Using directed networks to generate feedback and hints for mathematics

One challenge in automated feedback generation in education is the lack of scalable and transparent learner models that support feedback at multiple levels. We propose a directed network-based student modelling framework for automated feedback generation at two levels: guidance for problem-solving processes and feedback based on knowledge concept (KC) mastery and prerequisite learning needs. Guided by feedback intervention theory, Study 1 used the Bridge to Algebra 2006-2007 data set to construct a directed network of students’ step-level problem-solving trajectories and generate process-oriented feedback. Guided by knowledge space theory, Study 2 used the Eedi data set to construct a directed network by evaluating and pruning expert-defined prerequisite relationships among KCs and generating knowledge-oriented feedback. Study 1 supports the feasibility of generating process-oriented feedback at scale. Study 2 suggests that approximately half of the examinable expert-defined prerequisite relationships met predefined empirical criteria, and that the approach achieved full coverage for learners in the test set. Together, the studies introduce sequence – and structure-aware directed networks as interpretable student models, illustrate how feedback theories can guide automated feedback design, and propose a scalable framework for generating process – and knowledge-oriented feedback in technology-enhanced environments across different levels of the learning process.