On Characterization of Norm-Referenced Achievement Grading Schemes toward Explainability and Selectability

Grading is the process of interpreting learning competence to inform learners and instructors of the current learning ability levels and necessary improvement. For norm-referenced grading, the instructors use a conventionally statistical method, z score. It is difficult for such a method to achieve explainable grade discrimination to resolve dispute between learners and instructors. To solve such difficulty, this paper proposes a simple and efficient algorithm for explainable norm-referenced grading. Moreover, the rise of artificial intelligence nowadays makes machine learning techniques attractive to the norm-referenced grading in general. This paper also investigates two popular clustering methods, K-means and partitioning around medoids. The experiment relied on the data sets of various score distributions and a metric, namely, Davies–Bouldin index. The comparative evaluation reveals that our algorithm overall outperforms the other three methods and is appropriate for all kinds of data sets in almost all cases. Our findings however lead to a practically useful guideline for the selection of appropriate grading methods including both clustering methods and z score.