AN INVESTIGATION OF LOWER SECONDARY PUPILS' IMAGES OF MATHEMATICS AND MATHEMATICIANS

This thesis reports on a three-part research project in which the images of mathematics and mathematicians held by lower secondary pupils were investigated. A survey tool which asked pupils to draw a picture of a mathematician at work, and which included a Likert-type scale and open-ended writing prompts, was designed and developed for use in an international study of pupils in five countries (n = 476). The results indicate that while some pupils hold stereotypical images in common, all pupils appear to know very little about mathematicians and the work they do. Mathematicians' invisibility to pupils of this age appears to affect their images of mathematics. The tool was refined and utilised again as part of two interventions in the United States: the first attempted to see if images would be affected by a unit in graph theory and discrete mathematics topics (n = 28); the second brought pupils (n = 174) together with a panel of mathematicians. Each intervention had different strengths, but both widened pupils' views of mathematics, enabling them to see it as more than just a study of numbers. In a third small study, professionals in the mathematics field (n = 106) from ten countries were asked in a short survey to comment on Who is a mathematician? and Who may call oneself one? Findings of this portion of the study indicate a lack of a unified vision among members of the mathematics community and some evidence of an elitism which would restrict who may define themselves as a mathematician

Real-time programming and the big ideas of computational literacy

Thesis (Ph. D.)--Massachusetts Institute of Technology, School of Architecture and Planning, Program in Media Arts and Sciences, 2003.Includes bibliographical references (p. 115-121).Though notoriously difficult, real-time programming offers children a rich new set of applications, and the opportunity to engage bodily knowledge and experience more centrally in intellectual enterprises. Moreover, the seemingly specialized problems of real-time programming can be seen as keys to longstanding difficulties of programming in general. I report on a critical design inquiry into the nature and potential of real-time programming by children. A cyclical process of design, prototyping and testing of computational environments has led to two design innovations: a language in which declarative and procedural descriptions of computation are given equal status, and can subsume each other to arbitrary levels of nesting [and] a "live text" environment, in which real-time display of, and intervention in, program execution are accomplished within the program text itself. Based on children's use of these tools, as well as comparative evidence from other media and domains, I argue that the coordination of discrete and continuous process should be considered a central Big Idea in programming and beyond. In addition, I offer the theoretical notion of the "steady frame" as a way to clarify the user interface requirements of real-time programming, and also to understand the role of programming in learning to construct dynamic models, theories, and representations. Implications for the role of programming in education and for the future of computational literacy are discussed.by Christopher Michael Hancock.Ph.D

Bioinspired metaheuristic algorithms for global optimization

This paper presents concise comparison study of newly developed bioinspired algorithms for global optimization problems. Three different metaheuristic techniques, namely Accelerated Particle Swarm Optimization (APSO), Firefly Algorithm (FA), and Grey Wolf Optimizer (GWO) are investigated and implemented in Matlab environment. These methods are compared on four unimodal and multimodal nonlinear functions in order to find global optimum values. Computational results indicate that GWO outperforms other intelligent techniques, and that all aforementioned algorithms can be successfully used for optimization of continuous functions

Experimental Evaluation of Growing and Pruning Hyper Basis Function Neural Networks Trained with Extended Information Filter

In this paper we test Extended Information Filter (EIF) for sequential training of Hyper Basis Function Neural Networks with growing and pruning ability (HBF-GP). The HBF neuron allows different scaling of input dimensions to provide better generalization property when dealing with complex nonlinear problems in engineering practice. The main intuition behind HBF is in generalization of Gaussian type of neuron that applies Mahalanobis-like distance as a distance metrics between input training sample and prototype vector. We exploit concept of neuron’s significance and allow growing and pruning of HBF neurons during sequential learning process. From engineer’s perspective, EIF is attractive for training of neural networks because it allows a designer to have scarce initial knowledge of the system/problem. Extensive experimental study shows that HBF neural network trained with EIF achieves same prediction error and compactness of network topology when compared to EKF, but without the need to know initial state uncertainty, which is its main advantage over EKF