The Peer-to-Peer Learning Environment (P2PLE) is a proposed approach to helping learners co-construct their learning environment using recommendations about people, content, and tools. The work draws on current research on PLEs, and participant observation at the Peer-to-Peer University (P2PU). We are particularly interested in ways of eliciting explicit, coded, user feedback, and in monitoring the transitions from state to state within the PLE. We discuss the ways in which these ideas can inform the design of a platform for peer-supported study of university-level mathematics. (Contains 3 footnotes and 3 figures.)