Dissertation submitted in fulfilment of the requirements for the Master's Degree of Technology: Information Technology, Durban University of Technology, 2010. / The main purpose of this study was to examine how e-learning can help resolve some of the most acute problems that are specific to the nature of the outcomes-based education (OBE) system in developing countries. This was accomplished by investigating the relevant literature on OBE and by designing an e-learning content prototype for the South African version of OBE, with the focus on the training of Mathematics and Mathematical Literacy educators. OBE is an education system centred on the theory of mastery of learning introduced by Bloom in the 1950s. It has been implemented worldwide in primary and secondary schools and also in tertiary institutions. Some studies have shown that OBE is problematic, and that both educators and learners are opposed to this system of education. Existing research also reports that the quality of education in OBE is very poor as compared to that of the traditional education system. This study was an attempt to identify the most acute problems experienced by educators and learners in the OBE context and to design a prototype for e-learning content that can be used in courses in an attempt to solve these problems. The research population of the perceptions survey consisted of Mathematics and Mathematical Literacy educators and learners from the 6 000 primary and secondary schools of the KwaZulu- Natal (KZN) province of South Africa. Eighteen schools formed part of the research sample, with an average of two schools per region (the KZN province is divided into nine regions). Both private and public schools were included in the study. Data for the study were collected from March 2007 to August 2007 in the form of a perceptions survey of 104 educators and 288 learners, yielding an average of six educators and sixteen learners for each randomly selected school. Results from the perceptions survey show that educators and learners do not understand OBE terminology. In addition, educators claim that they are not sufficiently trained for OBE. Research iii participants also report that schools’ basic infrastructure is unsatisfactory, and that their classrooms are overcrowded. Mathematics is perceived as the most difficult subject by both educators and learners. The survey also reveals that most public schools do not have computers and that neither educators nor learners have access to computers in their public libraries. A SCORM- (Sharable Content Object Reference Model) compliant e-learning course was developed in this study to address the most acute problems identified by the survey, based on the Software Engineering Unified Model. The designed e-course contains OBE terminology such as learning outcomes, OBE principles, assessment standards, assessment methods, national curriculum statement and learning fields. The e-learning course content also contains the Mathematics and Mathematical Literacy curriculum for grades 11 and 12. It was constructed using 16 documents extracted from the National Department of Education’s website: 7 documents under Further Education and Training, 4 under Teacher Guide, and 5 under General Education and Training. The evaluation of the e-learning content prototype was conducted through a survey among 36 educators from different primary and secondary schools of the Mnquma Municipality of the Eastern Cape province of South Africa. They were trained in the SCORM-compliant e-learning course content at the Walter Sisulu University’s Butterworth campus. The training took place from 10 to 13 November 2009. After the training, educators filled out a questionnaire on their perceptions of the effectiveness of the proposed e-learning content prototype with regard to the practice of OBE. Results from the SCORM e-course evaluation survey showed that the proposed SCORM software artefacts allow educators to have a better understanding of OBE terminology. The proposed software artefact is user-friendly and educators recommended its use not only for Mathematics but for all subjects.

The purpose of this study was to evaluate the effectiveness of a short-term math/science inservice based upon the participants' perceived changes in attitude and behavior relevant to the projects' goals and objectives. One hundred and three elementary school teachers from twelve schools in an urban school district participated in the inservice. The treatments were administered during two eight hour days, one month apart. The project was designed to improve the participants' attitude and behavior relevant to ten goals that centered around increasing awareness and use of science process and math problem solving approaches to teaching. The evaluation instrument was a pre- and post-treatment survey. Seventy questions were created and apportioned to test twenty hypotheses. Two hypotheses were tested to determine the achievement of each goal. One hypothesis tested the teachers' perceived change in attitude and the other tested the teachers' perceived change in teaching behavior relevant to a specific goal. Goal achievement was determined by comparing changes (significant at the.05 level) in attitude and behavior. All ten attitude hypotheses indicated a significant positive change occurred in attitude. None of the behavior hypotheses showed a significant positive change. It was determined that the inservice was totally effective in changing the teachers' attitude, relevant to the goals, but it failed to make a positive impact upon the teachers' perceptions of their actual practice in the classroom. It was speculated that the failure to affect behavior change was a result of one or a combination of the following four factors: insufficient time lapse to affect behavior, more accurate reporting on the post test, retrenchment resulting from feelings of inadequacy, and fear of venturing out alone primarily due to the lack of organizational development. Suggestions for improving the inservice were based upon proposed remedies for the above four factors.

