Theorem-Prover (TP) based educational mathematics systems are able to cover all phases of stepwise problem solving, a TP checks user-input most generally and reliably; an additional feature is the ability to know the next step towards a solution. However, just presenting the next step is not motivating for the learner; so adaptive user guidance is required.
This paper describes a general approach to adaptive user guidance resulting from an interdisciplinary cooperation between Computer Mathematics and Cognitive Science. The former provides technologies for capturing a general notion of error-pattern and for general services to be used for user guidance by a dialogue component. The latter, Cognitive Science, addresses the dialogue component providing user guidance. After a brief review of guiding principles for learning an, architecture for the dialogue component in a prototype is presented. The interactions between mathematics engine, dialogue component and front-end are described as rules of a knowledge-based expert system.
The prototype is described to an extent which gives a proof of concept for both, the feasibility of general error-patterns in terms of Computer Mathematics as well as appropriateness of the respective services for adaptive user guidance in terms of Cognitive Science.