Teaching geometry and surfaces evaluation through graphic representation and dynamic paper models

Abstract

To make the geometrical cognitive process more interactive, we produced teaching aids (tangible models, graphic tablets) that help students in visualizing their geometrical-analytical investigations of the architectural artifacts and enhance their spatial prefiguration and critical form-reading skills, three-dimensional thinking and geometrical reading of shapes. Then, we looked for a medium suitable to create simple three-dimensional models, not only observable, like virtual models, not only tangible, like physical models proposed in the design studios, but also dynamic, using multiple media and languages in the same training message. As an example, we present here an interdisciplinary lesson between Calculus and Architectural Drawing and Survey Laboratory about developable surfaces, experimented on first year students of the bachelor program in Architecture. The lesson is based on the use of a graphic tablet and some origami inspired models: it summarizes the geometric description of a pyramid and a cloister vault of equal height and equal orthographic projection on the horizontal plane. We saw that tackling the same topic in both teaching contexts is not a useless overlap, but a stimulus to compare different languages and methods. 2D and 3D paper models of artifacts—and of projective reduction from 3D to the plane—aid spatial intuition and the subtle exercise of controlling mental images which replace artifacts, turning 3D configurations into signifying images. Moreover, this experience stimulates reading and evaluation of the drawn geometry (ruled surfaces, projections, developments), increasing critical sense in reading the built environment.