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As Generative Artificial Intelligence (GenAI) tools become more common in higher education, the need for AI literacy among students has grown. This study proposed and tested a theoretical framework linking individual factors—critical thinking and self-regulation—levels of engagement (deep and surface), and AI literacy. The sample consisted of 301 university students from Iran. Data were analyzed using structural equation modeling and mediation analysis across 12 hypotheses. Results showed that deep engagement, self-regulation, and critical thinking were positively associated with AI literacy, while surface engagement was not. Self-regulation was not significantly related to either engagement type, whereas critical thinking was linked to deep but not surface engagement. These findings offer insights for designing strategies to foster meaningful student interaction with GenAI tools.