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Variation Theory Meets Diagnostic Classification Models: The Case of Assessment in a Learning Study on Subtraction with Negative Numbers

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Title: Variation Theory Meets Diagnostic Classification Models: The Case of Assessment in a Learning Study on Subtraction with Negative Numbers
Language: English
Authors: Ahoo Sh Fard (ORCID 0000-0002-8860-8904), Frank Dige Bach (ORCID 0000-0001-5614-9064), Åke Ingerman (ORCID 0000-0002-0198-7631), Ulf Ryberg (ORCID 0009-0008-1277-7067)
Source: International Journal for Lesson and Learning Studies. 2026 15(5):17-32.
Availability: Emerald Publishing Limited. Howard House, Wagon Lane, Bingley, West Yorkshire, BD16 1WA, UK. Tel: +44-1274-777700; Fax: +44-1274-785201; e-mail: emerald@emeraldinsight.com; Web site: http://www.emerald.com/insight
Peer Reviewed: Y
Page Count: 16
Publication Date: 2026
Document Type: Journal Articles
Reports - Research
Education Level: Elementary Education
Grade 6
Intermediate Grades
Middle Schools
Descriptors: Subtraction, Numbers, Teacher Improvement, Teacher Collaboration, Grade 6, Foreign Countries, Statistical Analysis, Test Items, Models, Classification, Mathematics Tests, Learning Theories, Learning Objectives
Geographic Terms: Sweden
DOI: 10.1108/IJLLS-12-2024-0301
ISSN: 2046-8253
Abstract: Purpose: The study reports a learning study on subtraction with negative numbers based on Variation Theory (VT), with special focus on exploring the conditions for using diagnostic classification models (DCMs) for assessment. DCMs offer a multidimensional statistical modeling approach where the dimensions may mimic CAs (CAs) in VT. The study aims to within a learning study develop a knowledge test that meets DCM standards and to assess its usefulness in that context. Design/methodology/approach: Data comes from a learning study based on VT, in grade 6 in three Swedish schools. The developed teaching relied on four identified CAs that were also used to develop a knowledge test meeting the standards for DCM. The methodology involved iterative cycles of test development and statistical model evaluation, alongside qualitative methods such as think-aloud interviews. Findings: The developed test meets statistical standards implied by DCMs. Challenges in operationalizing CAs in test items are identified. Detailed information about how test-takers discerned CAs becomes available, which also may be used for the development of teaching and the articulation of CAs. In particular, the DCM analysis provided individual profiles regarding CAs, supporting a nuanced understanding of learning outcomes at the group level. Originality/value: The bridging VT and DCMs offer a comprehensive assessment of learning outcomes, emphasizing the importance of aligning tests with the object of learning. The findings suggest that DCMs can complement qualitative methods, providing a systematic and detailed analysis of students' knowledge.
Abstractor: As Provided
Entry Date: 20260101
Accession Number: EJ1503031
Database: ERIC
FullText Text:
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  Data: Variation Theory Meets Diagnostic Classification Models: The Case of Assessment in a Learning Study on Subtraction with Negative Numbers
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  Data: <searchLink fieldCode="AR" term="%22Ahoo+Sh+Fard%22">Ahoo Sh Fard</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-8860-8904">0000-0002-8860-8904</externalLink>)<br /><searchLink fieldCode="AR" term="%22Frank+Dige+Bach%22">Frank Dige Bach</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0001-5614-9064">0000-0001-5614-9064</externalLink>)<br /><searchLink fieldCode="AR" term="%22Åke+Ingerman%22">Åke Ingerman</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-0198-7631">0000-0002-0198-7631</externalLink>)<br /><searchLink fieldCode="AR" term="%22Ulf+Ryberg%22">Ulf Ryberg</searchLink> (ORCID <externalLink term="https://orcid.org/0009-0008-1277-7067">0009-0008-1277-7067</externalLink>)
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  Data: <searchLink fieldCode="SO" term="%22International+Journal+for+Lesson+and+Learning+Studies%22"><i>International Journal for Lesson and Learning Studies</i></searchLink>. 2026 15(5):17-32.
