Grey–Copula Dynamic Prediction of Hidden Learning Risk in Vocational Mathematics under Generative AI
Generative AI can raise students’ assignment marks while concealing a decline in their unaided problem solving. In vocational college mathematics, a semester supplies only twelve to sixteen weekly observations per student, so large-sample classifiers cannot be estimated reliably; risk appears as several indicators deteriorating together, so single-threshold rules overlook students approaching two limits at once; and dependence between indicators shifts once generative AI enters the classroom, so static models respond too slowly. This paper proposes a grey–Copula dynamic prediction method built around these three constraints. Four weekly indicators operationalise hidden learning risk as two conjunctive events; an improved grey model produces one-step forecasts and threshold-crossing probabilities from a few weeks of data; a rolling-window Copula couples paired indicators and is re-estimated weekly; and joint probabilities are mapped onto a three-tier alert. In a simulation of 15 scenarios and 1,600 replications, the joint probabilities were better calibrated than threshold and single-indicator rules (Brier score 0.115 against 0.177 and 0.262), and the rolling window recovered the post-break dependence within about 2.5 weeks. The Copula layer improved recall more than calibration, and an autoregressive alternative forecast better. No classroom validation is claimed.
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