An operational definition of Systemic Reform is used to document a case study of mathematics education reforms occurring in the mathematics classrooms of one middle school in one school division in one state. The middle school had two lead teachers who participated in the training component of a National Science Foundation-funded state-wide Systemic Reform Initiative. Systemic Reform conceptualized reform as combining bottom-up reform with top-down support. Therefore, the research methodology confronted the challenges of the breadth and complexity of Systemic Reform through the use of selective data in the form of artifacts, interviews, and observations from four populations: (1) classroom teachers, (2) building administrators, (3) district administrators, and (4) state-level staff. The study was conducted at four levels over a five-year period to provide the focus for longitudinal data collection to document: (1) the status of mathematics education during the 1995-96 primary data collection year, (2) the evolution of mathematics education reform over the course of the five year period, and (3) the manner in which Systemic Reform occurred. All levels of educators involved made an initial five-year commitment as active participants in the State's Systemic Reform Initiative, but only the Lead Teacher actually carried through with this commitment. After the first year division-level administrators shifted the focus of reform efforts to the elementary schools and discontinued support for the middle schools; after the second year both the division and state-level administrators withdrew all support. Although changes were made at the school level which supported reform in mathematics education (i.e., adoption of constructivist-type instructional materials, purchase of classroom sets of manipulatives and calculators, implementation of block scheduling, and the organization of teachers in interdisciplinary teams) the necessary changes in technology, curriculum and assessment were not in place to support the reform efforts. Through the perseverance of the Lead Teacher some changes in mathematics classrooms were documented, but the lack of consistent administrative leadership/support and emphasis on multiple reforms ended in the all to common bandwagon phenomena at the building, division and state levels so characteristic of change efforts in schools. / Ph. D.

Views of teaching: implications for the didactic training of mathematics teachers. School mathematics teaching is an essential learning area in South African schools. Owing to persistent traditional positivist-based views and approaches, it still suffers from a variety of teaching-learning problems. Various national attempts have already been made to develop an effective teaching-learning program for school mathematics. Prominent researchers reveal that the failure of teaching-learning programmes often have to be attributed to the lack of an underlying grounded didactic theory. Therefore this study focused on the development of a grounded teaching-theoretical framework for school mathematics teaching. A further problem regarding school mathematics is that its teaching and learning traditionally are viewed from a narrow school subject disciplinary perspective. Therefore this study departed from a general didactic-theoretical perspective, creating the opportunity to approach and solve problems from a wider angle. A constructivist-based post-positivist view of effective teaching was developed, before entering the field of school mathematics. In this way an integrated ontologicalcontextual view of teaching was developed in terms of six identified ontological essential features, and their contextual coherence, namely: intention, teacher, leamer, interaction, content and context. Contrary to traditional positivist views, no causal relationship between teaching and learning was imposed, and teaching was not qualified in terms of learning products. Instead, teaching was characterised and qualified on ontological grounds, departing from the phenomenon itself. In this way the limitations of positivist process-product views of teaching could be identified, explained and overcome. Alternatively, a dynamic integrated view of teaching as a human act, directed at the facilitation of relevant and meaningful learning, was grounded and developed. Based on this general ontological-contextually based view, a specific ontologicalcontextual view of effective school mathematics teaching was grounded and developed. To this end a variety of prominent contemporary views of and approaches to school mathematics, and its teaching and learning, needed to be analysed in a critical way. According to this analysis school mathematics, and its teaching and learning should be viewed and approached from a constructivist-based dynamic change-and-grow perspective as human acts. In addition, it could have been proved that the perspective concerned can facilitate the treatment and solving of the currently experienced teaching-learning problems. This requires the reconsideration, from a similar perspective, of the current school mathematics curriculum, as well as the preservice didactic training of mathematics teachers. Specific implications of the developed ontological-contextual view of effective school mathematics teaching were identified, and practically tested in the corresponding preservice didactic training situation in the North West Province. Based on this an integrated model for the training concerned was formulated. It was found that the current training largely contributed to the continuation of traditional views of and approaches to school mathematics teaching, and its essential features. From the developed integrated ontological-contextual perspective definitive proposals regarding the transformation of school mathematics teaching and the corresponding didactic training were made and motivated. Further areas for investigation and development, resulting from this study, were identified, as well. This study aimed at investigating, and revealing for further exploration, the specific and broadening interaction between the general teaching and subject didactical fields and research, particularly in the two contexts of effective school mathematics teaching and the corresponding preservice didactical training. A particular attempt was made to accomplish this in a grounded and integrated way, to the benefit of both fields. / Thesis (PhD)--PU for CHE, 1998.

