## Abstract

Digital learning environments that offer well-designed feedback have the potential to enhance mathematics education. Building such a system is typically a huge and complex undertaking. Generating informative feedback at the level of steps a student takes requires the encoding of expert knowledge about the problem domain in software. The software component that processes this knowledge is traditionally called a domain reasoner. Such a reasoner can produce various types of feedback, for example about the correctness of a step, common errors, hints about how to proceed, or complete worked-out solutions.

In this paper, we highlight the main domain reasoner components that are responsible for generating feedback: rules, problem-solving procedures, normal forms, buggy rules, and constraints. Examples are drawn from the Digital Mathematics Environment (DME), which uses feedback generated by specialized domain reasoners for solving equations and structuring hypothesis tests. Similar techniques have also been used in tutoring systems for domains outside mathematics.

Original language | English |
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Title of host publication | Proceedings of the 14th International Conference on Technology in Mathematics Teaching – ICTMT 14 |

Subtitle of host publication | Essen, Germany, 22nd to 25th of July 2019, University of Duisburg-Essen |

Editors | Bärbel Barzel, Ruth Bebernik, Lisa Göbel, Maximilian Pohl, Hana Ruchniewicz, Florian Schacht, Daniel Thurm |

Place of Publication | Essen, Germany |

Publisher | University of Duisburg-Essen |

Pages | 17-25 |

Number of pages | 9 |

ISBN (Print) | 978-3-940402-23-3 |

DOIs | |

Publication status | Published - 2020 |

Event | 14th International Conference on Technology in Mathematics Teaching - Universitat Duisburg-Essen, Essen, Germany Duration: 22 Jul 2019 → 25 Jul 2019 https://www.uni-due.de/didmath/veranstaltungen/tagungen/ictmt14/home.php |

### Conference

Conference | 14th International Conference on Technology in Mathematics Teaching |
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Abbreviated title | ICTMT 14 |

Country/Territory | Germany |

City | Essen |

Period | 22/07/19 → 25/07/19 |

Internet address |

## Keywords

- intelligent tutoring systems
- feedback generation
- expert domain knowledge