Organização e tratamento de dados recolhidos nas rotinas das crianças na sala dos quatro anos

Dissertação apresentada à escola Superior de Educação de Lisboa para obtenção de grau de mestre em Educação Matemática na Educação Pré-Escolar e nos 1º e 2º Ciclos do Ensino Básico

Generalizing repeating patterns: a study with children aged four

This paper presents part of a study that aimed to understand how the emergence of algebraic thinking takes place in a group of four-year-old children, as well as its relationship to the exploration of children‘s literature. To further deepen and guide this study the following research questions were formulated: (1) How can children's literature help preschoolers identify patterns?; (2) What strategies and thinking processes do children use to create, analyze and generalize repeating and growing patterns?; (3) What strategies do children use to identify the unit of repeat of a pattern? and (4) What factors influence the identification of patterns? The paper focuses only on the strategies and thinking processes that children use to create, analyze and generalize repeating patterns. The present study was developed with a group of 14 preschoolers in a private school in Lisbon, and it was carried out with all children. In order to develop the research, a qualitative research methodology under the interpretive paradigm was chosen, emphasizing meanings and processes. The researcher took the dual role of teacher-researcher, conducting the study with her own group and in her own natural environment. Participant observation and document analysis (audio and video recordings, photos and children productions) were used as data collection methods. Data collection took place from October 2013 to April 2014. The results of the study indicate that children master the concept of repeating patterns, and they are able to identify the unit of repeat, create and analyze various repeating patterns, evolving from simpler to more complex forms.

Práticas de avaliação formativa na aula de matemática: um estudo no 2º ciclo

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Educação Matemática na Educação Pré- Escolar e nos 1º e 2º Ciclo do Ensino Básico

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.

Fractional control of legged robots

Fractional calculus (FC) is being used in several distinct areas of science and engineering, being recognized its ability to yield a superior modelling and control in many dynamical systems. This article illustrates the application of FC in the area of robot control. A Fractional Order PDμ controller is proposed for the control of an hexapod robot with 3 dof legs. It is demonstrated the superior performance of the system by using the FC concepts.

Fitness function evaluation through fractional algorithms

This paper proposes a Genetic Algorithm (GA) for the design of combinational logic circuits. The fitness function evaluation is calculated using Fractional Calculus. This approach extends the classical fitness function by including a fractional-order dynamical evaluation. The experiments reveal superior results when comparing with the classical method.

Fractional control of dynamic systems

The concepts involved with fractional calculus (FC) theory are applied in almost all areas of science and engineering. Its ability to yield superior modeling and control in many dynamical systems is well recognized. In this article, we will introduce the fundamental aspects associated with the application of FC to the control of dynamic systems.

Fractional analysis of traffic dynamics

This article presents a dynamical analysis of several traffic phenomena, applying a new modelling formalism based on the embedding of statistics and Laplace transform. The new dynamic description integrates the concepts of fractional calculus leading to a more natural treatment of the continuum of the Transfer Function parameters intrinsic in this system. The results using system theory tools point out that it is possible to study traffic systems, taking advantage of the knowledge gathered with automatic control algorithms. Dynamics, Games and Science I Dynamics, Games and Science I Look Inside Other actions Export citation About this Book Reprints and Permissions Add to Papers Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn

A Review of Definitions for Fractional Derivatives and Integral

This paper presents a review of definitions of fractional order derivatives and integrals that appear in mathematics, physics, and engineering.

A didactic sequence of elementary geometric optics Informed by history and philosophy of science

The concepts and instruments required for the teaching and learning of geometric optics are introduced in the didactic processwithout a proper didactic transposition. This claim is secured by the ample evidence of both wide- and deep-rooted alternative concepts on the topic. Didactic transposition is a theory that comes from a reflection on the teaching and learning process in mathematics but has been used in other disciplinary fields. It will be used in this work in order to clear up the main obstacles in the teachinglearning process of geometric optics. We proceed to argue that since Newton’s approach to optics, in his Book I of Opticks, is independent of the corpuscular or undulatory nature of light, it is the most suitable for a constructivist learning environment. However, Newton’s theory must be subject to a proper didactic transposition to help overcome the referred alternative concepts. Then is described our didactic transposition in order to create knowledge to be taught using a dialogical process between students’ previous knowledge, history of optics and the desired outcomes on geometrical optics in an elementary pre-service teacher training course. Finally, we use the scheme-facet structure of knowledge both to analyse and discuss our results as well as to illuminate shortcomings that must be addressed in our next stage of the inquiry.

