published_or_final_version / abstract / toc / Education / Master / Master of Science in Information Technology in Education

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.

The Sediba project originated when investigations showed that there were many teachers in the North-West Province that did not possess sufficient subject knowledge to teach physical sciences and mathematics. In spite of many in-service training opportunities for teachers, the achievements of learners are still not satisfactory. From interviews with teachers in the Sediba Mathematics Programme the problem of unmotivated learners became apparent. From the literature it appeared that the motivation of teachers has an effect on the motivation of their learners. This study was undertaken as a result of those findings to determine whether the Sediba Mathematics Programme has an effect on the intrinsic motivation of the teachers in the programme. To understand the nature of motivation better, the motivation theories of Maslow, Herzberg, Adams and Vroom were investigated. This investigation made valuable contributions to the study and gave insight into the behaviour patterns of the teachers in certain situations. By means of the literature study a profile of a motivated mathematics teacher could be compiled. It was found that self-concept, self-efficacy, task value and the effect that change has on teachers, could be regarded as determinants of intrinsic motivation. Aided by a questionnaire, an empirical study was done to test the degree to which these determinants were present in the teachers. To bring about triangulation this was followed up by conducting interviews with a sample of the teachers. Furthermore, a mathematics competence test was done. Several models of in-service training were further investigated and the Sediba Mathematics Programme was evaluated on the basis of a set of essential elements for an ideal programme. It was found that the Sediba Programme fulfilled these requirements to a large degree. The empirical investigation, the mathematics competence test and the interviews that were held with teachers delivered the following results. It was found that the Sediba Mathematics Programme did have an effect on the intrinsic motivation of the teachers in the programme. The subject knowledge of the teachers improved significantly after only one year of study. The teachers' self-concept and self-efficacy improved, they regarded their task as important and endeavoured to implement change meaningfully in spite of existing uncertainties. Negative conditions such as overcrowded class-rooms, no/little aids, lack of safety and discipline at many schools that made it difficult for teachers to deliver quality teaching, could affect motivation negatively. Keywords for indexing: motivation, mathematics teacher, professional development, Sediba-program, in-service training and motivation, intrinsic motivation, extrinsic motivation, in-service training for mathematics teachers. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2008.

The purpose of the study is to determine the perception or views of mathematics and science educators on performance of grade 12 learners in Mafikeng district. Little has been written about secondary school educators' views with regard to performance of learners in Mathematics and Science in developing countries like South Africa. The survey method was used to gather data. A 31 item questionnaire was used to evaluate perception of educators in the areas of: Support for educators, Educator involvement, Conditions for teaching and Educators' perception on how educational change affects performance of learners in Mathematics and Science. The subjects of the study were 89 Mathematics and Science educators in the Mafikeng district. The sample was selected from the 31 high schools including senior secondary schools in the district. The empirical investigation conducted revealed that parental involvement in their children's studies is a serious problem that needs immediate attention, in addition to educator qualifications and lack of learning support materials. The study also revealed that improving performance of learners, responsibility and involvement of educators, learners, parents, government and community is essential. The conclusions drawn from the study show that educators' perceptions on performance of learners in Mathematics and Science entail cooperative and supportive structure, regular communication among staff and monitoring of school work for both educators and learners is very important. It is also important that the findings of the research be implemented to improve learner performance. / Thesis (MBA) North-West University, Mafikeng Campus, 2003

The Sediba project originated when investigations showed that there were many teachers in the North-West Province that did not possess sufficient subject knowledge to teach physical sciences and mathematics. In spite of many in-service training opportunities for teachers, the achievements of learners are still not satisfactory. From interviews with teachers in the Sediba Mathematics Programme the problem of unmotivated learners became apparent. From the literature it appeared that the motivation of teachers has an effect on the motivation of their learners. This study was undertaken as a result of those findings to determine whether the Sediba Mathematics Programme has an effect on the intrinsic motivation of the teachers in the programme. To understand the nature of motivation better, the motivation theories of Maslow, Herzberg, Adams and Vroom were investigated. This investigation made valuable contributions to the study and gave insight into the behaviour patterns of the teachers in certain situations. By means of the literature study a profile of a motivated mathematics teacher could be compiled. It was found that self-concept, self-efficacy, task value and the effect that change has on teachers, could be regarded as determinants of intrinsic motivation. Aided by a questionnaire, an empirical study was done to test the degree to which these determinants were present in the teachers. To bring about triangulation this was followed up by conducting interviews with a sample of the teachers. Furthermore, a mathematics competence test was done. Several models of in-service training were further investigated and the Sediba Mathematics Programme was evaluated on the basis of a set of essential elements for an ideal programme. It was found that the Sediba Programme fulfilled these requirements to a large degree. The empirical investigation, the mathematics competence test and the interviews that were held with teachers delivered the following results. It was found that the Sediba Mathematics Programme did have an effect on the intrinsic motivation of the teachers in the programme. The subject knowledge of the teachers improved significantly after only one year of study. The teachers' self-concept and self-efficacy improved, they regarded their task as important and endeavoured to implement change meaningfully in spite of existing uncertainties. Negative conditions such as overcrowded class-rooms, no/little aids, lack of safety and discipline at many schools that made it difficult for teachers to deliver quality teaching, could affect motivation negatively. Keywords for indexing: motivation, mathematics teacher, professional development, Sediba-program, in-service training and motivation, intrinsic motivation, extrinsic motivation, in-service training for mathematics teachers. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2008.

