Mathematical Communication, Conceptual Understanding, and Students' Attitudes Toward Mathematics

This action research study of my 8th grade classroom investigated the use of mathematical communication, through oral homework presentations and written journals entries, and its impact on conceptual understanding of mathematics. This change in expectation and its impact on students’ attitudes towards mathematics was also investigated. Challenging my students to communicate mathematics both orally and in writing deepened the students’ understanding of the mathematics. Levels of understanding deepened when a variety of instructional methods were presented and discussed where students could comprehend the ideas that best suited their learning styles. Increased understanding occurred through probing questions causing students to reflect on their learning and reevaluate their reasoning. This transpired when students were expected to write more than one draft to math journals. By making students aware of their understanding through communicating orally and in writing, students realized that true understanding did not come from mere homework completion, but from evaluating and assessing their own and other’s ideas and reasoning. I discovered that when students were challenged to communicate their reasoning both orally and in writing, students enjoyed math more and thought math was more fun. As a result of this research, I will continue to require students to communicate their thinking and reasoning both orally and in writing.

Motivating Middle School Mathematics Students

In this action research study I examined the relationship between the teacher, the students and the types of motivation used in mathematics. I specifically studied the mathematic teachers at my school and my seventh grade mathematics students. Motivating middle school students is difficult and the types of motivation can be as numerous as the number of students studied. I discovered that the teachers used multiple motivating tactics from praise, to extra time spent with a student, to extra fun activities for the class. I also discovered that in many instances, the students’ perception of mathematics was predetermined or predetermined by parental perceptions of mathematics. The social environment of the student and a sense of belonging also plays a role in how motivated a student stays. As a result of this research, I plan to notify the mathematics teachers at my school of the most effective types of motivation so we can become a more effective mathematics department.

Is Competition Making a Comeback? Discovering Methods to Keep Female Adolescents Engaged in STEM: A Phenomenological Approach

The decreasing number of women who are graduating in the Science, Technology, Engineering and Mathematics (STEM) fields continues to be a major concern. Despite national support in the form of grants provided by National Science Foundation, National Center for Information and Technology and legislation passed such as the Deficit Reduction Act of 2005 that encourages women to enter the STEM fields, the number of women actually graduating in these fields is surprisingly low. This research study focuses on a robotics competition and its ability to engage female adolescents in STEM curricula. Data have been collected to help explain why young women are reticent to take technology or engineering type courses in high school and college. Factors that have been described include attitudes, parental support, social aspects, peer pressure, and lack of role models. Often these courses were thought to have masculine and “nerdy” overtones. The courses were usually majority male enrollments and appeared to be very competitive. With more female adolescents engaging in this type of competitive atmosphere, this study gathered information to discover what about the competition appealed to these young women. Focus groups were used to gather information from adolescent females who were participating in the First Lego League (FLL) and CEENBoT competitions. What enticed them to participate in a curriculum that data demonstrated many of their peers avoided? FLL and CEENBoT are robotics programs based on curricula that are taught in afterschool programs in non-formal environments. These programs culminate in a very large robotics competition. My research questions included: What are the factors that encouraged participants to participate in the robotics competition? What was the original enticement to the FLL and CEENBoT programs? What will make participants want to come back and what are the participants’ plans for the future? My research mirrored data of previous findings such as lack of role models, the need for parental support, social stigmatisms and peer pressure are still major factors that determine whether adolescent females seek out STEM activities. An interesting finding, which was an exception to previous findings, was these female adolescents enjoyed the challenge of the competition. The informal learning environments encouraged an atmosphere of social engagement and cooperative learning. Many volunteers that led the afterschool programs were women (role models) and a majority of parents showed support by accommodating an afterschool situation. The young women that were engaged in the competition noted it was a friendly competition, but they were all there to win. All who participated in the competition had a similar learning environment: competitive but cooperative. Further research is needed to determine if it is the learning environment that lures adolescent females to the program and entices them to continue in the STEM fields or if it is the competitive aspect of the culminating activity. Advisors: James King and Allen Steckelberg

When the Practice of Theorizing Meets the Theorizing of Practice. Social Knowledge Making in Organization Science Academia and Managerial Communities

The aim of the present work is to contribute to a better understanding of the relation between organization theory and management practice. It is organized as a collection of two papers, a theoretical and conceptual contribution and an ethnographic study. The first paper is concerned with systematizing different literatures inside and outside the field of organization studies that deal with the theory-practice relation. After identifying a series of positions to the theory-practice debate and unfolding some of their implicit assumptions and limitations, a new position called entwinement is developed in order to overcome status quo through reconciliation and integration. Accordingly, the paper proposes to reconceptualize theory and practice as a circular iterative process of action and cognition, science and common-sense enacted in the real world both by organization scholars and practitioners according to purposes at hand. The second paper is the ethnographic study of an encounter between two groups of expert academics and practitioners occasioned by a one-year executive business master in an international business school. The research articulates a process view of the knowledge exchange between management academics and practitioners in particular and between individuals belonging to different communities of practice, in general, and emphasizes its dynamic, relational and transformative mechanisms. Findings show that when they are given the chance to interact, academics and practitioners set up local provisional relations that enable them to act as change intermediaries vis-a-vis each other’s worlds, without tying themselves irremediably to each other and to the scenarios they conjointly projected during the master’s experience. Finally, the study shows that provisional relations were accompanied by a recursive shift in knowledge modes. While interacting, academics passed from theory to practical theorizing, practitioners passed from an involved practical mode to a reflexive and quasi-theoretical one, and then, as exchanges proceeded, the other way around.

