The twenty-first century society demands a high level of mathematical literacy. This drove Korean educators to evaluate their students using international mathematics tests such as TIMSS, PISA and IMO. In these tests, Korean students ranked highly among the participating countries. Korean students, however, had done poorly in the application of mathematics in daily life situations as well as in their interest in mathematics in comparison to those of other countries. Based on these observations, the present study was an investigation on the contexts which Korean grade 8 to 10 students would prefer to deal with mathematics, in order to improve these weak points and thus increase their mathematical power. The aim of the study was to investigate mathematical literacy in connection with the relevance of mathematics and mathematical modelling. The study paid more attention to mathematics education in real life situations.

This half-thesis gives an overview of the influence of the microcomputer on the way in which mathematics is done, taught and learnt. The nature of mathematics and the nature of the tutor, tool and tutee modes of microcomputer usage are discussed as background. A case is made for the use of action research methods and a classroom-based curriculum development model to facilitate innovation and the integration of the microcomputer into the mathematics classroom. A curriculum development cycle of situation analysis. planning, trial and evaluation is advocated. This approach is used to develop a microcomputer-based course aimed at enhancing the reasoning skills of standard 7 pupils. Pupils, working in groups of three, interact with the PROLOG system to build up databases of facts and rules. The microcomputer is used in tutee mode. In "teaching" this tutee, pupils discover the need for formal language and logical reasoning. Active learning is promoted by pupils' interaction with the PROLOG system and by discussions within groups. In this environment the teacher becomes a consultant and constructive critic rather than a lecturer. Findings suggest that the microcomputer plays an important role in terms of pupil motivation and that the microcomputer-based course enables pupils to experience formal language usage and logical reasoning·as relevant activities. Pupil databases provide evidence of the pupils' ability to make appropriate use of rules and to distinguish between and-conditions and or-conditions. The objective of making pupils think was largely achieved. It is recommended that the course be incorporated in the standard 1 or standard 8 curriculum to complement or replace parts of the Euclidean geometry sections as a vehicle for developing logical reasoning skills. Suggestions for the further use of the microcomputer as an investigative tool in mathematics classes and for further microcomputer-inspired courses are also made. The provision of appropriate training to enable teachers to make effective and innovative use of the microcomputer in mathematics lessons is advocated.

The proliferation in the number of schools offering junior secondary education in Namibia since independence in 1990 has led to an increase in the number of learners in the classroom and has created a wide range of mathematical proficiency among learners entering senior secondary education in grade 11. This broad range of basic mathematical ability among these learners, together with increasing classroom numbers has caused problems for the senior secondary mathematics teachers (Batchelor, 2004). The study shows that diagnostic testing can prove to be useful in assessing learners’ mathematical preparedness by identifying learners’ areas of weakness, which have hindered their mathematics learning and performance. Taking the results of a diagnostic test into consideration could help teachers cater for their learners who need remediation classes as early as possible before extending the mathematics curriculum. Setting and using diagnostic testing requires careful consideration; there are many pitfalls that are highlighted in this research. These include question coverage and general analysis of category totals.

This study investigates the types of mathematics teaching aids available at both public and private secondary schools in Windhoek. The study characterises their usage and source as well as teachers’ perceptions towards the use of such teaching resources in the Mathematics classroom. The study is grounded in an interpretive paradigm and employed a mixed methods approach to generate both quantitative and qualitative data in two sequential phases. Phase 1 of the research process, which involved 75 Mathematics teachers, took the form of an audit of the availability and use of teaching aids at 25 secondary schools in Windhoek. A case study methodology was adopted in Phase 2 which focused on five purposively selected schools that displayed different characteristics in terms of the availability of teaching resources. The study found that the majority of teachers at secondary schools in Windhoek have a positive attitude towards the importance and role of teaching aids in Mathematics, seeing them as promoters of hands-on engagement, visual reasoning, active participation and motivation amongst learners. However, in some instances schools are underresourced with respect to certain types of teaching aids, specifically graph boards, geoboards, geometric models and computers. A need for appropriate in-school support on the use of teaching aids was also identified

The influence of modern technology on education is becoming more noticeable and has implications for the curriculum and the teaching methods of mathematics. The microcomputer can be used effectively as a powerful teaching and learning aid within the mathematics classroom. This study considers the role of the computer as an aid to teachers and pupils in the teaching and learning of mathematics and shows it as having great potential. At present relatively few schools in South Africa are using the computer as a teaching aid in the mathematics classroom. The researcher proposes that some reasons are a shortage of suitable programs, the fact that few teachers have adequate skills in educative uses of the computer and most teachers are not skilled in programming techniques. Based on this assessment of the problem, spreadsheet programs related to some mathematics lessons, together with teaching notes and pupils' material have been developed. Besides describing the potential of the computer in mathematics, this study outlines the development of three spreadsheet packages and suitable teaching methodologies used for each package, and assesses an action research investigation undertaken by the researcher, teachers and pupils when using these spreadsheet packages in six classes. The findings of the investigation are most encouraging. The overall conclusion is that computer spreadsheet packages can assist the teacher in making the learning of mathematics more effective, more interesting and more enjoyable.

