Representing Geometry Between Graphic Constructions and Mathematical Modeling

Our study exposes a search for specific pedagogical practices between mathematical modeling and visual thinking to support first-year Architecture to acquire spatial visualization and representation skills and abilities by exploiting the connections between mathematics and architecture. For this purpose, in our Architectural Drawing and Survey Laboratory, activities were designed, discussed and validated by various critical reading tools across the disciplinary fields involved: designing and building objects that have certain properties and that satisfy certain specifications, such as the construction of a graphic representation 2D of a 3D object, has been described by mathematical education scholars as a particular type of mathematical modeling process and by architects as a process of developing spatial prefiguration skills and visual thinking. The analysed case study, the different possible plane sections of cones and cylinders, allows us to discuss the difficulties in learning the relationships between theoretical and/or analytical information, 2D and/or 3D representations, physical and/or digital modeling, as well as to introduce the concept of rigour from the mathematical and drawing point of view. Moments of assessment and interaction have led to highlighting not only the strong link between synthetic and analytical treatment, between object and representation, but also the need to formally structure the monitoring/tutoring activities to support each of the students, so that they can become part of the community in formation.