Diversity and local democracy. The case of Republic of Macedonia - implications of ethnic diversity on municipal decision making and organizational performance

This research seeks to review the level of knowledge achieved in interpreting the relationship between the ethnic diversity at the workplace in the public sector and the organizational performance; as well as seeks to contribute in understanding the implications of this relationship. The study commenced with investigating the academic research in the relevant area addressing the following research questions: (a) How are diversity management and organizational performance conceptualized? (b) What are the existing findings of research concerning diversity at the workplace in the public organizations and organizational performance? (c) What factors intervene the relationship between the diversity and organizational performance? Based on the findings from the review of the academic research, this study seeks to contribute in understanding the ethnic diversity – performance relationship and its mplications at the local level in the Macedonian context. The reform process in Macedonia as a multicultural society, where for many years, inter-ethnic relations have been one of the most sensitive political issues, affecting both the stability of the country and the progress, focused mainly on the implementation of the decentralization and inclusion of ethnic minorities in the decision making process. With the implementation of the Ohrid Framework Agreement workforce at the units of local self-government in Republic of Macedonia is becoming more balanced with respect to ethnic minorities, with more workforce participation than ever by Albanians, Turks, Roma and other minorities. As public organizations at local level become more diverse along ethnic lines, it makes sense to pay more attention to how different ethnic groups interact with one another at work. Thus it gives additional importance on the research question addressed in the study and gives significance of the research in a broader scope.

Simulating dioxane transport in a heterogeneous glacial aquifer system (Washtenaw County, Michigan) using publicly available models and data

The primary challenge in groundwater and contaminant transport modeling is obtaining the data needed for constructing, calibrating and testing the models. Large amounts of data are necessary for describing the hydrostratigraphy in areas with complex geology. Increasingly states are making spatial data available that can be used for input to groundwater flow models. The appropriateness of this data for large-scale flow systems has not been tested. This study focuses on modeling a plume of 1,4-dioxane in a heterogeneous aquifer system in Scio Township, Washtenaw County, Michigan. The analysis consisted of: (1) characterization of hydrogeology of the area and construction of a conceptual model based on publicly available spatial data, (2) development and calibration of a regional flow model for the site, (3) conversion of the regional model to a more highly resolved local model, (4) simulation of the dioxane plume, and (5) evaluation of the model's ability to simulate field data and estimation of the possible dioxane sources and subsequent migration until maximum concentrations are at or below the Michigan Department of Environmental Quality's residential cleanup standard for groundwater (85 ppb). MODFLOW-2000 and MT3D programs were utilized to simulate the groundwater flow and the development and movement of the 1, 4-dioxane plume, respectively. MODFLOW simulates transient groundwater flow in a quasi-3-dimensional sense, subject to a variety of boundary conditions that can simulate recharge, pumping, and surface-/groundwater interactions. MT3D simulates solute advection with groundwater flow (using the flow solution from MODFLOW), dispersion, source/sink mixing, and chemical reaction of contaminants. This modeling approach was successful at simulating the groundwater flows by calibrating recharge and hydraulic conductivities. The plume transport was adequately simulated using literature dispersivity and sorption coefficients, although the plume geometries were not well constrained.

Predictors of satisfaction with treatment decision, decision-making preferences, and main treatment goals in patients with advanced cancer

Purpose This study investigated satisfaction with treatment decision (SWTD), decision-making preferences (DMP), and main treatment goals, as well as evaluated factors that predict SWTD, in patients receiving palliative cancer treatment at a Swiss oncology network. Patients and methods Patients receiving a new line of palliative treatment completed a questionnaire 4–6 weeks after the treatment decision. Patient questionnaires were used to collect data on sociodemographics, SWTD (primary outcome measure), main treatment goal, DMP, health locus of control (HLoC), and several quality of life (QoL) domains. Predictors of SWTD (6 = worst; 30 = best) were evaluated by uni- and multivariate regression models. Results Of 480 participating patients in eight hospitals and two private practices, 445 completed all questions regarding the primary outcome measure. Forty-five percent of patients preferred shared, while 44 % preferred doctor-directed, decision-making. Median duration of consultation was 30 (range: 10–200) minutes. Overall, 73 % of patients reported high SWTD (≥24 points). In the univariate analyses, global and physical QoL, performance status, treatment goal, HLoC, prognosis, and duration of consultation were significant predictors of SWTD. In the multivariate analysis, the only significant predictor of SWTD was duration of consultation (p = 0.01). Most patients indicated hope for improvement (46 %), followed by hope for longer life (26 %) and better quality of life (23 %), as their main treatment goal. Conclusion Our results indicate that high SWTD can be achieved in most patients with a 30-min consultation. Determining the patient’s main treatment goal and DMP adds important information that should be considered before discussing a new line of palliative treatment.

How Plankton Swim: An Interdisciplinary Approach for Using Mathematics & Physics to Understand the Biology of the Natural World

The authors have developed and field-tested high school-level curricular materials that guide students to use biology, mathematics, and physics to understand plankton and how these tiny organisms move in a world where their intuition does not apply. The authors chose plankton as the focus of their materials primarily because the challenges faced by plankton are novel problems to most students, forcing adoption of new perspectives and making the study of plankton exciting. Additional reasons that they chose plankton to focus on include their ecological importance, their availability to most teachers and students, the ease with which they can be collected and observed, and the current focus of some scientific researchers on their movement and behavior. These curricular materials include a series of inquiry-based, hands-on exercises designed to be accessible to students with a range of backgrounds. Many of these materials could be adapted for use by middle-school, and/or college-level students. In this article, the authors describe sample lessons, summarize what worked well, and flag obstacles they encountered while integrating mathematics and physics into the biology classroom.

The Learning of the Mathematical Models to Aid Decision Making in the High Level Engineering Schools?

At present, in the University curricula in most countries, the decision theory and the mathematical models to aid decision making is not included, as in the graduate program like in Doctored and Master´s programs. In the Technical School of High Level Agronomic Engineers of the Technical University of Madrid (ETSIA-UPM), the need to offer to the future engineers training in a subject that could help them to take decisions in their profession was felt. Along the life, they will have to take a lot of decisions. Ones, will be important and others no. In the personal level, they will have to take several very important decisions, like the election of a career, professional work, or a couple, but in the professional field, the decision making is the main role of the Managers, Politicians and Leaders. They should be decision makers and will be paid for it. Therefore, nobody can understand that such a professional that is called to practice management responsibilities in the companies, does not take training in such an important matter. For it, in the year 2000, it was requested to the University Board to introduce in the curricula an optional qualified subject of the second cycle with 4,5 credits titled " Mathematical Methods for Making Decisions ". A program was elaborated, the didactic material prepared and programs as Maple, Lingo, Math Cad, etc. installed in several IT classrooms, where the course will be taught. In the course 2000-2001 this subject was offered with a great acceptance that exceeded the forecasts of capacity and had to be prepared more classrooms. This course in graduate program took place in the Department of Applied Mathematics to the Agronomic Engineering, as an extension of the credits dedicated to Mathematics in the career of Engineering.