published_or_final_version / Curriculum Studies / Doctoral / Doctor of Philosophy

Teachers must have specific knowledge of a subject and how to teach it to promote learning in their students (also known as pedagogical content knowledge). Research has shown that project-based curriculum can be an effective way for teachers to leverage this knowledge into deeper student understanding and application readiness, but observations about when and how this happens in the classroom have not been adequately documented. In this study we will explore teaching and learning in a middle-school boat-building curriculum focused on real-world application of math concepts. The boat-building program took place over one week, included seven students, and was taught by three teachers. The teaching phase of this study examined how the three boat-building teachers applied their pedagogical content knowledge (PCK) through a participant observation case study. The three teachers had diverse training and teaching backgrounds. At the completion of the course these teachers were interviewed on their prior teaching experiences and training to determine how they acquired their pedagogical content knowledge. The learning part of this study involved a pre- and post-test application task completed by the students. After all students completed the application task, each was interviewed to see what, if any, knowledge or approach these teachers used had an impact on the ability of the students to do the task. Analysis of the pre-post assessments showed that students were not able to make statistically significant gains over the one week of instruction. However, students did note many aspects of instruction that they thought helped them. Additionally, students showed gains in assessing importance of geometry in design, the vocabulary associated with scale, geometry, and woodworking, and creating context for prior instruction. For the teachers, higher scores on the PCK rubric did align with a greater amount of experience teaching. Also, the two more experienced teachers influenced each other and the third teacher regarding student learning and instructional approach.

The purpose of this narrative inquiry study was to investigate the influence of curricular mandates on the teaching practices of high school mathematics teachers. Narrative inquiry, philosophically based on John Dewey’s theory of experience (Dewey, 1938), provides the intimate study of an individual's experience over time and in context(s) (Clandinin & Connelly, 2000). This study focused on the experiences of three high school mathematics teachers’ stories of educational change with data collected through interviews and personal documents. Socio-cultural narrative analysis was used to interpret the participants’ stories of adaptation. The data, presented as an ethnodrama, is composed of scenes taken from the interviews and interweaves the participants’ stories of evolution as they tackled the struggles of change on multiple levels: curriculum, student assessment, and teacher evaluation. Results indicated teachers adopt both traditional and reform strategies when deciding on appropriate teaching practices. Collaboration and professional development were two important aspects used by the participants to enlarge their toolbox of teaching practices when forced to challenge their existing beliefs. This study contributes to the scarce research on the impact of curricular mandates on teaching practices. It also highlights the experiences of high school mathematics teachers as they embrace the paradigm shift associated with the mandates and implement changes to their practices to promote a more student-centered, collaborative environment.

Robert Recorde (c. 1510-1557) was a pioneer in the teaching of mathematics in the English language. His attempt to popularize mathematics, in fact, was without precedent in any language. Mathematics in the 1500s was still exclusively reserved for mathematicians, and people in general had no interest in the subject. Within a hundred years after Recorde had popularized mathematics, however, this situation had changed. The scientific revolution of the seventeenth centuty occurred and mathematics became an indispensible aspect of man's knowledge. This thesis examines the background and development of Recorde's attempt to popularize mathematics and evaluates that attempt in terms of its relation to the position of science in the modern world.