There is a variety of possible ways in which computers can be used to enhance mathematics education. This thesis attempts to identify, analyse and classify these possibilities, particularly at the secondary school level. It describes and exemplifies applications ranging from drill-and-practice through games and simulations to problem solving by computer programming. Software evaluation procedures are considered in some depth. Illuminative evaluations of various items of software and there classroom use are reported. The underlying methodology is small-scale action research. Insights gained during the process of investigating each class of software lead to the eventual formulation of a scheme for classifying mathematics education software by means of 'multidimensional attributes'. It is contended that this scheme will help mathematics teachers to make well informed and sound professional judgements regarding the evaluation and use of computer programs for teaching/learning purposes. Also, it is hoped that this scheme and the thesis as a whole will contribute towards the establishment of well founded standards and procedures for software development in the field of mathematics education. Several implications of the computer for the mathematics curriculum in South Africa are suggested. A note of caution is sounded regarding possible detrimental effects of the computer and several questions requiring further research are posed. A recommendation arising from the thesis is that in-service training courses concerning computer applications in mathematics education should be run for secondary school teachers.

The investigator's experience of teaching mathematics at a college of education since 1983 has reinforced his conviction that trainee students come to college with significant gaps, weaknesses and faults in their (mathematical) conceptual structures, probably as a result of shortcomings in the mathematics teaching to which they have been exposed. The theme of this investigation is thus a natural choice that appeared to be of immediate relevance to secondary school mathematics teaching. The analysis of the issue leads to a unified perspective: the problem is placed in a theoretical framework where Bruner [spiral curriculum], Ausubel [structured learning] and Skemp [relational understanding] are brought together. How the curriculum, textbooks and examination influence school mathematics teaching is examined in some depth and the consequences investigated. Two specific topics, viz. the generalised Pythagorean relation and absolute value are investigated in relation to published work, curriculum and textbooks, and each (topic) is presented as a unifying theme in secondary mathematics to standard 9 pupils. The classroom exercise is assessed to test the hypothesis that structured, integrated presentation around a spiral curriculum promotes "relational understanding". Analysis of results supports the hypothesis.

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)

Thesis (MEd (Education))--Cape Peninsula University of Technology, 2016. / Education in South Africa is a concern to many stakeholders, including government, teachers, teacher unions and non-governmental organisations, owing to the poor academic performances of learners. Mathematics teachers, the focus of this study, are confronted with a constantly changing curriculum. Teachers are often targeted by the education authorities and general public as the primary cause of the poor outcomes of education in South Africa. This study considers the experiences of Grades 10–12 mathematics teachers in the Cape Winelands regarding curriculum change and its influence on their professional practice. The basic assumptions of social constructivism served as overarching theory. The researcher judged that a conceptual framework would make for a clearer and more systematic way of dealing with the constructs that underpin this study. The conceptual analysis framework, which was developed by combining the work of Rogan and Grayson, as well as that of Remillard, which is a perfect fit to this study, guided the interpretation and analysis of the data. A deductive approach in data analysis was applied in accordance with the conceptual framework used in this study. Being explorative in nature, this study is a qualitative design and therefore an interpretive methodological approach was followed. A purposive and convenience sampling method was used whereby teachers from six schools were pre-selected: two from ex-Model C schools, two from previously disadvantaged black schools and two from previously disadvantaged coloured schools. Semi-structured interviews were conducted. The findings of this study pointed to teachers’ acceptance of education reform and changes in the curriculum, provided they were not too radical. Teachers requested involvement on a broad spectrum throughout the planning and implementation process, and proper training and support prior to implementation. Factors that militated against implementation were, among others, poor facilities, resources and instructional aides; poorly trained change facilitators; poor leadership and management at schools; and the many constraints that the learners brought to the school and the classroom.

D.Ed. / Adolescents who achieve inadequately in mathematics often experience that the different aids available to assist them on their road to recovery are not sufficient. Most adolescents do not know how to bring about desired change. They are not aware what their problem areas are and how it should be addressed. Due to growing numbers in the classrooms in formal teaching, the teacher cannot assist the student individually on an ongoing basis. Factors within the student and his circumstances may also prevent him from benefiting from assistance. Furthermore, most adolescents in the senior secondary phase, who want to study further, are pressurized by educational bodies for higher marks. Therefore, limited time also becomes an issue. Although several studies have been carried out to investigate this matter and create models, the majority of practical programmes lacked depth and a holistic approach.