Automated feedback systems that rely on answer correctness will reinforce, rather than address, misconceptions when students reach the correct answer through flawed reasoning. We investigate automatic detection of these hidden misconceptions using 20,964 real student responses from the Eedi mathematics platform. Fine-tuned classifiers detect only 57% of these hidden misconceptions, and standard ML interventions do not improve on this. An open-weight reasoning model detects 84%, but at realistic prevalence, false alarms outnumber genuine detections roughly 8 to 1. We present a graduated assessment rubric that separates answer correctness from method validity, and propose a detect-verify-escalate pipeline that routes uncertain cases to diagnostic follow-up questions rather than directly to teachers. Two deployment modes adapt the pipeline: a teacher dashboard where the system filters a review queue, and an autonomous tutor where flags trigger low-cost formative follow-up.

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