Online games for the teaching of mathematics

In this article we present a didactic experience developed by the GIE (Group of Educational Innovation) “Pensamiento Matemático” of the Polytechnics University of Madrid (UPM), in order to bring secondary students and university students closer to Mathematics. It deals with the development of a virtual board game called Mate-trivial. The mechanics of the game is to win points by going around the board which consists of four types of squares identified by colours: “Statistics and Probability”, “Calculus and Analysis”, “Algebra and Geometry” and “Arithmetic and Number Theory ”. When landing on a square, a question of its category is set out: a correct answer wins 200 points, if wrong it loses 100 points, and not answering causes no effect on the points, but all the same, two minutes out of the 20 minutes that each game lasts are lost. For the game to be over it is necessary, before those 20 minutes run out, to reach the central square and succeed in the final task: four chained questions, one of each type, which must be all answered correctly. It is possible to choose between two levels to play: Level 1, for pre-university students and Level 2 for university students. A prototype of the game is available at the website “Aula de Pensamiento Matemático” developed by the GIE: http://innovacioneducativa.upm.es/pensamientomatematico/. This activity lies within a set of didactic actions which the GIE is developing in the framework of the project “Collaborative Strategies between University and Secondary School Education for the teaching and learning of Mathematics: An Application to solve problems while playing”, a transversal project financed by the UPM.

Exploring Cultural Heritage Resources in a 3D Collaborative Environment

Cultural heritage is a complex and diverse concept, which brings together a wide domain of information. Resources linked to a cultural heritage site may consist of physical artefacts, books, works of art, pictures, historical maps, aerial photographs, archaeological surveys and 3D models. Moreover, all these resources are listed and described by a set of a variety of metadata specifications that allow their online search and consultation on the most basic characteristics of them. Some examples include Norma ISO 19115, Dublin Core, AAT, CDWA, CCO, DACS, MARC, MoReq, MODS, MuseumDat, TGN, SPECTRUM, VRA Core and Z39.50. Gateways are in place to fit in these metadata standards into those used in a SDI (ISO 19115 or INSPIRE), but substantial work still remains to be done for the complete incorporation of cultural heritage information. Therefore, the aim of this paper is to demonstrate how the complexity of cultural heritage resources can be dealt with by a visual exploration of their metadata within a 3D collaborative environment. The 3D collaborative environments are promising tools that represent the new frontier of our capacity of learning, understanding, communicating and transmitting culture.

Plataformas experimentales para la formación en el área de la electrónica en entornos de e-learning

