Rank Aggregation for Course Sequence Discovery

TL;DR

This paper applies rank aggregation methods to analyze 15 years of student course data, revealing optimal course sequences and hidden prerequisites in the UCLA Mathematics curriculum.

Contribution

It adapts rank aggregation algorithms to university course sequencing, uncovering curriculum insights from large-scale student data.

Findings

Identified optimal course sequences using rank aggregation.

Revealed hidden prerequisites in the Mathematics curriculum.

Demonstrated differences in course orderings based on GPA subsets.

Abstract

In this work, we adapt the rank aggregation framework for the discovery of optimal course sequences at the university level. Each student provides a partial ranking of the courses taken throughout his or her undergraduate career. We compute pairwise rank comparisons between courses based on the order students typically take them, aggregate the results over the entire student population, and then obtain a proxy for the rank offset between pairs of courses. We extract a global ranking of the courses via several state-of-the art algorithms for ranking with pairwise noisy information, including SerialRank, Rank Centrality, and the recent SyncRank based on the group synchronization problem. We test this application of rank aggregation on 15 years of student data from the Department of Mathematics at the University of California, Los Angeles (UCLA). Furthermore, we experiment with the above approach on different subsets of the student population conditioned on final GPA, and highlight several differences in the obtained rankings that uncover hidden pre-requisites in the Mathematics curriculum.