Geometry to Build Models, Models to Visualize Geometry
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Geometry to Build Models, Models to Visualize Geometry Caterina Cumino 1 Ursula Zich 2
& Martino
Pavignano 2
& Maria
L. Spreafico 1
&
Accepted: 2 September 2020/ # The Author(s) 2020
Abstract In the seventeenth century, Guarino Guarini, mathematician and architect, affirmed that architecture, a discipline that primarily deals with measures, relies on geometry: therefore, the architect needs to know at least its basic principles. On behalf of Guarini’s words, we designed a set of interdisciplinary teaching experiences, between mathematics (via a calculus course) and drawing (via our Architectural Drawing and Survey Laboratory courses) that we proposed to first-year under graduate students studying for an Architecture degree. The tasks concern mathematical and representational issues about vaulted roofing systems and are based on the use of physical models in conjunction with digital tools, in order to make the cognitive geometric process more effective, thus following a consolidated tradition of both disciplines. Keywords Calculus . Architectural drawing . Developable surfaces . Representation issues
. Physical models . Undergraduate architecture
* Martino Pavignano [email protected] Caterina Cumino [email protected] Maria L. Spreafico [email protected] Ursula Zich [email protected]
1
Department of Mathematical Sciences “G. L. Lagrange” (DISMA), Politecnico di Torino, corso Duca degli Abruzzi 24, 10129 Torino, Italy
2
Department of Architecture and Design (DAD), Politecnico di Torino, viale Pier Andrea Mattioli 39, 10125 Torino, Italy
Digital Experiences in Mathematics Education
Introduction In this article, we describe and discuss a set of teaching experiences, presented to undergraduate students (in an Architecture degree, first year), that is a result of an interdisciplinary research project developed between mathematics and drawing. The students’ activity was focused on investigating mathematical and representational issues related to vaulted roofing systems, concerning vaults generated by cylinders and intersections between them. Our aim is to enhance students’ geometrical comprehension of architectural shapes, stimulating their spatial visualization ability, in the sense of Leopold (2015) and Nagy-Kondor (2007, 2010). In fact, in recent years, many scholars in different research fields have pointed out an increasing difficulty in geometric and spatial visualization by students starting their undergraduate studies (Ragni and Knauff 2013; Jones and Tzekaki 2016; Kovačević 2017), especially in places where geometry is still being reduced in favour of numeracy skills (Kovačević 2017). This trend is not so new, at least in the Italian context (Mammana and Villani 1998).In the Italian academic panorama, this is even truer if we analyse the situation of architectural studies, where most of the students do not perceive connections between mathematics and other disciplines (Cumino et al. 2019),1 for they have a tendency to compartmentalize knowledge (Hiebert and Lefevre 198
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