The introduction of graphing calculators into senior secondary schools and mandating of their use in high stakes assessment makes student expertise in finding a complete graph of a function essential. This thesis investigated the cognitive, metacognitive, mathematical, and technological processes senior secondary students used in seeking a complete graph of a difficult cubic function. A pretest of function knowledge was administered to two mixed ability classes in their final two years of secondary school. Five pairs of experienced users of TI-83 or 82 graphing calculators from these classes were audio and videotaped solving a problem task. Protocols were constructed and subjected to intensive qualitative macroanalysis and microanalysis using tools developed by the researcher from Schoenfeld’s work. / The findings were: (1)all students demonstrated understanding of the local and global nature of functions and the synthesis of these in determining a complete graph; (2) a range of mathematical and graphing calculator knowledge was applied in seeking a global view of the function with their combined application being more efficient and effective; (3) an understanding of automatic range scaling features facilitated efficient finding of a global view; (4) all pairs demonstrated having a clear mental image of the function sought and the possible positions of the calculator output relative to this; (5) students were able to resolve situations involving unexpected views of the graph to determine a global view; (6) students displayed understanding of local linearity of a function; (7) when working in the graphical representation, students used the algebraic but not the numerical representation to facilitate and support their solution; (8) scale marks were used to produce more elegant solutions and facilitate identification of key function features to produce a sketch but some students misunderstood the effect of altering these; (9) pairs differed in the proportion of cognitive and metacognitive behaviours demonstrated with question asking during evaluation supporting decision making; (10) correct selection of xxi an extensive range of graphing calculator features and use of dedicated features facilitated efficient and accurate identification of coordinates of key function features.

Text in English / In order to address the paucity of knowledge in regard to the psychological and physiological processes associated with lifelong weight loss (>20 years), this study adopts a qualitative approach informed by phenomenology to explore the experience of lifelong weight loss and maintenance of women who participated in the ITAND Programme. The research questions guiding the exploration of the current research are: (i) Which strategies from the ITAND Programme do women perceive as assisting with initial weight loss? (ii) What are the processes mediating lifelong weight loss? (iii) What strategies and skills mediate the maintenance of lifelong weight loss? (iv) What feelings or beliefs motivate women to continue attempts to lose weight after experiencing multiple failures on diets? and (v) Which psychological, cognitive and behavioural processes are identified as mediating lifelong weight loss? Eight overweight and obese women were invited to write their narratives and engage in interviews in regard to exploring their relationships with food, their bodies and their weight, after a period of more than 20 years following their participation in an integrative, transactional analysis, anti-diet programme (the ITAND Programme). Narratives were used to explore their beliefs about constructs, processes and strategies mediating long-term weight loss maintenance. The participants’ narratives and interviews were analysed through applying narrative analysis and interpretive phenomenological analysis. In addition to a non-diet paradigm, four processes definingweight loss maintenance were identified, including the adult learning process of transformative learning, the psychological process of transactional analysis, the physiological process of intuitive eating and the cognitive-behavioural processes relating to weight loss maintenance. This study contributes an integrative, transactional analysis, non-diet treatment model (ITAND model) which is enabled by the processes of transformative learning, intuitive eating and cognitive-behaviour modification to the successful long- term treatment of overweight and obesity. This model may be applied in whole or in part in a primary health care or community context. The findings of this study may be used to inform future research into the development and implementation of non-diet weight loss maintenance interventions in the treatment of overweight andobesity. / Psychology / D.Litt. et Phil. (Psychology)