8 after six chapters which describe relevant aspects

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8 After six chapters which describe relevant aspects of the philosophical, cultural, and intellectual environment within which probability has been taught, a "Broad-Spectrum Ecological Model" is developed to examine the forces which operate on a school system. The Model sees school systems and their various participants as operating according to general ecological principles, and interprets actions as responses to situations in ways which minimise energy expenditure and maximise chances of survival. The Model posits three principal forces- Physical, Social and Intellectual-as providing an adequate structure. The value of the Model as an interpretative framework is then assessed by examining three separate aspects of the teaching of probability. The first is a general survey of the history of the teaching of the topic from 1959 to 1994, paying particular attention to South Australia, but making some comparisons with other countries and other states of Australia. The second examines in detail attempts which have been made throughout the world to assess the understanding of probabilistic ideas. The third addresses the influence on classroom practice of research into the teaching and learning of probabilistic ideas. In all three situations the Model is shown to be a helpful way of interpreting the data, but to need some refinements. This involves the uniting of the Social and Physical forces, the division of the Intellectual force into Mathematics and Mathematics Education forces, and the addition of Pedagogical and Charismatic forces. A diagrammatic form of the Model is constructed which provides a way of indicating the relative strengths of these forces. The initial form is used throughout the thesis for interpreting the events described. The revised form is then defined and assessed, particularly against alternative explanations of the events described, and also used for drawing some comparisons with medical education. The Model appears to be effective in highlighting uneven forces and in predicting outcomes which are likely to arise from such asymmetries, and this potential predictive power is assessed for one small case study. All Models have limitations, but this one seems to explain far more than the other models used for mathematics curriculum development in Australia which have tended to see our practice as an imitation of that in other countries. JOHN M. TRURAN. SELECTED REFERENCES 1. TEXTBOOKS (1969). School Mathematics Project Book 5. Cambridge, United Kingdom: Cambridge University Press (with other authors). (1970). School Mathematics Project Book 3T. Cambridge, United Kingdom: Cambridge University Press (with other authors). (1970). School Mathematics Project Teacher’s Guide for Book 5. Cambridge, United Kingdom: Cambridge Uni- versity Press (with other authors).
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