Different forms of professional development online are becoming increasingly common for teachers and the aim of the thesis is to contribute knowledge about online professional development for mathematics teachers and the relationship between professional development, educational policy, and mathematics teaching practice. In the thesis, professional development refers to organized professional development in terms of university courses. The thesis consists of four studies, each of which has been presented in the form of an article. The four studies together explore transnational and national policy discourses, meaning-making activities that can be distinguished in online professional development, discourses pertaining to mathematics teaching in the classroom and in the subsequent seminar discussions in the course, and teachers’ experience of professional development online. The different arenas have been explored using the concept of discourse with reference to Fairclough, Gee, and Sfard. The term ”discourse” refers primarily to communication and language in use. The result of the studies indicates that the participants have not been offered enough opportunities to reflect on how or whether the use of several concepts and everyday life connections really deepened the students’ understanding of the mathematical content. Moreover, the analysis of the interviews with the participants shows that it was difficult for them to deepen their reflections in the synchronous communication online. There is a lack of reciprocal participation and reflection in the conversation and it is hard for the participants to get an idea of how the others respond to their messages. When a participant has completed his or her message the next speaker continues with a new message and as a result, the communication often takes a new direction instead of allowing in-depth reflection.

À un moment de développement technologique rapide et de réforme fréquente des programmes, l'abondance de ressources pédagogiques offre aux enseignants de nouvelles opportunités mais occasionne aussi une nouvelle complexité. Cette étude a pour objectif d’explorer l’expertise des enseignants en mathématiques nécessaire pour développer et interagir de manière collective avec des ressources. L'expertise étant contextualisée, cette recherche est conçue comme une étude de cas dans deux contextes contrastés (la Chine et la France). Basée sur l’approche documentaire du didactique et la théorie de l’activité culturelle et historique, l’étude propose un modèle pour l’expertise des enseignants de mathématiques interagissant avec des ressources, nommée expertise documentaire (ED). La démarche propose deux modèles successifs: le premier modèle de l’ED est basé sur une revue de la littérature et une étude pilote, le deuxième modèle repose sur une analyse de deux cas contrastés.Trois questions sont explorées: Comment définir l’ED ? Comment se développe l’ED dans le travail collectif ? Que peut-on apprendre du développement de l’ED à travers les deux cas? L'étude est basée sur la méthodologie d'investigation réflexive et adapte des outils d'entretiens, d'observation et d'analyse vidéo.Quelques résultats majeurs: (1) L’ED est définie par (i) une dimension statique à partir de la structure du système de ressources : l’ED se développe en maintenant vivant ce système, en reliant la conception des ressources à des considérations sur la didactique, le curriculum et les étudiants; (ii) une dimension dynamique à partir des schèmes de maintenance des systèmes de ressources et du travail documentaire : l’ED se développe en intégrant les ressources avec une perspective large en matière de recherche, une attitude critique lors de la sélection, une manière flexible d'adapter et une habitude à accumuler automatiquement. (2) Le travail collectif profite au développement de l’ED, en particulier au cours des phases collectives de conception des leçons, où les ressources et les schèmes d'utilisation sont questionnés pour des situations spécifiques. (3) Des conséquences sont tirées concernant la construction institutionnelle du travail collectif des enseignants (cas chinois) et des ressources en ligne de qualité (cas français). / In a time of fast technology development and frequent curriculum reform, the abundance of instructional resources brings teachers both chances and new complexity. This study aims at exploring mathematics teachers’ expertise required for, and developed in, interacting collectively with resources. Since expertise is contextualized, this research is designed as case study in two contrasting contexts (China and France). Based on Documentational Approach to Didactics and Cultural-historical Activity Theory, the study proposes a framework of mathematics teachers’ expertise interacting with resources, which is named as Documentation Expertise (DE). Efforts are made in two steps: a first DE framework based on literature review and pilot study, a refined framework after two contrasting cases analysis. Three questions are explored: How to define DE? How is DE developed through collective work? What can be learnt for developing DE through the two cases? The study is based on a methodology of reflective investigation, and adapts tools of interviews, observation and video analysis.It proposes some main results: (1) DE is evidenced from (i) a static dimension on resource system’s structure and components, DE develops in deliberately keeping the resource system lived by bridging resource design with considerations on didactics, curriculum and students; (ii) a dynamic dimension on schemes in resource system maintenance and documentation work, DE develops in integrating the resources with a broad view in searching, critical attitude in selecting, flexible way in adapting, and automatically habit in accumulating. (2) Collective work benefits DE development, especially collective lesson design, where resources and the schemes of usage are discussed concerning specific situations. (3) Implications are drawn concerning institutional construction of teacher collective work (Chinese case), and high-quality online-resources (French case). / 在科技迅速发展，课程改革频仍的时代，教学资源的极大丰富为教师的课程设计同时带来机遇和挑战。本研究围绕数学教师在文献纪录工作中的专长，旨在探索此种专长的成分构成及其集体工作环境下的发展路径。鉴于教师专长的情境性，本研究选择案例研究的方式对中法两组案例进行探索。基于教学的文献纪录法和文化历史活动两个理论框架，本研究提出了数学教师文献纪录专长的概念，意为数学教师在调用资源时所需要和发展而来的专长。研究工作分两步进行：通过文献梳理和预研究提出初步的文献纪录专长框架，再通过中法案例对初步框架进行修正补充，最终提出改进版的文献纪录专长框架。研究问题有三：何为文献纪录专长？文献纪录专长怎样在集体工作中得到发展？通过中法案例研究，在该专长的获得与发展方面可以为我们带来哪些启发？本研究采用反思性调查法，具体研究工具包括访谈法，自然观察法和视频分析法。研究结果如下：（1） 文献纪录专长可从静态和动态两个维度进行调查和表征：静态维度指资源系统的结构和成分，该专长主要体现在教师在教学资源的有意设计、组织、整理和积累中综合考量数学学科、教学法、课程和学生等要素；动态维度包括资源系统的管理维护，资源工作过程中对资源的开放式搜索、批判性选择、灵活修改与应用，以及自动化的资源归纳与积累习惯。（2） 集体工作有助于文献纪录专长的发展，尤其在集体备课活动中，针对具体情境下所需资源和应用图式的头脑风暴式讨论对参与教师获益均甚。（3） 中法案例对照下，也有一些针对制度环境的启发，例如中国案例中的教师集体工作制度系统，以及法国案例中的高质量网络资源建设。

