Modelling in Science Education and Learning - Vol. 12, Núm. 1 (2019)

Tabla de contenidos

¿Cómo modelizan los futuros profesores en situaciones de área y perímetro? El papel de las unidades y de las fórmulas
Análisis de redes sociales mediante cadenas de Markov
Computer Animation to teach interpolation from a modeling perspective
Una introducción a la modelización estocástica de subyacentes cotizados
Euclides no vivió en Manhattan: Geometría urbana
Modelización matemática en la educación secundaria: manual de uso
Modelización de cerámicas y transductores piezoeléctricos vibrando en espesor mediante matrices de transferencia
Un modelo de oferta y demanda con incertidumbre
La carta de Smith y sus generalizaciones

URI permanente para esta colecciónhttps://riunet.upv.es/handle/10251/118041

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Mostrando 1 - 9 de 9

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Animación por ordenador para enseñar inperpolación
(Universitat Politècnica de València, 2019-02-08) Pla-Castells, Marta; García-Fernández, Ignacio; Gimeno, Jesus; Ferrando, Irene
[EN] While mathematics courses are a basic topic in engineering studies, they are often considered as a difficult subject by students. In this work we present a learning experience based on computer animation and using the perspective of mathematical modelling. Our goal is to provide the students with a context that motivates the study of function interpolation. We present a problem statement that is intended to be solved by means of the Modeling Cycle. The development of the activity and the strategies identified during the process are presented and discussed.
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Modelización matemática en la educación secundaria: manual de uso
(Universitat Politècnica de València, 2019-02-08) Gallart, Cesar; Ferrando Palomares, Irene; García Raffi, Lluís Miquel
[EN] One of the main problems that arise when implementing a mathematical modeling task to the secondary classroom is the lack of a detailed description, from the didactic perspective, that helps and guides the in-service teachers in the implementation of this type of activity and that allows them to identify which are the learning objectives being pursued; if this kind of activities t within the oficial curriculum; the type of tasks that allow these objectives to be achieved; how to carry out their evaluation or what methodology to use. In this article we will address all these aspects from the perspective of a classroom experience, detailing each of the phases involved in the implementation of a modeling activity.
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Un modelo de oferta y demanda con incertidumbre
(Universitat Politècnica de València, 2019-02-08) Burgos-Simon, Clara; Cortés, J.-C.; Martínez-Rodríguez, David; Navarro Quiles, Ana; Villanueva Micó, Rafael Jacinto; Facultad de Administración y Dirección de Empresas; Departamento de Matemática Aplicada; Escuela Técnica Superior de Ingeniería Geodésica, Cartográfica y Topográfica; Instituto Universitario de Matemática Multidisciplinar; Departamento de Estadística e Investigación Operativa Aplicadas y Calidad; Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial
[EN] The stationary oer and supply models are useful in order to describe different macro-economical scenarios, for this reason they are one of the most essential tools in different subjects like Macroeconomics taught in the University degrees like Business Administration and Management and similar. The students of those degrees learn simultaneously mathematics and statistics, where they study deterministic and stochastic tools in order to apply them in that kind of models. In this work we present a simple example in order to work in a multidisciplinary way three different subjects, macroeconomics, mathematics and statistics. In particular, we will randomize the linear offer and supply model, considering that the parameters of the model are random variables instead single values. That is, because in some cases the parameters of the model have been tted using real data, and this data has an intrinsic randomness which it could begiven by two different factors, the device or the way we measure the data or the innate randomness to the consumer behaviour. Using the Random Variable Transformation Technique we can obtain the probability density function of the offer and supply functions. Moreover, we will obtain the distributions of the price and amount of equilibrium in the trade. Finally we will show the theoretical results with a numerical example.
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Modelización de cerámicas y transductores piezoeléctricos vibrando en espesor mediante matrices de transferencia
(Universitat Politècnica de València, 2019-02-08) Jiménez, Noé; Camarena, Francisco; Generalitat Valenciana; European Regional Development Fund; Agència Valenciana de la Innovació
[EN] In this work we present the modeling of a piezoelectric ceramic vibrating in thickness mode using transfer matrices. The complete modeling of the vibratory behavior of a piezoelectric ceramic is a complex problem.This is mainly due to the tensorial denition of the involved stresses and the anisotropy of the piezoelectric solids, both arising due to their intrinsic elastic and piezoelectric properties. This problem is recurrent when teaching of Acoustics and Ultrasound, Telecommunications and electronic sensors. The modeling using transfer matrices provides a simple but accurate method, since it captures the main physical phenomena of the electromechanical problem. In particular, the presented modeling allows a high degree of freedom to modify the design by adding layers of different materials and / or electronic components, with, in addition, it also allows the student to obtain an analytical model of the piezoelectric effect and the study of the electrical-elastic system.
