La transformación de rotación en el espacio: diseño curricular e integración en el aula del ambiente de geometría dinámica Cabri 3D

Se busca generar una discusión sobre el proceso de diseño y sistematización de una experiencia de aula en la cual se integra el Ambiente de Geometría Dinámica (AGD) Cabri 3D en el aprendizaje de la transformación de rotación en el espacio. En nuestra propuesta, encontramos investigaciones importantes en didáctica de las matemáticas que han puesto en evidencia las dificultades que los estudiantes presentan comúnmente en la exploración de propiedades de los objetos geométricos en el espacio, e incluso la representación de los mismos en él. Por lo cual, la comunicación se apoya en una aproximación instrumental que busca dar cuenta del papel mediador de Cabri 3D como un instrumento construido por el sujeto en el contexto de aprendizaje de la geometría. La propuesta se basa en el diseño de una situación didáctica en la que se integra el AGD Cabri 3D; hemos introducido una categoría que caracteriza el objeto matemático a movilizar en la secuencia de situaciones didácticas, esta categoría es la transformación de rotación en el espacio. La primera caracterización debe darse desde el reconocimiento de la Geometría transformacional como una alternativa para que los estudiantes construyan conocimiento del espacio a partir de la exploración y actuación sobre el mismo, así en la propuesta de la secuencia didáctica se tomara en consideración que la transformación de rotación posibilita la exploración de aspectos complejos tales como el sentido, la magnitud angular y la invarianza de propiedades. Esta última (la invarianza de propiedades) es uno de los aspectos más importante que se deberán distinguir en el diseño de la secuencia didáctica; en la composición de rotaciones por ejemplo, se reconoce como importante que los estudiantes tengan la capacidad de poder determinar cuáles objetos geométricos, puestos en juego en la transformación, conservan sus propiedades, así como poder determinar dentro de la rotación qué se conserva invariante. La segunda caracterización es el reconocimiento de la visualización como medio para que el estudiante interprete la información gráfica de conceptos matemáticos que se le presentan, con el fin de resolver un problema y realizar conjeturas acerca de la noción matemática que está trabajando. La pregunta central para animar la discusión en torno a nuestra comunicación es la siguiente: ¿Cómo influye el uso de Cabri 3D en el estudio del espacio y la exploración de la noción de transformación de rotación en el espacio?, ¿En la organización de la clase y los dispositivos que se deben implementar en la misma?

El modelado en Cabri de la función cuadrática como estrategia de verificación y generalización en la solución de un problema de optimización

Este articulo reporta el trabajo de estudiantes de noveno a undécimo grado en la solución de un problema de optimización, en donde el modelado juega un papel principal puesto que les permitió llegar a conclusiones y generalizaciones que no fueron posibles a través del lápiz y el papel. Se comentan las estrategias y procedimientos que siguieron los estudiantes y se destaca la importancia de la mediación instrumental a través de la modelación en el proceso de verificación de la solución del problema.

El estudio de los parámetros por medio de tecnologías híbridas

Los estudiantes de enseñanza media se enfrentan al uso e interpretación de los parámetros en funciones polinomiales, lugares geométricos y expresiones algebraicas. Este hecho conduce a la necesidad de diferenciar los parámetros de otro tipo de literales como variables o incógnitas. Esta investigación indaga sobre la influencia que pueden tener dos entornos tecnológicos sobre la comprensión de la polisemia de las literales, bajo el telón de fondo de los Modelos Teóricos Locales y de la Aproximación Instrumental.

La función seno mediada por la calculadora TI-92+

Se presentan en este reporte algunos resultados obtenidos en el aula de matemática a propósito del desarrollo de la situación problema: ¿Qué relación existe entre el ángulo en posición normal y el cociente del lado opuesto y la hipotenusa del triángulo rectángulo? (Fig. 1) Esta actividad se implementó con el objetivo de contribuir al desarrollo del pensamiento variacional de los alumnos de 10º grado jornada de la tarde del Colegio Nacional Loperena de Valledupar, a través de la mediación instrumental de la calculadora algebraica TI-92+ y el uso de las distintas representaciones semióticas para movilizar el aprendizaje de la red conceptual subyacente a la función Seno.