Resonancias de los paradigmas científicos en las arquitecturas de la Escuela de Madrid

Los años cincuenta y sesenta son los años de la incorporación definitiva de la arquitectura española al panorama internacional. Entre los arquitectos que protagonizan ese salto sin retorno, se encuentra el grupo de aquellos que unos años más tarde serán denominados por Juan Daniel Fullaondo como Escuela de Madrid. Carlos Flores, en su libro Arquitectura Española Contemporánea 1880-1950, se refiere a esos arquitectos como aquellos que se aplicaban a la difícil tarea de restablecer en España un tipo de arquitectura que conectaba con las teorías, soluciones y lenguajes establecidos por Europa durante las primeras décadas del siglo XX. Sigfried Giedion plantea en Espacio, Tiempo y Arquitectura el origen de una nueva tradición, surgida a partir de la revolución óptica de principios de siglo. Con tradición se refiere a una nueva cultura, que abarca la interrelación de las diferentes actividades del hombre: la similitud de los métodos que se usan en la arquitectura, la construcción, la pintura, el urbanismo o la ciencia. Esa novedad, fundamentada en su independencia y desvinculación con el periodo anterior, se inscribe dentro del esquema evolutivo que Thomas Kuhn plantea en su texto La Estructura de la Revoluciones Científicas, conforme a periodos no acumulativos. Kuhn habla del surgimiento de anomalías en cada periodo, origen de las crisis de pensamiento cuya explicación precisará un necesario cambio paradigmático. En la ciencia, en el campo de la óptica Thomas Young demuestra a principios del siglo XIX la naturaleza ondulatoria de la luz con su experimento de doble rendija; en el electromagnetismo se produce el salto conceptual que supone la postulación de la existencia del campo eléctrico por parte de Michael Faraday, y en termodinámica la consideración apuntada por Planck de que la radiación de la energía de produce de forma discreta, a través de cuantos. En las artes plásticas, paralelamente, Gleizes y Metzinger, en su recopilación de logros cubistas recogida en Sobre el Cubismo, hablan de la evolución sufrida durante el siglo XIX por la pintura: desde el idealismo de principios de siglo, para pasando por el realismo y la representación impresionista de la realidad, concluir prescindiendo de la perspectiva clásica. También la matemática, una vez desarrolladas por Gauss o Lobachevsky y Bolyai geometrías coherentes que incumplen el quinto postulado de Euclides, terminará dando validez a través de Riemann a los espacios ambiente en los que habitan dichas geometrías, desvinculando la relación directa entre espacio geométrico –el espacio ambiente al que da lugar un tipo de geometría- y el espacio físico. Capi Corrales refleja en su libro Contando el Espacio, cómo hasta la teoría de la relatividad y el cubismo, las geometrías no euclídeas no se hicieron notorias también fuera del campo de las matemáticas. El origen de la nueva tradición con la que Giedion se refiere a la nueva cultura de la modernidad coincide con los saltos paradigmáticos que suponen la teoría de la relatividad en las ciencias y el cubismo en las artes plásticas. Ambas se prolongan durante las primeras décadas hasta la teoría cuántica y la abstracción absoluta, barreras que los dos principales precursores de la relatividad y el cubismo, Einstein y Picasso, nunca llegan a franquear. En ese sentido Giedion habla también, además del origen, de su desarrollo, e incorpora las aportaciones periféricas en la arquitectura de Brasil, Japón o Finlandia, incluyendo por tanto la revisión orgánica propugnada por Zevi como parte de esa nueva tradición, quedando abierta a la incorporación tardía de nuevas aportaciones al desarrollo de esa cultura de la modernidad. Eliminado el concepto de la estética trascendental de Kant del tiempo como una referencia absoluta, y asumido el valor constante de la velocidad de la luz, para la teoría de la relatividad no existe una simultaneidad auténtica. Queda así fijada la velocidad de la luz como uno de los límites del universo, y la equivalencia entre masa y energía. En el cubismo la simultaneidad espacial viene motivada por la eliminación del punto de vista preferente, cuyo resultado es la multiplicidad descriptiva de la realidad, que se visualiza en la descomposición en planos, tanto del objeto como del espacio, y la consecuente continuidad entre fondo y figura que en arquitectura se refleja en la continuidad entre edificio y territorio. Sin la consideración de un punto de vista absoluto, no existe una forma auténtica. El cubismo, y su posterior desarrollo por las vanguardias plásticas, hacen uso de la geometría como mecanismo de recomposición de la figura y el espacio, adoptando mecanismos de penetración, superposición y transparencia. Gyorgy Kepes indica en El Lenguaje de la Visión que la descomposición cubista del objeto implica la sucesiva autonomía de los planos, hasta convertirse en elementos constituyentes. Algo que refleja las axonometrías arquitectónicas de Van Doesburg y que culmina con los espacios propuestos por Mies van der Rohe en sus primeros proyectos europeos. Estos mecanismos, encuentran eco en los primeros planteamientos de Javier Carvajal: en la ampliación del Panteón de españoles del cementerio de Campo Verano, un recinto virtual reconstruido mentalmente a partir del uso de tres únicos planos; o en el Pabellón de Nueva York, que organiza su planta baja desde el recorrido, introduciendo el parámetro temporal como una dimensión más. Al uso diferenciado del plano como elemento constituyente, Carvajal incorpora su plegado y su disposición conformando envolventes como mecanismo de cualificación espacial y formal, potenciando la prolongación entre arquitectura y territorio. Una continuidad que quedará culminada en las dos viviendas unifamiliares construidas en Somosaguas. La descomposición volumétrica conduce a unos niveles de abstracción que hace precisa la incorporación de elementos de la memoria -fuentes, patios, celosías…- a modo de red de señales, como las que Picasso y Braque introducen en sus cuadros para permitir su interpretación. Braque insiste en el interés por el espacio que rodea a los objetos. Una búsqueda de la tactilidad del espacio contraria a la perspectiva que aleja el objeto del observador, y que en los jardines de las viviendas de Somosaguas parece emanar de su propia materialidad. Un espacio táctil alejado del espacio geométrico y que Braque identifica con el espacio representativo en el que Poincaré, en La Ciencia y la Hipótesis, ubica nuestras sensaciones. Desdibujar los límites del objeto prolonga el espacio indefinidamente. Con el paso en el arte griego del mito al logos, se abre paso a la matemática como herramienta de comprensión de la naturaleza hasta el siglo XIX. Leon Lederman, en Simetría y la Belleza del Universo, apunta a que una de las mayores contribuciones de la teoría de Einstein es hacer cambiar el modo de pensar la naturaleza, orientándolo hacia la búsqueda de los principios de simetría que subyacen bajo las leyes físicas. Considerando que la simetría es la invariancia de un objeto o un sistema frente a una transformación y que las leyes físicas son las mismas en cualquier punto del espacio, el espacio de nuestro universo posee una simetría traslacional continua. En la ocupación del espacio de las primeras propuestas de Corrales y Molezún aparecen estructuras subyacentes que responden a enlosetados: paralelogramos sometidos a transformaciones continuas, que la naturaleza identifica tridimensionalmente con los grupos cristalográficos. Las plantas del museo de Arte Contemporáneo de la Castellana, la residencia de Miraflores, el pabellón de Bruselas o la torre Peugeot pertenecen a este grupo. La arquitectura como proceso de ocupación continua del territorio y de su trasposición al plano de cubierta, se materializa en líneas estructurales coincidentes con la estructura matemática de sus simetrías de traslación cuya posibilidad de prolongación infinita queda potenciada por el uso de la envolvente transparente. Junto a esta transparencia literal, inherente al material, Colin Rowe y Robert Slutzky nos alertan sobre otra transparencia inherente a la estructura: la transparencia fenomenal, ilustrada por los cuadros de Juan Gris, y cuya intuición aparece reflejada en la casa Huarte en Puerta de Hierro de Madrid. Corrales y Molezún insisten en una lectura de su volumetría alejada de la frontalidad, en la que los contornos de sus cubiertas inclinadas y las visuales tangenciales sugeridas por la organización de sus recorridos introducen una estructura diagonal que se superpone al entendimiento ortogonal de su planta, dibujando una intrincada red de líneas quebradas que permiten al espacio fluctuar entre las secuencia volumétrica propuesta. Los datos relativos al contenido energético de la luz y el concepto de átomo parten de la consideración de la emisión de energía en cuantos realizada por Planck, y concluyen con una circunstancia paradójica: la doble naturaleza de la luz -demostrada por la explicación de Einstein del efecto fotoeléctrico- y la doble naturaleza de la materia -asumida por Bohr y demostrada por el efecto Compton-. Schrödinger y Heisenberg formularán finalmente la ecuación universal del