Modelling in Science Education and Learning - Vol. 04, (2011)

Tabla de contenidos

Modelizacion para formar ciudadanos
Un singular desfile de modelos
Modelización matemática y álgebra: un tándem perfecto en la formación de ingenieros
La resolución de problemas como herramienta para la modelización matemática
Una propuesta de modelización en secundaria: problemas de estimación de magnitudes no alcanzables
Modelizando el cálculo de varias variablEEES en el aula
Semivariogram calculation optimization for object-oriented image classification
Un modelo de transmisión de plagas para la enseñanza del álgebra lineal en el contexto de estudios en ciencias ambientales
On the importance of metrics in practical applications
Modelos para distintas tecnologías de generación eléctrica y optimización de la demanda diaria
Utilización de un modelo compartimental de transporte de pesticidas en las prácticas de Química Agrícola y Ambiental
Proteine Bolognese
Matrices: un modelo para las fotografías digitales
Modelización con curvas y superficies de Bézier
Propuesta de modelización: Reflexión de ondas por una superficie rugosa
Simulación de esfuerzos en pórticos
Difract: Un nuevo laboratorio virtual para la modelización matemática de las propiedades de difracción de redes fractales
Un laboratorio virtual para la enseñanza de momentos de inercia de figuras planas
La diagonalización de matrices en arquitectura
Obtención de las características seccionales de secciones metálicas de pared delgada abiertas
Un problema a resolver con los algoritmos de caminos más cortos
Herramientas de la teoría de grafos para la modelización
Calculo de volúmenes en modelos remallados de elementos finitos
Modelización de superredes cuánticas con MathematicaQc
Applied mathematical modelling for Industrial Engineers
Cuatro métodos para medir la altura del campanario de Moixent
Trayectorias modelizadoras en la ESO
La modelización matemática en cuarto de la ESO

URI permanente para esta colecciónhttps://riunet.upv.es/handle/10251/100883

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Mostrando 1 - 20 de 28

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La modelización matemática en cuarto de la ESO
(Universitat Politècnica de València, 2011-06-05) Sierra, L.; Garcia-Raffi, L.M.; Gómez i Urgellés, Joan
[EN] In this paper we present an example of teaching mathematics from a different and motivating point of view for students of Compulsory Secondary Education (ESO). Mathematical modelling is a creative activity that properly directed, it could be introduced in the class- room in a easily and effectively way. This implies a renovation of both methodologies in the classroom and the type of skills evaluated on students. Mathematical modelling is a different way of presenting and working mathematics in the classroom, closer to the students interest, that has influence in the results achieved. This paper presents the experience that took place in the IES Moixent and the work already developed so far.
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Trayectorias modelizadoras en la ESO
(Universitat Politècnica de València, 2011-06-05) Sol, Manel; Giménez, Joaquín; Rosich, Núria
[EN] We present the results of our research about ESO student low attainers’ modelling competencies. We have analyzed their papers (dossiers) about the modelling activities they carried out. These modelling activities have been called Realistic modelling Project (RMP). We have studied specially the set of actions that students do when they carry out their projects. The sequence of all the actions has been called ‘Modelling Route”. In order to analyse it we have set out a hypothetical modelling route that ESO students, as non-expert modellers, can perform a whole modelling process. This hypothetical route, consists of 16 actions, which we have used as an instrument of analysis. Research results show that all students are able to carry out their mathematical projects but there are differences in the processes followed.
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Cuatro métodos para medir la altura del campanario de Moixent
(Universitat Politècnica de València, 2011-06-05) Sierra Galdón, Lorena
[EN] In this paper we present an activity realized at IES Moixent in Valencia during the 2009- 2010 academic year by ten students of the fourth course of Compulsory Secondary Education (ESO) in the subject of Mathematics. The activity consisted of estimating the height of the bell tower of the town of Moixent using four different mathematical methods. First, we explain the reasons drove us to organize this activity and then we briefly describe the methods used. We also present the methodology, the contents and the objectives to be achieved with this activity. Finally an sample of the results and comments produced by students is given.
