Thesis (Ph. D.)--Illinois State University, 2007. / Title from title page screen, viewed on April 8, 2008. Dissertation Committee: Edward S. Mooney (chair), Cynthia W. Langrall, Sherry L. Meier, Norma C. Presmeg. Includes bibliographical references (leaves 112-121) and abstract. Also available in print.

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The aim of the study is to investigate pre-service middle school mathematics teachers&rsquo / critical thinking processes through statistical and probabilistic knowledge in the context of popular media texts. The study was conducted with a qualitative case study method. Participants of the study consisted of four senior pre-service middle school mathematics teachers enrolled in a public university. Data were collected through in-depth interviews with the participants. Analysis of the data was conducted on the basis of two dimentions / critical thinking skills, and statistical and probabilistic knowledge. The results of the study indicated that pre-service middle school mathematics teachers reflected different critical thinking skills and made use of different statistical and probabilistic knowledge in different contexts. They mostly reflected interpretation skill on the basis of their statistical and probabilistic knowledge. Moreover, to what extent they made use of critical thinking skills was differentiated on the basis of their statistical and probabilistic knowledge. They reflected complicated critical thinking process dealing with conditional probability statements. They had difficulty with probabilistic statements underlying conditional probability especially in this process.

The aim of the study is to investigate pre-service middle school mathematics teachers&rsquo / critical thinking processes through statistical and probabilistic knowledge in the context of popular media texts. The study was conducted with a qualitative case study method. Participants of the study consisted of four senior pre-service middle school mathematics teachers enrolled in a public university. Data were collected through in-depth interviews with the participants. Analysis of the data was conducted on the basis of two dimentions / critical thinking skills, and statistical and probabilistic knowledge. The results of the study indicated that pre-service middle school mathematics teachers reflected different critical thinking skills and made use of different statistical and probabilistic knowledge in different contexts. They mostly reflected interpretation skill on the basis of their statistical and probabilistic knowledge. Moreover, to what extent they made use of critical thinking skills was differentiated on the basis of their statistical and probabilistic knowledge. They reflected complicated critical thinking process dealing with conditional probability statements. They had difficulty with probabilistic statements underlying conditional probability especially in this process.

Philosophiae Doctor - PhD / In this study the construct of personal theories is used to represent the teacher's conceptions, which are interpreted as the consciously held beliefs. The teacher's personal theories encompass beliefs, images, values and attitudes as well as understanding about teaching and learning. This study investigates the influence of the teacher's conceptions of mathematics, of the teaching and learning of mathematics and of the context before and after a structured learning experience. The interest in the teacher's conceptions is derived from the assumption that these serve as a primary component that influence how teachers think about their professional responsibilities and how they act in their classrooms. Furthermore, the extent of implementation of a new curriculum has been linked to the scope of congruence between the teachers' conceptions and the underpinning philosophy of the intended curriculum. The study of the teacher's conceptions is especially relevant during a time of educational reform, such as the current transition to an Outcomes Based Education curriculum in South Africa. The participants in this study consist of four primary school mathematics teachers with various educational backgrounds, who teach at schools situated in different physical environments. The conceptions that these teachers have of mathematics, of the teaching and learning of mathematics and the influence of the context are investigated using a variety of instruments. Data collection was done with a questionnaire, a repertory grid, a semi-structured interview and lesson observations. The teachers participated in the Teaching Intervention and Support Programme (TISP), as a structured teacher learning experience. The programme is centred on the integration of the developmental and socio-cultural perspectives on teacher learning. With the developmental perspective the focus is on the acquisition of intellectual skills, while the socio-cultural perspective emphasizes participation in social practice. Both are directed at effecting conceptual change. With the developmental approach the process of conceptual change involves the development of new conceptions from existing conceptions. From the socio-cultural perspective the context is paramount and conceptual change is seen as new ways of being and acting within a particular context. The teachers were invited to attend a two-week intervention session, followed by a six months support programme that was aimed at establishing a teacher learning community. The learning experiences provided during the intervention session were drawn mainly from Realistic Mathematics Education. On completion of the programme, the teachers' conceptions of mathematics, of the teaching and learning of mathematics and the influence of the context were again investigated. The results of this study show that two of the participants had highly mechanistic conceptions of mathematics, and the teaching and learning of mathematics. The remaining two had a more empiristic approach with its high focus on environmental activities. After the programme, the teachers with the mechanistic views adopted a mixed. conception with some of the mechanistic conceptions retained, but now interspersed with some empiristic and realistic conceptions. The participants with the empiristic conceptions adopted a more realistic conception, but again to varying degrees. Thompson's (1991) hierarchical structure for the development of conceptions was also used to describe the extent of conceptual change. However, it was found that a concentric, rather than a hierarchical representation is a more appropriate to describe these changes. With regards to the socio-cultural view of conceptual change, all the participants perceived the context differently. The teachers' actions were also more commensurate with the practices associated with teachers that encourage learner autonomy, mathematical investigations and a facilitative role for the teacher.