Design and Applications of a Generic and Heuristic Step-by-Step Problem Solver

Bernhard Zgraggen

Distance University of Applied Sciences of Switzerland

Abstract

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 on the basis of Mathematica.

The paper emphasizes the design and applications of a generic and heuristic algorithm that enables users to generate step-by-step solutions to problems according to their mathematical context by setting parameters for mathematical rules, complexity of expressions, and 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 them are dynamic lists or functional objects. The design of the algorithm corresponds to a heuristic best-first search; its functioning and parameters are explained in detail on the basis of examples from finding partial derivations and simplifying Boolean expressions. The conclusion of the paper deals with educational applications of the algorithm.