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Applied mathematical modelling for Industrial Engineers
(Universitat Politècnica de València, 2011-06-05) Mula, Josefa; Poler, Raúl; Departamento de Organización de Empresas; Centro de Investigación en Gestión e Ingeniería de Producción; Escuela Politécnica Superior de Alcoy
[EN] The learning of mathematical modelling techniques can result in a long and tedious process for Industrial Organization Engineering students. It is necessary to combine in a balanced way the theoretical teachings with the modelling of real study cases. In order to make more flexible the theoretical teaching process, multimedia tools of autodidactic learning are provided. A key factor is to evolve from simple models solved through educational programs, such as WinQSB or spreadsheets with embedded solvers to more complex models developed with a high level language of mathematical programming as MPL or GAMS where the models are solved with diverse commercial solvers (CPLEX, GUROBI, XPRESS, etc.) The objective of this paper is to present an innovative methodology to teach mathematical modelling techniques based in: (i) the balance of the theoretical and practical teachings; (ii) the use of multimedia autodidactic tools; and (iii) the formulation and resolution of real study cases through different solvers.
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Modelización de superredes cuánticas con Mathematica
(Universitat Politècnica de València, 2011-06-05) Monsoriu, J.A.; Giménez, M.H.; Giménez, F.; Marín, M.J.
[EN] Quantum superlattices are composite aperiodic structures comprised of alternating layers of several semiconductors following the rules of an aperiodic sequence. From a pedagogical point of view, it is easy to obtain the electronic scattering properties of these systems by means of the Transfer Matrix Method (TMM). In this work we present a TMM code developed in Mathematica that allows modeling periodic and aperiodic superlattices for motivating students of quantum physics by using unconventional geometries such as fractals or the Fibonacci sequence.
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Calculo de volúmenes en modelos remallados de elementos finitos
(Universitat Politècnica de València, 2011-06-05) Lapuebla-Ferri, Andrés; Giménez, Fernando; Jiménez, A.J.; Monsoriu, Juan A.; Pérez del Palomar, Amaya
[EN] Computer-assisted Finite Element Method is a widespread tool in the field of engineering. In certain applications, it is necessary to modify the mesh of the model during the analysis, which is known as ’remeshing’. In these situations, it is usually needed to perform some measurements, p.e., to calculate the volume of a region. Commercial packages can cover these needed, but they reveal to be limited in some situations. In this work, an application developed in MatlabQc is presented to approximately calculate the volume of a spatial region comprised between to meshes. The first is a quadrilateral finite element mesh, and the second mesh is topologically equivalent to the first and obtained through a remeshing process.
Access status: Abierto ,
Herramientas de la teoría de grafos para la modelización
(Universitat Politècnica de València, 2011-06-05) Jordan, Cristina; Torregrosa, Juan R.
[EN] In graph theory, networks play an important role in a lot of type of problems. In this paper we present some of them, sometimes without a clear relation with the classic definition of a network. They are enunciated in a real neighbourhood and the first step to solve them consists of translating the conditions of the problem to a graph. In order to get a good modelization, it must to take in mind the objective to reach. After the problem is modelized we apply the techniques or methods studied in graph theory. This type of problems increases the interest of the students, helps them to see the wide applicability of networks and trains them in the use of mathematical modelization.
Access status: Abierto ,
Un problema a resolver con los algoritmos de caminos más cortos
(Universitat Politècnica de València, 2011-06-05) Jordan, Cristina; Burriel, Jordi; Herráiz, Raquel
[EN] Graph theory solves, via a good modelization, a very large number of problems in different areas. This is why, this theory has been having an exponential increase in the last years. One of the basic problems that this theory solves is to obtain the shortest path between two points. In order to illustrate this problem, to motivate its study and to introduce the student in the world of the mathematical modelization and its large range of possibilities, we present a specific case: to help the police to catch the authors of a theft. The solution consists of representing the city where it took place by a no directed positive weighted graph and to apply the Floyd’s algorithm mixed with a reasoning of combinatorial type. At the end of the exercise, we can assure that the thieves cannot escape, by using another concept of graph theory, the vertex-cut.
Access status: Abierto ,
Obtención de las características seccionales de secciones metálicas de pared delgada abiertas
(Universitat Politècnica de València, 2011-06-05) Jimenez Mocholi, Antonio José; Giménez-Palomares, Fernando; Lapuebla-Ferri, Andrés; Departamento de Mecánica de los Medios Continuos y Teoría de Estructuras; Escuela Técnica Superior de Ingeniería Industrial
[EN] Thin-walled cold-formed steel sections are widely used in structural design. These sections, however, exhibit inestabilities that are caused by compression stresses when a structural member bends. For this reason, is necessary to know the effective values of the geometrical parameters of these sections, such as area section and moments of inertia. In addition, it is not recommended to choose open-shaped sections to sustain torsional loads, mostly if they are thin-walled sections. When designing a structure with thin-walled, open-shaped sections, it is necessary to use geometrical parameters such as torsional modulus, warping modulus, etc. In this job, an application designed in MatlabQc is presented in order to obtain such geometrical parameters. The geometry is discretised, and the algorithms are described. This application, implemented in a graphical way, is aimed to the students of subjects related to mechanical or industrial engineering.