National and international studies show that the standard of mathematics teaching and learning in South Africa is very low compared to other countries. These statistics are worrying because mathematics is one of the ‘gatekeeper’ subjects that determine learners’ access to higher learning and a better future. My study, aimed at exploring two Foundation Phase teachers’ selection and use of examples and representations when teaching number, forms part of a longitudinal study currently underway within the Wits Maths Connect Primary (WMC-P) Project. One of the broad aims of the WMC-P Project is to improve primary teachers’ mathematics content knowledge and also to see this translated into improved pedagogy on the ground. This qualitative study was carried out within the WMC-P Project’s 20-Day in-service training course and one of the ten government schools participating in the broader study. My study aimed to build on research that has been carried out on teachers’ use of examples and representations with a focus on the South African terrain. The dataset comprised of two Foundation Phase teacher’s pre-tests, course-work tasks, field notes, and transcripts of observed lessons. Data was analysed using an analytical framework based on current literature related to examples and representations within mathematics teaching. Findings from my study show possible associations between a higher content knowledge score and the extent of a teacher’s example space and more coherent connections between different representational forms. More studies around this topic are needed because research shows that teachers’ examples and representations in mathematics teaching are important for good teaching and conceptual understanding.

Thesis (Ph.D.)--University of the Witwatersrand, Faculty of Science, 2002.