La calculadora TI 92 plus y el CBR en la modelación del movimiento pendular

La introducción a la clase de matemáticas de la calculadora TI 92 Plus y otros dispositivos, tales como el CBR, están generando una nueva cultura matemática, caracterizar algunos rasgos de éste fenómeno educativo en la modelación del movimiento pendular es el propósito central de la presente investigación. El trabajo de los estudiantes permitió observar en la práctica los constitutivos del marco teórico del proyecto de incorporación de nuevas tecnologías al currículo de matemáticas de Colombia, como son: mediación instrumental, representaciones ejecutables, cognición situada, solución de problemas, fluidez algorítmica y fluidez conceptual.

Un esquema para la comprensión de la recta tangente en un entorno tecnológico

Presentamos una investigación cuyo objetivo es analizar la comprensión de la recta tangente en un entorno de aprendizaje en el que se puede usar un CAS. Desde las perspectivas históricas y cognitivas (APOS) analizaremos una serie textos de Bachillerato e Ingeniería que nos permitirá fijar una propuesta para la comprensión de la recta tangente como el límite de una sucesión de rectas secantes que tienen en común el punto de tangencia. Finalmente, mostramos unas herramientas diseñadas con el asistente matemático MATLAB© (génesis instrumental), accesibles online, que pueden ayudar a los estudiantes, especialmente en el registro gráfico, a construir los objetos cognitivos descritos en la descomposición genética.

Adaptación e implementación de recursos didácticos para la enseñanza de ecuaciones de primer y segundo grado a niños con discapacidad visual en un aula inclusiva

Los procedimientos, gráficos, operaciones y procesos en las matemáticas hacen necesaria la implementación de recursos didácticos que permitan facilitar el aprendizaje de los contenidos de ella. Por esto son indispensables en la enseñanza de las matemáticas como instrumentos de apoyo que favorecen el proceso de matematización y representación de ideas matemáticas. Esto es una gran dificultad para el niño con discapacidad visual ya que en la educación matemática hacen falta materiales didácticos adaptados lo cuales mejoren el ritmo de trabajo y rendimiento a la hora de aprender haciendo uso de una Didáctica Especial de la Matemática para ciegos que permita una adecuación de materiales pedagógicos e instrumental de trabajo para esta población.

L'histoire assassinee: Manfredo Tafuri and the present

Italian historian Manfredo Tafuri develops his ‘historical project’ in architecture during the 1960’s and 1970’s in three seminal books, which reach the English speaking specialist audience with a certain delay. Histories and Theories of Architecture (1968), which prepares the ground for the redefinition of a critical and independent history of architecture is first translated in English in 1979. Architecture and Utopia (Progetto e utopia, 1973) is translated in 1976, and becomes a point of reference for architectural histories and for the definition of architectural theories, mainly in the United States. The Sphere and the Labyrinth (1980), translated in 1987, is the text which formally defines and presents the ‘historical project’. Tafuri’s dense and highly politicized prose is often subjected in the English versions to numerous simplifications and reductive interpretations. Yet, the time lag and the space between languages that these translations occupy are inhabited by polemical and fertile reactions to the texts from the world of architectural design. Symptomatic of all, Aldo Rossi’s L’architecture assassinée, a rebuke in drawing to some of Tafuri’s remarks in Architecture and Utopia that seemed to suggest -but the interpretation is arguable– the ‘death’ of architecture as project (progetto). Tafuri’s texts instigate a dialogue between architectural history and practice, particularly relevant at a time in the development of the discipline when history was being redefined in its critical role as a ‘project’ –thus appropriating the active and propositional role traditionally assigned to architectural design–, while architectural design –still coping with the legacy of Modernism and with changed production systems- often found itself relegated to the paper of exhibitions, competitions and theoretical projects. This paper explores the relationship between architectural history and design in Tafuri’s work, focusing on recent reconsideration and interpretations of his work. It argues that, beyond instrumental simplifications, Tafuri’s ‘project’ remains active and essential in architecture’s critical culture today.

