This is an investigation explaining the relationship between the home environment and mathematics performance of 12 grade eight students from a high school in Durban, South Africa. One of the data collection methods was a 25-question test, based on the TIMSS test, namely a TIMSS equivalent mathematics test. The test was analysed and its relation to the South African syllabus, the students' familiarity with the type of questions and the multiple-choice mode of answer used in the TIMSS study, was investigated. The test scores were also used to identify high performing and low performing students to be interviewed about their mathematical, personal and home backgrounds. A student questionnaire was administered to these selected students as a basis for the interviews. An in depth one on one interview and records of the students' achievements in grade 7 and grade 8 in languages and mathematics, as well as school family records were used for the analysis. The life stories of the six high performing and six low performing students were then constructed and analysed with respect to: their achievements in mathematics and language; their home backgrounds; how their mathematics performance is affected by their home environments; and the effect of parental involvement in their lives. Finally research findings from the interviews on the home lives and experiences of the 12 grade 8 students from a high school in Durban are presented. Implications are put forward and recommendations made. / Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2006.

Mathematical modelling is an area in mathematics education that has been much researched but conspicuously absent from the South African curriculum. The last few years have seen a move towards re-inclusion of mathematical modelling in the South African school curriculum. According to the National Curriculum Statement (2003a), “mathematical modelling provides learners with the means to analyse and describe their world mathematically, and so allows learners to deepen their understanding of Mathematics while adding to their mathematical tools for solving real-world problems”. The purpose of this study was to explore pre-service mathematics teachers’ conception of mathematical modelling and the different strategies that pre-service mathematics teachers use when solving real-world mathematics problems. This study further investigated pre-service mathematics teachers’ ability to facilitate the understanding of specific mathematical modelling problems. Twenty-one fourth year Further Education and Training students from the Faculty of Education, University of KwaZulu-Natal participated in this study. In order to obtain appropriate data to answer the research questions, the researcher designed three different research instruments. The open-ended questionnaire and the task-based questionnaire were administered to all the participants, whilst ten participants were chosen to be interviewed. The data that was collected was analysed qualitatively. The research findings emanating from this study suggested that pre-service mathematics teachers did not have a suitable working knowledge of mathematical modelling, but were nonetheless able to use their mathematical competencies to solve the three real-world problems that formed part of the task-based questionnaire. It was found that although the participants were aware of different strategies to solve these real-world mathematics problems, they choose to use the ones that they were most familiar with. It is hoped that this study would prompt more universities to include mathematical modelling courses in the curriculum for prospective mathematics teachers. / Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2008.

This research study explores six primary school learners’ transition to secondary school and the influences that this may or may not have had on their mathematical performances. The study was carried out over a seven month period, that being the latter part of their final primary school year until the end of the first term of high school (October 2010 to April 2011). Various data collection methods were employed to retrieve information and much literature was used to inform this study. In the chapters to follow there are detailed descriptions of various stakeholders in the transition process as well as the factors that affect mathematics learning. The analysis of data reflects the findings of this study and discusses some of the implications regarding mathematics teaching and learning that should considered during the transitional period from primary school to secondary school. / Thesis (M.Ed.)-University of KwaZulu-Natal, Durban, 2011.

The quality of education in most historically black schools is a source of concern for many people. The high failure rate in mathematics in particular, is believed to result in part, from the inadequacy of the teacher preparation programs at many of the colleges of education in the country. Esikhawini College of Education in KwaZulu-Natal is one of the colleges which is involved in the preparation of secondary school mathematics teachers. The appropriateness of the mathematics curriculum of this College was the subject of the study. In particular, the study aimed at the following: (i) To analyse aims and philosophies underlying the prescribed mathematics curriculum of the College. (ii) To establish the teacher educators' and student teachers' perceptions of the appropriateness of the curriculum in general. (iii) To establish the teacher educators' and student teachers' perceptions of the mathematics curriculum content and processes. (iv) To establish the quality of available materials used at the College for realisation of the curriculum goals. (v) To offer proposals and recommendations for the improvement of the education of prospective secondary mathematics teachers. Data about the perceptions of the appropriateness of the mathematics curriculum was gathered through a questionnaire which was administered to one hundred and one student teachers. The issues that arose from the questionnaire study were followed up by an interview study. The interview schedule was administered to a sample of fourteen student teachers and all six mathematics teacher educators in the College. In addition, a survey of mathematics materials available at the College library and in the mathematics department was carried out to collect further data. Some of the significant findings of the, study were : • Limitations in the College mathematics curriculum in as far as the curriculum content and processes were concerned. • Inadequacy of mathematics curriculum materials that were available and used at the College. • Low attainment in mathematics at matriculation level of most of the student teachers. • Widespread dissatisfaction with the curriculum, especially that of Mathematics Didactics. The implications of the findings for the College were considered. Amongst other suggestions is the suggestion that the College introduces a preliminary STD course in which prospective student teachers' mathematics background is enriched to enable them to cope with the demands of the College curriculum.

