Metodología Multimedia y Evolución del Pensamiento Matemático Ordinal Prenumérico en escolares de 3 a 7 años

En esta investigación se aborda el problema de analizar y conocer una parte de la evolución del Pensamiento Ordinal prenumérico y recursivo en escolares de 3 a 7 años, como parte y fundamento de la evolución cognitiva del Pensamiento Numérico y Aritmético, y comprobar si la utilización de una metodología de investigación basada en la tecnología multimedia (Metodología Multimedia) proporciona información válida y relevante sobre dicha evolución. Para el desarrollo del estudio se ha empleado una metodología mixta con dos componentes principales: • La componente teórica, dirigida a fundamentar y validar el marco conceptual así como el procedimiento y los resultados obtenidos. Dicha fundamentación en los niveles matemático, epistemológico y fenomenológico se complementa con los antecedentes específicos de los dos campos básicos del estudio: pensamiento ordinal y tecnología multimedia. • La componente empírica, orientada a obtener información sobre los comportamientos de sujetos en torno a los aspectos fundamentales del problema de investigación, mediante la aplicación de los bloques de tareas multimedia, el análisis e interpretación de las respuestas, la identificación de las estrategias utilizadas y los errores cometidos, la determinación de perfiles y niveles de competencias ordinales y la determinación de las características básicas del desarrollo y la evolución con la edad de dichas capacidades y competencias. La culminación del estudio teórico ha consistido en la construcción de un modelo evolutivo de competencias ordinales y recursivas (MECOR) ), que proporciona un marco interpretativo de las características, regularidades y evolución del Pensamiento Ordinal Preinductivo en escolares de 3 a 7 años, y de un modelo general para el diseño del ítem multimedia (MGDIM) que permite establecer un procedimiento general que hemos definido y denominado "Metodología Multimedia" para la investigación en Educación Matemática, y en otras áreas educativas, idónea para su utilización en estudios de masas. Las construcciones anteriores han permitido, como consecuencia, la elaboración de un instrumento metodológico operativo para el estudio de las características del pensamiento ordinal y su evolución en sujetos de 3 a 7 años de edad. Desde el punto de vista empírico se aplica el instrumento multimedia construido incluyendo los mecanismos necesarios para el registro automático de todas las interacciones de los sujetos con todas y cada una de las tareas del estudio, minimizando la interacción investigador--sujeto, constatándose la libertad y espontaneidad de las respuestas de los sujetos, la gran variedad de datos obtenidos y la facilidad de análisis de los comportamientos que proporcionan los instrumentos utilizados. Además de las indicadas, la investigación realiza las siguientes aportaciones: • Una explicación detallada de la evolución de una parte de las capacidades ordinales y recursivas en escolares de 3 a 7 años. • Una caracterización de niveles de competencia y determinación de las edades más frecuentes en las que tienen lugar los cambios de nivel. • La detección y clasificación de los errores cometidos y las estrategias utilizadas. • La identificación de las edades a las que aparece: a) el uso de capacidades recursivas frente al mero etiquetaje, b) la distinción entre cantidad continua y discreta en la resolución de tareas ordinales, c) el conteo ordinal frente a otras estrategias en la resolución de tareas ordinales con cantidades discretas. • Una descripción general de las capacidades, competencias y estrategias asociadas a los estados del modelo (MECOR) por grupos de edad. • La determinación de modelos de ajuste no lineales para la evolución de las medias de las valoraciones por grupos de edad para cada una de las capacidades tratadas y la comprobación de que dichos modelos son más precisos que los ajustes lineales correspondientes. • Ejemplos prácticos de ítems multimedia para el desarrollo de investigaciones futuras. Sobre la relevancia de la investigación, podemos destacar entre otros los siguientes motivos: la necesidad de conocer en profundidad las características del pensamiento matemático de los alumnos de la etapa de Educación Infantil para mejorar el diseño y desarrollo didáctico del proceso formativo en dicha etapa, así como la necesidad de encontrar procedimientos y métodos orientados a disminuir los inconvenientes tradicionales que surgen en las investigaciones con sujetos de tan corta edad. Por otra parte creemos que el estudio es del máximo interés por la novedad de los instrumentos utilizados, la importancia del tema analizado y la proyección que los conocimientos pueden tener sobre nuevas formas de ver y tratar los contenidos matemáticos, nuevos métodos de investigación así como nuevas formas de abordar el diseño y desarrollo didáctico en las etapas de Educación Infantil y Primaria. Desde el punto de vista de la metodología, consideramos de vital importancia la validación de una metodología nueva que puede aportar información privilegiada sobre el aprendizaje y la cognición de sujetos cuyos comportamientos y respuestas se han caracterizado desde hace tiempo por su enorme dificultad de interpretación y, consecuentemente, por las dudas en cuanto a la validez y fiabilidad de los resultados. En este sentido creemos que estamos ante una de las metodologías que pueden aportar avances notables en el campo de la investigación en Educación Matemática.