Views of teaching: implications for the didactic training of mathematics teachers. School mathematics teaching is an essential learning area in South African schools. Owing to persistent traditional positivist-based views and approaches, it still suffers from a variety of teaching-learning problems. Various national attempts have already been made to develop an effective teaching-learning program for school mathematics. Prominent researchers reveal that the failure of teaching-learning programmes often have to be attributed to the lack of an underlying grounded didactic theory. Therefore this study focused on the development of a grounded teaching-theoretical framework for school mathematics teaching. A further problem regarding school mathematics is that its teaching and learning traditionally are viewed from a narrow school subject disciplinary perspective. Therefore this study departed from a general didactic-theoretical perspective, creating the opportunity to approach and solve problems from a wider angle. A constructivist-based post-positivist view of effective teaching was developed, before entering the field of school mathematics. In this way an integrated ontologicalcontextual view of teaching was developed in terms of six identified ontological essential features, and their contextual coherence, namely: intention, teacher, leamer, interaction, content and context. Contrary to traditional positivist views, no causal relationship between teaching and learning was imposed, and teaching was not qualified in terms of learning products. Instead, teaching was characterised and qualified on ontological grounds, departing from the phenomenon itself. In this way the limitations of positivist process-product views of teaching could be identified, explained and overcome. Alternatively, a dynamic integrated view of teaching as a human act, directed at the facilitation of relevant and meaningful learning, was grounded and developed. Based on this general ontological-contextually based view, a specific ontologicalcontextual view of effective school mathematics teaching was grounded and developed. To this end a variety of prominent contemporary views of and approaches to school mathematics, and its teaching and learning, needed to be analysed in a critical way. According to this analysis school mathematics, and its teaching and learning should be viewed and approached from a constructivist-based dynamic change-and-grow perspective as human acts. In addition, it could have been proved that the perspective concerned can facilitate the treatment and solving of the currently experienced teaching-learning problems. This requires the reconsideration, from a similar perspective, of the current school mathematics curriculum, as well as the preservice didactic training of mathematics teachers. Specific implications of the developed ontological-contextual view of effective school mathematics teaching were identified, and practically tested in the corresponding preservice didactic training situation in the North West Province. Based on this an integrated model for the training concerned was formulated. It was found that the current training largely contributed to the continuation of traditional views of and approaches to school mathematics teaching, and its essential features. From the developed integrated ontological-contextual perspective definitive proposals regarding the transformation of school mathematics teaching and the corresponding didactic training were made and motivated. Further areas for investigation and development, resulting from this study, were identified, as well. This study aimed at investigating, and revealing for further exploration, the specific and broadening interaction between the general teaching and subject didactical fields and research, particularly in the two contexts of effective school mathematics teaching and the corresponding preservice didactical training. A particular attempt was made to accomplish this in a grounded and integrated way, to the benefit of both fields. / Thesis (PhD)--PU for CHE, 1998.

This is a qualitative research that draws on Fairclough’s Critical Discourse Analysis methodology to analyze the discourse practices of the mathematics teacher educators in initial teacher training colleges in Malawi. The study involved four mathematics teacher educators in two teacher training colleges located in two different regions of Malawi. Specifically the study explored the following questions: 1) What are the discourse practices that mathematics teacher educators display in their descriptions of multilingual mathematics classrooms? 2) a) What are the discourse practices that mathematics teacher educators display in a college mathematics classroom? b) How do they make available the discourse practices for the student teachers to draw on? Data was collected through pre-observation interviews, classroom observations, reflective interviews and focus group discussions with the mathematics teacher educators. This study has shown that while there are some disconnections between the discourse practices produced in a school multilingual mathematics classroom and a college mathematics classroom, some of the discourse practices that mathematics teachers produced in a college mathematics classroom reinforces the common discourse practices being produced in multilingual mathematics classroom. There are three common discourse practices that were displayed in a college mathematics classroom. These discourse practices are: Initial-Response-Evaluation (Pimm, 1987), traditional lecturing and group discussions. I observed that the IRE and traditional lecturing discourse practices were accompanied by directive discourses for procedural control, and the procedural discourse was the prevalent discourse in all the discourse practices produced. iv Three major themes have emerged from the data analysis. Firstly, the research findings indicate that the mathematics teacher educators regard multilingualism and the language practices that come with it such as code-switching more as a problem rather than a resource for teaching and learning. Secondly, code-switching in college mathematics classroom is not as spontaneous as is research shows it to be in schools; rather it is very much controlled and restricted. Thirdly, the dilemmas of code-switching as discussed by Adler (1998, 2001) are more acute in teacher training colleges, mainly because of the mismatch in the Language-in-Education Policy (LiEP) in schools and tertiary level.