We present a new approach for the organization of schools, which we call the flexible scheduling paradigm (FSP). FSP improves student learning by dynamically redeploying teachers and other pedagogical resources to provide students with customized learning conditions over shorter time periods called "mini-terms" instead of semesters or years. By conceptualizing the school curriculum as a physical map, we can use technology from other sectors, such as project management, transportation, telecommunications networks, and the like, to customize the routing of students through curriculum using a core curriculum-targeted mastery-based approach, within current school budgetary and resource constraints. The maps are built from a unit-based curriculum, similar to current curricula, yet with the addition of more detailed unit dependency relationships. Our goal in this article is to introduce FSP and to establish a prima facie case for the new paradigm. (Contains 2 tables and 2 figures.)