Vocabulary Instruction as a Tool for Helping Students of Diverse Backgrounds and Ability Levels to Understand Mathematical Concepts

This action research project describes a research project designed and implemented specifically with an emphasis on the instruction of mathematical vocabulary. The targeted population was my second period classroom of sixth grade students. This group of seventeen students represented diverse socioeconomic backgrounds and abilities. The school is located in a community of a population of approximately 5,000 people in the Midwest. My research investigation focused on the use of specific methods of vocabulary instruction and students’ use of precise mathematical vocabulary in writing and speaking. I wanted to see what effects these strategies would have on student performance. My research suggested that students who struggle with retention of mathematical knowledge have inadequate language skills. My research also revealed that students who have a sound knowledge of vocabulary and are engaged in the specific use of content language performed more successfully. Final analysis indicated that students believed the use of specific mathematical language helped them to be more successful and they made moderate progress in their performance on assessments.

On the Mastering of Knowledge and Skills for Solving Mathematical Problems in the Context of the Relationship "Reflection–Synergy"

On the basis of topical investigations on the reflection in the mathematics education, in this article there are presented some contemporary ideas about refining the methodology of mastering knowledge and skills for solving mathematical problems. The thesis is developed that for the general logical and for some particular mathematical methods to become means of solving mathematical problems, first they need to be a purpose of the education.

Fractional order calculus: basic concepts and engineering applications

The fractional order calculus (FOC) is as old as the integer one although up to recently its application was exclusively in mathematics. Many real systems are better described with FOC differential equations as it is a well-suited tool to analyze problems of fractal dimension, with long-term “memory” and chaotic behavior. Those characteristics have attracted the engineers' interest in the latter years, and now it is a tool used in almost every area of science. This paper introduces the fundamentals of the FOC and some applications in systems' identification, control, mechatronics, and robotics, where it is a promissory research field.

Integrated care approaches and skills mix policies in Europe

ABSTRACT - Background: Integration of health care services is emerging as a central challenge of health care delivery, particularly for patients with elderly and complex chronic conditions. In 2003, the World Health Organization (WHO) already began to identify it as one of the key pathways to improve primary care. In 2005, the European Commission declared integrated care as vital for the sustainability of social protection systems in Europe. Nowadays, it is recognized as a core component of health and social care reforms across European countries. Implementing integrated care requires coordination between settings, organizations, providers and professionals. In order to address the challenge of integration in such complex scenario, an effective workforce is required capable of working across interdependent settings. The World Health Report 2006 noted that governments should prepare their workforce and explore what tasks the different levels of health workers are trained to do and are capable of performing (skills mix). Comparatively to other European countries, Portugal is at an early stage in what integrated care is concerned facing a growing elderly population and the subsequent increase in the pressure on institutions and professionals to provide social and medical care in the most cost-effective way. In 2006 the Portuguese government created the Portuguese Network for Integrated Care Development (PNICD) to solve the existing long-term gap in social support and healthcare. On what concerns health workforce, the Portuguese government already recognized the importance of redefine careers keeping professional motivation and satisfaction. Aim of the study: This study aims to contribute new evidence to the debate surrounding integrated care and skills mix policies in Europe. It also seeks to provide the first evidence that incorporates both the current dynamics of implementing integrated care in Portugal and the developments of international literature. The first ambition of our study is to contribute to the growing interest in integrated care and to the ongoing research in this area by identifying its different approaches and retrieve a number of experiences in some European countries. Our second goal of this research is to produce an update on the knowledge developed on skills mix to the international healthcare management community and to policy makers involved in reforming healthcare systems and organizations. To better inform Portuguese health policies makers in a third stage we explore the current dynamics of implementing integrated care in Portugal and contextualize them with the developments reported in the international literature. Methodology: This is essentially an exploratory and descriptive study using qualitative methodology. In order to identify integrated care approaches in Europe, a systematic literature review was undertaken which resulted in a paper published in the Journal of Management and Marketing in Health care titled: Approaches to developing integrated care in Europe: a systematic literature review. This article was recommended and included into a list of references identified by The King's Fund Library. A second systematic literature review was undertaken which resulted in a paper published in the International Journal of Healthcare Management titled: Skills mix in healthcare: An international update for the management debate. Semi-structured interviews were performed on experts representing the regional coordination teams of the Portuguese Network for Integrated Care Development. In a last stage a questionnaire survey was developed based on the findings of both systematic literature reviews and semi-structured interviews. Conclusions: Even though integrated care is a worldwide trend in health care reforms, there is no unique definition. Definitions can be grouped according to their sectorial focus: community-based care, combined health and social care, combined acute and primary care, the integration of providers, and in a more comprehensive approach the whole health system. Indeed, models that seek to apply the principles of integrated care have a similar background and are continually evolving and depend on the different initiatives taken at national level. . Despite the fact that we cannot argue that there is one single set typology of models for integrated care, it is possible to identify and categorize some of the basic approaches that have been taken in attempts to implement integrated care according to: changes in organizational structure, workforce reconfiguring, and changes in the financing system. The systematic literature review on skills mix showed that despite the widely acknowledged interest on skills mix initiatives there is a lack of evidence on skills mix implications, constraints, outcomes, and quality impact that would allow policy makers to take sustained and evidence-based decisions. Within the Portuguese health system, the integrated care approach is rather organizational and financial, whereas little attention is given to workforce integration. On what concerns workforce planning Portugal it is still in the stage of analyzing the acceptability of health workforce skills mix. In line with the international approaches, integration of health and social services and bridging primary and acute care are the main goals of the national government strategy. The findings from our interviews clarify perceptions which show no discrepancy with the related literature but are rather scarce comparing to international experience. Informants hold a realistic but narrow view of integrated care related issues. They seem to be limited to the regional context, requiring a more comprehensive perspective. The questionnaire developed in this thesis is an instrument which, when applied, will allow policy makers to understand the basic set of concepts and managerial motivations behind national and regional integrated care programs. The instrument developed can foster evidence on the three essential components of integrated care policies: organizational, financial, and human resources development, and can give additional input on the context in which integrated care is being developed, the type of providers and organizations involved, barriers and constraints, and the workforce skills mix planning related strategies. The thesis was successful in recognizing differences between countries and interventions and the instrument developed will allow a better comprehension of the international options available and how to address the vital components of integrated care programs.

Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications

Since no physical system can ever be completely isolated from its environment, the study of open quantum systems is pivotal to reliably and accurately control complex quantum systems. In practice, reliability of the control field needs to be confirmed via certification of the target evolution while accuracy requires the derivation of high-fidelity control schemes in the presence of decoherence. In the first part of this thesis an algebraic framework is presented that allows to determine the minimal requirements on the unique characterisation of arbitrary unitary gates in open quantum systems, independent on the particular physical implementation of the employed quantum device. To this end, a set of theorems is devised that can be used to assess whether a given set of input states on a quantum channel is sufficient to judge whether a desired unitary gate is realised. This allows to determine the minimal input for such a task, which proves to be, quite remarkably, independent of system size. These results allow to elucidate the fundamental limits regarding certification and tomography of open quantum systems. The combination of these insights with state-of-the-art Monte Carlo process certification techniques permits a significant improvement of the scaling when certifying arbitrary unitary gates. This improvement is not only restricted to quantum information devices where the basic information carrier is the qubit but it also extends to systems where the fundamental informational entities can be of arbitary dimensionality, the so-called qudits. The second part of this thesis concerns the impact of these findings from the point of view of Optimal Control Theory (OCT). OCT for quantum systems utilises concepts from engineering such as feedback and optimisation to engineer constructive and destructive interferences in order to steer a physical process in a desired direction. It turns out that the aforementioned mathematical findings allow to deduce novel optimisation functionals that significantly reduce not only the required memory for numerical control algorithms but also the total CPU time required to obtain a certain fidelity for the optimised process. The thesis concludes by discussing two problems of fundamental interest in quantum information processing from the point of view of optimal control - the preparation of pure states and the implementation of unitary gates in open quantum systems. For both cases specific physical examples are considered: for the former the vibrational cooling of molecules via optical pumping and for the latter a superconducting phase qudit implementation. In particular, it is illustrated how features of the environment can be exploited to reach the desired targets.

New readers, new reading skills and meaning: challenges for media and information literacy

Recognizing the importance of developing the information and media literacy in contemporary society, this article discusses the scenario of hybrid languages born on cyberspace, hypertext and the new types of readers who interact with information, now disseminated by digital media. As theoretical references authors such as Lucia Santaella, we develop arguments that present the headquarters of language and thought within a semiotic support. Matrices help to understand the phenomenon of hybrid language in hypertext. Therefore, we emphasize that the development of skills associated with the new reading environments propitiated by the virtual environment requires the understanding of language, which is one of the concepts used within the media and information literacy (MIL) proposal of Unesco, which combines the two concepts and skills of information and media literacy. It is hoped that this article motivate scholars and practitioners of education and information to take responsibility to educate for information environments that arise with new media and technologies, emphasizing the issue of reading and language.

