Supplementary file 1_Enhancing EFL vocabulary and psychological well-being in Chinese undergraduates through adaptive digital games with mind mapping and Runge–Kutta modeling.docx

In China’s exam-oriented EFL education system, undergraduates face high academic pressure, hindering vocabulary mastery and psychological well-being; this study introduces an adaptive framework to address these challenges. This study presents a groundbreaking approach to improving English as a Foreign Language (EFL) vocabulary mastery and psychological well-being among Chinese undergraduate students by combining an adaptive computer agent-based digital game (ACA-DG) with mind mapping and Runge–Kutta Pairs of Orders 6(5) modeling. Adaptive agents customize interventions to align with students’ learning and emotional requirements, mind mapping structures vocabulary knowledge, and Runge–Kutta methods simulate dynamic learning and psychological processes. A 12-week experimental study at a Chinese university compared an experimental group (ACA-DG with mind mapping, n = 75) to a control group (standard DGBL, n = 75). Vocabulary assessments, motivation, self-efficacy, anxiety, and life satisfaction scales, alongside interviews and observations, revealed a 30.2% vocabulary score improvement, increased motivation, and reduced anxiety in the experimental group. The Runge–Kutta model predicted learning paths with 95% accuracy. This interdisciplinary framework provides innovative tools for EFL educators, merging computational accuracy with emotional support, and advocates for scalable technology-driven learning solutions.