Variables, funciones y cambios: ¿qué conocen nuestros alumnos?

El estudio de la matemática permite la modelización de situaciones que conducen a la resolución de problemas. Por esto, es primordial que los estudiantes analicen los cambios que ocurren en diferentes fenómenos biológicos, económicos y sociales. Sin embargo, durante la escuela media, no se favorece demasiado el desarrollo del pensamiento y lenguaje variacional, base para la comprensión de los conceptos de la matemática de la variación y el cambio, es decir el cálculo. Por este motivo, este trabajo, enmarcado en el proyecto de investigación “Pensamiento y lenguaje variacional: bases para la construcción de conceptos del cálculo diferencial”, tiene como objetivo el análisis y valoración de los resultados obtenidos en una experiencia de aula centrada en el diseño, implementación y corrección de una guía de actividades que indaga las nociones que tienen los alumnos que ingresan al nivel universitario con respecto a variables, cambios, funciones, imagen, gráficas, expresión analítica, valor numérico y comportamiento de funciones.

Variación y variables con geometría dinámica

Este trabajo es parte de un proyecto de investigación sobre la aplicación de tecnología computacional en la enseñanza y aprendizaje de matemáticas con alumnos de nivel medio básico o secundaria (séptimo a noveno grado) y nivel medio superior o bachillerato (décimo a doceavo grado), en particular, trata de entender la función mediadora del efecto de “arrastre” del software de geometría dinámica en la cognición de sujetos que estudian las nociones de variación y variable. Aquí reportamos los resultados de una exploración, usando Cabri, en el aprendizaje de esas nociones con estudiantes de nivel medio básico de 13-14 años de edad. Se describen las actividades, las respuestas de los estudiantes y una experiencia que sugiere el potencial de la verbalización de los resultados por los estudiantes en el proceso de simbolización algebraica.

Incursión en el ámbito de las dos variables: optimización usando argumentos gráficos

Cuando enseñamos a los alumnos a resolver problemas, solemos abusar de la utilización de algoritmos encaminados a encontrar la solución óptima, evitando las dificultades que puede suponer la introducción de reglas más o menos complejas en el diseño de dicho algoritmo. Pero resolver un problema es mucho más que aplicar un algoritmo de forma mecánica, supone encontrar una respuesta coherente a una serie de datos relacionados dentro de un contexto. Es por esto que presentamos esta práctica, donde la utilización de un algoritmo para resolver un problema nos lleva a encontrar soluciones que descartaremos como útiles.

El método de discretización en varias variables

El artículo presenta un método, de naturaleza indirecta, que puede ayudar a probar ciertos resultados que involucran sucesiones y funciones continuas que frecuentemente aparecen en la topología de R^n.

Relating plankton assemblages to environmental variables using instruments towed by ships-of-opportunity

Undulating Oceanographic Recorders (UORs) and Continuous Plankton Recorders (CPRs) equipped with a suite of sensors were towed by merchant vessels in the North Sea between 1988 and 1991, recording a range of environmental variables. These were used to interpret the results of analyses of the plankton taken on CPR tows off the northeast coast of the UK in 1989 and in the Skagerrak and Kattegat in July 1988 and through 1989. Correlations were found between the biota and the environmental variables. The tidal front off the northeast coast of the UK and the front between the low salinity water in the Kattegat and the higher salinity water in the Skagerrak were dominant factors correlating with the distribution of the plankton assemblages. Discontinuities, defining the positions of the fronts, in the values of physical variables (temperature and, where measured, salinity and turbidity) were closely identified with geographical divisions between plankton assemblages. Measures of irradiance were found to be important on several occasions, presumably due to diel migrations of the zooplankton.

The ESA Climate Change Initiative: Satellite Data Records for Essential Climate Variables

Observations of Earth from space have been made for over 40 years and have contributed to advances in many aspects of climate science. However, attempts to exploit this wealth of data are often hampered by a lack of homogeneity and continuity and by insufficient understanding of the products and their uncertainties. There is, therefore, a need to reassess and reprocess satellite datasets to maximize their usefulness for climate science. The European Space Agency has responded to this need by establishing the Climate Change Initiative (CCI). The CCI will create new climate data records for (currently) 13 essential climate variables (ECVs) and make these open and easily accessible to all. Each ECV project works closely with users to produce time series from the available satellite observations relevant to users' needs. A climate modeling users' group provides a climate system perspective and a forum to bring the data and modeling communities together. This paper presents the CCI program. It outlines its benefit and presents approaches and challenges for each ECV project, covering clouds, aerosols, ozone, greenhouse gases, sea surface temperature, ocean color, sea level, sea ice, land cover, fire, glaciers, soil moisture, and ice sheets. It also discusses how the CCI approach may contribute to defining and shaping future developments in Earth observation for climate science.

