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

Cheng-Hsuan Li, Yi-Jin Ju and Pei-Jyun Hsieh
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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

Sustainability, 2022, vol. 14, issue 10, 1-17

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.

Keywords: nonparametric cognitive diagnosis; skill; misconception; error pattern; small class (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2022
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