Interlocking directorships

[Introduction] When a director of one company at the same time serves on the board of another company, the two companies are said to be interlocked by that director. Through this linkage each company has potential access to information about the activities of the other, either explicitly as intelligence transferred by the director or implicitly in shaping the director’s perspective and general views. Director interlocks formed by executive directors, employed by the firm, are generally interpreted as more instrumental for the firm than those formed by non-executive directors. Firms are often interlocked with more than one other firm and those firms, in turn, with others; a web of social relationships envelops business.

Elemental analysis of soil samples for forensic purposes by inductively coupled plasma spectrometry - precision considerations

Major and trace elemental composition provides a powerful basis for forensic comparison of soils, sediments and rocks. However, it is important that the potential 'errors' associated with the procedures are fully understood and quantified, and that standard protocols are applied for sample preparation and analysis. This paper describes such a standard procedure and reports results both for instrumental measurement precision (repeatability) and overall 'method' precision (reproducibility). Results obtained both for certified reference materials and example soils show that the instrumental measurement precision (defined by the coefficient of variation, CV) for most elements is better than 2-3%. When different solutions were prepared from the same sample powder, and from different sub-sample powders prepared from the same parent sample, the CV increased to c. 5-6% for many elements. The largest variation was found in results for certified reference materials generated from 23 instrument runs over an 18 month period (mean CV=c. 11%). Some elements were more variable than others. W was found to be the most variable and the elements V, Cr, Co, Cu, Ni and Pb also showed higher than average variability. SiO2, CaO, Al2O3 and Fe2O3, Rb, Sr, La, Ce, Nd and Sm generally showed lower than average variability, and therefore provided the most reliable basis for inter-sample comparison. It is recommended that, whenever possible, samples relating to the same investigation should be analysed in the same sample run, or at least sequential runs.

Evaluation of the new ESR network software for the retrieval of direct sun products from cimel ce318 and prede pom01 sun-sky radiometers.

The European Skynet Radiometers network (EuroSkyRad or ESR) has been recently established as a research network of European PREDE sun-sky radiometers. Moreover, ESR is federated with SKYNET, an international network of PREDE sun-sky radiometers mostly present in East Asia. In contrast to SKYNET, the European network also integrates users of the CIMEL CE318 sky–sun photometer. Keeping instrumental duality in mind, a set of open source algorithms has been developed consisting of two modules for (1) the retrieval of direct sun products (aerosol optical depth, wavelength exponent and water vapor) from the sun extinction measurements; and (2) the inversion of the sky radiance to derive other aerosol optical properties such as size distribution, single scattering albedo or refractive index. In this study we evaluate the ESR direct sun products in comparison with the AERosol RObotic NETwork (AERONET) products. Specifically, we have applied the ESR algorithm to a CIMEL CE318 and PREDE POM simultaneously for a 4-yr database measured at the Burjassot site (Valencia, Spain), and compared the resultant products with the AERONET direct sun measurements obtained with the same CIMEL CE318 sky–sun photometer. The comparison shows that aerosol optical depth differences are mostly within the nominal uncertainty of 0.003 for a standard calibration instrument, and fall within the nominal AERONET uncertainty of 0.01–0.02 for a field instrument in the spectral range 340 to 1020 nm. In the cases of the Ångström exponent and the columnar water vapor, the differences are lower than 0.02 and 0.15 cm, respectively. Therefore, we present an open source code program that can be used with both CIMEL and PREDE sky radiometers and whose results are equivalent to AERONET and SKYNET retrievals.

The emergence of automated high-frequency flow cytometry: revealing temporal and spatial phytoplankton variability

Phytoplankton observation is the product of a number of trade-offs related to sampling processes, required level of diversity and size spectrum analysis capabilities of the techniques involved. Instruments combining the morphological and high-frequency analysis for phytoplankton cells are now available. This paper presents an application of the automated high-resolution flow cytometer Cytosub as a tool for analysing phytoplanktonic cells in their natural environment. High resolution data from a temporal study in the Bay of Marseille (analysis every 30 min over 1 month) and a spatial study in the Southern Indian Ocean (analysis every 5 min at 10 knots over 5 days) are presented to illustrate the capabilities and limitations of the instrument. Automated high-frequency flow cytometry revealed the spatial and temporal variability of phytoplankton in the size range 1−∼50 μm that could not be resolved otherwise. Due to some limitations (instrumental memory, volume analysed per sample), recorded counts could be statistically too low. By combining high-frequency consecutive samples, it is possible to decrease the counting error, following Poisson’s law, and to retain the main features of phytoplankton variability. With this technique, the analysis of phytoplankton variability combines adequate sampling frequency and effective monitoring of community changes.

