Knowledge distillation from large reasoning models (LRMs) often uses raw teacher trajectories as supervision. However, this practice creates a mismatch between the goal of distillation and the nature of teacher trajectories. Advanced LRMs typically improve their reasoning capabilities through reward-driven post-training, such as RLHF. This training optimizes them as strong solvers, rather than as teachers that produce reasoning processes smaller models can easily learn. Since smaller models have different "cognitive capacities" compared to their larger teachers, directly imitating raw teacher trajectories can sometimes be ineffective and often requires a substantial number of high-quality samples. To bridge this mismatch, we propose Cognition-Aligned Reasoning Distillation (CARD), an RL-based framework that transforms solver trajectories into teaching trajectories aligned with the student's cognition. Avoiding expensive resampling, our framework directly transforms existing trajectories. We optimize CARD with two reward signals: (1) a Distribution Alignment Reward that matches the student's predictive distribution, and (2) a Logical Coherence Reward that reduces misleading failed reasoning steps. Comprehensive evaluations across multiple student models and settings demonstrate that CARD outperforms distillation from raw teacher trajectories in in-domain settings while achieving substantial gains in out-of-distribution performance. Code is available at https://github.com/LiteSSLHub/CARD.

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