Exploring the Influence of Vocabulary Instruction on Students’ Understanding of Mathematical Concepts

In this action research study of my classroom of 8th grade mathematics, I investigated the influence of vocabulary instruction on students’ understanding of the mathematics concepts. I discovered that knowing the meaning of the vocabulary did play a major role in the students’ understanding of the daily lessons and the ability to take tests. Understanding the vocabulary and the concepts allowed the students to be successful on their daily assignments, chapter tests, and standardized achievement tests. I also discovered that using different vocabulary teaching strategies enhanced equity in my classroom among diverse learners. The knowledge of the math vocabulary increased my students’ confidence levels, which in turn increased their daily and test scores. As a result of this research, I plan to find ways to incorporate the vocabulary teaching strategies I have used into current math curriculum. I will start this process at the beginning of the next school year, and will continue looking for new strategies that will promote math vocabulary retention.

Concepts and methods of quantitative assessment of risk to groundwater resources

This work presents a two-dimensional approach of risk assessment method based on the quantification of the probability of the occurrence of contaminant source terms, as well as the assessment of the resultant impacts. The risk is calculated using Monte Carlo simulation methods whereby synthetic contaminant source terms were generated to the same distribution as historically occurring pollution events or a priori potential probability distribution. The spatial and temporal distributions of the generated contaminant concentrations at pre-defined monitoring points within the aquifer were then simulated from repeated realisations using integrated mathematical models. The number of times when user defined ranges of concentration magnitudes were exceeded is quantified as risk. The utilities of the method were demonstrated using hypothetical scenarios, and the risk of pollution from a number of sources all occurring by chance together was evaluated. The results are presented in the form of charts and spatial maps. The generated risk maps show the risk of pollution at each observation borehole, as well as the trends within the study area. This capability to generate synthetic pollution events from numerous potential sources of pollution based on historical frequency of their occurrence proved to be a great asset to the method, and a large benefit over the contemporary methods.

On the solubility of proteins as a function of pH: Mathematical development and application

Thermodynamic relations between the solubility of a protein and the solution pH are presented in this work. The hypotheses behind the development are that the protein chemical potential in liquid phase can be described by Henry`s law and that the solid-liquid equilibrium is established only between neutral molecules. The mathematical development results in an analytical expression of the solubility curve, as a function of the ionization equilibrium constants, the pH and the solubility at the isoelectric point. It is shown that the same equation can be obtained either by directly calculating the fraction of neutral protein molecules or by integrating the curve of the protein average charge. The methodology was successfully applied to the description of the solubility of porcine insulin as a function of pH at three different temperatures and of bovine beta-lactoglobulin at four different ionic strengths. (C) 2011 Elsevier B.V. All rights reserved.

Concepts and tools for comprehensive sustainability assessments for tourism destinations: a comparative review

This paper reviews a wide range of tools for comprehensive sustainability assessments at whole tourism destinations, covering socio-cultural, economic and environmental issues. It considers their strengths, weaknesses and site specific applicability. It is intended to facilitate their selection (and combination where necessary). Tools covered include Sustainability Indicators, Environmental Impact Assessment, Life Cycle Assessment, Environmental Audits, Ecological Footprints, Multi-Criteria Analysis and Adaptive Environmental Assessment. Guidelines for evaluating their suitability for specific sites and situations are given as well as examples of their use.

Reputations, self-concepts and coping strategies of volatile solvent users

Data pertaining to the reputations, self-concepts and coping strategies of thirty-one secondary school Volatile Solvent Users (VSUs), forty-four ex-VSUs, and forty-eight non-VSUs in the Perth Metropolitan area of Western Australia were obtained using the High School Student Activity Questionnaire. Findings revealed that significant differences between current VSUs, ex-VSUs, and non-VSUs were more attributable to factors of reputation enhancement than to factors of either self-concept or coping strategies. Current VSUs identified themselves as both having and wanting to have a more non-confronting reputation, and as admiring drug-related activities significantly more than both ex-VSUs and non-VSUs. Two coping variables were also found to be significant indicating that females use more nonproductive coping strategies and external coping strategies than males. No interaction effects were identified. The implications for drug education and further research are discussed.