Multidisciplinary Practices for First Engineering Levels: Collection and Mathematical Treatment of Topographic Data Obtained with Ultrasonic Techniques
The role of skills in higher education and their corresponding accreditation are becoming increas... more The role of skills in higher education and their corresponding accreditation are becoming increasingly important in the context of the knowledge society and lifelong learning strategies and policies. It begins with a first definition of the notion of skill, distinguishing between transversal or generic competencies and specific skills. The hypothesis held in this paper is that the transversal competences can be achieved and accredited whenever conditions of possibility are created for this. The obligation to assess is a reflection of what has been called the evaluating state and the emphasis on accountability, which emphasizes accountability and results, without paying attention to the processes. Faced with this tendency, the authors argue for the need to promote institutional measures and favorable learning environments so that the students' abilities have their best development and recognition not only formal, but substantive, in academic terms and in the labour market. The transversal competences project launched at the Polytechnic University of Valencia (UPV) (http://www.upv.es/contenidos/COMPTRAN/) has as its main objective to accredit these competences to the students graduated in its official degree programs. The present work focuses on establishing a strategy for the evaluation of transversal competences to accredit their acquisition in three subjects in the area of mathematics in a first degree course. The strategies used for the teaching of competences are those based on collaborative learning and through the study of cases. The above is based on teamwork, which helps to develop several transversal skills at the same time. In addition, this method forces to question, to recognize the relevant knowledge, and to reorganize these skills, which abound in the analysis and resolution of problems in general, being this another important transversal skill. This paper describes the experience carried out in the subjects of Algebra, Calculus and Mathematical Methods, analyzing the results obtained from a qualitative and also quantitative point of view, carrying out the evaluation by means of global and analytical rubrics. It also analyzes how far the preparation of these tasks has helped to create necessary study habits in students, to promote effective cooperation between them and to obtain better academic results. We also analyze what other social and educational factors would be necessary to achieve the proposed objectives.
La clotoide, también conocida como radioide de arcos o espiral de Cornu, recibe su nombre del voc... more La clotoide, también conocida como radioide de arcos o espiral de Cornu, recibe su nombre del vocablo griego Klothó que significa "hilandera". Su utilización más inmediata está en los trazados en planta de obras lineales como curva de transición (para unir tramos rectos con tramos curvos o para conectar dos tramos circulares de curvaturas distintas).Ésta es su característica más importante, ya que el radio de curvatura disminuye de manera inversamente proporcional a la distancia recorrida sobre ella y esto permite al conductor adaptarse de forma suave al cambio de trayectoria. Los nuevos trazados de carreteras están diseñados incluyendo una sucesión de clotoides con curvatura grande lo que se traduce en mayor distancia de visibilidad y fácil adaptación al terreno. En este trabajo partimos de la propiedad geométrica que define una clotoide y obtenemos su ecuación a partir de las llamadas integrales de Fresnel. En segundo lugar, representamos geométricamente las propiedades que se derivan y obtenemos una aproximación numérica de la clotoide. Porúltimo, utilizamos esas aproximaciones para presentar un ejemplo. Clothoids, also known as radius of curvature or Cornu spirals, take their name from the greek word Klothó, meaning, weaver. They are also widely used as transition curves in railroad or highway engineering for connecting and transiting the geometry between a tangent and a circular curve (to join straight sections with curve transitions or to connect two circular sections of different curvatures). This is their most relevant characteristic, since the radius of curvature diminishes in inverse proportion to the distance run over it, and that allows the driver to adapt slowly to the change in the trajectory. The new highways are designed including a series of clothoids with a large curvature which involves a greater visibility in the distance and easy adaptation to the track. In this paper we take into account the geometric property which defines clothoids and we obtain its equation from Fresnel integrals. Secondly, we represent the properties derived geometrically and obtain a numerical approximation of the clothoid. Finally, we use these approximations to present an example.
The achievement of a comprehensive education of the students to provide a global knowledge that a... more The achievement of a comprehensive education of the students to provide a global knowledge that allows them to make appropriate decisions in the framework of their future work is one of the most important challenges of the Engineering degrees, especially in basic subjects as Physics or Mathematics. In this sense, a great effort has to be done by the teachers of the first year where the subjects are generally quite abstract and, as a consequence, the motivation of the students is hard to attain. Several are the conditions to obtain this goal successfully: First, a correct cross-coordination and a well-designed teaching of the basis subjects to avoid undesirable repetition of some concepts under different point of view and to show the basic knowledge as a uniform conceptual body ready to be applied to real situations. Second, the need to make attractive the study of these basic and abstract subjects by proposing the resolution of real problems related with the goals of each particular Degree, and adapted to the knowledge of the student of the first level. These problems have to be solved involving different branch of the basic subjects as Physics or Mathematics. In this paper we present a real project related to the professional skills of the Geomatic and Topography Degree, adapted for the first level, and involving three core subjects namely, Algebra, Calculus and Mechanics. The approach of this real project, proposed as an interdisciplinary practice, is related with the path followed by a rocket that puts a satellite in orbit. In real situations, sixteen are the steps of the protocol to achieve this goal, from the takeoff of the rocket to its entrance on the final elliptic orbit. To adapt this complicated protocol to our purposes, we have simplified the steps considering finally only four: (i) the takeoff of the rocket; (ii) the change of the upright path at a predetermined height from the ground to approach to the elliptical orbit; (iii) the link between the rise of the rocket and its placing in elliptical orbit; (iv) the putting into the elliptical orbit itself. Analysis of classic geometric figures as the conics, with their different forms of representation, becomes necessary to be able to develop this practice, since they adapt to the forms described by orbits of the satellites. Modeling makes it necessary to use different reference systems and their relationship between them. In addition, the simplified study of the satellite position vector in its different phases provides fundamental data such as speed, acceleration or balance of forces, related with the subjects of Dynamic or Kinematics, and where the concept of derivative plays a fundamental role. A later detailed study on the motion of the satellite would lead to propose systems of differential equations that relate the elements studied and whose complexity requires numerical methods for their resolution.
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Papers by Emilio Checa