arXiv:2610.37238v1 Announce Type: new Abstract: In early mathematics, children learn abstract concepts through concrete representations, such as manipulating objects, drawing, and speaking. Learning with peers can enrich this process by exposing children to diverse strategies and enabling them to exchange ideas through interaction. We realized this potential with virtual peers in Peers4U, a multimodal learning system to enhance children's mathematical conceptual understanding. Virtual peers driven by LLMs are personalized to the learner's cognitive level and assigned multimodal solutions with inspectable processes. During learning, peers engage in mixed-initiative interactions by responding, initiating topics, and advancing discussions along a pedagogical progression. A user study with 22 children and two experts showed our learner-centered topic orchestration significantly outperformed a persona-centered baseline, and children spontaneously authored new artifacts to demonstrate inspired ideas or share their own strategies, producing significantly more solutions when grouped with more Leading Peers. We contribute design insights for multimodal, learner-centered virtual peer systems.