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.

Over many years the practice or art of teaching Mathematics posed itself as, not only being different from the practice of teaching any other subject, but to have many challenges and opportunities that ask for exploration and understanding. Just after independence in 1990, Namibia has embarked upon a reform process for the entire education system. Many changes were brought about to create a uniform, equal system for all. However, many challenges still remain to be addressed. Mathematics education remains one of the key areas where Namibian teachers can contribute towards the improvement of the subject. Unsatisfactory results, under-qualified teachers, and a negative disposition towards Mathematics are some of the challenges. These challenges are not unique to Namibia. Across the globe psychologists, philosophers and educators continue to engage in debates and research projects in search of answers and solutions for the improvement of Mathematics education. Despite encountering numerous obstacles, many teachers are dedicated and achieve outstanding results with their learners. This thesis reports on a research project that focused on the Mathematics teaching practice of two teachers whose experiences can make a positive contribution to the improvement of Mathematics teaching in Namibia. Furthermore, this case study investigated and attempted to understand the Mathematics teaching practices of two proficient teachers who each claimed to have a specific and unique approach to teaching Mathematics. The one claimed to be mainly procedural in her Mathematics teaching, while the other one claimed to teach mainly in a conceptual manner. Both achieve very good results with their classes and attribute their own teaching orientations to a process of several experiences they went through as students and in their careers. The study revealed that both claims are substantiated and that each teacher was consistent in her claimed approach. Many challenges and constraints were encountered by both teachers, but in their unique and specific ways each teacher’s chosen teaching approach supported them to overcome these. It was evident from the findings that each teacher’s practice came about as an evolutionary process over an extended period of time. As many challenges and limitations are universal, it is believed that in sharing experiences, teachers can benefit from each other by improving their practice. It was clearly stated by both participants that the re-thinking of and reflecting on their own practices provided them with new insights and motivation. Peer support and sharing of practices contribute positively towards the improvement of the teachers’ classroom practices.

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.

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The study investigated the effectiveness of Problem-based learning (PBL) in the Further Mathematics classrooms in Nigeria within the blueprint of pre-test-post-test non-equivalent control group quasi-experimental design. The target population consisted of all Further Mathematics students in the Senior Secondary School year one in Ijebu division of Ogun State, Nigeria. Using purposive and simple random sampling techniques, two schools were selected from eight schools that were taking Further Mathematics. One school was randomly assigned as the experimental while the other as the control school. Intact classes were used and in all, 96 students participated in the study (42 in the experimental group taught by the researcher with the PBL and 54 in the control group taught by the regular Further Mathematics teacher using the Traditional Method (TM)). Four research questions and four research hypotheses were raised, answered, and tested in the study. Four research instruments namely pre-test manipulated at two levels: Researcher-Designed Test (RDT) (r = 0.87) and Teacher- Made Test (TMT) (r = 0.88); post-test manipulated at two levels: RDT and TMT; pre-treatment survey of Students Beliefs about Further Mathematics Questionnaire (SBFMQ) (r = 0.86); and post-treatment survey of SBFMQ were developed for the study. The study lasted thirteen weeks (three weeks for pilot study and ten weeks for main study) and data collected were analysed using Mean, Standard deviation, Independent Samples t-test statistic, and Analysis of Variance. Results showed that there were statistically significant differences in the mean post-test achievement scores on TMT (t=-3.58, p<0.05), mean post-test achievement scores on RDT (t=-5.92, p<0.05) and mean post-treatment scores on SBFMQ (t=-6.22, p<0.05) between students exposed to the PBL and those exposed to the TM, all in favour of the PBL group. Results also revealed that there was statistically significant difference in the post-test achievement scores on TMT at knowledge (t= -23.97, p<0.05) and application (t= -11.41, p<0.05) but not at comprehension (t= -0.50, p>0.05, ns) levels of cognition between students exposed to the PBL and the TM. Based on the results, the study recommended that the PBL should be adopted as alternative instructional strategy to the TM in enhancing meaningful learning in Further Mathematics classrooms and efforts should be made to integrate the philosophy of PBL into the pre-service teachers’ curriculum at the teacher-preparation institutions in Nigeria. / Science and Technology Education / D. Phil. (Mathematics, Science and Technology Education)

This thesis is the partial product of a project begun in an effort to build a unified course in advanced high school mathematics beyond the first two years of elementary study. It is a course intended for the academic student who is preparing for the fields of engineering, the sciences, or pure mathematics. It is a course aimed at a unification and greater correlation of the various courses and topics, and at an association on the various mathematical processes involved in the various fields. It is also a course aimed at mastery of mathematics and of its operations as a whole, as a unity not as separate compartments. Furthermore, it is a course which aims to give individual instruction in a classroom situation and to meet as nearly as possible the individual needs and abilities of the students in the class. For the present, attention has been focused upon the problem of unification of the units and topics as presented in the traditional courses in advanced high school mathematics - intermediate algebra, trigonometry, and solid geometry.

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