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Learning from errors: co-clustering students' answer types in a digital learning environment to verify task design on linear equations.

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Title: Learning from errors: co-clustering students' answer types in a digital learning environment to verify task design on linear equations.
Authors: Elkjær, Morten1 (AUTHOR) meh@alinea.dk, Mørup, Morten2 (AUTHOR)
Source: Scandinavian Journal of Educational Research. Jun2026, Vol. 70 Issue 4, p797-814. 18p.
Subject Terms: *Digital learning, Linear equations, Data mining, Design, Cluster analysis (Statistics)
Abstract: This study is concerned with establishing a means to generate better methods to analyse and learn about task design for digital learning environments. Specifically, we utilise data consisting of over 2 million unique answers from a popular Danish digital learning environment, matematikfessor.dk, to solve 892 unique tasks dealing with linear equations. Utilising the Multinomial Infinite Relational Model (MIRM), which can account for extensive didactical coding of the five most popular answers to each of the 892 tasks, we successfully co-clustered students and tasks into groups for further analysis. The results showed that the analysis of these clusters of tasks can provide access to valuable information on the difficulties students in four respective groups face and what kind of specific tasks and knowledge pertinent to what types of tasks actually affect students' problems or difficulties anticipated by the task designer. [ABSTRACT FROM AUTHOR]
Copyright of Scandinavian Journal of Educational Research is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Education Research Complete
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  Data: Learning from errors: co-clustering students' answer types in a digital learning environment to verify task design on linear equations.
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  Data: <searchLink fieldCode="AR" term="%22Elkjær%2C+Morten%22">Elkjær, Morten</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> meh@alinea.dk</i><br /><searchLink fieldCode="AR" term="%22Mørup%2C+Morten%22">Mørup, Morten</searchLink><relatesTo>2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Scandinavian+Journal+of+Educational+Research%22">Scandinavian Journal of Educational Research</searchLink>. Jun2026, Vol. 70 Issue 4, p797-814. 18p.
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  Data: *<searchLink fieldCode="DE" term="%22Digital+learning%22">Digital learning</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+equations%22">Linear equations</searchLink><br /><searchLink fieldCode="DE" term="%22Data+mining%22">Data mining</searchLink><br /><searchLink fieldCode="DE" term="%22Design%22">Design</searchLink><br /><searchLink fieldCode="DE" term="%22Cluster+analysis+%28Statistics%29%22">Cluster analysis (Statistics)</searchLink>
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  Label: Abstract
  Group: Ab
  Data: This study is concerned with establishing a means to generate better methods to analyse and learn about task design for digital learning environments. Specifically, we utilise data consisting of over 2 million unique answers from a popular Danish digital learning environment, matematikfessor.dk, to solve 892 unique tasks dealing with linear equations. Utilising the Multinomial Infinite Relational Model (MIRM), which can account for extensive didactical coding of the five most popular answers to each of the 892 tasks, we successfully co-clustered students and tasks into groups for further analysis. The results showed that the analysis of these clusters of tasks can provide access to valuable information on the difficulties students in four respective groups face and what kind of specific tasks and knowledge pertinent to what types of tasks actually affect students' problems or difficulties anticipated by the task designer. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  Data: <i>Copyright of Scandinavian Journal of Educational Research is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1080/00313831.2025.2516437
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      – Code: eng
        Text: English
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        PageCount: 18
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      – SubjectFull: Digital learning
        Type: general
      – SubjectFull: Linear equations
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      – SubjectFull: Data mining
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      – SubjectFull: Design
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      – SubjectFull: Cluster analysis (Statistics)
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      – TitleFull: Learning from errors: co-clustering students' answer types in a digital learning environment to verify task design on linear equations.
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              Text: Jun2026
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              Y: 2026
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