movimiento que rige en las ondas de materia, y cuya representación matemática es lo que se conoce como función de onda. El objeto es así identificado con su función de onda. Su ondulatoriedad expresará la probabilidad de encontrarse en un lugar determinado. Gyorgy Kepes subraya la necesidad de simplificar el lenguaje para pasar de la objetividad que aún permanece en la pintura cubista a la abstracción total del espacio. Y es así como los artistas plásticos reducen los objetos a simples formas geométricas, haciendo aflorar a la vez, las fuerzas plásticas que los tensionan o equilibran, en un proceso que acaba por eliminar cualquier atisbo de materia. Robert Rosenblum en La Pintura Moderna y la Tradición del Romanticismo Nórdico habla de cómo ese rechazo de la materia en favor de un vacío casi impalpable, campos luminosos de color denso que difunden un sereno resplandor y parecen engendrar las energías elementales de la luz natural, está directamente vinculado a la relación con la naturaleza que establece el romanticismo nórdico. La expresión de la energía de la naturaleza concentrada en un vacío que ya había sido motivo de reflexión para Michael Faraday en su postulación del concepto de campo eléctrico. Sáenz de Oíza incide en la expresión de la condición material de la energía en su propuesta junto a José Luis Romany para la capilla en el Camino de Santiago. La evocación de diferentes fuerzas electromagnéticas, las únicas junto a las gravitatorias susceptibles de ser experimentadas por el hombre, aparecerán visualizadas también en el carácter emergente de algunas de sus obras: el Santuario de Aránzazu o Torres Blancas; pero también en la naturaleza fluyente de sus contornos, la dispersión perimetral de los espacios -el umbral como centro del universoo la configuración del límite como respuesta a las tensiones germinales de la naturaleza. Miguel Fisac, a la vuelta de su viaje a los países nórdicos, aborda una simplificación lingüística orientada hacia la adecuación funcional de los espacios. En el Instituto de Daimiel, el Instituto de formación del profesorado o los complejos para los Padres Dominicos en Valladolid o Alcobendas, organiza progresivamente la arquitectura en diferentes volúmenes funcionales, incidiendo de un modo paralelo en la manifestación de los vínculos que se establecen entre dichos volúmenes como una visualización de las fuerzas que los tensionan y equilibran. En ellos la prolongación de la realidad física más allá de los límites de la envolvente ya es algo más que una simple intuición. Un proceso en el que el tratamiento de la luz como un material de construcción más, tendrá un especial protagonismo. En la iglesia de la Coronación, la iluminación del muro curvo escenifica la condición ondulatoria de la luz, manifestándose como si de un patrón de interferencia se tratara. Frente a la disolución de lo material, el espacio se manifiesta aquí como un medio denso, alejado de la tradicional noción de vacío. Una doble naturaleza, onda y partícula, que será intuido también por Fisac en la materia a través de su uso comprometido del hormigón como único material de construcción. Richard Feynmann nos alerta de la ocupación del espacio por multitud de fuerzas electromagnéticas que, al igual que la luz, precisan de receptores específicos para captar su presencia. Sus célebres diagramas suponen además la visualización definitiva de los procesos subatómicos. Al igual que la abstracción absoluta en las artes plásticas, esas representaciones diagramáticas no son asimilables a imágenes obtenidas de nuestra experiencia. Una intuición plasmada en el uso del diagrama, que irán adquiriendo progresivamente los dibujos de Alejandro de la Sota. La sección del gimnasio Maravillas recoge los trazos de sus principales elementos constructivos: estructura, cerramientos, compartimentaciones…, pero también, y con la misma intensidad, los de las fuerzas que generan su espacio, considerando así su condición de elementos constituyentes. El vacío, nos deja claro Sota, es el lugar donde habitan dichas tensiones. La posterior simplificación de las formas acompañadas de la obsesión por su aligeramiento, la casi desaparición de la envolvente, incide en aquella idea con la que Paul Klee define la actividad del artista en su Teoría del Arte Moderno, y en la que se transmite el distanciamiento hacia lo aparente: No se trata de reproducir lo visible, se trata de volver visible. Así, en Bankunión y Aviaco, como en tantos otros proyectos, frente al objetivo de la forma, Sota plantea el límite como la acotación de un ámbito de actuación. Su propia representación aséptica y diagramática transmite la renuncia a una especificidad espacial. Gilles Deleuze expresa ese posicionamiento en Pintura, el Concepto de Diagrama: el diagrama como la posibilidad de cuadros infinitos, o la posibilidad infinita de cuadros. Aparece así una concepción probabilística del espacio en la que frente a la renuncia por la forma, la tendencia al aligeramiento, y lo difuso de su definición – ideas claras, definición borrosa, en palabras de Llinás referidas al modo de operar de Sota-, la insistente atención a algunos elementos como escaleras, protecciones o miradores parece trasmitir la idea de que la arquitectura queda condensada en aquellos acontecimientos que delatan su condición dinámica, transitoria. Primando la relación frente al objeto, el vínculo frente a lo tangible. English summary. The fifties and sixties were the years of the final incorporation of Spanish architecture to the international scene. Among the architects who star that no return leap, is the group of those who a few years later will be named by Juan Daniel Fullaondo as Escuela de Madrid. Carlos Flores, in his book Arquitectura Española Contemporánea 1880-1950, refers to those architects as those that applied to the difficult task of restoring in Spain an architecture that connected with theories, solutions and established languages in Europe during the first decades of the twentieth century. Sigfried Giedion proposes in Space, Time and Architecture, the origin of a new tradition, arising from the optical revolution at the beginning of the century. With tradition he refers to a new culture, covering the interplay of different human activities: the similarity of the methods used in architecture, building, painting, urban planning or science. This new feature, based on its independence and detachment from the previous period, is part of the evolutionary scheme that Thomas Kuhn proposes in his text The Structure of Scientific Revolutions, according to non-accumulative periods. Kuhn talks about the emergence of anomalies in each period, origin of thought crisis whose explanation will require a paradigm shift needed. In science, in the field of optical Thomas Young demonstrates at the early nineteenth century the wave nature of light with its double-slit experiment , in electromagnetism the postulation of the existence of the electric field by Michael Faraday involves a conceptual leap, and in thermodynamic, the consideration pointed by Planck about quantum energy radiation. In the arts, in a parallel process, Gleizes and Metzinger , in his collection of cubism achievements on their book Du Cubisme, speak of evolution occurring during the nineteenth century by the painting: from the idealism of beginning of the century, going for realism and impressionist representation of reality, and finishing regardless of the classical perspective . Mathematics also, once developed by Gauss and Lobachevsky and Bolyai consistent geometries that violate Euclid's fifth postulate , will end validating Riemann’s ambient spaces in which these geometries inhabit, decoupling the direct relationship between geometric space -the space environment that results in a type of geometry- , and physical space. Capi Corrales reflectes in his book Contando el Espacio, that non-Euclidean geometries were not noticeable outside the field of mathematics until the theory of relativity and cubism. The origin of the new tradition that Giedion relates to the new culture of modernity coincides with paradigmatic leaps pointed by the theory of relativity in science and Cubism in the visual arts. Both are extended during the first decades until quantum theory and absolute abstraction, barriers that the two main precursors of relativity and cubism, Einstein and Picasso never overcome. In that sense Giedion speaks about the origin, but also the development, and incorporates peripheral inputs from Brazil, Japan and Finland architecture, thus including organic revision advocated by Zevi as part of this new tradition, being open to the late addition of new contributions to the development of that culture of modernity. Removed the concept of Kant's transcendental aesthetics, of time as an absolute reference, and assumed the constant value of the speed of light, theory of relativity says there is no authentic concurrency. It is thus fixed the speed of light as one of the limits of the universe, and the equivalence of mass and energy. In cubism, spatial simultaneity results from the elimination of preferential points of view, resulting in the multiplicity descriptive of reality, which is displayed in decomposition levels, both the object and the space, and the