<p>Handwritten mathematical expression recognition (HMER) is a highly challenging task, as it involves not only distinguishing visually similar characters but also interpreting complex structures. Even for humans, it sometimes requires several rounds of confirmation to arrive at a recognition result. Iterative self-refinement is a strategy frequently employed by humans when tackling complex tasks. Inspired by this, we put forward a self-reflective, closed-loop feedback architecture for HMER. Specifically, a compatible <b>Confidence-Guided Self-Correction Module (CGSCM)</b> is proposed to endow existing end-to-end HMER models with self-correcting capabilities. CGSCM evaluates the semantic consistency between the preceding token predictions and the original handwritten image; it accordingly assigns confidence scores that reflect the visual consistency of each token. These scores guide the model in rethinking its previous predictions, placing greater emphasis on low-confidence tokens in the next refinement step. Furthermore, we incorporate self-correction into the training phase by introducing a token replacement strategy that forces the model to learn to distinguish between visually similar symbols. Extensive experiments conducted on the public CROHME, HME100K, and QA-HME datasets demonstrate that CGSCM can consistently enhance end-to-end HMER performance across different state-of-the-art model backbones, thus achieving new benchmark performance. Considering the expression level, the accuracy has achieved an average improvement of 1.01% across datasets and backbones, with the maximum improvement reaching 2.19%. Our work has verified the effectiveness of introducing the iterative self-refinement mechanism in the HMER task. The proposed CGSCM provides valuable insight for building robust self-refining models in complex tasks. The code is available at: <a href="https://github.com/Jzliu-dl/CGSCM">https://github.com/Jzliu-dl/CGSCM</a></p>