The teaching of probability in schools provides a good opportunity for examining how a new topic is integrated into a school curriculum. Furthermore, because probabilistic thinking is quite different from the deterministic thinking traditionally found in mathematics classrooms, such an examination is particularly able to highlight significant forces operating within educational practice. 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, where 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. / Thesis (Ph.D.)--Graduate School of Education and Department of Pure Mathematics, 2001.

In many command and control situations the understanding of dynamic events is crucial. With today’s development of hard- and software architecture, we have the possibility to visualize data in two-dimensional (2D) and three-dimensional (3D) images. The aim of this thesis is therefore to investigate different approaches to visualizing dynamic events. The visualization techniques investigated include 2D animation and time representations as markings on a 2D map. In 3D the visualization technique investigated is the “space time-cube” A further aim is to study whether the Cue Probability Learning (CPL) paradigm can be used to evaluate visualizations. By mapping time onto a spatial dimension, in the 2D visualization as lines with different densities and in 3D as height over the map, a simultaneous visualization of space and time is possible. The findings are that this mapping of time onto space is beneficial to users as compared with animations, but the two mapping techniques are not interchangeable. If a task requires judgments of metric spatial properties, a 2D visualization is more beneficial; however, if the task only requires judgments of more qualitative aspects, a 3D visualization is more beneficial. When we look at a 3D visualization, we utilize different sources of depth information. These sources are always present and each defines either a 3D scene or a projection surface. By using these different sources of depth information wisely, a visualization can be created that efficiently shows relevant information to a user while requiring a minimal amount of specialized hardware. Finally, the CPL paradigm seems to be a worthwhile option as an experimental paradigm in visualization experiments. One of the advantages of CPL is that novice users can be trained to be task experts in a controlled and time-efficient way.

Thesis (doctoral)--University of Uppsala, 1983. / Thesis t.p. laid in. Includes bibliographical references (p. 157-163).

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Designers do not merely develop concepts; they are increasingly involved in testing product concepts and learning consumer preference. However, designers’ decision making processes in these tasks have been little studied. In the two essays, I apply decision making frameworks to concept testing and preference learning to study consumer’s and designer’s biases. In my first essay, I study consumer bias in concept testing. When consumers test new products, they are often asked to choose which product they prefer. However, a choice question can elicit biased preference because consumers simply choose the product that is superior on the attribute serving their purchase purpose. My studies show that when consumers are asked to predict which product they will enjoy more, they are more likely to prefer the product that actually reflects their consumption utility. These findings suggest that making trade-offs is avoided in the choice question, but is encouraged in the enjoyment prediction question. Thus, a simple change of question format, in otherwise identical product comparisons, elicits different answers. This holds true when product attributes are easy to evaluate; when product attributes are hard to evaluate, changing question format does not affect consumer choice. My second essay examines designer bias in preference learning. When designers predict consumer preference for a product, they often base their predictions on consumer preference for similar products. However, this categorization-based strategy can result in biased predictions because categorical similarity is not diagnostic for preference prediction. I conducted two studies by applying a Multiple Cue Probability Learning experiment to a designer’s prediction task. I found that when subjects used a sequential learning strategy, making a sequence of predictions and receiving feedback, they increased prediction accuracy by 14% on average. When they made predictions with multiple sets, with a break between each set during which they reflected on what they had learned, their prediction accuracy further improved by 7% on average. In sum, I demonstrate bias and propose approaches to avoid them in two design tasks. My two essays show that the decision making frameworks are crucial in understanding and improving the successful outcome of the design process.

Designers do not merely develop concepts; they are increasingly involved in testing product concepts and learning consumer preference. However, designers’ decision making processes in these tasks have been little studied. In the two essays, I apply decision making frameworks to concept testing and preference learning to study consumer’s and designer’s biases. In my first essay, I study consumer bias in concept testing. When consumers test new products, they are often asked to choose which product they prefer. However, a choice question can elicit biased preference because consumers simply choose the product that is superior on the attribute serving their purchase purpose. My studies show that when consumers are asked to predict which product they will enjoy more, they are more likely to prefer the product that actually reflects their consumption utility. These findings suggest that making trade-offs is avoided in the choice question, but is encouraged in the enjoyment prediction question. Thus, a simple change of question format, in otherwise identical product comparisons, elicits different answers. This holds true when product attributes are easy to evaluate; when product attributes are hard to evaluate, changing question format does not affect consumer choice. My second essay examines designer bias in preference learning. When designers predict consumer preference for a product, they often base their predictions on consumer preference for similar products. However, this categorization-based strategy can result in biased predictions because categorical similarity is not diagnostic for preference prediction. I conducted two studies by applying a Multiple Cue Probability Learning experiment to a designer’s prediction task. I found that when subjects used a sequential learning strategy, making a sequence of predictions and receiving feedback, they increased prediction accuracy by 14% on average. When they made predictions with multiple sets, with a break between each set during which they reflected on what they had learned, their prediction accuracy further improved by 7% on average. In sum, I demonstrate bias and propose approaches to avoid them in two design tasks. My two essays show that the decision making frameworks are crucial in understanding and improving the successful outcome of the design process.