resulting continuity between figure and background that architecture is reflected in the continuity between building and land. Without the consideration of an absolute point of view, there isn’t an authentic shape. Cubism, and its subsequent development by the vanguard arts, make use of geometry as a means of rebuilding the figure and space, taking penetration mechanisms, overlapping and transparency. Gyorgy Kepes suggest in Languaje of Vision, that cubist decomposition of the object involves successive planes autonomy, to become constituent elements. Something that reflects the Van Doesburg’s architectural axonometrics and culminates with the spaces proposed by Mies van der Rohe in his first European projects. These mechanisms are reflected in the first approaches by Javier Carvajal: the extension of Spanish Pantheon in Campo Verano Cemetery, virtual enclosure mentally reconstructed from 24 the use of only three planes, or in the Spanish Pavilion of New York, which organizes its ground floor from the tour, introducing the time parameter as an additional dimension. Carvajal adds to the differential use of the plane as a constituent, Carvajal incorporates its folding and forming enclosures available as a mechanism for spatial and formal qualification, promoting the extension between architecture and territory. A continuity that will be completed in the two houses built in Somosaguas. Volumetric decomposition, as the fragmentation achieved in the last cubist experiences, needs the incorporation of elements of memory - fountains, patios, shutters...- as a network of signals, such as those introduced by Picasso and Braque in their paintings to allow their interpretation. Braque insists in his interest in the space surrounding the objects. A search of the tactility of space contrary to the perspective, which moves the observer away from the object, and that in the gardens of Somosaguas seems to emanate from its own materiality. A tactile space away from the geometric space and Braque identified with the representative space in which Poincaré in La Science et l´hypothèse, located our feelings. To blur those boundaries of the object extends the space indefinitely. With the passage in Greek art from myth to logos, it opens up to mathematics as a tool for understanding the nature until the nineteenth century. Leon Lederman, in Symmetry and beautiful Universe, suggests that one of the greatest contributions of Einstein's theory is to change the mindset of nature, namely the search for symmetry principles that underlie physical laws. Considering that symmetry is the invariance of an object or system from a transformation and that physical laws are the same at any point in space, the space of our universe has a continuous translational symmetry. In the space occupation of the first proposals by Corrales and Molezún underlying structures appear that match enlosetados: parallelograms under continuous transformations, which nature identifies tridimensionally with the crystallographic groups. Plants in the Contemporary Art Museum in La Castellana, the residence in Miraflores, the Brussels pavilion or the Peugeot tower belong to this group. The architecture as a process of continuous occupation of the territory and of its transposition to the deck, embodied in structural lines coincide with the mathematical structure of the translational symmetry and infinite extension whose possibility is enhanced by the use of the transparent cover. Alongside this literal transparency inherent to the material, Colin Rowe and Robert Slutzky alert us another transparency inherent in the structure: phenomenal transparency, illustrated by the Juan Gris’ works, and whose intuition is reflected in the Huarte’s house in Puerta de Hierro in Madrid. Corrales and Molezún insist on a reading of its volume away from the frontal, in which the outline of their inclined roofs and tangential visual suggested by the organization of his circulations introduce a diagonal structure which overlaps the orthogonal understanding of its plant, drawing an intricate web of broken lines that allow the space fluctuate between the volumetric sequence proposal. Information concerning to the energy mean of light and the concept of atom start from the consideration by Plank about the energy emission, and conclude with a paradoxical situation: the dual nature of light - demonstrated by the explanation of Einstein's photoelectric effect-, and the dual nature of matter -assumed by Bohr and demonstrated by the Compton effect-. Finally, Schrödinger and Heisenberg will formulate the universal movement equation governing in undulatory matter, whose mathematical representation is what is known as a wave function. The object is thus identified with its wave function. Its undulatory expression speaks about the probability of being found in a certain place. Gyorgy Kepes emphasizess the need to simplify the language to move from the objectivity that still remains in the cubist painting to the total abstraction of the space. And this is how artists reduced the objects to simple geometric shapes, making emerge at a time, the plastic forces that tense or balance them, in a process that eventually eliminate any trace of matter. Robert Rosenblum in Modern Painting and the Northern Romantic Tradition. Friedrich to Rothko talks about how this rejection of matter in an almost impalpable vacuum: dense color light fields that broadcast a serene glow and seem to generate the elemental energies of natural light is directly linked to the relationship with nature that sets the northern romanticism. An expression of the power of nature concentrated in a vacuum which had been reason for thought by Michael Faraday in his application of the concept of electric field. Saenz de Oíza touches upon the material expression of the energy in its proposal with Jose Luis Romany to the chapel on the Camino de Santiago. The presence of electromagnetic forces, the only ones with the gravitational one capable of being experienced by the man will also visualize in the emerging nature of some of his works: the sanctuary of Aránzazu or Torres Blancas, but also in the flowing nature of its contours, and the inclusion of interest in the realization of space fluctuating boundary: the threshold as the center of the universe. Miguel Fisac, back from his trip to the Northern Countries, starts on a linguistic simplification oriented to the functional adequacy of spaces. In the Daimiel Institute, in the Institute to Teacher Formation or in the complex to the Dominican Fathers in Valladolid or Alcobendas, progressively organized into different functional volumes architecture, focusing in a parallel way in the manifestation of the links established between these volumes as a visualization of the forces that tense and balance them. The prolongation of the physical reality beyond the limits of the envelope is already something more than a simple intuition. A process in which the treatment of light as a construction material, have a special role. In the Coronation church, curved wall lighting dramatizes the undulatory condition of the light, manifesting as if an interference pattern is involved. Versus the dissolution of the material, the space is expressed here as a dense atmosphere, away from the traditional notion of the vacuum. A dual nature, wave and particle, which is also sensed by Fisac in his committed use of concrete as a unique construction material. Richard Feynman alerts us to the occupation of space by many electromagnetic forces, which like the light, require specific receptors to capture their presence. His famous diagrams also involve the final visualization of atomic processes. As absolute abstraction in the visual arts, these representations are not assimilated to images obtained from our experience. A diagrammatic nature, abstracted from figuration, which will obtein the pictures of Alejandro de la Sota. The section of Maravillas gym collects traces of its main building blocks: structure, enclosures... but also, and with the same intensity, of the forces that generate their space as constituent elements. Sota makes it clear: the vacuum is where inhabit these tensions. The subsequent simplification of forms, accompanied by the obsession with his lightening, the near disappearance of the envelope, touches upon that idea which Paul Klee defines the activity of the artist in his Modern Art Theory, the spacing out to the apparent: it is not to reproduce the visible, it is to turn visible. Thus, in Bankunión and Aviaco, as in many other projects, against the shape, raises the limit as the dimension of a scope. His own aseptic and diagrammatic representation transmits waiver to a spatial specificity that Gilles Deleuze clearly expressed in Painting. The Concept Diagram: The diagram as the possibility of infinite pictures, or infinite possibility of the picture. Thus appears the probabilistic concept of space in which, opposite to the diffuse of its definition -clear ideas, diffuse definition, as Llinas said- the insistent attention to some elements like stairs, guards or lookouts seems to concentrate the architecture in its dynamic condition, transitional. The relationship opposite the object, the link opposite the tangible.

