SPARK-KT: Illuminating Student Cognition through Stepwise Prerequisite-Aware Reasoning in Knowledge Tracing

Understanding how students think—not merely what they know—remains the central challenge of knowledge tracing. Current approaches model knowledge as a flat collection of concepts and are fundamentally unable to capture the hierarchical reasoning processes that govern human problem-solving. We introduce SPARK-KT ( S tepwise P rerequisite- A ware R easoning for K nowledge T racing), a framework that reconceptualizes knowledge tracing through the lens of cognitive dependency structures. SPARK-KT leverages Large Language Models to automatically decompose each question into a Directed Acyclic Graph of reasoning steps, where nodes represent atomic cognitive operations and edges encode prerequisite constraints. A novel dependency-aware mastery propagation mechanism ensures that a student’s competence on any step is bounded by their weakest prerequisite—mirroring the pedagogical reality that complex skills cannot be deployed without foundational mastery. Through a dual-stream architecture that disentangles conceptual knowledge from procedural structure, SPARK-KT improves predictive accuracy while providing fine-grained interpretability: it identifies not just whether a student will succeed, but which specific reasoning step constitutes their cognitive bottleneck. Experiments across three diverse educational domains demonstrate consistent improvements over sixteen state-of-the-art baselines, with particularly strong gains on multi-step reasoning problems. Beyond prediction, SPARK-KT enables actionable diagnostics—revealing latent potential masked by prerequisite gaps and informing precisely targeted interventions.