Matemática na Educação Pré-Escolar : A ordem das dezenas

O nosso sistema numérico é um sistema posicional e de base dez. É posicional porque o valor dos símbolos depende da posição que ocupam. É de base dez por serem necessárias dez unidades de ordem inferior para compor uma de ordem imediatamente superior. Embora consideremos este sistema simples e natural quando o utilizamos no dia a dia, não nos devemos esquecer de como é sofisticado e engenhoso. A humanidade demorou muito a ter um sistema numérico como o que utilizamos presentemente. Houve mesmo épocas em que civilizações avançadas utilizavam diferentes sistemas em simultâneo. Alguns consideravelmente piores do que o atual. Por isso, não podemos almejar que uma criança em idade pré-escolar possa compreender totalmente o sistema decimal. De facto, a temática das ordens numéricas e, em particular, a da ordem das dezenas, é consideravelmente delicada. Neste artigo, exploraremos algumas formas de abordar o conceito de ordem das dezenas junto de crianças a partir dos cinco anos de idade. As ideias apresentadas são inspiradas no Singapore Math, método utilizado para o ensino da matemática inicial em Singapura, um exemplo bem-sucedido da abordagem "concreto-pictórico-abstrato".

Frações (parte I)

A temática das frações é provavelmente o assunto mais delicado no que diz respeito ao ensino da matemática inicial. Por terem múltiplas aplicações, contextos e sentidos, as frações pedem um ensino altamente especializado e esmerado. Há que modelar de forma cuidadosa o conceito de fração, fasear e ordenar os nós conceptuais ao longo dos anos e dosear o caráter abstrato/concreto dos exemplos e atividades. Muito se testou, teorizou e escreveu sobre esta temática. Este trabalho consiste num resumo alargado sobre o ensino das frações, documentado em literatura especializada e ilustrado através de exemplos concretos retirados de manuais do Singapore Math, um dos mais cotados métodos de ensino do mundo.

Contribution of traffic and tobacco smoke in the distribution of polycyclic aromatic hydrocarbons on outdoor and indoor PM2.5

Traffic emissions and tobacco smoke are considered two main sources of polycyclic aromatic hydrocarbons (PAHs) in indoor and outdoor air. In this study, the impact of these sources on the level of fine particulate matter (PM2.5) and on the distribution of 15 PAHs regarded as priority pollutants by the US-EPA on PM2.5 were evaluated and compared. Outdoor and indoor PM2.5 samples were collected during winter 2008 in Oporto city in Portugal, for sampling periods of 12 and 24 hours, respectively. The outdoor PM2.5 were sampled at one site directly influenced by traffic emissions and the indoor PM2.5 samples were collected at one home directly influenced by tobacco smoke and another one without smoke. A methodology based on microwave-assisted extraction and liquid chromatography with fluorescence detection was applied for the efficient PAHs determination in indoor and outdoor PM2.5. PAHs in indoor PM2.5 concentrations were significantly influenced by the presence of traffic and tobacco smoking emissions. The mean of ΣPAHs in the outdoor traffic PM2.5 was not significantly different from the value attained in the indoor without smoking site. The tobacco smoke increased significantly PAHs concentrations on average about 1000 times more, when compared with the outdoor profile samples suggesting that tobacco smoking may be the most important source of indoor PAHs pollution.

Copper, nickel and zinc removal by peanut hulls: batch and column studies in mono, tri-component systems and with real effluent

The main goal of this research study was the removal of Cu(II), Ni(II) and Zn(II) from aqueous solutions using peanut hulls. This work was mainly focused on the following aspects: chemical characterization of the biosorbent, kinetic studies, study of the pH influence in mono-component systems, equilibrium isotherms and column studies, both in mono and tri-component systems, and with a real industrial effluent from the electroplating industry. The chemical characterization of peanut hulls showed a high cellulose (44.8%) and lignin (36.1%) content, which favours biosorption of metal cations. The kinetic studies performed indicate that most of the sorption occurs in the first 30 min for all systems. In general, a pseudo-second order kinetics was followed, both in mono and tri-component systems. The equilibrium isotherms were better described by Freundlich model in all systems. Peanut hulls showed higher affinity for copper than for nickel and zinc when they are both present. The pH value between 5 and 6 was the most favourable for all systems. The sorbent capacity in column was 0.028 and 0.025 mmol g-1 for copper, respectively in mono and tri-component systems. A decrease of capacity for copper (50%) was observed when dealing with the real effluent. The Yoon-Nelson, Thomas and Yan’s models were fitted to the experimental data, being the latter the best fit.