Access status: Abierto ,
La diagonalización de matrices en arquitectura
(Universitat Politècnica de València, 2011-06-05) Jiménez Fernández, E.
[EN] In this work we use a beam problem as an application of diagonalization of symmetric matrices.
Access status: Abierto ,
Un laboratorio virtual para la enseñanza de momentos de inercia de figuras planas
(Universitat Politècnica de València, 2011-06-05) Giménez, Fernando; Monsoriu, Juan A.; Lapuebla-Ferri, Andrés; Jiménez, Antonio José; Departamento de Mecánica de los Medios Continuos y Teoría de Estructuras; Escuela Técnica Superior de Ingeniería Industrial
[EN] In this work, we present a graphic user interface (Gui) developed in MatlabQc to easily obtain the gravity center and the matrix of inertia of a plane domain. It is allowed to include holes, an also to consider curved or straight edges. The application represents graphically the domain, the position of the centre of gravity and the principal axes of inertia. From a pedagogical point of view, it can be usefully employed in the context of different subjects in university teaching, such as: Physics, Strength of Materials, Structural Analysis, etc.
Access status: Abierto ,
Difract: Un nuevo laboratorio virtual para la modelización matemática de las propiedades de difracción de redes fractales
(Universitat Politècnica de València, 2011-06-05) Giménez, M.H.; Monsoriu, J.A.; Giménez, F.; Pons, A.; Barreiro, J.C.; Furlan, W.D.
[EN] This work presents a new virtual laboratory, Difract, developed with Easy Java Simulations, for using in Optics courses as a computer tool for the mathematical modelling of the diffraction properties of 1D and 2D fractal gratings. This virtual laboratory enables students to quickly and easily analyze the influence on the Fraunhofer diffraction pattern of the different construction parameters of the fractal grating. As an application example, the Cantor fractal set has been considered.
Access status: Abierto ,
Simulación de esfuerzos en pórticos
(Universitat Politècnica de València, 2011-06-05) Giménez, Fernando; Lapuebla-Ferri, Andrés; Jiménez, Antonio José; Monsoriu, Juan A.; Departamento de Mecánica de los Medios Continuos y Teoría de Estructuras; Escuela Técnica Superior de Ingeniería Industrial
[EN] Virtual laboratories are a very powerful tool to help in transmitting scientific knowledge. Within the actual framework of university teaching, such tools are of great value due to its capabilities of self-teaching to the students of technical studies. In the present work, the authors describe a virtual laboratory developed with the Graphical User Interface (Gui) of the MatlabQc package. The aim of this virtual laboratory is to obtain the diagrams (i.e., graphical representation) of axial forces, shear forces and bending moments in plane, two-dimensional frames.
Access status: Abierto ,
Propuesta de modelización: Reflexión de ondas por una superficie rugosa
(Universitat Politècnica de València, 2011-06-05) Garcia-Raffi, L.M.; Romero-García, V.
[EN] Within the framework of the new curriculum, where active learning is the student, we propose a practice of modelling in science education to work with basics of mathematics and physics. The practice involves the modelling of wave reflection by rough surfaces. In a first stage, the reflection is analysed by a completely flat surface using geometric and physical concepts. The wave reflected from the surface is calculated from the waves emitted by a virtual source placed at the position symmetrical to the source position with respect to the mirror surface. To calculate the reflected wave, probability concepts are introduced. The wave reflection by a rough surface is obtained from the waves emitted by different sources for virtually every point of reflection. Courses in architecture and basic engineering, or even a master of acoustics are exceptional framework for the implementation of this practice.
Access status: Abierto ,
Modelización con curvas y superficies de Bézier
(Universitat Politècnica de València, 2011-06-05) Galdames Bravo, Orlando
[EN] The Bézier curves, a mathematical tool used in construction of curves and surfaces, was born as concrete application within the car industry. The present paper expects to recover this example for show how some mathematical tools can be used in the university teaching. We explain how and why these arise and also its mathematical formulation with the troubles that set out. We finalize describing an experience in the classroom and we extract some conclusions respect to supposing the incorporation of a subject oriented to solve a design using Bézier curves and surfaces.