This qualitative study examines the use of Visual Technology for the Autonomous Learning of mathematics (VITALmaths) video clips in three Grade 9 classrooms in the Eastern Cape, South Africa, two of which are in well-resourced ex-Model C schools and one in a semi-rural township school. The rapid development of mobile technology, especially in Africa, has opened up previously unexplored avenues in economy, communication and education (Aker & Mbiti, 2010), with a number of mobile learning initiatives being launched in South Africa (Botha & Ford, 2007; Vosloo & Botha, 2009). The VITALmaths project was developed collaboratively between the University of Applied Sciences Northwestern Switzerland and Rhodes University in South Africa (Linneweber-Lammerskitten, Schäfer and Samson, 2010). As the main platform for dissemination of the video clips is the cell phone, the study looked at the various aspects involved in the use of cell phones by learners in the classroom, as well as the incorporation of the clips into the teaching of three teachers. Consideration was given to whether or not the clips assisted the teachers in teaching, as well as whether or not they encouraged further exploration. The study was divided into six stages during which data was collected and analysed using an interpretive approach throughout. Data collection methods included semistructured interviews, questionnaires, observation, journals and reflective essays. The study revealed the participating teachers, having incorporated the clips into several lessons, found that these had a meaningful effect on their teaching practice, as well as on the engagement of the learners in the lessons. The majority of the learners involved in the study had access to cell phones, either their own or borrowed, and were able to download the video clips onto their phones from the website (www.ru.ac.za/vitalmaths). A number of learners found that the clips helped them find examples of specific mathematical concepts outside of the classroom, thus leading to further enquiry and exploration, while several learners downloaded and viewed additional clips. Overall findings showed that the VITALmaths video clips could be incorporated into teaching with relative ease.

The study reported here utilised a theory of levels of geometric thinking. This theory was proposed and developed by two Dutch mathematics educators, Pierre van Hiele and his wife, Dina van Hiele-Geldof. The van Hiele theory enables investigations into why many students experience difficulties in learning geometry. In many nations, such as the UK, the USA, Netherlands, the USSR and to a certain extent, Nigeria and South Africa, research evidence has indicated that the overall students’ mathematical competencies are linked to their geometric thinking levels. This study is the first of its kind to apply the van Hiele theory of geometric thinking in the Namibian context to analyse geometrical conceptualisation in Grade 12 mathematics students. In all, 50 Grade 12 students (20 from School A and 30 from School B) were involved in this study. These students wrote a van Hiele Geometry Test adapted from the Cognitive Development and Achievement in Secondary School Geometry test items. Thereafter, a clinical interview with the aid of manipulatives was conducted. The results from this study indicated that many of the School A and School B students who participated in the research have a weak conceptual understanding of geometric concepts: 35% of the School A and 40% of the School B subsamples were at the prerecognition level. 25% and 30% of the School A, and 20% and 23.3% of the School B students were at van Hiele levels 1 and 2 respectively. An equal number of students but different in percentages, 2 (10%) in School A and 2 (6.7%) in School B, were at van Hiele level 3. Only one student from School B attained van Hiele level 4. These results were found to be consistent with those of previous similar studies in UK, USA, Nigeria and South Africa. The findings of this study also highlight issues of how the Namibian Grade 12 geometry syllabus should be aligned with the van Hiele levels of geometric thinking as well as the use of appropriate and correct language in geometrical thinking and problem solving.