Electroanalytical determination of oxadiazon and characterization of its base-catalyzed ring-opening products

The electrochemical behavior of the hydrolysis products of oxadiazon was studied by cyclic and square-wave voltammetry using a glassy carbon electrode. Maximum currents were obtained at pH 12.8 in an aqueous electrolyte solution containing 30% ethanol and the current did not decrease with time showing that there was little adsorption of the reaction products on the electrode surface. The hydrolysis products of oxadiazon were identi®ed, after isolation and puri®cation, as 1-trimethylacetyl-2-(2,4-dichloro-5-isopropoxyphenyl)-2-ethoxycarbonylhydrazine (Oxa1) and 1-trimethylacetyl-2-(2,4-dichloro-5-isopropoxyphenyl) hydrazine (Oxa2) with redox potentials 0.6Vand 70.1V (vs. Ag=AgCl), respectively. Based on the electrochemical behavior of 1-trimethylacetyl-2-(2,4-dichloro-5-isopropoxyphenyl) hydrazine (Oxa2) a simple electroanalytical procedure was developed for the determination of oxadiazon in commercial products used in the treatment of rice crops in Portugal that contain oxadiazon as the active ingredient. The detection limit was 161074 M, the mean content and relative standard deviation obtained for seven samples of two different commercial products by the electrochemical method were 28.4 0.8% (Ronstar) and 1.9 0.2% (Ronstar GR), and the recoveries were 100.3 5.4% and 101.1 5.3 %, respectively.

Shane Meadows’ country: analysis of the film this is England (2006)

This Is England is social realist film portraying racism and poverty in 1980s Britain through the eyes of Shaun, a 12 year old boy, who has lost his father in the Falklands war and as to come to terms with his own identity, the difficult transition from childhood to adolescence and the need to fit in a determined group/tribe/gang. The following article aims at analysing relevant aspects depicted from the film emphasizing the so much debated reality of life during 80s. In This is England Shane Meadows manages to rediscover his own self geography, by revisiting his adolescent years. It is a biographical film about the importance of peer pressure and the results of an excess of nationalism, at the same time it typifies some issues related to the 80s youth culture.

Prática de ensino supervisionado no 1.º e 2.º ciclo do ensino básico: calculo mental: um estudo sobre as estratégias utilizadas por alunos do 1.º e do 2.º ciclo do ensino básico

Relatório de Estágio apresentado à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ensino do 1.º e do 2.º Ciclo do Ensino Básico

Débora, qual foi o livro que trouxeste hoje? A potencialidade dos livros na educação pré-escolar

Relatório da UC Seminário de Apoio à Prática Profissional Supervisionada Mestrado em Educação Pré-Escolar

Desenvolvimento do sistema de controlo de um braço robotizado e respetiva interface com o utilizador

A robótica tem evoluído de forma significativa nos últimos anos e passa a ser indispensável em várias aplicações nas áreas da engenharia, aeronáutica, medicina, entre outras. O estado da arte do presente trabalho está dividido em duas partes, uma que aborda vários aspetos relacionados com a robótica e outra com os aspetos da fundamentação matemática por de trás da robótica, porque para controlar o robô é necessário implementar expressões matemáticas para o poder controlar. Neste trabalho é apresentado um sistema de controlo do braço robótico MENTOR e o desenvolvimento de uma interface para o utilizador. Para o controlo do braço robótico foi necessário calcular a cinemática direta e inversa, para que se possa obter os ângulos das juntas para uma dada posição ou qual é a posição final do braço robótico para um valor das juntas. O sistema é bastante flexível e foi desenvolvido para ser utilizado essencialmente para aprendizagem de robótica, podendo no entanto ser utilizado em outras aplicações.

A divisão no 4º ano de escolaridade

Dissertação apresentada para obtenção do grau de Mestre em Educação Matemática na Educação Pré-Escolar e nos 1.º e 2.º Ciclos do Ensino Básico

A survey in Portuguese X-ray fluoroscopy equipment: dose rates and image quality

X-ray fluoroscopy is essential in both diagnosis and medical intervention, although it may contribute to significant radiation doses to patients that have to be optimised and justified. Therefore, it is crucial to the patient to be exposed to the lowest achievable dose without compromising the image quality. The purpose of this study was to perform an analysis of the quality control measurements, particularly dose rates, contrast and spatial resolution of Portuguese fluoroscopy equipment and also to provide a contribution to the establishment of reference levels for the equipment performance parameters. Measurements carried out between 2007 and 2013 on 143 fluoroscopy equipment distributed by 34 nationwide health units were analysed. The measurements suggest that image quality and dose rates of Portuguese equipment are congruent with other studies, and in general, they are as per the Portuguese law. However, there is still a possibility of improvements intending optimisation at a national level.

