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The purpose of this paper was to analyze the structure of difficult concepts learning within the classroom. The sample of the study was 18 fourth grade students in Central Taiwan, and the exam tools were produced by teachers for math exams. In this paper, a combination of the Rasch Model GSP chart analysis theory, the misconception domain, the Interpretive Structural Modeling (ISM) and Grey Structural Model (GSM) was used. The results are as follows: (1) Based on the change in students' average grade and the difficulty between problems of Rasch Line = 0.5, the effect of the remedial teaching will be known. (2) Through the GSM structural graphs, the misconception domain structure of students can be identified. (3) The problemconcept relationship of misconception domain can reveal the structure of misconceptions through the GSM structural graph. This structure is capable of identifying the learning sequence of the difficult concepts. (4) Upon comparing the GSM structural graph of misconception domain before and after remedial teaching, it became clear which concepts made learning more effective, and which concepts needed to be developed more. (5) The research method for a small amount of people and problems can still systematic point out the structure of concepts which need in this class.

The study analyzed students' misconception based on rough set theory and combined with interpretive structural model (ISM) to compare students' degree of two classes. The study then has provided an effective diagnostic assessment tool for teachers. The participants were 30 fourth grade students in Central Taiwan, and the exam tools were produced by teachers for math exams. The study has proposed three methods to get common misconception of the students in class. These methods are "Deleting conditional attributes", "Using Boolean logic to calculate discernable matrix", and "Calculating significance of conditional attributes." The results showed that students of Class A had common misconceptions but students of Class B had not common misconception. In addition, the remedial decision-making for these two classes of students is pointed out. While remedial decision-making of two classes corresponded to structural graph of concepts, it can be found the overall performance of the Class B was higher than Class A.

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ÖzBu araştırmada, aynı evrenden tesadüfi olarak seçilen örneklemlerden elde edilen Maddeler için Sınırlandırılmış Gri İlişki Derecelerinin (MİSGİD) tutarlılığının ve Madde Uyarı İndeksleri (MUİ) aracılığı ile gerçekleştirilen madde sınıflandırmaları arasındaki uyumun incelenmesi amaçlanmıştır. Bu amaç doğrultusunda, 20 madde ve bu maddelere dayalı 1000 adet yanıt örüntüsü simülasyon yoluyla elde edilmiş, yanıt örüntüleri içerisinden seçkisiz olarak seçilen ve 30 yanıt örüntüsü içeren 10 farklı veri seti (örneklem) oluşturulmuştur. Örneklemlerin her birinden elde edilen MİSGİD değerlerinin farklı örneklemler arası tutarlılığının belirlenebilmesi amacıyla Spearman Sıra Farkları Korelasyon Katsayıları hesaplanmış ve buna ek olarak değer ortalamaları arasındaki farkın anlamlılığı Kruskal Wallis-H Testi ile incelenmiştir. Ayrıca örneklemlerden elde edilen MUİ ile yapılan sınıflandırmaların ne oranda uyum gösterdiği yüzde oranlar yardımıyla incelenmiştir. Elde edilen bulgular, Sato Test Kuramında maddelerin kalitesinin belirlenebilmesi için üretilen MİSGİD parametrelerinin ve MUİ parametresine dayalı yapılan sınıflandırmaların tutarlı sonuçlar verdiğini göstermiştir.