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Design and Applications of a Generic and Heuristic Step-by-Step Problem Solver
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| Organization: | Distance University of Applied Sciences of Switzerland |
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2004 International Mathematica Symposium
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Banff, Canada
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The material presented in this paper is part of a research project of the Swiss Distance University of Applied Sciences called webSolutions [www.webmath.ch] which deals with the development and deployment of programs interactively generating detailed and dynamic step-by-step solutions to typical problems in higher mathematical education, based on Mathematica. The paper puts the emphasis on the design and applications of a generic and heuristic algorithm which enables users to generate step-by-step solutions to problems according to their mathematical context by setting parameters for mathematical rules, complexity of expressions, possible solutions and heuristics, as well as for mathematical notations and layout. The interface of the algorithm provides a wide range of parameters, many of which are dynamic lists or functional objects. The design of the algorithm corresponds to a heuristic best-first search. Its parameters and the way it functions are explained in detail using examples from finding partial derivations and simplifying Boolean expressions. The closing part of the paper deals with educational applications of the algorithm.
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step-by-step solutions, webMathematica, heuristic algorithm, complexity of expressions, mathematical notations
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http://www.webmath.ch/
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