Knowledge tracing is a key component of intelligent educational systems. However, most existing methods mainly focus on response prediction, providing limited support for explaining predicted outcomes and improving students'learning states. This paper proposes Diagnostic and Interpretable Knowledge Tracing (DIKT), which integrates response prediction, skill-level diagnosis, and model-based learning analysis. DIKT generates bounded cognitive-state trajectories and decomposes the final response probability into skill-wise probabilities. The trajectories reveal students'evolving strengths and weaknesses, while the skill-wise probabilities identify the skills that most strongly constrain the prediction. Based on these diagnostic results, DIKT supports direct cognitive-state intervention and effective-learning-duration-based what-if analysis to examine how hypothetical adjustments affect current predictions and subsequent state evolution. DIKT combines Bayesian multi-head attention, conditional variational recurrent inference, a logistic-growth decoder, and multiplicative skill-wise prediction. Experiments on three benchmark datasets show that DIKT outperforms all evaluated baselines, with an average absolute AUC gain of 2.04 percentage points. Other experiments further demonstrate that DIKT supports educationally meaningful diagnostic analysis and provides informative diagnostic indicators for downstream applications, extending knowledge tracing from response prediction to interpretable diagnosis and model-based learning analysis.

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