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La carta de Smith y sus generalizaciones
(Universitat Politècnica de València, 2019-02-08) Perez-Peñalver, M.Jose; Sanabria-Codesal, Esther; Müller, Andrei A.; Departamento de Matemática Aplicada; Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial; Ministerio de Economía y Competitividad
[EN] Smith's chart is a graphical tool, classically used in the analysis and design of microwave circuits, based on the mathematical idea of inverting the positive semi-plane to the unit circle through the transformation of Möebius$M(z)=\frac{z-1}{z+1}.$ One of its main advantages is that it provides an excellent visual approach to high-frequency problems and, although its usefulness has survived to this day, it has some drawbacks that have been alleviated by successive generalizations. In Muller et al., 2011, the authors proposed a generalizationof Smith's chart in space: the Smith 3D chart, where they use the stereographic projection of the sphere in the plane. This new model unies the design of the circuits, keeping unchanged all the properties of the original Smith chart. In addition, these authors developed a CAD tool www.3dsmithchart.com to facilitate the measurements and graphics in it. This is not the only possible generalization, in this work we present other possibilities using hyperbolic geometry. This geometry was explored by M. C. Escher, in some of his best known illustrations, as well as being closely related to original Smith's chart (Gupta, 2006).
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Euclides no vivió en Manhattan: Geometría urbana
(Universitat Politècnica de València, 2019-02-08) Gómez Urgellés, Joan Vicenç
[EN] The Voronoi diagrams and the taxi distance are presented as models to solve a situation in which three assistance centers have to be located. The project was carried out by engineering students at the EPSEVG-UPC. At a cognitive and formal level, work is being done on Minkowski's L1 metric space as a differentialelement with respect to the Euclidean metric in order to visualize other metrics and use Geogebra as a tool to solve problems from reality, thus showing in this way the epistemological aspect of mathematics.
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¿Cómo modelizan los futuros profesores en situaciones de área y perímetro? El papel de las unidades y de las fórmulas
(Universitat Politècnica de València, 2019-02-08) Montejo-Gámez, Jesús; Fernández-Ahumada, Elvira; Adamuz-Povedano, Natividad
[EN] This study explores those skills associated with modeling that preservice primary and secondary teachers develop when working with measure. The sample was made up of a total of 12 master's degree students and 13 primary school teacher students, who worked in groups to solve a task, which was specically designed to develop skills associated with measure through modeling. The analysis of the models produced by the prospective teachers revealed a great wealth of ideas and evidence of the dependence on formulae for the calculation and estimation of areas. Results also indicate relationship between the model's closeness to the real situation and the tendency of participants to validate it, as well as the importance of the layout of the task on the produced models.
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Una introducción a la modelización estocástica de subyacentes cotizados
(Universitat Politècnica de València, 2019-02-08) Calatayud, Julia; Cortés, Juan Carlos; Jornet Sanz, Marc; Villanueva, Rafael; Agencia Estatal de Investigación
[EN] The aim of this paper is to show a methodology, based on the so-called Lognormal Model, to describe the dynamics of underlying assets by taking into account the uncertainty of nancial markets. In spite of its simple formulation, the Lognormal Model is a valuable tool from a formative standpoint becauseit provides an excellent basis to study more advanced models. The proposed approach has been put into practice by the authors in their teaching in both undergraduate and postgraduate studies. We present the model and its application to describe the dynamics of real data of an asset traded in the Spanish stock market index IBEX35.
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Análisis de redes sociales mediante cadenas de Markov
(Universitat Politècnica de València, 2019-02-08) Carreño Sanchez, Amanda; Sanabria-Codesal, Esther; Departamento de Matemática Aplicada; Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial; Ministerio de Economía y Competitividad
[EN] The main aim of this paper is shown a mathematical model about the social networks that enhances the interest of the Mathematics' students that are in rst course. This model is based on Markov chains. Its approach and resolution permit to illustrate the applicability of the discrete equation systems and toemphasize the concepts studied about eigenvalue problems and diagonalization. Furthermore, all results are computed with the Mathematica software.

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