Thesis--University of Illinois. / Vita. Photocopy of typescript. Ann Arbor, Mich., University Microfilms, 1972.

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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.

Transformation geometry has been neglected in our schools because teachers are often not proficient enough to teach it, as it was not part of the syllabus during their training. The study investigates effective ways of teaching transformation geometry in grade 9, applying van Hiele’s theory (1986) of geometry teaching and learning and Kilpatrick’s model of mathematical proficiency. The teaching programme activities require consistent use of physical manipulatives by the teacher for effective teaching, learning and understanding of geometric concepts. The type of study is a case study. Data collection tools are: - baseline evaluation, teacher & learner interviews (pre & post programme intervention) and observation (pre & post) during the implementation of the teaching programme. Results were analysed both qualitatively and quantitatively. My research findings show some improvement of learner performance after the application of the programme. Baseline evaluation shows that some learners attained below and above 30%. Interviews showed that some learners had problems before the implementation of the programme and some problems were eliminated by the use of the programme activities and learning progression was evident. Learner performance showed that learners had acquired some knowledge and critical thinking and reasoning skills, reflection skills, communication through LOLT improved, commitment to activities of the programme and teaching practice had improved. Learner performance showed that a learner can be in two different levels at the same time. Consistent use of manipulatives resulted in effective teaching and learning of geometry in grade 9. The results of this research support other researchers’ views of teaching geometry using van Hiele’s theory (1986) and Kilpatrick et al. (2001). Shaw (2002) argues that teaching geometry with manipulatives enhances conceptual understanding by the learner. In my opinion, it also promotes immediate intervention by the teacher as soon as the learner picks an incorrect object. The project enhanced and improved levels of communication between the learner, teacher and others in the classroom.

Made available in DSpace on 2016-04-27T16:33:25Z (GMT). No. of bitstreams: 1 Ana Claudia Caldas de Arruda Leite.pdf: 161304 bytes, checksum: 3fcc7f1788ee6fb26577233250e14dfe (MD5) Previous issue date: 2007-08-08 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / This work, carried through from social sciences circumscribed education issues, has as object of study the concept of project, its introduction in the educational context, and its relation with modernity. Moreover, it is based on the project method , developed in 1918 by William Heard Kilpatrick, due to its contribution for the understanding of the nexuses established between psychology and education. Also, this method allows analyzing the input of the education and psychology in the history of teaching based on projects. The conception of project in modernity reveals two main features from the XVI century: the ascension of the individual and the development of the capitalism. From the hypothesis that the concept of projects evidences the lack of synchronism produced in this period, between the emphasis on the individual and on the transformations of the modes of production. Thus, it turns the making of this self-governing reasoning oriented person unachievable. In order to analyze the idea of project, Kilpatrick essays on the project method were used as primary reference source. Finally, the theoretical referential which support this work were Karl Marx and the authors of the critical theory / Este trabalho, realizado a partir de problemas circunscritos às ciências sociais da educação, tem como objeto de estudo a noção de projeto, sua relação com a modernidade e introdução no contexto educacional, com base no método de projeto , elaborado em 1918 por William Heard Kilpatrick. A escolha por esta concepção justifica-se na medida em que o método de projeto contribui para o entendimento dos nexos estabelecidos entre a psicologia e a educação, bem como possibilita analisar a entrada de ambas na história do ensino por projetos. Na modernidade, a noção de projeto relaciona-se com dois aspectos constituídos desde o século XVI, quais sejam: a ascensão do indivíduo e o desenvolvimento do capitalismo. Baseia-se na hipótese de que o conceito de projeto evidencia o descompasso, produzido neste período, entre a centralidade atribuída ao indivíduo e as transformações no modo de produção. Os conceitos básicos que orientam a análise do material são: experiência, formação, liberdade e indivíduo, definidos com base nos autores da teoria crítica e em Karl Marx. No intuito de analisar a noção de projeto, em particular sua introdução na educação, no início do século XX, utilizaram-se os ensaios de Kilpatrick sobre o método de projeto