ARTICLE
26 July 2026

Grey–Copula Dynamic Prediction of Hidden Learning Risk in Vocational Mathematics under Generative AI

Yan Wang1*
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1 School of Humanities, Sichuan Vocational College of Information Technology, Guangyuan 628000, Sichuan, China
EIR 2026 , 4(7), 159–166; https://doi.org/10.26689/EIR.v4i7.16067
© 2026 by the Author. Licensee: Bio-Byword Scientific Publishing Pty Ltd, Australia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License ( https://creativecommons.org/licenses/by/4.0/ )
Abstract

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.

Keywords
Generative artificial intelligence
Vocational college mathematics
Learning risk
Grey prediction model
Copula function
References

[1] Bastani H, Bastani O, Sungu A, et al., 2025, Generative AI Without Guardrails Can Harm Learning: Evidence From High School Mathematics. PNAS, 122(26): e2422633122.

[2] Fan Y, Tang L, Le H, et al., 2025, Beware of Metacognitive Laziness: Effects of Generative Artificial Intelligence on Learning Motivation, Processes, and Performance. British Journal of Educational Technology, 56(2): 489–530.

[3] Sklar A, 1959, Fonctions de Répartition à N Dimensions et Leurs Marges. Publications de l’Institut de Statistique de l’Université de Paris, 8: 229–231.

[4] Nelsen RB, 2006, An Introduction to Copulas. 2nd ed. New York: Springer.

[5] Deng JL, 1982, Control Problems of Grey Systems. Systems & Control Letters, 1(5): 288–294.

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