Access status: Abierto ,
Matrices: un modelo para las fotografías digitales
(Universitat Politècnica de València, 2011-06-05) Domínguez Jiménez, María Elena
[EN] In this work we emphasize the relationship between two -apparently very different- disciplines: digital photography and mathematics. In fact, digital images -that everybody handles nowadays- are mathematically modeled by matrices. Moreover, all the manipulations over digital pictures can be expressed by means of matricial operations. In particular, here we set a problem of compression of digital images, based in the SVD (singular value decomposition), a concept learnt by the students of Linear Algebra courses. In this way, the students discover, by themselves, some important issues that teachers want to transmit to them: on one hand, that the theoretical concepts of Linear Algebra are directly applied to the technology that surrounds them everyday in our digital world; on the other hand, how mathematical modelization provides a powerful tool for the resolution of real practical problems.
Access status: Abierto ,
Proteine Bolognese
(Universitat Politècnica de València, 2011-06-05) Cubarsi, R.; Vázquez, E.; Villaverde, A.; Ministerio de Ciencia e Innovación
[EN] The penetration of a modified version of a green fluorescent protein called GFP in the cytoplasm and nucleus of a mammalian cell is modelled. The mathematical model provides a first approach to the experiment, with a progressive decreasing rate of fluorescence as the total luminosity increases until saturation. However, a local deviation from the proposed model is detected, due to a process that takes place in a non-differentiable way. The phenomenon is explained from the sudden entrance of GFP into the cytoplasm and nucleus by the weakening or permeabilization of their membranes, and from the obstruction of GFP flux by the nuclear membrane. Thus, the mathematical model provides relevant information on the deviation from the pattern that has been adopted. To unify the European Higher Education Area (EHEA), and in accordance with the guidelines of the Bologna Process, the subjects of new curricula have under- gone a thorough review of their contents. So the new methodology be fruitful, a highly optimized agenda must be designed by linking every topic with topics from other subjects. The case presented evidences how Mathematical Modelling is useful to implement and review lessons learned in various subjects, from maths and biology in the current case, besides being an effective way to stimulate learning, since it is showing the usefulness of what is studied.
Access status: Abierto ,
Utilización de un modelo compartimental de transporte de pesticidas en las prácticas de Química Agrícola y Ambiental
(Universitat Politècnica de València, 2011-06-05) Contreras, W.A.; Bautista-Carrascosa, I.; Lidón, Antonio; Ginestar, D.; Instituto Universitario de Ingeniería del Agua y del Medio Ambiente; Departamento de Química; Escuela Técnica Superior de Ingeniería Agronómica y del Medio Natural
[EN] Computational models are useful tools in most of the knowledge areas and can be easily used to visualize the behaviour of complex systems. In this work, we present a simple com- partmental model to simulate the dynamics of the concentration of a given pesticide in a rice crop. The model considers different compartments such as: air, water, rice plants and sediments, which are coupled with a soil column modelled by means of a convection-advection equation. The model has been implemented in MatlabQc and has a Graphical User Interface (Gui) that allows to change easily the value of different parameters of the model and to obtain graphical representations of the results. Different possible applications of the model for a practical class of the subject Environmental and Agricultural Chemistry are proposed.
Access status: Abierto ,
Modelos para distintas tecnologías de generación eléctrica y optimización de la demanda diaria
(Universitat Politècnica de València, 2011-06-05) Carlos, Sofia
[EN] The short term load dispatch using different energy technologies is a technical problem of great interest. This problem is addressed to Industrial Engineers, as some lectures about energy technologies and the electric market can be found among the subjects of this degree. The work proposed consists of performing the optimization of the power generated by different plants to satisfy a dairy demand curve taking into consideration only thermal and hydropower plants. A simple mathematical model has been developed to quantify the power generated for each kind of plant that takes into consideration all of their supply restrictions. To perform the optimization, a genetic algorithm has been used. Thus, the students are introduced in a type of heuristic optimization techniques to solve a quite complicated problem due to the non-linearity and restrictions present in the problem.
Access status: Abierto ,
On the importance of metrics in practical applications
(Universitat Politècnica de València, 2011-06-05) Camarena, Joan-Gerard; Morillas, Samuel; Cisneros, F.J.; Departamento de Matemática Aplicada; Instituto Universitario de Matemática Pura y Aplicada; Escuela Técnica Superior de Ingeniería Informática
[EN] Students motivation for learning mathematical concepts can be increased when showing the usefulness of these concepts in practical problems. One important mathematical concept is the concept of metric space and, more related to the applications, the concept of metric function. In this work we aim to illustrate how important is to appropriately choose the metric when dealing with a practical problem. In particular, we focus on the problem of detection of noisy pixels in colour images. In this context, it is very important to appropriately measure the distances and similarities between the image pixels, which is done by means of an appropriate metric. We study the performance of different metrics, including recent fuzzy metrics, within a specific filter to show that it is indeed a critical choice to appropriately solve the task.

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