M.Ed. / In South Africa outcomes-based education with Curriculum 2005 brought great changes to learners, educators and parents. The purpose of this investigation was in the first place to determine the influence of OBE on the classroom management of the Mathematics educator in the senior phase. Secondly this research was to determine effective classroom management guidelines. Data was collected before and after the implementation of OBE. The respondents were Grade 8 and 9 educators in four different schools, situated in four different urban communities, respresentative of the broader South African nation. Data was collected by means of focus group interviews, analyzed by means of content analysis and conducted by the researcher and an independent analyst. Teachers identified problems regarding classroom management, existing support factors and support factors that they would like to have. Many of the problems identified by the respondents were common before and after the implementation of OBE. Some of these problems were the learners lack of interest in their work, communication difficulties between the educator and learners from township communities, lack of a learning culture, a very low interest in school activities by parents, absence of resources and lack of support by the Department of Education. Educators mentioned some other problems that occurred after the implementation of OBE. A big issue to educators is overcrowding of classes and the amount of work that comes along with it. They find it impossible to teach Mathematics effectively in such big classes. Contributing to this problem are the negative attitudes of learners towards the learning situation. In OBE, the learners' input is important, and educators struggled to get them to work. Almost all the respondents require effective guidelines for teaching and the necessary resources. Educators as well as the learners struggle with the increased workload. In view of the findings, it is clear that teachers require the necessary skills for implementing OBE effectively. Enough resources, smaller classes and enough textbooks are important necessities. From this study it appeared that learners should be actively involved in the learning process, and educators have to be very well prepared for everyday's class. Well-prepared groupwork by educators provides for active involvement of the learners in the learning process and the opportunity for the learner to accept responsibility for his/her own learning success as well as that of his/her fellow-learners. Mathematics teachers need to spend more time on basic number skills, assessment of new work and should be very strict on homework. Educators in the Mathematics class have to motivate learners and this requires motivated educators. The enjoyment of learning should be a very important factor. The correct steps need to be taken by the Department of Education to ensure a positive learning experience by educator and learner.

M.Ed. / The objective of this study was to explore the possibilities of applying and using the computer in the Mathematics classroom. The effectiveness of the various possibilities of this application was of particular importance, as the main motivation for the use of the computer as educational aid in the Mathematics classroom was to promote learning effectively and to transform learners from passive to active participators in the learning environment. A literary study was assigned to a broad discussion of three learning theorems. The behaviourist, information processing and constructivist learning theories were weighed up against one another. The distinguishing characteristics of each one, as well as implications thereof on the effective learning of Mathematics, were analysed. The nature of mathematical knowledge serves ultimately as criteria for effective learning. A list of criteria and guidelines, which the learning situation had to meet, in order to promote effective learning in Mathematics, was presented before the computer could be considered as an alternative teaching strategy. In the course of the study, there was regular reference to the computer as a tutor. Varius advantages and disadantages of computer aided instruction (CAI) in the Mathematics classroom were discussed thoroughly. Four types of CAI approaches were seen as alternatives to traditional teaching methods. Each of these approaches was weighed up against the suggested/recommended list of criteria which the learning situation should meet in order to promote effective learning. As an alternative to these approaches, the possibilities of application software were considered. This study focused particularly on the possibilities of the use of spreadsheets in the Mathematics classroom. Various advantages and disadvantages of the implementation of spreadsheets in the Mathematics classroom were discussed thoroughly. During an empirical study, a lesson unit, implementing spreadsheets as teaching aid, was put to the test and its value assessed. The success of this lesson unit was evaluated according to a West. In conclusion, it can be assumed that constructivist learning theory principles served as a foundation for this study which effectively promoted learning. The learners were constructively active, on the computer, and were guided in their construction of knowledge with the assistance of inductive questions and observation of the spreadsheet generated graphs. In a group situation, the learners supported one another and the teacher acted merely as facilitator. By using spreadsheets in the Mathematics classroom as an alternative to the traditional CAI material, learning could be effectively promoted as the progression of lesson aspects and phases depended on the foundation of constructivism.

M.Ed. (Subject Didactics) / Mathematics, which plays a vital role in modern man's working 1ife and which is also of great· importance in his dai ly social life, raises many problems at the secondary and tertiary education levels. The question has arisen as to what degree the teacher's instruction in the junior primary phase is responsible for spesific problems relating to insight of the four main operations, considering that mathematical content~ from the beginning stages, is continuous and inter-related, so that one insight serves as a prerequisite to the next. The aim of the study was to form a picture, on a small scale,of the incidence of specific teaching faults and deficiencies in the tuition of the four main operations in the junior primary school phase that inhibit understanding. It is hoped that this may be of practical benefit for teacher training and the formulation of related documents, and may also stimulate further extensive research...

