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This study investigates how collaborative intelligence emerges through interactions among students, a classroom teacher, and a conversational AI agent, MathPal, in high school math classes. Drawing on distributed cognition theory, it examines how instructional roles are dynamically restructured within a triadic system. Using a qualitative case study design, data from student–AI conversations, interviews, and computational analyses (LSA, ENA) reveal distinct learner profiles, adaptive teacher orchestration, and shared cognitive labor. Findings highlight four core mechanisms—division of labor, coordination protocols, information integration, and system enhancement—that underpin collaborative intelligence. This work contributes new insights into the implementation of AI-supported learning environments and offers practical implications for scaling individualized support in secondary mathematics classrooms.