This paper explores educational interactions involving humans and artificial intelligences not as sequences of prompts and responses, but as a social process of conversation and exploration. In this conception, learners continually converse with AI language models within a dynamic computational medium of internet tools and resources. Learning happens when this distributed system sets goals, builds meaning from data, consolidates understanding, reconciles differences, and transfers knowledge to new domains. Building social generative AI for education will require development of powerful AI systems that can converse with each other as well as humans, construct external representations such as knowledge maps, access and contribute to internet resources, and act as teachers, learners, guides and mentors. This raises fundamental problems of ethics. Such systems should be aware of their limitations, their responsibility to learners and the integrity of the internet, and their respect for human teachers and experts. We need to consider how to design and constrain social generative AI for education.

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