Architectural Drawing and Mathematical Modelling: Conics, GeoGebra and More

This contribution is part of an ongoing research and concerns the 2D graphic representation of a 3D object. The participants are the students of a course of architectural drawing and survey, in the first year of an architecture bachelor’s degree. In such an extra-mathematical educational environment, a mathematical modelling perspective of prescriptive type (Niss, 2015) appears as a tool of investigation and as an educational goal, since students are involved in solving mathematical problems in the design phase of an architectural project, developing a rudimental modelling cycle to go from a real-world object to its mathematization and to the critical interpretation of modelling outcomes. The research questions are: Which are students’ recurring misconceptions and difficulties intertwined with mathematical thinking? How to improve students’ understanding of drawing as a tool to communicate and visualize objects and their geometrical properties? A joint intervention of teachers of architectural drawing and mathematics took place during regular drawing lessons on conics and surfaces; a GeoGebra applet was proposed to show an ellipse as draggable object to highlight shape variations and invariant properties with respect to movements of the foci. At the end of the first teaching period, students’ understanding was tested, asking a 2D representation of a barrel vault with semi-elliptical cross section, covering a rectangular base gallery. Two surveys were conducted: a satisfaction one and a questionnaire with dichotomous and multiple-choice questions about synthetic 2D/3D geometry. It seems that students’ main difficulties lie in a lack of identification of mathematical objects and in the inability to use their mathematical knowledge in the critical interpretation of their outcomes. This may be since mathematics traditionally is thought at any level as a separate discipline and calls for further investigations. The satisfaction questionnaire shows a positive attitude about the joint intervention: 98% of them think that it is useful to better understand other topics of the course and 93,8% of them find the use of a dynamical geometric software (like GeoGebra) very helpful.