Um caso multimédia na formação inicial: contributos para o conhecimento sobre o ensino exploratório da Matemática

Este artigo tem como foco o uso de casos multimédia na formação inicial de professores e procura analisar o seu contributo para o desenvolvimento do conhecimento didático de futuras professoras acerca do ensino exploratório da Matemática, bem como apreciar as suas perspetivas sobre as mais-valias do caso multimédia utilizado como recurso formativo. Analisam-se questionários e relatórios de treze alunas do Mestrado em Educação Pré-Escolar e Ensino do 1.º Ciclo da Universidade de Évora, que trabalharam sobre um caso multimédia que retrata a prática de ensino de uma professora de 1º ciclo. O caso inclui recursos diversificados, sendo os vídeos de sala de aula complementados com o plano da aula, as resoluções da tarefa pelos alunos, as reflexões da professora sobre a sua prática, um quadro de referência sobre o ensino exploratório da Matemática e artigos teóricos sobre ensino de natureza exploratória da Matemática. As alunas em formação apreciaram conhecer e explorar o caso multimédia, ressaltando a possibilidade de através dele conhecerem uma nova prática real de ensino da Matemática; sublinharam a importância de ouvirem as reflexões da professora para dotar de sentido a respetiva prática, revelando as intenções das suas ações; aprenderam também conhecimentos relevantes para pôr em prática o ensino exploratório, nomeadamente relativos ao conhecimento do processo instrucional, tanto no diz respeito à planificação, como à condução da aula.

Percursos de vida profissional: da formação inicial à entrada na carreira

Dissertação apresentada à Escola Superior de Educação de Lisboa para a obtenção do Grau de Mestre em Ciências da Educação - especialidade Supervisão em Educação

O jogo e o desenvolvimento do raciocínio matemático na educação pré-escolar e no ensino do 1.º ciclo do ensino básico

Mestrado (PES II), Educação Pré-Escolar e Ensino do 1º Ciclo do Ensino Básico, 13 de Fevereiro de 2015, Universidade dos Açores.

Patterns, mathematics and culture : the search for symmetry in Azorean sidewalks and traditional crafts

In the hustle and bustle of daily life, how often do we stop to pay attention to the tiny details around us, some of them right beneath our feet? Such is the case of interesting decorative patterns that can be found in squares and sidewalks beautified by the traditional Portuguese pavement. Its most common colors are the black and the white of the basalt and the limestone used; the result is a large variety and richness in patterns. No doubt, it is worth devoting some of our time enjoying the lovely Portuguese pavement, a true worldwide attraction. The interesting patterns found on the Azorean handicrafts are as fascinating and substantial from the cultural point of view. Patterns existing in the sidewalks and crafts can be studied from the mathematical point of view, thus allowing a thorough and rigorous cataloguing of such heritage. The mathematical classification is based on the concept of symmetry, a unifying principle of geometry. Symmetry is a unique tool for helping us relate things that at first glance may appear to have no common ground at all. By interlacing different fields of endeavor, the mathematical approach to sidewalks and crafts is particularly interesting, and an excellent source of inspiration for the development of highly motivated recreational activities. This text is an invitation to visit the nine islands of the Azores and to identify a wide range of patterns, namely rosettes and friezes, by getting to know different arts and crafts and sidewalks.

Mathematical education and interdisciplinarity : promoting public awareness of mathematics in the Azores

Mathematical literacy in Portugal is very unsatisfactory in what concerns international standards. Even more disturbingly, the Azores archipelago ranks as one of the worst regions of Portugal in this respect. We reason that the popularisation of Mathematics through interactive exhibitions and activities can contribute actively to disseminate mathematical knowledge, increase awareness of the importance of Mathematics in today’s world and change its negative perception by the majority of the citizens. Although a significant investment has been undertaken by the local regional government in creating several science centres for the popularisation of Science, there is no centre for the popularisation of Mathematics. We present our first steps towards bringing Mathematics to unconventional settings by means of hands-on activities. We describe in some detail three activities. One activity has to do with applying trigonometry to measure distances in Astronomy, which can also be applied to Earth objects. Another activity concerns the presence of numerical patterns in the Azorean flora. The third activity explores geometrical patterns in the Azorean cultural heritage. It is our understanding that the implementation of these and other easy-to-follow and challenging activities will contribute to the awareness of the importance and beauty of Mathematics.

