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A Nonparametric Weighted Cognitive Diagnosis Model and Its Application on Remedial Instruction in a Small-Class Situation

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  • Cheng-Hsuan Li

    (Graduate Institute of Educational Information and Measurement, National Taichung University of Education, Taichung City 40306, Taiwan)

  • Yi-Jin Ju

    (Graduate Institute of Educational Information and Measurement, National Taichung University of Education, Taichung City 40306, Taiwan)

  • Pei-Jyun Hsieh

    (Graduate Institute of Educational Information and Measurement, National Taichung University of Education, Taichung City 40306, Taiwan)

Abstract

CDMs can provide a discrete classification of mastery skills to diagnose relevant conceptions immediately for Education Sustainable Development. Due to the problem of parametric CDMs with only a few training sample sizes in small classroom teaching situations and the lack of a nonparametric model for classifying error patterns, two nonparametric weighted cognitive diagnosis models, NWSD and NWBD, for classifying mastery skills and knowledge bugs were proposed, respectively. In both, the variances of items with respect to the ideal responses were considered for computing the weighted Hamming distance, and the inverse distances between the observed and ideal responses were used as weights to obtain the probabilities of the mastering attributes of a student. Conversely, NWBD can classify students’ “bugs”, so teachers can provide suitable examples for precision assistance before teaching non-mastery skills. According to the experimental results on simulated and real datasets, the proposed methods outperform some standard methods in a small-class situation. The results also demonstrate that a remedial course with NWSD and NWBD is better than one with traditional group remedial teaching.

Suggested Citation

  • Cheng-Hsuan Li & Yi-Jin Ju & Pei-Jyun Hsieh, 2022. "A Nonparametric Weighted Cognitive Diagnosis Model and Its Application on Remedial Instruction in a Small-Class Situation," Sustainability, MDPI, vol. 14(10), pages 1-17, May.
    • Handle: RePEc:gam:jsusta:v:14:y:2022:i:10:p:5773-:d:812396
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    References listed on IDEAS

    as
    1. Chia-Yi Chiu & Yan Sun & Yanhong Bian, 2018. "Cognitive Diagnosis for Small Educational Programs: The General Nonparametric Classification Method," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 355-375, June.
    2. Tobias Hoppe & Alexander Renkl & Tina Seidel & Stephanie Rettig & Werner Rieß, 2020. "Exploring How Teachers Diagnose Student Conceptions about the Cycle of Matter," Sustainability, MDPI, vol. 12(10), pages 1-15, May.
    3. Laine Bradshaw & Jonathan Templin, 2014. "Combining Item Response Theory and Diagnostic Classification Models: A Psychometric Model for Scaling Ability and Diagnosing Misconceptions," Psychometrika, Springer;The Psychometric Society, vol. 79(3), pages 403-425, July.
    4. Susan Embretson (Whitely), 1984. "A general latent trait model for response processes," Psychometrika, Springer;The Psychometric Society, vol. 49(2), pages 175-186, June.
    5. Jimmy de la Torre, 2011. "The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 179-199, April.
    6. Gisela Cebrián & Ramon Palau & Jordi Mogas, 2020. "The Smart Classroom as a Means to the Development of ESD Methodologies," Sustainability, MDPI, vol. 12(7), pages 1-18, April.
    7. Shiyu Wang & Jeff Douglas, 2015. "Consistency of Nonparametric Classification in Cognitive Diagnosis," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 85-100, March.
    8. Chia-Yi Chiu & Jeff Douglas, 2013. "A Nonparametric Approach to Cognitive Diagnosis by Proximity to Ideal Response Patterns," Journal of Classification, Springer;The Classification Society, vol. 30(2), pages 225-250, July.
    9. Jimmy Torre, 2011. "Erratum to: The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 510-510, July.
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