Conjeturación del teorema del valor medio para derivadas: Un acercamiento desde la detección de invariantes en dispositivos móviles con GeoGebra

This article presents the results of a research project whose main objective was to describe the mediating role of GeoGebra’s “Graphing Calculator” mobile application on the conjecturing processes of the mean value theorem for derivatives by the use of some dragging tools, which combines dynamic geometry and infinitesimal calculus. By means of a qualitative case study, involving students from aeronautical engineering, research efforts were carried out looking forward to get evidence that allow the judgement of a hypothesis involving a positive influence of a mobile learning strategy on conjecturing processes in the context of a calculus course. The results obtained allowed us to conclude significant advances in the conjecturing process of the above-mentioned theorem for the solving-problems process in engineering. The discussion of how this type of digital resources, through a dynamic geometry environment in mobile devices, could favor the learning of calculus, is also addressed.Este artículo presenta los resultados de un proyecto de investigación cuyo objetivo fue describir el papel mediador de la aplicación móvil “Calculadora Gráfica” de GeoGebra sobre los procesos de conjeturación del teorema del valor medio para derivadas mediante la detección de invariantes a través de herramientas de arrastre, combinando geometría dinámica con cálculo infinitesimal. A través de un estudio de caso cualitativo, que involucró estudiantes de Ingeniería Aeronáutica, se dinamizaron los esfuerzos investigativos con el propósito de validar la hipótesis relacionada con una influencia positiva de una estrategia de aprendizaje móvil sobre el proceso de conjeturación en un curso de Cálculo Diferencial. Los resultados obtenidos permitieron evidenciar avances significativos en la conjeturación del teorema mencionado para la resolución de problemas en ingeniería y se discute cómo este tipo de recursos digitales, a través de un entorno de geometría dinámica en dispositivos móviles, puede servir como mediación para favorecer el aprendizaje del cálculo

Noción de aproximación del área bajo la curva utilizando la aplicación Calculadora Gráfica de GeoGebra

Este artículo presenta los resultados de un proyecto de investigación desarrollado en la Facultad de Ingeniería y Ciencias Básicas de la Fundación Universitaria Los Libertadores de Bogotá. El objetivo era describir y analizar los efectos de implementar una unidad didáctica para la enseñanza de la noción de área bajo la curva en un curso de cálculo integral, a partir de la integración de teléfonos inteligentes durante la experiencia de aprendizaje. Para tal fin, se realizó un diseño experimental de cuatro grupos de Solomon con el propósito de determinar la influencia de una intervención mediada por la aplicación móvil Calculadora Gráfica de GeoGebra y verificar los efectos de un pretest sobre la cantidad de respuestas correctas en el postest. Los resultados se analizaron mediante la aplicación de una prueba ANOVA de dos vías. Se encontró que el pretest tuvo una influencia directa en los resultados del postest y que los dos grupos que recibieron la intervención mediada por la aplicación móvil de GeoGebra obtuvieron mejor rendimiento en el postest que aquellos grupos que tuvieron una intervención con calculadora científica tradicional

Noción de aproximación del área bajo la curva utilizando la aplicación Calculadora Gráfica de GeoGebra

