Adapting Mathematical Domain Reasoners

TL;DR

This paper presents a method for adapting mathematical domain reasoners in learning environments by allowing users to explicitly configure and communicate the components used for solving exercises, enhancing flexibility.

Contribution

It introduces a framework enabling users to adapt and configure domain reasoners through explicit communication of solving components, improving customization for diverse educational needs.

Findings

Users can tailor domain reasoners to specific exercise requirements

The approach supports combining multiple mathematical domains

Enhanced flexibility in mathematical learning environments

Abstract

Mathematical learning environments help students in mastering mathematical knowledge. Mature environments typically offer thousands of interactive exercises. Providing feedback to students solving interactive exercises requires domain reasoners for doing the exercise-specific calculations. Since a domain reasoner has to solve an exercise in the same way a student should solve it, the structure of domain reasoners should follow the layered structure of the mathematical domains. Furthermore, learners, teachers, and environment builders have different requirements for adapting domain reasoners, such as providing more details, disallowing or enforcing certain solutions, and combining multiple mathematical domains in a new domain. In previous work we have shown how domain reasoners for solving interactive exercises can be expressed in terms of rewrite strategies, rewrite rules, and views. This paper shows how users can adapt and configure such domain reasoners to their own needs. This is achieved by enabling users to explicitly communicate the components that are used for solving an exercise.