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.

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 research study is to describe and analyze the self-reported experiences of exemplary high school mathematics teachers who underwent personal and professional transformations in order to develop and use a standards-based, constructivist (SBC) teaching paradigm in their classrooms. These teachers were all past recipients of the Presidential Award for Excellence in Mathematics and Science Teaching (PAEMST), an award that required them to demonstrate that their mathematics instruction was rigorous in the manner described by the NCTM standards. The following research questions are addressed: (a) What are the paths SBC secondary mathematics teachers who received the PAEMST pursued to become highly effective?, (b) What obstacles and challenges did they encounter and how were these obstacles overcome?, and (c) What sustained them on their journeys? The research methodology used to be a narrative inquiry. Following a wide survey of PAEMST recipients, five volunteer participants were chosen for the study. Data were collected from each participant using a one-to-one interview and the written section of each participant's PAEMST application. A narrative was written for each participant describing the path they had followed to become a highly effective high school mathematics teacher. The narrative was sent to each participant, and a follow-up interview was conducted via telephone amending the narrative to reflect the participant's additions and deletions. From the five amended narratives, eight themes were identified: (a) influences; (b) education; (c) professional development; (d) NCTM standards; (e) teaching style: beginning, current, or end of a career; (f) obstacles; (g) personality traits and personal beliefs; and (h) student influence. Several of the themes were supported by previous research. However, this research study discovered two new findings. First, the five participants had common characteristics and beliefs: (a) belief in their students, (b) persistence, (c) belief that professional development is vital for teacher growth, and (d) passion about mathematics and about conveying that passion to their students. The second research finding pertained to the influence that their own students had on all of the five participants. All the participants purposely sought out their students' thoughts about the classroom curriculum and about the instruction they received. The teachers considered their students part of the classroom learning community, and they honored and acted on their input. Finally, in addition to describing the trajectory of five PAEMST winning teachers, this study offers recommendations for students studying to become high school mathematics teachers, teacher educators, and educational researchers. For these students, their teaching preparation courses need to be taught adhering to the four principles of learning: activity, reflection, collaboration and community. According to this research, the model of teacher preparation courses that emphasize the teaching of the above four principles using a traditional teacher-directed method does not prepare future mathematics teachers for the use of SBC teaching in their classrooms. Suggestions about further research are addressed.

This study aimed to increase efficacy for teaching mathematics in pre-service early childhood teachers through the presentation of five video lessons on topics in early childhood mathematics. Each lesson entailed reading a short essay on a topic related to children's mathematical thinking and then watching a short video of a child engaged in a relevant task and a clinical interview with an adult. This study also examined pre-service teachers' knowledge of mathematical development (KMD) and intellectual modesty, or the awareness of the limits of one's knowledge, as possible mediators of change in efficacy. Results showed that the video lessons did significantly increase efficacy for teaching mathematics, but that KMD and intellectual modesty were not significant mediators of the change in efficacy. In effect, confidence appeared disconnected from competence. Follow-up analyses revealed the importance of rich mathematical content within the videos in producing increased confidence and competence.

Education plays a vital role in any society; so much so, that countries strive to have not only adequate, but excellent educators in their classrooms. The aim of this study was to understand how beginning secondary mathematics teachers define success and to what experiences they attribute that success. Specifically, the central research question addressed was, "To what degree were significant attributes or experiences, important to the success of the first year teaching, learned pre-teacher education program, during a program, or post-program?" The practical goal of filling classrooms with great educators needs to be informed by research on how best to recruit highly qualified candidates into the field of mathematics education and how best to facilitate the teacher preparation process. This study employed a mixed methodology, using a sample of beginning secondary mathematics teachers to gather both quantitative and qualitative data on when they reported gaining influential knowledge or experiences. In particular, input from those who have had some success as beginning mathematics teachers was desired. The interview protocol designed for these participants added depth to the survey responses. Emphasis was placed on the relative importance of the three stages, pre-, during, and post-program, in developing common attributes associated with good teaching. Two characteristics were generally discussed as developing pre-program: being a self-starting and hard-working individual, and holding a belief that every student can learn. Beginning teachers viewed these traits as important for their success. Participants also felt that they acquired both practical classroom tools and educational theory from their teacher education program; having program instructors model pedagogy and mathematical instruction, and having opportunities to practice incorporating theory into their teaching were also seen as important. These aspects distinguished particularly prominent roles that the teacher education program played in shaping its graduates. Classroom management and being flexible and adaptive to different contexts were the most notable qualities frequently reported as being learned post-program. The study's results have implications for informing the types of students a mathematics education program should try to attract or recruit and defining areas where practicum or internship components might be incorporated into the teacher education process.

