Constructing the shortest path on a cylindrical surface

Digital media warrant a reappraisal of established conceptual fields and a search for new ones densely providing access to powerful mathematical ideas. This study reports secondary students' meaning making around the notion of intrinsically defined curvature in space by means of a tool integrating programming, dynamic manipulation of variable values and a simulation of 3D space. The study involved 15 ninth grade school students’ attempt to design the shortest path between two points on a cylindrical surface are presented in this paper. Camera perusal and zoom allow for a change of viewpoints of the constructed figure. The findings yield meanings around concepts notoriously difficult even in undergraduate mathematics, such as differential stereometry, limits and curvature as systematic trihedron state change