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This study investigates how teachable agents’ personality traits influence students’ achievement emotions, engagement, and learning in mathematics. We randomly assigned students to teach six AI agents—five emphasizing each of the Big Five personality traits and one non-personality-emphasis agent. Results indicated that agent personality traits influenced students’ achievement emotions, with agreeableness promoting positive activating emotions, conscientiousness reducing negative activating emotions and nearly eliminating positive deactivating emotions, and openness increasing negative deactivating emotions. Among these emotions, positive activating emotions were associated with greater engagement and higher learning outcomes; negative activating emotions, though detrimental to in-task engagement, also predicted learning performance. These findings underscore the complex interplay among agent personality, student emotion, and learning, informing the development of emotionally adaptive learning environments.