Course-prerequisite networks for analyzing and understanding academic curricula

Creators: Stavrinides, Pavlos; Zuev, Konstantin M.

Abstract

Understanding a complex system of relationships between courses is of great importance for the university's educational mission. This paper is dedicated to the study of course-prerequisite networks (CPNs), where nodes represent courses and directed links represent the formal prerequisite relationships between them. The main goal of CPNs is to model interactions between courses, represent the flow of knowledge in academic curricula, and serve as a key tool for visualizing, analyzing, and optimizing complex curricula. First, we consider several classical centrality measures, discuss their meaning in the context of CPNs, and use them for the identification of important courses. Next, we describe the hierarchical structure of a CPN using the topological stratification of the network. Finally, we perform the interdependence analysis, which allows to quantify the strength of knowledge flow between university divisions and helps to identify the most intradependent, influential, and interdisciplinary areas of study. We discuss how course-prerequisite networks can be used by students, faculty, and administrators for detecting important courses, improving existing and creating new courses, navigating complex curricula, allocating teaching resources, increasing interdisciplinary interactions between departments, revamping curricula, and enhancing the overall students' learning experience. The proposed methodology can be used for the analysis of any CPN, and it is illustrated with a network of courses taught at the California Institute of Technology. The network data analyzed in this paper is publicly available in the GitHub repository.

Additional Information

© The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. We thank Gloria Brewster and Kimberley Mawhinney for providing us with a database of Caltech courses, Eric V. Smith for the valuable help with the toposort module, Justin Bois for useful feedback on the first draft of the paper, and Liza Bradulina and Sophia Zueva for stimulating discussions. We also thank the anonymous reviewers for useful comments and suggestions. This work was supported by the Carver Mead Discovery Grant and the Information Science and Technology (IST) initiative at Caltech. Contributions. KZ designed the study, proposed the methods, and supervised the research; PS cleaned the data, created the network and its visualizations, and developed the code; KZ and PS performed research, analyzed the data, and wrote the manuscript; both authors read and approved the final manuscript. Availability of data and materials. The network data analyzed in this study is available in the GitHub repository, https://github.com/pstavrin/Course-Prerequisite-Networks. The authors declare that they have no competing interests.

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