A arte/expressão plástica numa inter-relação com a matemática/geometria: Um projeto no jardim de infância

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Educação Artística, na Especialização de Artes Plásticas na Educação

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

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

A theoretical study on modelling the respiratory tract with ladder networks by means of intrinsic fractal geometry

Fractional order modeling of biological systems has received significant interest in the research community. Since the fractal geometry is characterized by a recurrent structure, the self-similar branching arrangement of the airways makes the respiratory system an ideal candidate for the application of fractional calculus theory. To demonstrate the link between the recurrence of the respiratory tree and the appearance of a fractional-order model, we develop an anatomically consistent representation of the respiratory system. This model is capable of simulating the mechanical properties of the lungs and we compare the model output with in vivo measurements of the respiratory input impedance collected in 20 healthy subjects. This paper provides further proof of the underlying fractal geometry of the human lungs, and the consequent appearance of constant-phase behavior in the total respiratory impedance.

Acylated cyanoimido-complexes trans-[Mo(NCN){NCN(O)R}(DPPE)(2)]Cl and their reactons with electrophiles: Chemical, electrochemical and theoretical study

Treatment of a dichloromethane solution of trans-[Mo(NCN){NCNC(O)R}(dppe)(2)]Cl [R = Me (1a), Et (1b)] (dppe = Ph2PCH2CH2PPh2) with HBF4, [Et3O][BF4] or EtC(O)Cl gives trans-[Mo(NCN)Cl-(dppe)(2)]X [X = BF4 (2a) or Cl (2b)] and the corresponding acylcyanamides NCN(R')C(O)Et (R' = H, Et or C(O)Et). X-ray diffraction analysis of 2a (X = BF4) reveals a multiple-bond coordination of the cyanoimide ligand. Compounds 1 convert to the bis(cyanoimide) trans-[Mo(NCN)(2)(dppe)(2)] complex upon reaction with an excess of NaOMe (with formation of the respective ester). In an aprotic medium and at a Pt electrode, compounds 1 (R = Me, Et or Ph) undergo a cathodically induced isomerization. Full quantitative kinetic analysis of the voltammetric behaviour is presented and allows the determination of the first-order rate constants and the equilibrium constant of the trans to cis isomerization reaction. The mechanisms of electrophilic addition (protonation) to complexes 1 and the precursor trans[Mo(NCN)(2)(dppe)(2)], as well as the electronic structures, nature of the coordination bonds and electrochemical behaviour of these species are investigated in detail by theoretical methods which indicate that the most probable sites of the proton attack are the oxygen atom of the acyl group and the terminal nitrogen atom, respectively.

Redox-active cytotoxic diorganotin(IV) cycloalkylhydroxamate complexes with different ring sizes: Reduction behaviour and theoretical interpretation

Two series of new diorganotin(IV) cycloalkylhydroxamate complexes with different ring sizes (cyclopropyl, cyclobutyl, cyclopentyl and cyclohexyl), formulated as the mononuclear [R2Sn(HL)(2)] (1:2) (a, R=Bu-n and Ph) and the polymeric [R2SnL](n) (1:1) (b, R=Bu-n) compounds, were prepared and fully characterized. Single crystal X-ray diffraction for [(Bu2Sn)-Bu-n{C5H9C(O)NHO}(2)] (3a) discloses the cis geometry and strong intermolecular NH center dot center dot center dot O interactions. The in vitro cytotoxic activities of the complexes were evaluated against HL-60, Bel-7402, BGC-823 and KB human tumour cell lines, the greater activity concerning [(Bu2Sn)-Bu-n(HL)(2)] [HL=C3H5C(O)NHO (1a), C6H11C(O)NHO (4a)] towards BGC-823. The complexes undergo, by cyclic voltammetry and controlled-potential electrolysis, one irreversible overall two-electron cathodic process at a reduction potential that does not appear to correlate with the antitumour activity. The electrochemical behaviour of [R2Sn(C5H9C(O)NHO)(2)] [R=Bu-n (3a), Ph (7a)] was also investigated using density functional theory (DFT) methods, showing that the ultimate complex structure and the mechanism of its formation are R dependent: for the aromatic (R = Ph) complex, the initial reduction step is centred on the phenyl ligands and at the metal, being followed by a second reduction with Sn-O and Sn-C ruptures, whereas for the alkyl (R=Bu-n) complex the first reduction step is centred on one of the hydroxamate ligands and is followed by a second reduction with Sn-O bond cleavages and preservation of the alkyl ligands. In both cases, the final complexes are highly coordinative unsaturated Sn-II species with the cis geometry, features that can be of biological significance.

