Exploring the structure of the school curriculum with graph neural networks.

School curricula guide the daily learning activities of millions of students. They embody the understanding of the education experts who designed them of how to organize the knowledge that students should acquire in a way that is optimal for learning. This can be viewed as a learning 'theory' which is, nevertheless, rarely put to the test. Here, we model a data set obtained from a Computer-Based Formative Assessment system used by thousands of students. The student-item response matrix is highly sparse and admits a natural representation as a bipartite graph, in which nodes stand for students or items and an edge between a student and an item represents a response of the student to that item. To predict unobserved edge labels (correct/incorrect responses) we resort to a graph neural network (GNN), a machine learning method for graph-structured data. Nodes and edges are represented as multidimensional embeddings. After fitting the model, the learned item embeddings reflect properties of the curriculum, such as item difficulty and the structure of school subject domains and competences. Simulations show that the GNN is particularly advantageous over a classical model when group patterns are present in the connections between students and items, such that students from a particular group have a higher probability of successfully answering items from a specific set. In sum, important aspects of the structure of the school curriculum are reflected in response patterns from educational assessments and can be partially retrieved by our graph-based neural model.