A INFLUÊNCIA DAS PRÁTICAS PEDAGÓGICAS DOCENTES E DAS BARREIRAS DISCENTES SOBRE O DESENVOLVIMENTO DA CRIATIVIDADE DO FUTURO ADMINISTRADOR

As empresas que almejam garantir e melhorar sua posição dentro de em um mercado cada vez mais competitivo precisam estar sempre atualizadas e em constante evolução. Na busca contínua por essa evolução, investem em projetos de Pesquisa & Desenvolvimento (P&D) e em seu capital humano para promover a criatividade e a inovação organizacional. As pessoas têm papel fundamental no desenvolvimento da inovação, mas para que isso possa florescer de forma constante é preciso comprometimento e criatividade para a geração de ideias. Criatividade é pensar o novo; inovação é fazer acontecer. Porém, encontrar pessoas com essas qualidades nem sempre é tarefa fácil e muitas vezes é preciso estimular essas habilidades e características para que se tornem efetivamente criativas. Os cursos de graduação podem ser uma importante ferramenta para trabalhar esses aspectos, características e habilidades, usando métodos e práticas de ensino que auxiliem no desenvolvimento da criatividade, pois o ambiente ensino-aprendizagem pesa significativamente na formação das pessoas. O objetivo deste estudo é de identificar quais fatores têm maior influência sobre o desenvolvimento da criatividade em um curso de graduação em administração, analisando a influência das práticas pedagógicas dos docentes e as barreiras internas dos discentes. O referencial teórico se baseia principalmente nos trabalhos de Alencar, Fleith, Torrance e Wechsler. A pesquisa transversal de abordagem quantitativa teve como público-alvo os alunos do curso de Administração de uma universidade confessional da Grande São Paulo, que responderam 465 questionários compostos de três escalas. Para as práticas docentes foi adaptada a escala de Práticas Docentes em relação à Criatividade. Para as barreiras internas foi adaptada a escala de Barreiras da Criatividade Pessoal. Para a análise da percepção do desenvolvimento da criatividade foi construída e validada uma escala baseada no referencial de características de uma pessoa criativa. As análises estatísticas descritivas e fatoriais exploratórias foram realizadas no software Statistical Package for the Social Sciences (SPSS), enquanto as análises fatoriais confirmatórias e a mensuração da influência das práticas pedagógicas e das barreiras internas sobre a percepção do desenvolvimento da criatividade foram realizadas por modelagem de equação estrutural utilizando o algoritmo Partial Least Squares (PLS), no software Smart PLS 2.0. Os resultados apontaram que as práticas pedagógicas e as barreiras internas dos discentes explicam 40% da percepção de desenvolvimento da criatividade, sendo as práticas pedagógicas que exercem maior influencia. A pesquisa também apontou que o tipo de temática e o período em que o aluno está cursando não têm influência sobre nenhum dos três construtos, somente o professor influencia as práticas pedagógicas.