Electrorheology study of a series of LC cyanobiphenyls: Experimental and theoretical treatment

In this work we study the electro-rheological behaviour of a series of four liquid crystal (LC) cyanobiphenyls with a number of carbon atoms in the alkyl group, ranging from five to eight (5CB–8CB). We present the flow curves for different temperatures and under the influence of an external electric field, ranging from 0 to 3 kV/mm, and the viscosity as a function of the temperature, for the same values of electric field, obtained for different shear rates. Theoretical interpretation of the observed behaviours is proposed in the framework of the continuum theory of Leslie–Ericksen for low molecular weight nematic LCs. In our analysis, the director alignment angle is only a function of the ratio between the shear rate and the square of the electric field – boundary conditions are neglected. By fitting the theoretical model to the experimental data, we are able to determine some viscosity coefficients and the dielectric anisotropy as a function of temperature. To interpret the behaviour of the flow curves near the nematic–isotropic transitions, we apply the continuum theory of Olmsted–Goldbart, which extends the theory of Leslie–Ericksen to the case where the degree of alignment of the LC molecules can also vary.

The computational role of short-term plasticity and the balance of excitation and inhibition in neural microcircuits: experimental and theoretical analysis

The computations performed by the brain ultimately rely on the functional connectivity between neurons embedded in complex networks. It is well known that the neuronal connections, the synapses, are plastic, i.e. the contribution of each presynaptic neuron to the firing of a postsynaptic neuron can be independently adjusted. The modulation of effective synaptic strength can occur on time scales that range from tens or hundreds of milliseconds, to tens of minutes or hours, to days, and may involve pre- and/or post-synaptic modifications. The collection of these mechanisms is generally believed to underlie learning and memory and, hence, it is fundamental to understand their consequences in the behavior of neurons.(...)

XII Iberian-Italian Congress of Financial and Actuarial Mathematics

"The purpose of the XII Iberian-Italian Congress of Financial and Actuarial Mathematics is to provide a meeting point for researchers in Financial Economics from different countries and research backgrounds in universities, government or financial institutions. In fact, the Congress which is currently taking place in Lisbon has been organized to encourage communication and debate among the participants as well as to reinforce the bonds between us.The current edition of the Congress is characterized by the quality and diversity of the papers that have been submitted with special attention to the International Financial Crisis and measures of risk in different financial markets. However, as the Congress Program indicates, there are also parallel sessions about traditional topics in finance such as asset pricing, insurance, corporate finance, etc.Although this Congress has always been organized alternately between Spain and Italy, this year we have the great pleasure of celebrating it in Portugal which will be included as a permanent partner." [prefácio]

Diffusion and efficiency of ISO 9001 in Portugal: a qualitative and quantitative study from a holistic theoretical perspective

Purpose – the aim of this paper is to analyse the diffusion and efficiency of ISO 9001 on different sectors of activity Design/methodology/approach – for that purpose, a holistic an integrative theoretical approach was based on the scope of the Contingency theory, the Institutional theory and the Resources-Based View (RBV). This theorethical perspective was used in a broad empirical study, using a qualitative and quantitative methodology, concerning Portuguese companies from different sectors of activity. Findings – according to the findings from both perspectives, a ranked combination of the named theoretical frame was constructed. Research limitations/implications – as to the analysis of the efficiency of ISO 9000, one of the limitations of this study lays in the consideration of just two sectors of activity, and another relates to its domestic geographical placement. Practical implications – this study used the ISO 9001 structure for the interviews and this has revealed very useful for the organizations to grasp the matters inquired. Originality/value – a relevant contribution to the state of art is achieved through the considered theoretical scope of analysis