Submitted by DANIELA MIRANDA FERNANDES SANTOS null (danymifesa@gmail.com) on 2016-05-20T01:00:42Z No. of bitstreams: 1 tese_doutorado_daniela_miranda_fernandes_santos.pdf: 2659899 bytes, checksum: a862ae59b25bd39008f6030cb06e5bc4 (MD5) / Approved for entry into archive by Felipe Augusto Arakaki (arakaki@reitoria.unesp.br) on 2016-05-23T20:12:23Z (GMT) No. of bitstreams: 1 santos_dmf_dr_prud.pdf: 2659899 bytes, checksum: a862ae59b25bd39008f6030cb06e5bc4 (MD5) / Made available in DSpace on 2016-05-23T20:12:23Z (GMT). No. of bitstreams: 1 santos_dmf_dr_prud.pdf: 2659899 bytes, checksum: a862ae59b25bd39008f6030cb06e5bc4 (MD5) Previous issue date: 2016-03-31 / Secretaria da Educação do Estado de São Paulo / A presente pesquisa, vinculada à linha “Processos Formativos, Ensino e Aprendizagem”, foi implusionada pela questão: Qual a relação entre a álgebra acadêmica e a álgebra escolar expressa nas concepções dos licenciandos e professores do curso de licenciatura em matemática? E, teve como objetivo geral investigar a relação entre a álgebra acadêmica e a álgebra escolar expressa nas concepções de álgebra e do seu ensino entre professores e licenciandos matriculados no curso de licenciatura em matemática da FCT – Unesp de Presidente Prudente, tendo em vista subsidiar reflexões sobre a formação inicial de professores de matemática. O referencial teórico constitui-se das teorias da educação matemática acerca da álgebra, da relação entre álgebra acadêmica e álgebra escolar, das concepções de álgebra e do seu ensino e da formação inicial de professores de matemática. Com abordagem qualitativa e delineamento descritivo analítico, a pesquisa teve como procedimentos metodológicos: análise documental, questionário e entrevista, realizados ao longo do curso. O material de análise incluiu o Projeto Pedagógico do referido curso, os questionários aplicados aos licenciandos no 1º e 3º ano, as entrevistas realizadas com os licenciandos no 2º e 4º ano do curso bem como as entrevistas realizadas com professores que ministraram disciplinas diretamente relacionadas à álgebra. A análise documental associada às entrevistas realizadas com professores e licenciandos indicou que o curso atende às orientações legais vigentes. No entanto, não há justificativa para a escolha de disciplinas da grade curricular, tendo em vista a sua relevância para a formação do futuro professor. Nas proposituras do plano de ensino das disciplinas Álgebra Elementar e Álgebra I observou-se nuances da relação entre a álgebra acadêmica e a álgebra escolar, mas o seu desenvolvimento mostrou-se incoerente com tais proposituras. Na prática, priorizava-se o ensino do conhecimento matemático, caracterizando-se no modelo da racionalidade técnica, reforçando procedimentos vivenciados e internalizados durante o processo de escolarização anterior à licenciatura. No curso analisado, a ênfase curricular, quando se trata de álgebra, recaiu sobre a álgebra das estruturas. Relacionando os modelos relativos ao ensino de álgebra destacados pelos licenciandos em diversos momentos ao longo do curso, foi possível perceber que se trata de modelos pautados na definição, seguida de exemplos, resolução de exercícios, que no geral, se aproximam expressivamente da álgebra acadêmica. Quando os licenciandos definem álgebra, salienta-se à concepção estrutural. Por outro lado, ao se referirem à aplicabilidade da álgebra, destaca-se a concepção ferramenta. Considerando que a concepção ferramenta se sobressaiu entre as demais, conclui-se que as concepções dos licenciandos encontram-se em consonância com a álgebra escolar, com algumas marcas da álgebra acadêmica, representada pela concepção estrutural. As concepções de álgebra dos professores se aproximaram à concepção estrutural. Explicitam que, para ser um bom professor de matemática basta ter domínio sólido de conteúdo e saber ensinar; desse modo apontaram a supervalorização das disciplinas específicas em detrimento das disciplinas pedagógicas, enfatizando a álgebra acadêmica. O presente estudo concluiu que a relação entre a álgebra acadêmica e álgebra escolar na formação inicial do licenciando não é significativa a ponto de ressignificar os conhecimentos sobre ensino de álgebra do futuro professor. / This research, linked to the line "Formative Processes, Teaching and Learning," was driven by the question: What is the relationship between academic algebra and school algebra expressed in the conceptions of undergraduate and professors of mathematics degree course? And has had as general goal to investigate the relationship between academic algebra and school algebra expressed in algebra concepts and their teaching between professors and undergraduates enrolled in the Mathematics degree of FCT - UNESP of Presidente Prudente, in order to subsidize reflections on initial training of mathematics teachers. The theoretical framework was constituted of mathematics educational theories about algebra, the relationship between academic algebra and school algebra, the algebra concepts and their education and initial training of mathematics teachers. Using qualitative approach and descriptive analytic design, the research has had as methodological procedures: document analysis, questionnaire and interview, conducted throughout the course. The analysis material included the pedagogical project of that course, the questionnaires given to undergraduates in the 1st and 3rd year, interviews with undergraduates on the 2nd and 4th year of the course as well as interviews with teachers who taught subjects directly related to algebra. The documentary analysis associated with interviews carried out with professors and undergraduates indicated that the course meets the statutory guidelines. However, there is no justification for the choice of the curriculum subjects, in view of its relevance to the formation of the future teacher. In the propositions of the teaching plan of the subjects elementary algebra and Algebra I, it was observed nuances of the relationship between academic algebra and school algebra, but its development was found to be inconsistent with such propositions. In practice, the mathematical knowledge education was prioritized, and characterizing itself in the model of technical rationality, reinforcing procedures experienced and internalized during the process prior to the school degree. Over this course, the curricular emphasis when it comes to algebra, has fell on the structures algebra. Relating the models to the teaching of algebra highlighted by undergraduates at several points along the course, it was revealed that it is guided by models in the definition, followed by examples, exercises solving, which overall approach expressively of academic algebra. When the undergraduates define algebra, structural design is stressed. On the other hand, when referring to the algebra applicability, the design tool is highlighted. Considering that the tool design stood out among the others, it is concluded that the conceptions of undergraduates are in line with the school algebra, with some marks of academic algebra, represented by the structural design. The algebra concepts of the teachers have approached to the structural design. They explain that to be a good mathematics teacher it‟s just necessary to have solid domain content and know how to teach; thereby they pointed to the overvaluation of specific subjects at the expense of educational disciplines, emphasizing academic algebra. This study has concluded that the relationship between academic algebra and school algebra in the initial formation of the undergraduate is not significant enough to reframe the future teacher‟s knowledge related to the algebra teaching.

