CQSA-KT: Research on personalized knowledge tracing based on quantum-constructivism in sparse learning environments

Knowledge tracing (KT), as a key technology to enable personalized instruction, faces the challenges of data sparsity and insufficient personalization modeling in large-scale instructional environments. To this end, this paper proposes a constructivist-inspired quantum self-attention knowledge tracing model (CQSA-KT). The deep mapping relationship between Constructivist Learning Theory (CLT) and Quantum Computing (QC) is established by characterizing the multilevel nature of learning states through quantum states, modeling knowledge associations through quantum entanglement, and simulating the assessment process through quantum measurements. The model contains four core modules: The quantum knowledge representation embedding module (QKREM) utilizes quantum complex embedding to achieve a high-dimensional representation of knowledge states; the quantum attention interaction module (QAIM) applies quantum entanglement to model the non-local nature of knowledge associations; the quantum measurement module (QMM) introduces the quantum measurement theory for learning assessment; and the hybrid cognitive feature fusion module (HCFFM) integrates classical and quantum features. Experiments on three publicly available datasets show that CQSA-KT maintains better performance under high sparsity (>98 %) conditions, significantly outperforming ten existing benchmark models. Especially in extremely sparse scenarios (only 20 % training data), the model’s AUC improves by 8.5 percentage points over the benchmark models. This theory-driven technological innovation validates the application potential of QC in education and provides a new theoretical framework for the development of intelligent education.