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  Data: Emerald Publishing Limited. Howard House, Wagon Lane, Bingley, West Yorkshire, BD16 1WA, UK. Tel: +44-1274-777700; Fax: +44-1274-785201; e-mail: emerald@emeraldinsight.com; Web site: http://www.emerald.com/insight
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  Data: <searchLink fieldCode="DE" term="%22Subtraction%22">Subtraction</searchLink><br /><searchLink fieldCode="DE" term="%22Numbers%22">Numbers</searchLink><br /><searchLink fieldCode="DE" term="%22Teacher+Improvement%22">Teacher Improvement</searchLink><br /><searchLink fieldCode="DE" term="%22Teacher+Collaboration%22">Teacher Collaboration</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+6%22">Grade 6</searchLink><br /><searchLink fieldCode="DE" term="%22Foreign+Countries%22">Foreign Countries</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+Analysis%22">Statistical Analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Test+Items%22">Test Items</searchLink><br /><searchLink fieldCode="DE" term="%22Models%22">Models</searchLink><br /><searchLink fieldCode="DE" term="%22Classification%22">Classification</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Tests%22">Mathematics Tests</searchLink><br /><searchLink fieldCode="DE" term="%22Learning+Theories%22">Learning Theories</searchLink><br /><searchLink fieldCode="DE" term="%22Learning+Objectives%22">Learning Objectives</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Sweden%22">Sweden</searchLink>
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  Data: 10.1108/IJLLS-12-2024-0301
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  Data: Purpose: The study reports a learning study on subtraction with negative numbers based on Variation Theory (VT), with special focus on exploring the conditions for using diagnostic classification models (DCMs) for assessment. DCMs offer a multidimensional statistical modeling approach where the dimensions may mimic CAs (CAs) in VT. The study aims to within a learning study develop a knowledge test that meets DCM standards and to assess its usefulness in that context. Design/methodology/approach: Data comes from a learning study based on VT, in grade 6 in three Swedish schools. The developed teaching relied on four identified CAs that were also used to develop a knowledge test meeting the standards for DCM. The methodology involved iterative cycles of test development and statistical model evaluation, alongside qualitative methods such as think-aloud interviews. Findings: The developed test meets statistical standards implied by DCMs. Challenges in operationalizing CAs in test items are identified. Detailed information about how test-takers discerned CAs becomes available, which also may be used for the development of teaching and the articulation of CAs. In particular, the DCM analysis provided individual profiles regarding CAs, supporting a nuanced understanding of learning outcomes at the group level. Originality/value: The bridging VT and DCMs offer a comprehensive assessment of learning outcomes, emphasizing the importance of aligning tests with the object of learning. The findings suggest that DCMs can complement qualitative methods, providing a systematic and detailed analysis of students' knowledge.
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  Data: 20260101
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  Data: EJ1503031
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      – Type: doi
        Value: 10.1108/IJLLS-12-2024-0301
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 16
        StartPage: 17
    Subjects:
      – SubjectFull: Subtraction
        Type: general
      – SubjectFull: Numbers
        Type: general
      – SubjectFull: Teacher Improvement
        Type: general
      – SubjectFull: Teacher Collaboration
        Type: general
      – SubjectFull: Grade 6
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      – SubjectFull: Foreign Countries
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      – SubjectFull: Statistical Analysis
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      – SubjectFull: Test Items
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      – SubjectFull: Models
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      – SubjectFull: Classification
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      – SubjectFull: Mathematics Tests
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      – SubjectFull: Learning Theories
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      – SubjectFull: Learning Objectives
        Type: general
      – SubjectFull: Sweden
        Type: general
    Titles:
      – TitleFull: Variation Theory Meets Diagnostic Classification Models: The Case of Assessment in a Learning Study on Subtraction with Negative Numbers
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              Y: 2026
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