluncedo kulabo abayizimpumputhe, ikakhulukazi lolu cwaningo lumayelana nokufundisa kanye nokufundwa kwesifundo sezibalo esikoleni sabakhubazekile endaweni yasemakhaya ngaseNamibia. Inkinga lapha ukusweleka kocwaningo lwangaphambili olumayelana nemithintela yohlelo lobuchwepheshe oluncedayo losolwazi abangama-contructivists ngokuhola izikole zabakhubazekile zaseNamibia kanye nabafundisi. Inhloso kwaye kuwukwenza ucwaningo oluphathekayo kanye nabafundi abakhubazeke amehlo kanye nenhlolovo nothisha ababandakanyekayo, ngokusebenzisa ucwaningo oluxubile, oluxuba idatha mayelana nempumelelo kwezemfundo kanye nedatha yezamanani yenhlolovo. . Okutholwe wucwaningo kuchaza ukuthi kunomthelela obonakalayo wezamanani mayelana nempumelelo yekhono lokuphindaphinda kanye nokwehlukanisa, kodwa hayi impumelelo yabo ngokwekhono lokuhlanganisa kanye nokunciphisa. Izigaba ezihambisana nosolwazi abakhasayo zisebenza ngokuncedana, ngokusebenzisana, ngokuvumbulula, ngokuzihlola wena siqu sakho, ngokufunda ngokwenza amaphutha, ngokucinga ulwazi ngokuzimela, ngokuzenzela imigomo, ngokubheka impumelelo yakho, ngokucabangisisa ngokusebenzisa ulwazi kanye nokuzibhekisisa. Lolu lwazi lwezesayensi lunomthelela emkhakheni kanti lususelwa endleleni esebenzayo ngokubuyekeza kanye nokukhetha ithiyori yokufunda efanele kanye nohlelo oluncedayo lobuchwepheshe. / Die studie het ’n ondersoek na bystandstegnologie vir dowes, spesifiek ten opsigte van hoe dit in die onderrig en leer van wiskunde by ’n landelike spesiale laerskool in Namibië toegepas word, behels. Die navorsingsprobleem was die gebrek aan navorsing oor die effek van konstruktivistiese bystandstegnologie wat leiding aan Namibiese spesiale skole en opvoeders kan bied. Die navorsingsdoelwit was om ’n eksperiment met dowe leerders uit te voer en onderhoude met die betrokke onderwysers te voer as deel van ’n gemengdemetodestudie, wat die insameling van kwantitatiewe data oor akademiese prestasie en kwalitatiewe onderhouddata behels het. Die bevindings van die studie dui op ’n statisties beduidende effek op die leerders se prestasie met betrekking tot vermenigvuldiging en deling, maar nie hulle prestasie met betrekking tot optel en aftrek nie. Die voortkomende konstruktivisties-verwante kategorieë is meewerking, samewerking, verkenning, selfassessering, die vermoë om uit foute te leer, ’n onafhanklike soeke na kennis, selfregulering, selfbesinning, metakognitiewe denke en selfbewussyn. Hierdie wetenskaplike insigte lewer ’n bydrae tot die studieveld en spruit uit ’n nuttige metode vir die beoordeling en seleksie van geskikte leerteorieë en bystandstegnologie. / School of Computing / M. Sc. (Computing)

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This research investigates the relationship between the attitude of senior secondary mathematics educators towards school and the achievement of their learners. A literature study examined research into the relationships between an educator's attitude towards his or her school management team, colleagues, learners, parents, the subject of mathematics and the factors influencing mathematics achievement. An empirical investigation used a quantitative research design to collect data from selected senior secondary schools in the Eastern Cape Province of South Africa. A questionnaire was used to gather data and a statistical data analysis was conducted to calculate frequencies and test hypotheses. Findings indicated the existence of a relationship between educators' attitudes towards school and the achievement of their learners. It was therefore recommended that school managers should be very sensitive to the climate prevailing in their schools in order to encourage mathematics educators and thus, indirectly, learners in this vital subject. / Educational Studies / M. Ed. (Didactics)

In this study, senior certificate (standard 10) pupils' attainment of the cognitive and affective aims and objectives of the senior certificate mathematics curriculum was investigated. With regard to the attainment of the cognitive objectives and aims, senior certificate pupils' performance in their mathematics examination, in terms of three broad categories of cognitive abilities (lower level, middle level and higher level mathematical abilities) was analysed and examined. As no norms (criteria) for mathematical attainment in respect of these three categories of cognitive abilities could be identified, these norms had to be firstly developed by the researcher. However, suitable standardised scales were identified and administered to determine senior certificate pupils' attainment of the affective aims and objectives (attitude towards and interest in mathematics). Besides the quantitative analysis, qualitative assessments of senior certificate pupils' attainment of the cognitive and affective aims and objectives were also made using information obtained, by way of a questionnaire, from teachers of senior certificate mathematics classes. The main findings that emerged from this investigation were: * The senior certificate pupils are attaining the desired proficiency levels in the cognitive objectives and aims of the senior certificate mathematics curriculum. However, these pupils are not adequately attaining the affective aims and objectives of the mathematics curriculum. * Qualitative information elicited from senior certificate teachers of mathematics tends to support the above findings which were obtained from the quantitative analysis. * There is a need for curriculum development in certain areas of the senior certificate mathematics curriculum, particularly in Euclidean geometry, for standard grade pupils. In terms of the general findings, certain recommendations were also formulated. In several ways, the present research is a pioneering effort in evaluating the efficacy of the cognitive and affective aims and objectives of the senior certificate mathematics curriculum. It is hoped that this study will serve as a catalyst for future research. / Curriculum and Instructional Studies / D. Ed. (Didactics)

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 explored factors that affect academic achievements in Grade 6 mathematics classrooms in a case of solving word problems. It investigated empirically the causes and perceptions that lead to difficulties in solving word problems and eventually identified strategies for teaching them. The constructivist philosophy was adopted. The study used the mixed-method design with quantitative data complementing the qualitative information. In gathering data, a word problem task, questionnaires, a class observation schedule, face-to-face and focus group interviews were used, focusing on SFS (pseudo) school learners and their teachers as a convenient sample. Data analysis was done in an integrated fashion where concurrent triangulation was followed. The statistics results illustrate that factors such as English language proficiency adversely affect the academic achievements of Grade 6 learners when solving word problems. Reading instructions aloud repeatedly and explaining key mathematical concepts have emerged as key strategies in understanding and solving word problems in mathematics. / Inclusive Education / M. Ed. (Inclusive Education)