Parent Loss in Adolescence and its Impact on Sense of Self: When an Adolescent Boy Loses His Mother.

Adolescence is a developmental phase that involves physical, emotional, and cognitive changes. Often this period is one of transition that requires significant adjustment both with the individual and the family. It is considered to start with puberty, sometime between the ages of 10 and 13, and end with the transition into adulthood (Kruse & Walper, 2008). Puberty is a term that is used to describe the physical changes that generally occur during adolescence. It is an aspect of the changes that occur during the overarching phase of development. Within adolescence, individuals are confronted with many developmental tasks such as establishing an individual identity, making decisions about the future, and moving from dependence on families to independence (Austrian, 2008).There are many changes that occur during adolescence, including sexual maturation and functioning, endocrine developments, and skeletal and muscular changes. Boys will see a growth of body, pubic, and facial hair, their voice will deepen, and they will begin having erections and wet dreams (Kruse & Walper, 2008). The accelerated transformation of this phase generally has an emotional impact and individuals may feel concerned or self-conscious about their appearance. Ausubel, Montemayor, and Svajian (1977) suggest that adolescents may be more sensitive during this period of development. This sensitivity may be in part due to the rapid growth resulting in a sense of awkwardness in appearance and physical coordination.

Earth’s Rotation: A Challenging Problem in Mathematics and Physics

A suitable knowledge of the orientation and motion of the Earth in space is a common need in various fields. That knowledge has been ever necessary to carry out astronomical observations, but with the advent of the space age, it became essential for making observations of satellites and predicting and determining their orbits, and for observing the Earth from space as well. Given the relevant role it plays in Space Geodesy, Earth rotation is considered as one of the three pillars of Geodesy, the other two being geometry and gravity. Besides, research on Earth rotation has fostered advances in many fields, such as Mathematics, Astronomy and Geophysics, for centuries. One remarkable feature of the problem is in the extreme requirements of accuracy that must be fulfilled in the near future, about a millimetre on the tangent plane to the planet surface, roughly speaking. That challenges all of the theories that have been devised and used to-date; the paper makes a short review of some of the most relevant methods, which can be envisaged as milestones in Earth rotation research, emphasizing the Hamiltonian approach developed by the authors. Some contemporary problems are presented, as well as the main lines of future research prospected by the International Astronomical Union/International Association of Geodesy Joint Working Group on Theory of Earth Rotation, created in 2013.

