Os programas de matemática do ensino básico de 1990 e de 2007 e o processo de implementação do programa de 2007, no 1º ciclo do Ensino Básico

Mestrado em Educação Matemática na Educação Pré – Escolar e nos 1.º e 2.º Ciclos do Ensino Básico

O pensamento algébrico e a descoberta de padrões na formação de professores

Este texto incide sobre o tema do pensamento algébrico nos primeiros anos de escolaridade ao nível da formação contínua de professores. Na abordagem apresentada o tema dos padrões surge como contexto estruturante para o desenvolvimento do pensamento algébrico. Começa-se por fazer um enquadramento dos referenciais teóricos que fundamentam a adoção de uma proposta didática desenvolvida nesse âmbito, recorrendo em seguida a um estudo empírico que foi desenvolvido, do qual se relata aqui uma parte centrada nas práticas de sala de aula de uma professora do primeiro ciclo em formação, de modo a poder confirmar a eficácia da proposta no ensino e desenvolvimento do pensamento algébrico dos alunos. Os resultados permitem concluir que a professora interiorizou e projetou na sua prática os aspetos essenciais que conduziram ao desenvolvimento do pensamento algébrico nos alunos. O texto termina com algumas conclusões e implicações para a formação de professores.

Estudo da divergência entre duas vias que curvam em sentidos contrários

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Civil na Área de Especialização de Vias de Comunicação e Transportes

Texture zeros and weak basis transformations

We investigate the physical meaning of some of the "texture zeros" which appear in most of the Ansatze on quark masses and mixings. It is shown that starting from arbitrary quark mass matrices and making a suitable weak basis transformation one can obtain some of these sets of zeros which therefore have no physical content. We then analyse the physical implications of a four-texture zero Ansatz which is in agreement with all present experimental data. (C) 2000 Elsevier Science B.V. AU rights reserved.

An Evaluation of Local Feature Combiners for Robot Visual Localization

In the last decade, local image features have been widely used in robot visual localization. To assess image similarity, a strategy exploiting these features compares raw descriptors extracted from the current image to those in the models of places. This paper addresses the ensuing step in this process, where a combining function must be used to aggregate results and assign each place a score. Casting the problem in the multiple classifier systems framework, we compare several candidate combiners with respect to their performance in the visual localization task. A deeper insight into the potential of the sum and product combiners is provided by testing two extensions of these algebraic rules: threshold and weighted modifications. In addition, a voting method, previously used in robot visual localization, is assessed. All combiners are tested on a visual localization task, carried out on a public dataset. It is experimentally demonstrated that the sum rule extensions globally achieve the best performance. The voting method, whilst competitive to the algebraic rules in their standard form, is shown to be outperformed by both their modified versions.

Lendo e explorando histórias: a emergência do pensamento algébrico em crianças de 4 anos

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

The influence of count's number in myocardium in the determination of reproducible parameters in Gated-SPECT studies simulated with GATE

Myocardial Perfusion Gated Single Photon Emission Tomography (Gated-SPET) imaging is used for the combined evaluation of myocardial perfusion and left ventricular (LV). The purpose of this study is to evaluate the influence of the total number of counts acquired from myocardium, in the calculation of myocardial functional parameters using routine software procedures. Methods: Gated-SPET studies were simulated using Monte Carlo GATE package and NURBS phantom. Simulated data were reconstructed and processed using the commercial software package Quantitative Gated-SPECT. The Bland-Altman and Mann-Whitney-Wilcoxon tests were used to analyze the influence of the number of total counts in the calculation of LV myocardium functional parameters. Results: In studies simulated with 3MBq in the myocardium there were significant differences in the functional parameters: Left ventricular ejection fraction (LVEF), end-systolic volume (ESV), Motility and Thickness; between studies acquired with 15s/projection and 30s/projection. Simulations with 4.2MBq show significant differences in LVEF, end-diastolic volume (EDV) and Thickness. Meanwhile in the simulations with 5.4MBq and 8.4MBq the differences were statistically significant for Motility and Thickness. Conclusion: The total number of counts per simulation doesn't significantly interfere with the determination of Gated-SPET functional parameters using the administered average activity of 450MBq to 5.4MBq in myocardium.

Reproducibility of simulated myocardial lesions simulated on a virtual phantom

Human virtual phantoms are being widely used to simulate and characterize the behavior of different organs, either in diagnosis stages but also to enable foreseeing the therapeutic effects obtained on a certain patient. In the present work a typical patient’s heart was simulated using XCAT2©, considering the possibility of a lesion and/or anatomical alteration being affecting the myocardium. These simulated images, were then used to carry out a set of parametric studies using Matlab©. Although performed in controlled sceneries, these studies are very important to understand and characterize the performance of the methodologies used, as well as to determine to what extent the relations between the perturbation introduced at the myocardium and the resulting simulated images can be considered conclusive.

Desenvolvendo o pensamento algébrico no 2.º ciclo do ensino básico: o sentido dos símbolos e da generalização

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção do grau de mestre em Educação Matemática na Educação Pré-escolar e nos 1.º e 2.º 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.

A Logic and tool for local reasoning about security protocols

Trabalho apresentado no âmbito do Mestrado em Engenharia Informática, como requisito parcial para obtenção do grau de Mestre em Engenharia Informática

On the analysis of compensation correctness

One fundamental idea of service-oriented computing is that applications should be developed by composing already available services. Due to the long running nature of service interactions, a main challenge in service composition is ensuring correctness of transaction recovery. In this paper, we use a process calculus suitable for modelling long running transactions with a recovery mechanism based on compensations. Within this setting, we discuss and formally state correctness criteria for compensable processes compositions, assuming that each process is correct with respect to transaction recovery. Under our theory, we formally interpret self-healing compositions, that can detect and recover from faults, as correct compositions of compensable processes. Moreover, we develop an automated verification approach and we apply it to an illustrative case study.

Crossing balanced and stair nested desings

Balanced nesting is the most usual form of nesting and originates, when used singly or with crossing of such sub-models, orthogonal models. In balanced nesting we are forced to divide repeatedly the plots and we have few degrees of freedom for the first levels. If we apply stair nesting we will have plots all of the same size rendering the designs easier to apply. The stair nested designs are a valid alternative for the balanced nested designs because we can work with fewer observations, the amount of information for the different factors is more evenly distributed and we obtain good results. The inference for models with balanced nesting is already well studied. For models with stair nesting it is easy to carry out inference because it is very similar to that for balanced nesting. Furthermore stair nested designs being unbalanced have an orthogonal structure. Other alternative to the balanced nesting is the staggered nesting that is the most popular unbalanced nested design which also has the advantage of requiring fewer observations. However staggered nested designs are not orthogonal, unlike the stair nested designs. In this work we start with the algebraic structure of the balanced, the stair and the staggered nested designs and we finish with the structure of the cross between balanced and stair nested designs.

Periodic paths on nonautonomous graphs

We define nonautonomous graphs as a class of dynamic graphs in discrete time whose time-dependence consists in connecting or disconnecting edges. We study periodic paths in these graphs, and the associated zeta functions. Based on the analytic properties of these zeta functions we obtain explicit formulae for the number of n-periodic paths, as the sum of the nth powers of some specific algebraic numbers.

Study of the interactions in a three-way crossed classification model

Crossed classification models are applied in many investigations taking in consideration the existence of interaction between all factors or, in alternative, excluding all interactions, and in this case only the effects and the error term are considered. In this work we use commutative Jordan algebras in the study of the algebraic structure of these designs and we use them to obtain similar designs where only some of the interactions are considered. We finish presenting the expressions of the variance componentes estimators.