Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (leaves 157-163).

Thesis (M.Ed.)--University of Hong Kong, 1992. / Includes bibliographical references (leaf 103-108). Also available in print.

Thesis (M. Ed.)--University of Hong Kong, 1996. / Includes bibliographical references (leaf 147-152).

Thesis (M.Ed.)--University of Hong Kong, 1996. / Includes bibliographical references (leaves 147-152). Also available in print.

This research report focuses on an investigation of the prevalence and nature of code switching practices in grade 8 mathematics classrooms in the Ohangwena region of Namibia. The existence of code switching in these classrooms was established by administering a survey to all grade 8 teachers in the region, while the nature of these practices was explored by interviewing and observing selected teachers using a case study research methodology. The data from the survey was analysed quantitatively using descriptive statistics, while the qualitative data from the case study which comprised of audio and video transcripts was analysed within the framework of Probyn’s (2006) code switching categories. These categories looked at code switching in terms of: explaining concepts; clarifying statements or questions; emphasising points; making connections with learners’ own contexts and experiences; maintaining the learners’ attention with question tags; classroom management and maintaining discipline; and affective purposes. The study found that code switching is widespread in most of the grade 8 mathematics classrooms in the Ohangwena region. It also revealed that the teachers’ code switching practices aligned well with most of Probyn’s framework. The criterion of maintaining learner’s attention with question tags was however not found in this study. The results of the study showed that teachers code switch because the majority of the learners’ language proficiency is not good. Code switching is mostly used as a strategy to support and promote learners understanding in mathematics. The study recommends that it is high time that code switching is acknowledged as a legitimate practice and recognised as an important and meaningful teaching strategy to assist learners who are learning mathematics in their second language. Code switching needs to be de-stigmatised and teachers should be supported in using this practice effectively and efficiently.

Quality mathematics education relies on effective pedagogy which offers students appropriate and rich opportunities to develop their mathematical proficiency (MP) and intellectual autonomy in learning mathematics. This qualitative case study aimed to explore and analyse selected effective mathematics teachers' proficiency in the area of geometry in five secondary schools in five different Namibia educational regions. The sample was purposefully selected and comprised five mathematics teachers, identified locally as being effective practitioners by their peers, Education Ministry officials and the staff of the University of Namibia (UNAM). The schools where the selected teachers taught were all high performing Namibian schools in terms of students' mathematics performance in the annual national examinations. The general picture of students' poor performance in mathematics in Namibia is no different to other sub-Saharan countries and it is the teachers who unfortunately bear the brunt of the criticism. There are, however, beacons of excellence in Namibia and these often go unnoticed and are seldom written about. It is the purpose of this study to focus on these high achievers and analyse the practices of these teachers so that the rest of Namibia can learn from their practices and experience what is possible in the Namibian context. The mathematical content and context focus of this study was geometry. This qualitative study adopted a multiple case study approach and was framed within an interpretive paradigm. The data were collected through individual questionnaires, classroom lesson observations and in-depth open-ended and semi-structured interviews with the participating teachers. These interviews took the form of post lesson reflective and stimulated recall analysis sessions. An adapted framework based on the Kilpatrick, Swafford and Findell's (2001) five strands of teaching for MP was developed as a conceptual and analytical lens to analyse the selected teachers' practice. The developed coding and the descriptive narrative vignettes of their teaching enabled a qualitative analysis of what teachers said contributed to their effectiveness and how they developed MP in students. An enactivist theoretical lens was used to complement the Kilpatrick et al.'s (2001) analytical framework. This enabled a deeper analysis of teacher teaching practice in terms of their embodied mathematical knowledge, actions and interactions with students. procedural fluency (PF) and productive disposition (PD), were addressed regularly by all five participating teachers. Evidence of addressing either the development of students' strategic competence (SC) or adaptive reasoning (AR) appeared rarely. Of particular interest in this study was that the strand of PD was the glue that held the other four strands of MP together. PD was manifested in many different ways in varying degrees. PD was characterised by a high level of content knowledge, rich personal experience, sustained commitment, effective and careful preparation for lessons, high expectations of themselves and learners, collegiality, passion for mathematics and an excellent work ethic. In addition, the teachers' geometry teaching practices were characterised by making use of real-world connections, manipulatives and representations, encouraging a collaborative approach and working together to show that geometry constituted a bridge between the concrete and abstract. The findings of the study have led me, the author, to suggest a ten (10) principles framework and seven (7) key interrelated factors for effective teaching, as a practical guide for teachers. This study argues that the instructional practices enacted by the participating teachers, who were perceived to be effective, aligned well with practices informed by the five strands of the Kilpatrick et al.'s (2001) model and the four concepts of autopoesis, co-emergence, structural determinism and embodiment of the enactivist approach. The study concludes with recommendations for effective pedagogical practices in the teaching of geometry, and opportunities for further research.

In the study the researcher has investigated the effectiveness of the use of the balanced score card as a performance management tool for grade 12 mathematics teachers at Amajingqi Secondary School in Adelaide, in the Fort Beaufort district, circuit 8. Thirty learners, four principals, four educators who teach mathematics and the mathematics Head of Department in the schools were selected as participants in this research. A questionnaire (Appendix A) was handed out to principals, HOD’s, mathematics educators and learners doing mathematics in the four schools (4) selected for the study. The main findings of this study were: Mathematics teachers had an average of sixteen years of experience in the subject. Maths teachers do no pay much attention to slow learners. Learners are demotivated and need motivation to perform above average. Learners do not practice mathematics enough. Parental involvement is lacking in assisting learners with schoolwork let alone mathematics. Maths teachers are overloaded with work as in the schools researched one teacher would teach mathematics from Gr. 8 to 12.