Cross-scale knowledge tracking: A joint time-frequency modeling approach for global cycles and local fluctuations

With the development of online education and the growing demand for personalized learning, characterizing the dynamic evolution of students’ knowledge states across multiple timescales has become a critical issue. Educational psychology and nonlinear dynamics theory indicate that the process of knowledge acquisition is not a simple linear accumulation but a complex system shaped by the nonlinear coupling of long-term trends (slow variables) and short-term fluctuations (fast variables). However, existing knowledge tracking methods often focus either on long-term trends or short-term fluctuations, struggling to simultaneously capture their nonlinear interactions while also exhibiting inconsistent feature distribution across scales. To address these limitations, this paper proposes the cross-scale knowledge tracking model WFTKT: it employs Fourier Transform combined with Hypergraph Neural Networks (FT-HGNN) to extract long-term rhythms and higher-order dependencies, simulating slow variables during the learning process; It employs a wavelet transform combined with a dynamic graph convolutional network (WT-GCN) to analyze short-term perturbations and local diffusion, characterizing fast variables; through a dynamic fusion mechanism (DFF), it adaptively allocates weights between long-term and short-term branches across different learning scenarios, and utilizes CORAL loss to align cross-scale feature distributions, thereby simulating the nonlinear coupling mechanism between fast and slow variables. Experiments on four benchmark datasets demonstrate that WFTKT outperforms existing strong baseline models in both prediction accuracy and periodic behavior characterization, validating its ability to model cross-scale nonlinear learning dynamics.