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

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Orynbassar A., Sapazhanov Y., Kadyrov S., Lyublinskaya I.

MATHEMATICS, vol.10, no.12, 2022 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 12
  • Publication Date: 2022
  • Doi Number: 10.3390/math10122084
  • Journal Name: MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded, Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: curriculum design, prerequisite, ROC curve analysis, Youden index, undergraduate education, mathematics education, binary classification, CONFIDENCE-INTERVALS, YOUDEN INDEX, AREA


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.