Correia Dias, Angela Alvares; (1996) Ways of seeing geometrical meaning in different situations. Doctoral thesis , Institute of Education, University of London.

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Abstract

This thesis set out to challenge the traditional approach to the study of geometrical understanding which has assumed that conceiving and interpreting shapes or forms is the result of logical and mental interaction between an individual and geometrical objects and that the production of geometrical meaning is motivated by the stimulus of the external structure of a visual text. By way of contrast, this study makes the case that geometrical meaning is socially and contextually produced. The research has two interconnected strands. The first strand is theoretical aiming to develop a framework for the study of geometrical understanding drawing on concepts from Mikhail Bakhtin, Umberto Eco and Gunther Kress. The second is empirical aiming to collect data whose analysis will inform and be informed by this theoretical framework. For this study, three groups of people who differed radically in terms of their geometrical experiences, socio-economic and educational backgrounds were interviewed in order to examine their interpretations of geometrical elements exhibited in different settings. The theoretical work of this thesis led to a framework for understanding geometry comprising 'sign', 'sign-functions', 'visual text', and 'heteroglossia'. Analysis of the data from empirical study in terms of this framework revealed the importance of the dynamics for visual experience as a process for communicating and of signifying, and how this relationship was itself dependent on the material conditions and contextual dynamics in which the meanings were constructed. The thesis concludes with an assessment of its potential contribution to redress the balance between learning about geometry and learning through geometry.

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