What is good mathematics teaching? The answer depends on whom you are asking. Teachers, researchers, policymakers, administrators, and parents usually provide their own view on what they consider is good mathematics teaching and what is not. The purpose of this study was to determine how beginning teachers define good mathematics teaching and what they report as being the most important attributes at the secondary level. This research explored whether there was a relationship between the demographics of the participants and the attributes of good teaching. In addition, factors that influence the understanding of good mathematics teaching were explored. A mixed methodology was used to gather information from the research participants regarding their beliefs and classroom practices of good mathematics teaching. The two research instruments used in this study were the survey questionnaire and a semi-structured interview. Thirty-three respondents who had one to two years of classroom experience comprised the study sample. They had graduated from a school of education in an eastern state and had obtained their teacher certification upon completing their studies. The beginning mathematics teachers selected these four definitions of good teaching as their top choices: 1) have High Expectations that all students are capable of learning; 2) have strong content knowledge (Subject Matter Knowledge); 3) create a Learning Environment that fosters the development of mathematical power; and 4) bring Enthusiasm and excitement to classroom. The three most important attributes in good teaching were: Classroom Management, Motivation, and Strong in Content Knowledge. One interesting finding was the discovery of four groups of beginning teachers and how they were associated with specific attributes of good mathematics teaching according to their demographics. Beginning teachers selected Immediate Classroom Situation, Mathematical Beliefs, Pedagogical Content Knowledge, and Colleagues as the top four factors from the survey analysis that influenced their understanding of good mathematics teaching. The study's results have implications for informing the types of mathematical knowledge required for pre-service teachers that can be incorporated into teacher education programs and define important attributes of good mathematics teaching during practicum.

The release of the Common Core State Standards for Mathematics in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by teachers about mathematical models and modeling in order to aid in the development of teacher education and professional development programs. The study used a mixed methods approach. Quantitative data were collected through an online survey of a large sample of practicing and prospective secondary teachers of mathematics in the United States. The purpose of this was to gain an understanding of the conceptions held by the general population of United States secondary mathematics teachers. In particular, basic concepts of mathematical models, mathematical modeling, and mathematical modeling in education were analyzed. Qualitative data were obtained from case studies of a small group of mathematics teachers who had enrolled in professional development which had mathematical models or modeling as a focus. The purpose of these case studies was to give an illustrative view of teachers regarding modeling, as well as to gain some understanding of how participating in professional development affects teachers' conceptions. The data showed that US secondary mathematics teachers hold several misconceptions about models and modeling, particularly regarding aspects of the mathematical modeling process. Specifically, the majority of teachers do not understand that the mathematical modeling process always requires making choices and assumptions, and that mathematical modeling situations must come from real-world scenarios. A large minority of teachers have misconceptions about various other characteristics of mathematical models and the mathematical modeling process.

The purpose of this study is to determine how well traditional elementary preparation programs and alternative elementary certification programs are perceived by teacher candidates, to prepare them to teach mathematics to the standards required today. Using a qualitative design, this study examines how various ranked elementary teacher preparation programs and alternative certification programs are preparing elementary teachers to teach the mathematics envisioned in the CCSSM. Participants in this study all attended an undergraduate elementary teacher preparation program or an alternate route certification program. To paint a holistic picture of elementary teacher preparation in mathematics, each undergraduate elementary teacher preparation programs was ranked in a different level in the NCTQ Teacher Preparation Review. Qualitative surveys and interviews were used to gather data on participants' perceptions of their preparation in mathematics. Twenty-five participants agreed to take part in this study. Participants filled out a two-part survey. The first part of the survey asked background questions on their coursework and field experiences in mathematics along with a survey on their beliefs about their ability to teach mathematics. The second part was a pedagogy survey that asked participants how they would teach particular mathematics concepts that now require a conceptual understanding in the CCSSM. Seven participants agreed to participate in a follow up interview to further investigate their experiences in mathematics preparation in their teacher education programs. The data showed that there is little consistency in the mathematics education of elementary teachers within a teacher preparation program and across different teacher preparation programs. There is little standardization in the coursework for participants from different preparation programs and participants within the same program. The interviews revealed that the degree to which participants were able to teach mathematics in their field experiences also varied within and across teacher preparation programs. Furthermore, the interviews also unveiled that the CCSSM were also studied and utilized in different capacities within and across institutions. Lastly, the data from the surveys disclosed that the majority of participants feel that they have the ability to be effective teachers of mathematics yet the majority of participants teach mathematics for a procedural understanding.

The purpose of this study was to develop a valid and reliable, instrument for determining the mathematics subject matter knowledge of Thai preservice elementary teachers at eight (8) teachers' colleges in eight (8) provinces in northern Thailand. The focus of the content of interest was the operation of division of rational numbers in the context of an appropriate taxonomy of the cognitive domain categories suggested by Wilson (1971). The Delphi technique, item analysis, and "known group" techniques were utilized in the instrument development phases of the study. Hypotheses were tested to determine whether significant differences existed between colleges and between teachers with different backgrounds. The dependent variable was the mean test score for preservice teachers at eight Thai teachers' colleges. The study included the testing of significance for colleges, background, and whether there was significant interaction between colleges and teachers' backgrounds (liberal arts and science). The pilot instrument consisted of 52 items representing four cognitive levels (computation, comprehension, application, and analysis). Based on an analysis of pilot test data, 10 items were eliminated. The final draft instrument consisted of 42 items and was administered to 272 preservice elementary teachers. When field test data were analyzed and compared to "known group" data, 10 items were found to be outside of the acceptability range for difficulty. Item difficulty was used for selecting items for inclusion in the final instrument to measure the operation of division of rational numbers with Thai college preservice elementary teachers. This step in the research served to reduce the number of test items to 32, which constituted the content for the final instrument. The internal consistency reliability was .81 for the 42-item instrument. Content and construct validity were verified by various procedures. / Graduation date: 1994

The purpose of this study was to initiate integration of HIV and AIDS curriculum in / Thesis (Ph.D.) - University of KwaZulu-Natal, Durban, 2008.