Clos network

Dependency graph

Mathematics education

Link analysis

Social psychology

Theoretical computer science

Bipartite graph

Telecommunications

Set (abstract data type)

Computer science

Psychology

Graph

Mathematics

Interlacing

Artificial intelligence

Strengths and weaknesses

Programming language

Dependency (UML)

Machine learning

Journal of Computing in Higher Education

Depicting the reason for the mismatch between instructor expectations of students’ performance in advanced courses and their actual performance has been a challenging issue for a long time, which raises the question of why such a mismatch exists. An implicit reason for this mismatch is the student’s weakness in prerequisite course skills. To solve this challenge, this research proposes a new graph mining algorithm combined with statistical analysis to reveal the dependency relationships between Course Learning Outcomes (CLOs) of prerequisite and advanced courses. In addition, a new model is built to predict students’ performance in the advanced courses based on prerequisites. The contributions of this research are threefold: (1) Modeling: three models are built based on bipartite graphs. The first model is a bipartite graph to model the relationships between the CLOs of different courses. This bipartite graph is constructed using a new calculated dependency measure based on a statistical analysis of students’ grades. Then the relationships between the Learning Outcomes are discovered by extracting the maximal bipartite cliques in the graph. The second model is built to model the relationships between students and the prerequisite CLOs. The maximal bipartite cliques are then extracted from this graph to discover the maximal set of students who share the same study weaknesses. The third model is built to model the relationships between students and the advanced CLOs. The maximal bipartite cliques are then extracted to discover the maximal set of students who are expected to share the same study weaknesses in the advanced course. Therefore, the same remedial actions can be used towards this group of students. (2) Algorithm: A new maximal bipartite cliques enumeration algorithm is proposed to extract the targeted patterns and relationships between CLOs themselves and between students and CLOs. (3) Applicability: The proposed models and algorithm have been applied using a real educational data set collected from one university. Other real datasets are used to conduct an empirical evaluation to assess the maximal bipartite enumeration algorithm’s correctness, the running time of the inflation and enumeration steps, and the overhead of the inflation algorithm on the size of the generated general graph. The evaluation proves that the proposed algorithm is accurate, efficient, effective, and applicable to real-world graphs more than the traditional algorithm.

A framework to capture the dependency between prerequisite and advanced courses in higher education