D.Ed. / During the past few years the teaching of mathematics has been characterized by a move away from the traditional teaching methods. With a view to improving the effectiveness of teaching and learning mathematics, the emphasis has shifted from the product to the process. The mathematical skills that need to be developed in pupils include strategies for the solving of real problems. This represents a shift from the application of mathematics to solve problems to problem solving as a teaching method. The application of a problemcentred approach in the teaching of mathematics has given rise to a need for instruments that will facilitate multidimensional assessment. This requires the revision, adaptation and expansion of the structure of existing assessment techniques. A need was identified for the formulation of clear guidelines for the assessment of pupils' mathematical competericies. Data obtained from relevant literature and from questionnaires designed for the purpose of this study were used to compile guidelines for the assessment and evaluation of mathematics pupils. New assessment methods make new demands on the designers and users of assessment instruments, and the assessment of pupils' problem solving skills make high demands on mathematics teachers. It requires a thorough knowledge of, and insight into how pupils learn mathematics. The teacher is a facilitator, a catalyst and a provider of information who teaches pupils the language of mathematics by teaching them the necessary terminology and symbolism. Because of the diversity that is present in the way pupils respond, the assessment of their problem-solving ability is a complex process. It is therefore very important that mathematics teachers be equipped with extensive assessment skills. Assessment is a complete reporting on the knowledge of the pupils; it is the tool employed to measure progress. It describes the present situation by collecting the data required for evaluation. Evaluation can be defined as the awarding of a value to progress made and conclusions arrived at on the basis of the total body of information collected. Every single facet that influences the pupils' achievement in mathematics must be assessed in order to form a complete image of their mathematical abilities. It is therefore essential to assess both cognitive and the affective facets. To ensure the reliability of the data collected with a view to assessment, a variety of assessment techniques need to be employed. Any report on the pupils' demonstration of the achievement of the desired outcomes must be more comprehensive than a single mark or symbol. Separate reports must be compiled in respect of cognitive progress and affective aspects. Pupils should receive clear guidelines on what the expected outcomes are, and on how and when assessment will be conducted. Criteria for monitoring the standard of assess .- ment must be formulated by the teacher, whose duty it is to inform the pupils fully on these. Validity and reliability are important considerations in testing. Assessment serves to emphasize the most important mathematics to be learned. The choice of assessment techniques is extremely important. A policy of continuous assessment ensures that the final decision is not based on the result of a single examination. However, promotion or the awarding of credits must be based on more than the result of a continuous formative assessment. Summative final examination assessment place the final stamp on knowledge, without which it would have been impossible to conduct an evaluation.

M.Ed. (Curriculum Studies) / Problem solving is potentially one of the most valuable skills that can be acquired in the primary school. In spite of it's value problem solving was not successful implemented in overseas countries. Schools in South-Africa have just started to implement problem solving techniques in the primary school. To ensure successful implementation of problem solving in South-Africa this study examines possible reasons for it's failure in the primary school. Success in Problem solving depends on the correct perspectives to problem solving and the feeling of success by the teachers and pupils. This implies that the teachers and pupils must see progress by using problem solving in the mathematics class. A new teaching model was designed to prevent or eliminate the failure of problem solving in the classroom. This model was developed from a problem solving perspective and can be described as a Social Constructivistic model. This model includes lesson structures, worksheets and a proposed teaching style. The.basis of the model is real world problems. It was found that after nine weeks of implementation the children were positive toward problem solving and mathematics. An empirical investigation showed that children. can become beter problemsolvers in a relative short time span. This study suggests a holistic approach to implementing problem solving in mathematics. This approach includes a change in the whole educational situation. The teacher needs maximum assistance through tutorial programs, worksheets and staff supervision.

M.Ed. (Education) / Please refer to full text to view abstract

D.Ed.

M.Ed. / Please refer to full text to view abstract

The general understanding of mathematics as a subject and its implications is, in reality alarmingly low. Evidence of this is evident in learners’ performance and their reaction towards the subject. Fractions as a domain of Mathematics are no exception. The majority of the learners do not learn Fractions comfortably. The causes of this may be varied. However, it is believed that one way of ensuring meaningful teaching and learning is to make use of appropriate connections. The significance and the important role of the teacher in making mathematical connections in learning for understanding are well documented in the literature. This study focuses on the nature of mathematical connections selected Grade 7 teachers make when teaching Fractions, as well as their perceptions of the importance of making such connections. This qualitative case study was conducted in three schools in the Oshana region. The purpose was to investigate how mathematics teachers make connections in fractions. Underpinned by an interpretive paradigm, the study made use of observations and interviews to generate data. The framework borrowed from Businkas’ (2008) study was used in analysing and coding the nature of connections used in the lessons observed. An individual conversation on the nature and perceptions of the connections made in the observed lessons was undertaken with each teacher followed by a focus group discussion that aimed at analysing deeper perceptions on connections. The main findings of the study revealed that teachers made use of all the different types of connections as per Businkas’s framework. The frequency of occurrence showed that Instruction-Oriented Connection and Multiple Representation connections topped the list of connections used. Teachers pointed out that connections to prior knowledge and making multiple representations were most significant, as they related to learners’ existing knowledge and pointed to different ways of solving a problem. The teachers were, however, not familiar with the other connections identified as this was their first experience of interrogating connections. They, however, agreed on the importance of making those connections. The teachers agreed that meaningful connections indeed helped with their conceptual understanding of Mathematics. They believed that connections can increase learners’ interest in school and help reduce negative views of fractions, in particular, and mathematics in general. However, they felt that the limited number of resources, poor teaching approaches and the inability of creating fraction sense may hinder them from making appropriate connections.

This case study, involving six Grade 10 learners, investigates how a peer tutoring programme could shape the mathematical experience and disposition of the participating tutors. The study is grounded in an interpretive paradigm and data was collected in four sequential phases. The Mathematics Dispositional Functions Inventory (MDFI) instrument was completed by the tutors prior to commencement of the tutoring programme. The tutoring sessions then took place over a three week period during which time each tutor kept a reflective journal. Semi-structured interviews were then conducted, after which each tutor completed the MDFI instrument again in order to track any potential changes in their mathematical disposition. The study found that the participating tutors showed an improved mathematics disposition after the peer tutoring experience. Not only was the peer tutoring programme an empowering experience for the tutors, it also had a positive influence on both the tutors’ self-confidence as well as their perceived mathematical ability.