The purpose of this study was to cooperate student-problem chart (S-P Chart) and ordering theory (OT) as an integrated method of cognition diagnosis. S-P chart was used to classify students into proper learning styles, In order to use OT to determine existing hierarchies among items with specifically learning style. Furthermore, an empirical data of capacity concepts testing for fundamental mathematics learning was analyzed based on the integrated method. The results showed that cognition diagnosis would be feasible for remedial teaching and design of teaching materials.

Euclidean distance function based fuzzy clustering algorithms can only be used to detect spherical structural clusters. Gustafson-Kessel (GK) clustering algorithm and Gath-Geva (GG) clustering algorithm were developed to detect non-spherical structural clusters by employing Mahalanobis distance in objective function, however, both of them need to add some constrains for Mahalanobis distance. In this paper, the authors’ improved Fuzzy C-Means algorithm based on common Mahalanobis distance (FCM-CM) is used to identify the mastery concepts in linear algebra, for comparing the performances with other four partition algorithms; FCM-M, GG, GK, and FCM. The result shows that FCM-CM has better performance than others.

In this paper, an extensional item relational structure theory based on the improved nonparametric item response theory is proposed. Item relational structure theory (Takeya, 1991) was developed to detect item relational structures of a group of subjects. The differences of these structures and experts knowledge structures can provide more information for planning remedial instruction, developing instruction materials, or educational researches. In this study, Lius improved nonparametric item response theory ( Liu, 2000, 2013) without the local independence assumption is used to estimate the joint probability of two items, and construct personal item relational structures. A Mathematics example is also provided in this paper to illustrate the advantages of the proposed method

In this paper, an improved polytomous item relational structure theory based on Q-matrix theory is proposed, using Tatsuoka’s Q-matrix theory, we can construct the test with all efficient items which are fitting in with the given relational structure of cognitive attributes, and then, before the test, using Liu’s before-test item ordering theory, an ideal relational structural graph of itemscan be constructed, and the real efficient items can be obtained accordingly. After testing the students, an after-test structure of items can be estimated by using the Liu’s polytomous item relational structure theory. Furthermore, using Liu’s criterion related validity index, we can evaluate the estimated item relational structure of the test, and the results could be useful for cognitive diagnosis and remedial instruction.

No abstract