Automated feedback for mathematical learning environments

Bastiaan Heeren*, Johan Jeuring

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference Article in proceedingAcademicpeer-review


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 languageEnglish
Title of host publicationProceedings of the 14th International Conference on Technology in Mathematics Teaching – ICTMT 14
Subtitle of host publicationEssen, Germany, 22nd to 25th of July 2019, University of Duisburg-Essen
EditorsBärbel Barzel, Ruth Bebernik, Lisa Göbel, Maximilian Pohl, Hana Ruchniewicz, Florian Schacht, Daniel Thurm
Place of PublicationEssen, Germany
PublisherUniversity of Duisburg-Essen
Number of pages9
ISBN (Print)978-3-940402-23-3
Publication statusPublished - 2020
Event14th International Conference on Technology in Mathematics Teaching - Universitat Duisburg-Essen, Essen, Germany
Duration: 22 Jul 201925 Jul 2019


Conference14th International Conference on Technology in Mathematics Teaching
Abbreviated titleICTMT 14
Internet address


  • intelligent tutoring systems
  • feedback generation
  • expert domain knowledge


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