El campo de estudio relacionado con los laboratorios remotos en el ámbito educativo de las ciencias y la ingeniería está sufriendo una notable expansión ante la necesidad de adaptar los procesos de aprendizaje en dichas áreas a las características y posibilidades de la formación online. Muchos de los recursos educativos basados en esta tecnología, existentes en la actualidad, presentan ciertas limitaciones que impiden alcanzar las competencias que se deben adquirir en los laboratorios de ingeniería. Estas limitaciones están relacionadas con diferentes aspectos de carácter técnico y formativo. A nivel técnico las limitaciones principales se centran en el grado de versatilidad que son capaces de proporcionar comparado con el que se dispone en un laboratorio tradicional y en el modo de interacción del usuario, que provoca que el estudiante no distinga claramente si está realizando acciones sobre sistemas reales o simulaciones. A nivel formativo las limitaciones detectadas son relevantes para poder alcanzar un aprendizaje significativo. En concreto están relacionadas principalmente con un escaso sentimiento de inmersión, una reducida sensación de realismo respecto a las operaciones que se realizan o la limitada posibilidad de realizar actividades de forma colaborativa. La aparición de nuevas tecnologías basadas en entornos inmersivos, unida a los avances producidos relacionados con el aumento de la capacidad gráfica de los ordenadores y del ancho de banda de acceso a Internet, han hecho factible que las limitaciones comentadas anteriormente puedan ser superadas gracias al desarrollo de nuevos recursos de aprendizaje surgidos de la fusión de laboratorios remotos y mundos virtuales 3D. Esta tesis doctoral aborda un trabajo de investigación centrado en proponer un modelo de plataformas experimentales, basado en la fusión de las dos tecnologías mencionadas, que permita generar recursos educativos online que faciliten la adquisición de competencias prácticas similares a las que se consiguen en un laboratorio tradicional vinculado a la enseñanza de la electrónica. El campo de aplicación en el que se ha focalizado el trabajo realizado se ha centrado en el área de la electrónica aunque los resultados de la investigación realizada se podrían adaptar fácilmente a otras disciplinas de la ingeniería. Fruto del trabajo realizado en esta tesis es el desarrollo de la plataforma eLab3D, basada en el modelo de plataformas experimentales propuesto, y la realización de dos estudios empíricos llevados a cabo con estudiantes de grado en ingeniería, muy demandados por la comunidad investigadora. Por un lado, la plataforma eLab3D, que permite llevar a cabo de forma remota actividades prácticas relacionadas con el diseño, montaje y prueba de circuitos electrónicos analógicos, aporta como novedad un dispositivo hardware basado en un sistema de conmutación distribuido. Dicho sistema proporciona un nivel de versatilidad muy elevado, a nivel de configuración de circuitos y selección de puntos de medida, que hace posible la realización de acciones similares a las que se llevan a cabo en los laboratorios presenciales. Por otra parte, los estudios empíricos realizados, que comparaban la eficacia educativa de una metodología de aprendizaje online, basada en el uso de la plataforma eLab3D, con la conseguida siguiendo una metodología clásica en los laboratorios tradicionales, mostraron que no se detectaron diferencias significativas en el grado de adquisición de los resultados de aprendizaje entre los estudiantes que utilizaron la plataforma eLab3D y los que asistieron a los laboratorios presenciales. Por último, hay que destacar dos aspectos relevantes relacionados directamente con esta tesis. En primer lugar, los resultados obtenidos en las experiencias educativas llevadas a cabo junto a valoraciones obtenidas por el profesorado que ha colaborado en las mismas han sido decisivos para que la plataforma eLab3D se haya integrado como recurso complementario de aprendizaje en titulaciones de grado de ingeniería de la Universidad Politécnica de Madrid. En segundo lugar, el modelo de plataformas experimentales que se ha propuesto en esta tesis, analizado por investigadores vinculados a proyectos en el ámbito de la fusión nuclear, ha sido tomado como referencia para generar nuevas herramientas de formación en dicho campo. ABSTRACT The field of study of remote laboratories in sciences and engineering educational disciplines is undergoing a remarkable expansion given the need to adapt the learning processes in the aforementioned areas to the characteristics and possibilities of online education. Several of the current educational resources based on this technology have certain limitations that prevent from reaching the required competencies in engineering laboratories. These limitations are related to different aspects of technical and educational nature. At the technical level, they are centered on the degree of versatility they are able to provide compared to a traditional laboratory and in the way the user interacts with them, which causes the student to not clearly distinguish if actions are being performed over real systems or over simulations. At the educational level, the detected limitations are relevant in order to reach a meaningful learning. In particular, they are mainly related to a scarce immersion feeling, a reduced realism sense regarding the operations performed or the limited possibility to carry out activities in a collaborative way. The appearance of new technologies based on immersive environments, together with the advances in graphical computer capabilities and Internet bandwidth access, have made the previous limitations feasible to be overcome thanks to the development of new learning resources that arise from merging remote laboratories and 3D virtual worlds. This PhD thesis tackles a research work focused on the proposal of an experimental platform model, based on the fusion of both mentioned technologies, which allows for generating online educational resources that facilitate the acquisition of practical competencies similar to those obtained in a traditional electronics laboratory. The application field, in which this work is focused, is electronics, although the research results could be easily adapted to other engineering disciplines. A result of this work is the development of eLab3D platform, based on the experimental platform model proposed, and the realization of two empirical studies with undergraduate students, highly demanded by research community. On one side, eLab3D platform, which allows to accomplish remote practical activities related to the design, assembling and test of analog electronic circuits, provides, as an original contribution, a hardware device based on a distributed switching system. This system offers a high level of versatility, both at the circuit configuration level and at the selection of measurement points, which allows for doing similar actions to those conducted in hands-on laboratories. On the other side, the empirical studies carried out, which compare the educational efficiency of an online learning methodology based on the use of eLab3D platform with that obtained following a classical methodology in traditional laboratories, shows that no significant differences in the acquired degree of learning outcomes among the students that used eLab3D platform and those that attended hands-on laboratories were detected. Finally, it is important to highlight two relevant aspects directly related with this thesis work. First of all, the results obtained in the educational experiences conducted, along with the assessment from the faculty that has collaborated in them, have been decisive to integrate eLab3D platform as a supplementary learning resource in engineering degrees at Universidad Politecnica de Madrid. Secondly, the experimental platform model originally proposed in this thesis, which has been analysed by nuclear fusion researchers, has been taken as a reference to generate new educational tools in that field.