Integration of a CAS/DGS as a CAD system in the mathematics curriculum for architecture students

Abstract

Students of Architecture and Building Engineering Degrees work withComputer Aided Design systems daily in order to design and model architectonic constructions. Since this kind of software is based on the creation and transformation of geometrical objects, it seems to be a useful tool in Maths classes in order to capture the attention of the students. However, users of these systems cannot display the set of formulas and equations which constitute the basis of their studio. Moreover, if they want to represent curves or surfaces starting from its corresponding equations, they have to define specific macros which require the knowledge of some computer language or they have to create a table of points in order to convert a set of nodes into polylines, polysolids or splines. More specific concepts, like, for instance, those related to differential geometry, are not implemented in this kind of software, although they are taught in our Maths classes. In a very similar virtual environment, Computer Algebra and Dynamic Geometry Systems offer the possibility of implementing several concepts which can be found in the usual mathematics curriculum for Building Engineering: curves, surfaces and calculus. Specifically, the use of sliders related to the Euler's angles and the generation of tools which project 3D into 2D, facilitate the design and model of curves and rigid objects in space, by starting from their parametric equations. In this article, we show the experience carried out in an experimental and control group in the context of the Maths classes of the Building Engineering Degree of the University of Seville, where students have created their own building models by understanding and testing the usefulness of the mathematical concepts.

Linking diversity in learning Geometry: Exploring tessellation in techno-based mathematical tasks

“…A study conducted by Tatar et al (2014) revealed the positive effect of using dynamics software in learning geometry. Another study also indicates the positive contribution of dynamics geometry software in mathematics classrooms which is useful to create and transform any geometrical objects (Falcón, 2011). Furthermore, we took this as an opportunity to utilize dynamics geometry software in tessellation activities, especially to facilitate students with easier manipulation and transformations of polygons inspired by Falcón's research (2011).…”

Modelado paramétrico de edificios en el aula de matemáticas

“…Sin embargo, ésta no es mostrada de forma explícita al usuario, quien a la hora de modelar una determinada forma geométrica no tiene más que realizar una serie de operaciones intuitivas con el ratón e introducir a lo más unos ciertos parámetros con ayuda del teclado. Desde el punto de vista de la enseñanza de las Matemáticas en Arquitectura y Edificación es interesante no obstante hacer ver al alumnado el fuerte vínculo que tiene esta disciplina con los programas de diseño gráfico (Falcón, 2011). Basta ver en la red por ejemplo cualquier galería de imágenes elaboradas por el software libre Surfer (Instituto Matemático de Oberwolfach, 2008), el cual representa tridimensionalmente con alta resolución cualquier superficie asociada a una determinada ecuación implícita en tres variables (x, y, z), siendo de hecho precisamente dicha calidad de imagen una de las características que lo distingue de otros programas matemáticos (Figura.…”

“…En este sentido, ya en el Curso Académico 2009-2010 se planteó la posibilidad de realizar como actividad el modelado tridimensional de edificios desde el punto de vista matemático. Sin embargo, el software que se utilizó en dicha ocasión fue GeoGebra 3, que es un programa de geometría dinámica diseñado para trabajar únicamente en dos dimensiones, con lo que gran parte del tiempo asociado a dicha actividad se dedicó a convertir dicho programa en uno de tipo CAD que permitiese realizar gráficos tridimensionales a partir de proyecciones ortogonales (Falcón, 2011). Si bien dicho proceso de conversión fue en sí mismo de gran interés didáctico y los diseños se ajustaron a las expectativas (Figura.…”