Faculty of Education - Theses

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Author: Kelly, Lynne Sandra × Start date: 1990 × Type: Masters Coursework thesis × Subject: Education × Subject: Gifted children ×

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    The investigation into the application of chaos theory and fractal geometry as a cross-curricular enrichment theme for highly able students
    Kelly, Lynne Sandra ( 1994)
    Chaos theory and fractal geometry is investigated as an interdisciplinary enrichment theme for gifted students. A literature search revealed the recommendation that this topic be introduced into secondary schools, but no references could be found to a suitable course. Hence an action research group of highly able secondary school students aged from twelve to seventeen was established to help develop just such a course. It was found to be necessary to divide the emergent curriculum into seven streams to satisfy the individual needs of the students. The streams were mathematics, science, programming, software, history and philosophy, communications and art. The mathematics stream formed the basis introducing concepts such as iteration, deterministic systems, iterated function systems, complex numbers, the Cantor, Mandelbrot and Julia Sets, The Koch curve, fractal dimensions, period doubling and phase space. Some students programmed the mathematical procedures in both Quick Basic and Turbo Pascal. The applications in science, including weather forecasting, dissecting lungs, chemical reactions, astronomy, population dynamics and magnetic pendulums were investigated using practical methods wherever possible. Software packages were explored as were the historical, philosophical, sociological and artistic questions which arose during the action research phase. Modern communications were used to gain programs and information over Internet. Links with people of similar interests around the world were established. Through these activities, a final course of eighty work sheets and supporting reference sheets was developed. This course is presented in Volume Two. Students and the candidate maintained journals and these, along with a questionnaire and other documentary data, were analysed using a grounded theory methodology. As a result, chaos theory and fractal geometry was shown to be a suitable and stimulating theme for cross-curricular enrichment of highly able students.