Extremum estimators and stochastic optimization methods

Submitted in partial fulfillment for the Requirements for the Degree of PhD in Mathematics, in the Speciality of Statistics in the Faculdade de Ciências e Tecnologia

Literacia em saúde e alimentação saudável : os novos produtos e a escolha dos alime

Resumo Com o objectivo de contribuir para entender o nível de literacia em saúde dos consumidores e verificar a relação entre esta e o comportamento no consumo de alimentos (consumerismo), foi efectuado um inquérito por questionário que incluiu a tradução para Português do Newest Vital Sign,© (2008) Pfizer Inc. Used with permission (NVS). Este instrumento foi aplicado a uma amostra estratificada, de 384 indivíduos com mais de 15 anos de idade, da região da Grande Lisboa, distribuída de acordo com o Census 2001. A nível de literacia em saúde foi avaliado através da versão Portuguesa do NVS que consiste numa “ferramenta” onde se fornece aos inquiridos uma série de informações relacionadas com a saúde, nomeadamente a informação nutricional constante de um rótulo, devendo estes fazer a demonstração das suas capacidades de utilização dessa informação respondendo a questões. Dos resultados recolhidos verifica-se que existe uma relação directa entre a literacia em saúde e a escolaridade, constatou-se ainda uma associação entre a literacia em saúde e o comportamento consumerista no consumo de alimentos assim como com um comportamento de consumo pautado pela consciência ecológica. De salientar ainda a relação estatisticamente significativa entre a literacia em saúde e a neofilia alimentar. No entanto os indivíduos mais idosos, com menores habilitações literárias e de menor rendimento são mais neofóbicos Não existe relação entre o género e a literacia em saúde. O NVS, agora disponível na língua portuguesa, constitui num contexto de promoção da saúde, uma ajuda em termos de Saúde Pública. Abstract Aiming to contribute to the understanding of consumer’s health literacy, and to verify the relation between health literacy and consumerism in food consumption, a validation of an inquiry, that include the Portuguese version of the Newest Vital Sign, © (2008) Pfizer Inc. Used with permission (NVS) was performed. Afterwards this epidemiologic instrument was applied to a convenience sample (384 individuals, over 15 years old) of the population of “Grande Lisboa”, distributed accordingly to Census 2001. Health literacy was evaluated by the Portuguese version of NVS and consists in a tool by which a number of health-related information, in this case nutritional information written in a food label, is used to demonstrate one’s ability to use that information answering to questions. From the results it is possible to verify that there is a close relation between health literacy and general literacy (school years), it was also possible to observe an association among health literacy, consumer behaviour and ecological consumption of food products. It is of relevance the fact that an association between health literacy and food neophilia is statistically significant. Nevertheless older individuals, with lower health literacy and income are the most neophobic. There is no statistical association between gender and health literacy. The Portuguese version of NVS is an essential tool to evaluate the population health literacy in a hea

Power indices applied to Portuguese Parliament

In this paper, we apply the following four power indices to the Portuguese Parliament: Shapley–Shubik index, Banzhaf index, Deegan–Packel index and Public Good Index. We also present the main notions related with simple games and discuss the features of each power index by means of their axiomatic characterizations.

Formação para a literacia da informação: uma interactividade necessária com os media

Our aim is to analyse the relationship between interactive media and its use in Education when applied to formal training for information literacy. Contextualizing the notion of literacy in an evolving framework and emphasizing the recognition of its importance, we highlight some desirable skills in the current information society, including, inevitably, technological competencies. When considering the notion of literacy within an evolving framework and emphasizing the acknowledgement of its significance some desirable skills stand out in the current information society including, inevitably, the technological skills. We emphasize media literacy and select some strategies for teaching and learning practices recommended for the development of new skills, highlighting the contribution of some international literacy standards and describing some of the good practices in Education. We also underline the need for training within an holistic perspective, integrating student’, teachers and staff cooperation in the educational process. In this process, the potential of the Web 2.0, which grants the new information users – the prosumers (consumers and producers) a new statute, new powers and obligations, is indeed worth mentioning. Regarding the situation, we shall quote the reports on the experiences of virtual learning communities that use the moodle platform and mention several activities and programs managed by the Portuguese government to increase the citizens’ literacy’s levels. In conclusion, we point out the need for lifelong learning and the ability of individuals to “learn to learn” who therefore provide literacy with a dynamic component.

Exploring the long-term associations between adolescents’ music training and academic achievement

There is a positive relationship between learning music and academic achievement, although doubts remain regarding the mechanisms underlying this association. This research analyses the academic performance of music and non-music students from seventh to ninth grade. The study controls for socioeconomic status, intelligence, motivation and prior academic achievement. Data were collected from 110 adolescents at two time points, once when the students were between 11 and 14 years old in the seventh grade, and again 3 years later. Our results show that music students perform better academically than non-music students in the seventh grade (Cohen’s d = 0.88) and in the ninth grade (Cohen’s d = 1.05). This difference is particularly evident in their scores in Portuguese language and natural science; the difference is somewhat weaker in history and geography scores, and is least pronounced in mathematics and English scores (η2 p from .09 to .21). A longitudinal analysis also revealed better academic performance by music students after controlling for prior academic achievement (η2 p = .07). Furthermore, controlling for intelligence, socioeconomic status and motivation did not eliminate the positive association between music learning from the seventh to the ninth grade and students’ academic achievement (η2 p = .06). During the period, music students maintained better and more consistent academic standing. We conclude that, after controlling for intelligence, socioeconomic status and motivation, music training is positively associated with academic achievement.