Application of ROC Curve Analysis for Predicting Students’ Passing Grade in a Course Based on Prerequisite Grades

Alibek Orynbassar, Yershat Sapazhanov, Shirali Kadyrov and Irina Lyublinskaya
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Alibek Orynbassar: Department of Natural Sciences and Mathematics Education, Faculty of Education and Humanities Sciences, Suleyman Demirel University, Kaskelen 040900, Kazakhstan
Yershat Sapazhanov: Department of Natural Sciences and Mathematics Education, Faculty of Education and Humanities Sciences, Suleyman Demirel University, Kaskelen 040900, Kazakhstan
Shirali Kadyrov: Department of Mathematics and Natural Sciences, Faculty of Engineering and Natural Sciences, Suleyman Demirel University, Kaskelen 040900, Kazakhstan
Irina Lyublinskaya: Department of Mathematics, Science, and Technology, Teachers College, Columbia University, New York, NY 10027, USA

Mathematics, 2022, vol. 10, issue 12, 1-11

Abstract: Determining prerequisite requirements is vital for successful curriculum development and student on-schedule completion of the course of study. This study adapts the Receiver Operating Characteristic (ROC) curve analysis to determine a threshold grade in a prerequisite course necessary for passing the next course in a sequence. This method was tested on a dataset of Calculus 1 and Calculus 2 grades of 164 undergraduate students majoring in mathematics at a private university in Kazakhstan. The results showed that while the currently used practice of setting prerequisite grade requirements is accurately identifying successful completions of Calculus 2, the ROC method is more accurate in identifying possible failures in Calculus 2. The findings also indicate that prior completion of Calculus 1 is positively associated with success in a Calculus 2 course. Thus, this study contributes to the field of mathematics education by providing a new data-driven methodology for determining the optimal threshold grade for mathematics prerequisite courses.

Keywords: curriculum design; prerequisite; ROC curve analysis; Youden index; undergraduate education; mathematics education; binary classification (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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