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This study explores how multi-agent, generative AI platforms affect cognitive load and affective states in elementary learners. In a 10-day classroom study with 160 students, participants engaged with a multi-agent AI system embedded in the Math Nation platform. Pre/post surveys assessed confidence, anxiety, and cognitive load. We trained machine learning models—including a LLaMA-based model—on AI dialogue data to predict students' internal states. Results showed increased AI confidence and critical awareness, but also heightened extraneous cognitive load. The LLaMA model achieved an F1 score of 81.7%, highlighting the potential of multi-agent interactions to support unobtrusive, language-based assessment of cognitive and emotional factors in learning.