Design and educational Applications of a generic Step-by-Step Solver for mathematical Problems based on Mathematica

Abstract

The starting point of this paper is a project at the Distance University of Applied Sciences of Switzerland 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 Wolfram Research, Inc.'s Mathematica. The first part of the paper explains an approach for a generic step-by-step solver and its interface enabling tutors to create step-by-step solutions according to their mathematical context by an appropriate setting of parameters (mathematical rules, complexity parameters, parameters for solutions, general stop conditions, rules for output and display of expressions and mathematical explanations). The functioning of such an algorithm and its parameters are explained in detail on the basis of examples from distinct mathematical areas. The second part of the paper puts the emphasis on web-based applications of such a solver system in higher mathematical education.