Two rational partial scoring methods for sorting problems are the "Maximum Relative Chaining Spectrum" (MRS) and the "Linear Rank Matrix Method" (LM), as proposed by the presenter. Both are models based on mathematical operations that reflect the cognitive burden during the task. MRS is a simple measurement method as it is practically equivalent to the minimum edit distance, but it could not evaluate the movement and aggregation distance from each test-taker's answer to the chain of correct answers. On the other hand, LM, an approximate version of MRS, is a general form of Kendall's rank correlation coefficient and allows for the setting of element-to-element distance weights that are not present in Kendall's coefficients. In this study, the superiority of LM considering element-to-element distance was verified using actual test data on historical events from 122 university students. Here, it was confirmed that element clusters were stably formed by applying multidimensional scaling to data that had undergone a certain transformation to the distance (mean value) between sorting elements. In particular, items that fell outside the cluster appeared in the lower-performing group, revealing areas where the learners' understanding was insufficient.
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