The Math Teaching Atlas: Trails, Anchors, and Compass in Action

Abstract

Mathematics is a mountain, but students need more than descriptions of the view: they need a trail they can actually walk. This paper presents the Math Teaching Atlas, a framework for mathematical exposition built around route units (single steps with explicit justifications), routeways (chains of route units), and roadmaps of multiple valid routeways to the same destination. New ideas are introduced through familiar anchors, while a mathematical compass (motivation) and driving simulations (concrete examples) help students extend known routeways and construct new ones. The paper also develops a route geometry on pedagogical route graphs, thereby beginning a mathematization of mathematics pedagogy itself. Taken together, the framework aims to make mathematical explanations more visible, navigable, and teachable.