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.

The purpose of this case study was to investigate the experience of six Foundation Phase teachers implementing the Singapore Mathematics Curriculum (SMC). The study makes use of Kilpatrick, Findell & Swafford‟s (2001) framework for teaching for mathematical proficiency as a conceptual lens to analyse teaching practice in the classroom. The study took place in two schools currently implementing the SMC in East London, in the Eastern Cape Province of South Africa. This qualitative study was framed within an interpretive paradigm. It relies on data collected in semistructured interviews, individual questionnaires, focus group interviews, journals and presentations. In general, the SMC was well received, and the participating teachers isolated the following as particularly positive features of their experience: - The teachers and students were enjoying the discovery of mathematics using a variety of manipulatives as stipulated when using the SMC; - The use of the model method, a specific feature of the SMC, to solve problems helped students visualise the problem; - The teachers‟ understanding of teaching for mathematical proficiency was enhanced; - The spiral curriculum informed teaching practice by allowing for building on to concepts already mastered, creating a logical flow of ideas and careful progression; - Whilst the SMC provides a more structured approach to the teaching and learning of mathematics, it provides constant opportunities for creativity and logical thinking; and - The change in attitude of both students and teachers has resulted in a greater confidence when non-routine, openended problem solving activities are engaged in. From a critical perspective the participants found the following problematic when implementing the SMC: - The teachers felt that there was insufficient drill and practice once the concept was understood. More practice and exercises were called for; - The whole class teaching approach with every student having a textbook and workbook pertaining to the lesson required a change to classroom management; and - To obtain a deeper understanding of number concepts was time consuming and re-teaching the weaker students called for additional time and adjustments to the timetable.

The study was an investigation into the teaching decisions that mathematics teachers make over time. I view a mathematics classroom as a didactical system of teacher, learners and content within an educational institution, where content is the material that brings teachers and learners together. Within such a system I view the teacher's role as making content available to learners. Prior research has often investigated the teacher's role by comparing teaching practices nationally or internationally, but these comparisons have tended to use the lesson as the unit of analysis. I propose that how teachers make content available can change over the course of a series of lessons and so my study used the lesson series as the unit of analysis. I purposefully designed the study so that it involved four cases, which allowed me to explore the role of the teacher and the topic in how content was made available. To investigate how teachers made content available to learners in each case, I developed an analytical approach from which I could study the modes of teacher interaction that featured across the lesson series, the forms of mathematical content made available and the sequencing of these forms. Attending to forms of content - rather than content itself - allowed for comparison of teaching of different topics. This original analytical approach represents a contribution to both mathematics education and mixed methods research. Within this small sample of cases, quantifiable differences were identified in how content was made available between classwork and seatwork, from lesson to lesson and between cases. Between-case differences in the nature of teaching 'between-the-desks' during seatwork were also identified. These differences illuminated teaching decisions to which teachers and classroom researchers may not routinely attend. The findings therefore contribute - and identify additional lines of enquiry that might contribute further - to a more extensive understanding of teaching practices.

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.