Stevenson, Ian.; (1995) Constructing curvature: the iterative design of a computer-based microworld for non-Euclidian geometry. Doctoral thesis , Institute of Education, University of London.

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Abstract

The study charts the iterative development of a computer-based microworld for noneuclidean geometry. Its aim was to explore the possibilities for constructing a suitable context that simultaneously articulated the processes of teaching and learning using computer-based versions of euclidean models for non-euclidean geometry, and the construction of the context. Using the microworld paradigm as the basis for a model of a computer-based learning environment, the study defines a microworld not only in terms of the computational and non-computational tools available to the learner, but also with reference to its pedagogical intentions and cognitive pre-suppositions. The model of the microworld that was created was then used to guide its design and development. The computational element of the microworld employed an object-oriented version of the Lisp-based programming language Logo to implement Turtle Graphics in a non-euclidean context. The design process for the microworld was iterative. Activities, which brought together software and specific pedagogic approaches to non-euclidean geometry, were trialled and modified in the light of learners' experiences with the microworld. Organised into three developmental cycles, the study describes and analyses each iteration under three interrelated categories: technical refinement of the software and non-computational objects, structuring of the pedagogical framework, and the cognitive development of the learners mediated by their experience of the microworld. The study concludes with an appreciation of this iterative development process. It proposes a framework for microworld creation based on the principles of design and of learning as the exploration of a knowledge domain.

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