This study reports on the extent to which selected mathematics teachers facilitate the teaching and learning of geometry at the van Hiele levels 1 and 2 at a Grade 10 level in selected schools in Namibia. It also addresses and explores the teaching strategies teachers employ in their classrooms. Kilpatrick et al.’s model for proficient teaching and the van Hiele model of geometric thinking were used to explore the type of teaching strategies employed by selected mathematics teachers. These two models served as guidelines from which interview and classroom observation protocols were developed. Given the continuing debate across the world about the learning and teaching of geometry, my thesis aims to contribute to a wider understanding of the teaching of geometry with regard to the van Hiele levels 1 and 2. There are no similar studies on the teaching of geometry in Namibia. My study concentrates on selected Grade 10 mathematics teachers and how they teach geometry using the van Hiele theory and the five Kilpatrick components of proficient teaching. As my research looks at teaching practice it was important to deconstruct teaching proficiency with a view to understanding what makes good teachers effective. The results from this study indicated that the selected Grade 10 mathematics teachers have a good conceptual understanding of geometry as all of them involved in this study were able to facilitate the learning and teaching of geometry that is consistent with the van Hiele levels 1 and 2.

The research presented in this thesis is a case study located in the interpretive paradigm of qualitative research. The focus is on the use of van Hiele's theory to explore problems encountered in circle geometry by grade 11 learners and making some policy recommendations concerning the curriculum structure and teaching of the geometry at all grades. The interpretation is based to the learners' background in geometry i.e. their prior knowledge and experience of learning geometry. The study was carried out over a period of three years. The data collection process took a period of two months (April and May 2003) with a group of 21 grade 11 mathematics learners in a rural senior secondary school in the Eastern Cape. The researcher used document analysis, worksheets, participants' observation, van Hiele tests, a questionnaire and semi-structured interviews to collect data. The study showed that the structure of the South African geometry syllabus consists of a some what disorganized mixture of concepts. It is not sequential and hierarchical and it sequences concepts in a seemingly unrelated manner. The study revealed that the South African high school geometry curriculum is presented at a higher van Hiele level than what the learners can attain. The findings of the study showed that many of the grade 11 learners were under-prepared for the study of more sophisticated geometry concepts and proofs. Three categories of reasons could be ascribed to this: Firstly, there was insufficient preparation of learners during the primary and senior phases. Secondly the study indicated that there is overload of geometry at the high school level in the South African mathematics curriculum. Thirdly, the over-reliance on the traditional approach to teaching geometry, poor presentation of mathematical technical concepts and language problems, were identified as possible additional reasons for the poor learner understanding of geometry in general and circle geometry in particular. The study recommends that the structure of the South African geometry curriculum should be revisited and redesigned. Teachers should be empowered and developed to be more effective in teaching geometry through further studies in mathematics and in-service workshops. They should also be engaged in the process of implementing the van Hiele's theory in the teaching of geometry in their classrooms.

This study provides a qualitative examination of the role of visualization through an understanding of the thought processes that occur during visualization when Grade 9 learners engage in data handling and spatial tasks. Data were gathered in a problem-centred context from learners' written responses in order to determine the students' visuality. Visuality is defined as how often learners used visualization. In addition interviews were conducted with the learners who described the thought processes that they engaged in during visualization while involved in problem solving. The role of visualization was highlighted through the processes that learners described during the interviews. The tasks which provided manipulative materials helped learners create visual images which promoted the process of visualization. Certain recommendations were made. Knowledge of the role of visualization enables the educator to encourage the use of visualization during the teaching of mathematics. / Educational Studies / M.Ed. (Mathematical Education)

The Lesotho Junior Secondary Examination Analysis (2009 and 2010) revealed that students performance in Mathematics in general and Transformation geometry of rotation in particular was generally poor. Only a few number of students that sat for the final Form C Examination passed. This study employed the van Hiele’s levels of learning to investigate and describe the difficulties students have in the learning of rotational transformation geometry. Both a written test and interview were used to solicit information regarding students’ difficulties. This information was collected from 90 students from Qaoling Secondary School in Maseru district in Lesotho. Findings from the study revealed that students had difficulties in identifying and naming transformation of rotation, finding the centre, angle of rotation and locating the exact image of a rotated figure after rotation. Also, they had greater difficulties when using transformation to do proof. The analysis showed that students mostly had difficulties at the level of Abstraction and Deduction. This gave an indication that the vast majority of the students in Form C are reasoning at the lowest two levels of the van Hiele’s model which are Visualization and Description. For these students’ difficulties to be curbed, the analysis demonstrated amongst others that teachers needed to use Manipulative materials and Information Communication Technology (ICT) during the process of teaching and learning. Manipulative materials provide experience in which students can transfer their understanding smoothly from one concept to another. / Mathematics Education / M. Ed. (Mathematics Education)