Preparing children and youth for a world of growing complexity, diversity, and mobility requires fresh educational approaches and deliberate pedagogies. In this article, we explore the role of storytelling in making sense of crucial global transformations affecting children's lives. We examine how migrant children and their peers in two classrooms -- in the United States and Greece -- learn to listen to, co-construct, and share stories of migration. The article draws on a comparative case study and action research approach to advance a novel "Collective Stories of Voice and Influence" pedagogy. We find four qualities that render Collective Stories of Voice and Influence pedagogically effective: they are collaboratively constructed, multivoiced, materially grounded, and civically empowering. The proposed pedagogy can inform educators interested in novel teaching designs that use narratives to help children address complex global issues while creating safe conditions to navigate moments of vulnerability.