This article presents the results of research project developed at the Faculty of Engineering and Basic Sciences of the Fundación Universitaria los Libertadores (Bogotá, D.C.) whose main goal was to describe and to analyze the effects of implementing a didactic strategy for teaching the concept of area under the curve, in the context of an Integral Calculus course. Cell phones devices were used as a tool intended to support the learning process considering that these devices might not be as harmful or distracting as others and, as well, that respond to the new ways of recognizing and integrating into alternative Learning communities. An experimental design of four Solomon groups was carried out with the purpose of determining the influence of an intervention mediated by the GeoGebra “Graphing Calculator” mobile application, also considering the effect of an entrance test. The results found indicate that the two groups that had the intervention based on the mobile application obtained better performance in the exit test than those groups that had an intervention with a traditional scientific calculator.Este artículo presenta los resultados de un proyecto de investigación desarrollado en la Facultad de Ingeniería y Ciencias Básicas de la Fundación Universitaria Los Libertadores (Bogotá, D.C.) cuyo objetivo consistió en describir y analizar los efectos de implementar una estrategia didáctica para la enseñanza de la noción de área bajo la curva, durante un curso de Cálculo Integral, a partir de la integración de teléfonos celulares como dispositivos que pueden apoyar el proceso de aprendizaje y no como artefactos nocivos o distractores y que responden a nuevas formas de reconocerse e integrarse a comunidades alternativas de aprendizaje. Se realizó un diseño experimental de cuatro grupos de Solomon con el propósito de determinar la influencia de una intervención mediada por la aplicación móvil “Calculadora Gráfica” de GeoGebra considerando también el efecto de una prueba de entrada. Los resultados encontrados señalan que los dos grupos que tuvieron la intervención mediada por la aplicación móvil obtuvieron mejor rendimiento en la prueba de salida que aquellos grupos que tuvieron una intervención con calculadora científica tradicional.Cet article présente les résultats d'un projet de recherche développé à la Faculté d'Ingénierie et de Sciences Fondamentales de la Fundación Universitaria los Libertadores (Bogotá, DC) dont l'objectif était de décrire et d'analyser les effets d'une stratégie didactique pour enseigner la notion de l’aire sous la courbe, pendant un cours de calcul intégral, avec l'utilisation des téléphones cellulaires en tant qu'appareils capables de supporter le processus d'apprentissage et non comme des appareils nuisibles ou gênants, et, aussi,  répondant à de nouvelles façons de reconnaître et d'intégrer des communautés alternatives d'apprentissage. Une conception expérimentale de quatre groupes de Solomon a été réalisée dans le but de déterminer l’influence d’une intervention médiatisée par l’application mobile «Graphing Calculator» de GeoGebra, tenant également compte de l’effet d’un test d’entrée. Les résultats obtenus indiquent que les deux groupes pour lesquels l'intervention mobile a été médiée par l'application mobile ont obtenu de meilleures performances au test de sortie que ceux des groupes ayant de l’intervention avec une calculatrice scientifique traditionnelle

El Aprendizaje Móvil en Educación Superior: Una Experiencia desde la Formación de Ingenieros

This article presents the results of a research project performed at the Faculty of Engineering and Basic Sciences of the Fundación Universitaria Los Libertadores, Bogotá., whose objective was to describe the effects and experiences of incorporating the GeoGebra “Graphing Calculator” app on learning the notion of limit from the integration of mobile devices in the classroom. A sequential explanatory design was used in order to judge the hypothesis linking a positive influence of the use of smartphones and tablets and academic performance. In the quantitative stage, an experimental design of four Solomon groups was carried out and during the qualitative stage, an attitudinal test was applied and semi-structured interviews were carried out with students who participated in the treatment with the mobile application. The results obtained in the postest by the experimental groups surpassed those obtained by the control groups that participated in an intervention based on traditional teaching resources. The students who received the experimental treatment showed greater interest and motivation for learning about the topic addressed, so it can be inferred that the integration of mobile devices in the classroom promotes other innovative ways of learning calculus.Este artículo presenta los resultados de un proyecto de investigación desarrollado en la Facultad de Ingeniería y Ciencias Básicas de la Fundación Universitaria Los Libertadores, Bogotá. cuyo objetivo fue describir los efectos y las experiencias de la incorporación de la aplicación “Calculadora Gráfica” de GeoGebra sobre el aprendizaje de la noción de límite a partir de la integración de dispositivos móviles al aula de clase. Se empleó un diseño explicativo secuencial con el ánimo de validar la hipótesis relacionada con una influencia positiva del aprovechamiento de teléfonos inteligentes y tabletas en el desempeño académico. En la etapa cuantitativa se realizó un diseño experimental de cuatro grupos de Solomon y durante la etapa cualitativa se aplicó un test actitudinal y se desarrollaron entrevistas semiestructuradas con estudiantes que participaron del tratamiento con la aplicación móvil. Los resultados obtenidos en el postest por los grupos experimentales superaron a los obtenidos por los grupos control que participaron de una intervención mediada por recursos didácticos tradicionales. Los estudiantes que recibieron el tratamiento experimental demostraron mayor interés y motivación por el aprendizaje del tema abordado, por lo que se puede inferir que la integración de dispositivos móviles en el aula promueve otras formas innovadoras de aprender cálculo

Spatial Transmission of 2009 Pandemic Influenza in the US

The 2009 H1N1 influenza pandemic provides a unique opportunity for detailed examination of the spatial dynamics of an emerging pathogen. In the US, the pandemic was characterized by substantial geographical heterogeneity: the 2009 spring wave was limited mainly to northeastern cities while the larger fall wave affected the whole country. Here we use finely resolved spatial and temporal influenza disease data based on electronic medical claims to explore the spread of the fall pandemic wave across 271 US cities and associated suburban areas. We document a clear spatial pattern in the timing of onset of the fall wave, starting in southeastern cities and spreading outwards over a period of three months. We use mechanistic models to tease apart the external factors associated with the timing of the fall wave arrival: differential seeding events linked to demographic factors, school opening dates, absolute humidity, prior immunity from the spring wave, spatial diffusion, and their interactions. Although the onset of the fall wave was correlated with school openings as previously reported, models including spatial spread alone resulted in better fit. The best model had a combination of the two. Absolute humidity or prior exposure during the spring wave did not improve the fit and population size only played a weak role. In conclusion, the protracted spread of pandemic influenza in fall 2009 in the US was dominated by short-distance spatial spread partially catalysed by school openings rather than long-distance transmission events. This is in contrast to the rapid hierarchical transmission patterns previously described for seasonal influenza. The findings underline the critical role that school-age children play in facilitating the geographic spread of pandemic influenza and highlight the need for further information on the movement and mixing patterns of this age group

