Abstract
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.
Highlights
In both formal and informal education, grading is the process of interpreting learning competence to inform learners and instructors of current learning ability levels and necessary improvement. ere are basically two types of nonbinary grading systems [1]: criterion-referenced grading and norm-referenced grading. e former normally calculates the percentage of a learning score and maps it to the predefined percent range of a specific grade. is grading system is suitable for an examination that covers all content topics of learning and requires long exam-taking as well as answer-checking times
The performance of each grading method is represented with clustering quality. e quality of clustering results can be measured by using a well-known metric namely Davies–Bouldin index (DBI)
Z score method, K-means, and Partitioning around medoids (PAM) in norm-referenced unconditional grading
Summary
In both formal and informal education, grading is the process of interpreting learning competence to inform learners and instructors of current learning ability levels and necessary improvement. ere are basically two types of nonbinary grading systems [1]: criterion-referenced grading and norm-referenced grading. e former normally calculates the percentage of a learning score and maps it to the predefined percent range of a specific grade. is grading system is suitable for an examination that covers all content topics of learning and requires long exam-taking as well as answer-checking times. . ., performing the norm-referenced grading on such a score series by using a traditional method may result in grades . E main contributions of this paper are a simple and efficient grading algorithm and a novel insight into the performance of statistical method, machine learning methods, and our algorithm in unconditionally norm-referenced grading. To the best of our knowledge, we demonstrate for the first time the applicability of K-means and PAM clustering techniques for norm-referenced grading. Is paper significantly extends our immature work [10] with a full-fledged algorithm, a newly practical data set, a newly experimented machine learning method, a set of new findings, and a novel guideline for method selection
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