Quantifying the impact of environmental variables upon catch-per-unit-effort of the Blue Shark Prionace glauca in the Western English Channel

The effect of environmental variables on blue shark Prionace glauca catch per unit effort (CPUE) in a recreational fishery in the western English Channel, between June and September 1998–2011, was quantified using generalized additive models (GAMs). Sea surface temperature (SST) explained 1·4% of GAM deviance, and highest CPUE occurred at 16·7° C, reflecting the optimal thermal preferences of this species. Surface chlorophyll a concentration (CHL) significantly affected CPUE and caused 27·5% of GAM deviance. Additionally, increasing CHL led to rising CPUE, probably due to higher productivity supporting greater prey biomass. The density of shelf-sea tidal mixing fronts explained 5% of GAM deviance, but was non-significant, with increasing front density negatively affecting CPUE. Time-lagged frontal density significantly affected CPUE, however, causing 12·6% of the deviance in a second GAM and displayed a positive correlation. This outcome suggested a delay between the evolution of frontal features and the subsequent accumulation of productivity and attraction of higher trophic level predators, such as P. glauca.

Quantifying the impact of environmental variables upon catch-per-unit-effort of the Blue Shark Prionace glauca in the Western English Channel

The effect of environmental variables on blue shark Prionace glauca catch per unit effort (CPUE) in a recreational fishery in the western English Channel, between June and September 1998–2011, was quantified using generalized additive models (GAMs). Sea surface temperature (SST) explained 1·4% of GAM deviance, and highest CPUE occurred at 16·7° C, reflecting the optimal thermal preferences of this species. Surface chlorophyll a concentration (CHL) significantly affected CPUE and caused 27·5% of GAM deviance. Additionally, increasing CHL led to rising CPUE, probably due to higher productivity supporting greater prey biomass. The density of shelf-sea tidal mixing fronts explained 5% of GAM deviance, but was non-significant, with increasing front density negatively affecting CPUE. Time-lagged frontal density significantly affected CPUE, however, causing 12·6% of the deviance in a second GAM and displayed a positive correlation. This outcome suggested a delay between the evolution of frontal features and the subsequent accumulation of productivity and attraction of higher trophic level predators, such as P. glauca.

Spatio-temporal Bayesian network models with latent variables for revealing trophic dynamics and functional networks in fisheries ecology

Ecosystems consist of complex dynamic interactions among species and the environment, the understanding of which has implications for predicting the environmental response to changes in climate and biodiversity. However, with the recent adoption of more explorative tools, like Bayesian networks, in predictive ecology, few assumptions can be made about the data and complex, spatially varying interactions can be recovered from collected field data. In this study, we compare Bayesian network modelling approaches accounting for latent effects to reveal species dynamics for 7 geographically and temporally varied areas within the North Sea. We also apply structure learning techniques to identify functional relationships such as prey–predator between trophic groups of species that vary across space and time. We examine if the use of a general hidden variable can reflect overall changes in the trophic dynamics of each spatial system and whether the inclusion of a specific hidden variable can model unmeasured group of species. The general hidden variable appears to capture changes in the variance of different groups of species biomass. Models that include both general and specific hidden variables resulted in identifying similarity with the underlying food web dynamics and modelling spatial unmeasured effect. We predict the biomass of the trophic groups and find that predictive accuracy varies with the models' features and across the different spatial areas thus proposing a model that allows for spatial autocorrelation and two hidden variables. Our proposed model was able to produce novel insights on this ecosystem's dynamics and ecological interactions mainly because we account for the heterogeneous nature of the driving factors within each area and their changes over time. Our findings demonstrate that accounting for additional sources of variation, by combining structure learning from data and experts' knowledge in the model architecture, has the potential for gaining deeper insights into the structure and stability of ecosystems. Finally, we were able to discover meaningful functional networks that were spatially and temporally differentiated with the particular mechanisms varying from trophic associations through interactions with climate and commercial fisheries.