Estimating the Timing of Mother-to-Child Transmission of the Human Immunodeficiency Virus Type 1 Using a Viral Molecular Evolution Model

Background: Mother-to-child transmission (MTCT) is responsible for most pediatric HIV-1 infections worldwide. It can occur during pregnancy, labor, or breastfeeding. Numerous studies have used coalescent and molecular clock methods to understand the epidemic history of HIV-1, but the timing of vertical transmission has not been studied using these methods. Taking advantage of the constant accumulation of HIV genetic variation over time and using longitudinally sampled viral sequences, we used a coalescent approach to investigate the timing of MTCT. Materials and Methods Six-hundred and twenty-two clonal env sequences from the RNA and DNA viral population were longitudinally sampled from nine HIV-1 infected mother-and-child pairs [range: 277–1034 days]. For each transmission pair, timing of MTCT was determined using a coalescent-based model within a Bayesian statistical framework. Results were compared with available estimates of MTCT timing obtained with the classic biomedical approach based on serial HIV DNA detection by PCR assays. Results: Four children were infected during pregnancy, whereas the remaining five children were infected at time of delivery. For eight out of nine pairs, results were consistent with the transmission periods assessed by standard PCR-based assay. The discordance in the remaining case was likely confused by co-infection, with simultaneous introduction of multiple maternal viral variants at the time of delivery. Conclusions: The study provided the opportunity to validate the Bayesian coalescent approach that determines the timing of MTCT of HIV-1. It illustrates the power of population genetics approaches to reliably estimate the timing of transmission events and deepens our knowledge about the dynamics of viral evolution in HIV-infected children, accounting for the complexity of multiple transmission events

Planetary Exploration Horizon 2061 Report, Chapter 3: From science questions to Solar System exploration

This chapter of the Planetary Exploration Horizon 2061 Report reviews the way the six key questions about planetary systems, from their origins to the way they work and their habitability, identified in chapter 1, can be addressed by means of solar system exploration, and how one can find partial answers to these six questions by flying to the different provinces to the solar system: terrestrial planets, giant planets, small bodies, and up to its interface with the local interstellar medium. It derives from this analysis a synthetic description of the most important space observations to be performed at the different solar system objects by future planetary exploration missions. These observation requirements illustrate the diversity of measurement techniques to be used as well as the diversity of destinations where these observations must be made. They constitute the base for the identification of the future planetary missions we need to fly by 2061, which are described in chapter 4. Q1- How well do we understand the diversity of planetary systems objects? Q2- How well do we understand the diversity of planetary system architectures? Q3- What are the origins and formation scenarios for planetary systems? Q4- How do planetary systems work? Q5- Do planetary systems host potential habitats? Q6- Where and how to search for life?Comment: 107 pages, 37 figures, Horizon 2061 is a science-driven, foresight exercise, for future scientific investigation

Influenza A Gradual and Epochal Evolution: Insights from Simple Models

The recurrence of influenza A epidemics has originally been explained by a “continuous antigenic drift” scenario. Recently, it has been shown that if genetic drift is gradual, the evolution of influenza A main antigen, the haemagglutinin, is punctuated. As a consequence, it has been suggested that influenza A dynamics at the population level should be approximated by a serial model. Here, simple models are used to test whether a serial model requires gradual antigenic drift within groups of strains with the same antigenic properties (antigenic clusters). We compare the effect of status based and history based frameworks and the influence of reduced susceptibility and infectivity assumptions on the transient dynamics of antigenic clusters. Our results reveal that the replacement of a resident antigenic cluster by a mutant cluster, as observed in data, is reproduced only by the status based model integrating the reduced infectivity assumption. This combination of assumptions is useful to overcome the otherwise extremely high model dimensionality of models incorporating many strains, but relies on a biological hypothesis not obviously satisfied. Our findings finally suggest the dynamical importance of gradual antigenic drift even in the presence of punctuated immune escape. A more regular renewal of susceptible pool than the one implemented in a serial model should be part of a minimal theory for influenza at the population level