The biogeochemical structuring role of horizontal stirring: Lagrangian perspectives on iron delivery downstream of the Kerguelen Plateau

Field campaigns are instrumental in providing ground truth for understanding and modeling global ocean biogeochemical budgets. A survey however can only inspect a fraction of the global oceans, typically a region hundreds of kilometers wide for a temporal window of the order of (at most) several weeks. This spatiotemporal domain is also the one in which the mesoscale activity induces through horizontal stirring a strong variability in the biogeochemical tracers, with ephemeral, local contrasts which can easily mask the regional and seasonal gradients. Therefore, whenever local in situ measures are used to infer larger-scale budgets, one faces the challenge of identifying the mesoscale structuring effect, if not simply to filter it out. In the case of the KEOPS2 investigation of biogeochemical responses to natural iron fertilization, this problem was tackled by designing an adaptive sampling strategy based on regionally optimized multisatellite products analyzed in real time by specifically designed Lagrangian diagnostics. This strategy identified the different mesoscale and stirring structures present in the region and tracked the dynamical frontiers among them. It also enabled back trajectories for the ship-sampled stations to be estimated, providing important insights into the timing and pathways of iron supply, which were explored further using a model based on first-order iron removal. This context was essential for the interpretation of the field results. The mesoscale circulation-based strategy was also validated post-cruise by comparing the Lagrangian maps derived from satellites with the patterns of more than one hundred drifters, including some adaptively released during KEOPS2 and a subsequent research voyage. The KEOPS2 strategy was adapted to the specific biogeochemical characteristics of the region, but its principles are general and will be useful for future in situ biogeochemical surveys.

Could benzalkonium chloride be a suitable alternative to mercuric chloride for preservation of seawater samples?

Instrumental equipment unsuitable or unavailable for fieldwork as well as lack of ship space can necessitate the preservation of seawater samples prior to analysis in a shore-based laboratory. Mercuric chloride (HgCl2/ is routinely used for such preservation, but its handling and subsequent disposal incur environmental risks and significant expense. There is therefore a strong motivation to find less hazardous alternatives. Benzalkonium chloride (BAC) has been used previously as microbial inhibitor for freshwater samples. Here, we assess the use of BAC for marine samples prior to the measurement of oxygen-to-argon (O2 = Ar) ratios, as used for the determination of biological net community production. BAC at a concentration of 50 mg dm-3 inhibited microbial activity for at least 3 days in samples tested with chlorophyll a (Chl a) concentrations up to 1 mgm-3. BAC concentrations of 100 and 200 mg dm

Biomonitoring of air pollutants by using lichens (Evernia prunastri) in areas between Kenitra and Mohammedia cities in Morocco.

In this study, Evernia prunastri, a lichen growing in its natural habitat in Morocco was analysed for the concentration of five heavy metals (Fe, Pb, Zn, Cu and Cr) from eleven sites between Kenitra and Mohammedia cities. The control site was Dar Essalam, an isolated area with low traffic density and dense vegetation. In the investigated areas, the concentration of heavy metals was correlated with vehicular traffic, industrial activity and urbanization. The total metal concentration was highest in Sidi Yahya, followed by Mohammedia and Bouznika. The coefficient of variation was higher for Pb and lower for Cu, Zn and Fe. The concentrations of most heavy metals in the thalli differed significantly between sites (p<0.01). Principal component analysis (PCA) revealed a significant correlation between heavy metal accumulation and atmospheric purity index. This study demonstrated also that the factors most strongly affecting the lichen flora were traffic density, the petroleum industry and paper factories in these areas. Overall, these results suggest that the index of atmospheric purity and assessment of heavy metals in lichen thalli are good indicators of the air quality at the studied sites.