Individual Differences in Dimensions of Information Processing, Self-esteem and Secondary School Students' Multiplicatne Knowledge in Basic Arithmetical Problems

Abstract

This thesis examined individual differences in cognition and affect in secondary school students' multiplicative knowledge structures of basic mathematics problems. The study was set in a metropolitan State High School in Brisbane, Queensland, Australia which draws students from a mix of demographic and socio-economic areas. <br/> Four quantitative studies examined models of cognition, affect and knowledge structures of basic mathematics problems and their inter-relationships. <br/> The first study used Luria's 'whole brain' theory of Information Processing abilities or preferences. This theory describes two ways in which people input, store and analyse sensory data. According to Luria's model, information is processed successively (sequential and primarily temporal) and simultaneously ( continuous and primarily spatial.) The second study used Marsh's multi-dimensional model of Self-Esteem which describes academic and non-academic dimensions as measures of Self-Image. The academic dimensions of Maths and Verbal Self-Esteem can be linked directly to performance in mathematics problems. Basic mathematics items used in Queensland and other parts of Australia provided a measure of student performance on four arithmetical operations of addition, subtraction, multiplication and division of positive integers and non-integers. The fourth study showed that individual differences in Information Processing Preferences and the academic dimensions of Maths and Verbal Self-Esteem were related significantly to increasingly complex multiplicative knowledge structures in basic mathematics problems. <br/> A later Phase 2 qualitative study supplemented and complimented the significant findings of the four Phase 1 studies. This fifth study incorporated semi-structured interviews of 22% of the cohort. This was a selective sample drawn from Years 8 and 9 only and was informed by the findings of the Phase 1 quantitative results. The interviews focussed on individual differences of Simultaneous and Successive Information Processing Preferences and affect in the inter-connectedness of multiplicative knowledge structures that students use in solving basic mathematics problems. <br/> Procedural and Conceptual knowledge aspects of multiplicative structures were analysed within a proceptual framework described by Gray and Tall ( 1994 ). Simultaneous Information Processing Preferences were found to be essential in enabling connectedness of the more conceptual aspects of multiplicative knowledge. Successive Information Processing Preferences were found to be essential in enabling connectedness of the more procedual aspects of multiplicative knowledge inherent in algorithmic processes. An expanded model of Proceptual Multiplicative Knowledge proposed that flexibility, inherent in Simultaneous Information Processing Preferences, is the catalyst for enabling more complex multiplicative knowledge structures in basic mathematics problems. <br/> The relationship between these cognitive aspects and the academic dimension of Maths Self-Esteem, while generally related positively to differences in Simultaneous Information Processing Preferences, is not as clearly defined with idiosyncratic behaviours apparent in higher levels of Simultaneous Information Processing Preferences. <br/> This significant finding of individual differences in Information Processing Preferences and Maths Self-Esteem in proceptual aspects of multiplicative knowledge structures of basic mathematics problems provided a sound basis for further major research within the disciplines of psychology, mathematics and mathematics education.