The autonomy of the EU legal order and the law-making activities of international organizations. Some examples regarding the Council most recent practice. Research Papers in Law 03/2012

[Introduction.] It is generally believed that while the principle of the autonomy of the EU legal order, in the sense of constitutional and institutional autonomy that is to say what concerns the autonomous decision-making of the EU, has been clearly strengthened by the most recent jurisprudence of the Court of Justice (eg. Moxplant3, Intertanko or the Kadi/Al Baraakat judgements or the Opinion 1/2009 of the CJEU etc.) as well as, in my opinion, in many aspects by the Treaty of Lisbon, it is still valid to add that the principle of a favourable approach, stemming from the Court jurisprudence, for the enhanced openness of the EU legal order to international law has remained equally important for the EU4. On the other hand, it should be also seen that in a globalized world, and following the increased role of the EU as an international actor, its indispensable and crucial role concerning the creation of world (legal) order in many policy fields ( for example let's think about the G20 issues, the global economic and financial crisis, the role of the EU in promoting and protecting human rights worldwide, the implementation of the multilateral or regional conventional law, developed in the framework the UN (e.g. in the field of agriculture or environment etc) or what concerns the Kyoto process on climate change or the conservation of marine biological resources at international level etc), it seems reasonable and justified to submit that the influence, for example, of the law-making activities of the main stakeholder international organizations in the mentioned policy-areas on the EU (especially on the development of its constantly evolving legal order) or vice-versa the influence of the EU law-making practice on these international organizations is significant, in many aspects mutually interdependent and more and more remarkable. This tendency of the 21st century doesn't mean, however, in my view, that the notion of the autonomy of the EU legal order would have been weakened by this increasing interaction between international law and EU law over the passed years. This contribution is going to demonstrate and prove these departuring points by giving some concrete examples from the most recent practice of the Council (all occuring either in the second half of 2009 or after the entry into force of the Lisbon Treaty), and which relate to two very important policy areas in the EU, namely the protection of human rights and the Common Fishery Policy.

L’importance du rendement, du soutien des adultes, des attentes de réussite et de la valeur accordée aux mathématiques dans les choix de filières de formation préuniversitaire des étudiantes issues des séquences de mathématiques enrichies

La présente étude s’intéresse aux choix de filières de formation des filles comparées aux garçons. La présence des filles dans les filières de formation dans le domaine des sciences, de la technologie, du génie et de la mathématique (STGM) est moins importante que celle des garçons. Ce fait est documenté dans la plupart des pays industrialisés (OCDE, 2013). Les décideurs sont préoccupés par cette sous-représentation des filles et des femmes dans ces domaines et s’affairent à comprendre le phénomène, dans le but d’agir pour changer la situation (Drouin et al., 2008; MCCCF, 2011). Or, les facteurs d’influence pour expliquer cet écart entre les garçons et les filles sont nombreux et ne font pas l’objet d’un consensus dans la littérature (Ceci et al., 2009). Toutefois, plusieurs s’entendent pour dire que les mathématiques, importantes dans les profils de formation en STGM, et la façon dont les filles les perçoivent pourraient expliquer, en partie, leurs choix (Rowan-Kenyon et al., 2012 et Wang et al., 2013). Ces auteurs ont aussi suggéré que le contexte social et les croyances des filles au sujet des mathématiques seraient déterminants dans le processus de choix impliquant cette discipline. Un modèle théorique sociocognitif, inspiré par les travaux de Lent et al, (1994-2006), expliquant le processus de choix scolaires et professionnels a permis de conceptualiser les liens entre les déterminants socio-motivationnels spécifiques aux mathématiques. L’objectif général de la présente étude était de mieux documenter l’importance des mathématiques dans les choix de filières de formation menant aux carrières en STGM. Spécifiquement, nous avons examiné les relations entre le rendement en mathématiques, la perception des élèves quant au contexte social (soutien des parents et enseignants), leurs attentes de réussite, la valeur qu’ils accordent aux mathématiques (sentiment d’autoefficacité, anxiété, perception de l’utilité et intérêt) et les choix de filières de formation générale après leur secondaire (sciences humaines sans mathématiques, sciences humaines avec mathématiques, sciences de la santé et sciences pures). Nous avons exploré les distinctions entre les filles et les garçons. Pour ce faire, 1129 élèves finissants ont été questionnés au sujet de leurs motivations en mathématiques et de leurs intentions de formation post-secondaire. Par la suite, une comparaison entre les 583 filles et les 543 garçons a été réalisée par des analyses de régression logistiques multinomiales. Les résultats montrent que plusieurs déterminants permettent de dégager des similitudes et des différences quant aux choix de filières de formation des filles et des garçons. D’abord, il semble que pour la plupart des élèves, filles ou garçons, un rendement élevé et un important soutien des enseignants tel que perçu par les élèves à la fin du secondaire est davantage lié aux choix de filières en sciences pures et en sciences de la santé qu’en sciences humaines avec ou sans mathématiques. Toutefois, le soutien des parents perçu est plus déterminant pour les filles qui choisissent les sciences de la santé que pour les garçons. Le soutien des enseignants perçu est plus déterminant pour les garçons qui choisissent les sciences humaines que pour les filles. Aussi, un faible sentiment d’autoefficacité en mathématiques serait associé au choix de filières en sciences humaines, alors qu’une forte anxiété en mathématiques chez les filles serait associée aux filières en sciences de la santé. Pour les garçons, c’est davantage l’intérêt en mathématiques qui est déterminant pour choisir la filière des sciences pures. La perception de l’utilité des mathématiques est déterminante à la fois pour les garçons et pour les filles qui choisissent les filières de sciences les menant à des carrières en STGM. En somme, nos résultats suggèrent que le soutien en mathématiques de la part des adultes significatifs, tel que perçu par les élèves, est moins prépondérant que les attentes de réussite (sentiment d’autoefficacité et anxiété) et la valeur accordée aux mathématiques (intérêt et utilité perçue) pour comparer les garçons et les filles dans leurs choix de filières. À la lumière des résultats obtenus, il nous semble que l’implantation de mesures, dans les milieux scolaires, pour renforcer le sentiment d’autoefficacité des jeunes filles en mathématiques et surtout pour diminuer leur taux d’anxiété dans cette matière serait une voie prometteuse pour atteindre la parité entre les garçons et les filles dans les filières en STGM.