Estudo Estratigráfico e Paleontológico do Jurássico do Algarve Ocidental

Algarve Province, Southern Portugal, corresponds in part to a meso-cenozoic basin running along the coast from Cabo S. Vicente to beyond Spanish border. Structurally it is a big monocline plunging southwards much deformed mainly by two East-West longitudinal flexures. Lithostratigraphical and chronostratigraphical studies dealt specially with Jurassic formations. This and the geological mapping of the post-Hercynian sedimentary formations allow us to define the following units: Triassic-Lower Liassic Arenitos de Silves (Silves sandstones sensu P. Choffat, pro parte) - At their base the Silves sandstones (0-150m) are represented mainly by cross-bedded red sandstones. This unit is Upper Triassic (Keuper) in age, on the evidence of some Brachiopoda. Complexo margo-carbonatado de Silves (Silves marl-limestone complex=Silves sandstones sensu P. Choffat, pro parte) (80-200m) overlies the preceding, it may be reported to the Upper Triassic-Hettangian. It consists of a thick pelite-marl-dolomite-limestone series with many intercalations of greenstones. Since no fossils were found it is not possible to conclude whether it is still Hettangian or if it does correspond, in the whole or in part, already to the Sinemurian. Liassic Dolomitos e calcários dolomíticos de Espiche (Espiche dolomite-rocks and dolomitic-limestones) - The usually massive and finely crystalline or saccharoidal dolomites and dolomitic-limestones are the toughest strata of the Algarve margin giving rise to several hills. Its thickness attains in certain points 60 metres at least. Based on geometry and on lithological similarities with the carbonated complex of the northern basin of Tagus river (Peniche, São Pedro de Muel, Quiaios), this formation can be accepted as Sinemurian in age. As it happens with the carbonated complex, here also the first dolomite beds are non-isochronal throughout the region; upper time-limit of the dolomitic facies is either Lower Carixian, Lower Toarcian or even Lower Dogger. The dolomitization is secondary but not much later than sedimentation. However, between Cabo S. Vicente-Vila do Bispo there is evidence of an even later secondary dolomitization related to the regional fault complex. Calcário dolomítico com nódulos de silex da praia de Belixe (Belixe beach dolomitic-limestone with silex nodules) (50-55m) - Ascribed to Lower or Middle Carixian on the basis of Platypleuroceras sp., Metaderoceras sp. nov. and M. gr. Venarense. Calcário cristalino compacto com Protogrammoceras, Fuciniceras e ? Argutarpites de Belixe (Belixe compact crystalline limestone with Protogrammoceras, Fuciniceras and ? Argutarpites) (30m) - Ascribed to Lower Domerian. Middle and Upper Domerian are indicated but by a single specimen of ? Argutarpites. Calcários margosos e margas com Dactylioceras semicelatum e Harpoceratídeos de Armação Nova (Armação Nova marly limestones and marls with D. semicelatum and Harpoceratidae) (25m) -Ascribed to Lower Toarcian. Middle and Upper Toarcian formations are not known in the Algarve. Dogger Calcários oolíticos, c. corálicos, c. pisolíticos, c. calciclásticos, c. dolomíticos e dolomitos de Almadena (Almadena oolitic-limestones, coral-reef-limestones, pisolite-limestones, limeclastic-limestones, dolomitic-limestones and dolomite-rocks) (more than 50 metres), with lagoonal facies. Ascribed to Aalenian-Bathonian-? Callovian. Margas acinzentadas e calcários detríticos com Zoophycos da praia de Mareta (Mareta beach greyish marls and detritical limestones with Zoophycos) (40m) - Pelagic transreef facies with Upper Bajocian and Bathonian ammonites. Calcários margosos e margas da praia de Mareta (Mareta beach pelagic marly-limestones and marls) (110m) - Ascribed to the Callovian on its ammonites. Malm Near Cabo S. Vicente and Sagres the first Upper Jurassic level consists of a yellowish-brown nodular, compact, locally phosphated and ferruginous, sometimes conglomeratic, marly limestone (0,35-1,50m) containing a rich macrofauna, which includes: 1) Callovian forms unknown at Lower Oxfordian; 2) Upper Callovian forms that still survived in Lower and Middle Oxfordian; 3) Lower Oxfordian forms (Mariae and Cordatum Zones); 4) Lower and Middle Oxfordian forms (Mariae to Plicatilis Zone); 5) Middle Oxfordian forms (plicatilis Zone), and some ones appearing in Middle Oxfordian. This condensed deposit is therefore dated from Middle Oxfordian (Plicatilis Zone). The other Upper Jurassic lithostratigraphical units were also mapped but their detailed study is not presented in this work. Correlations between lithostratigraphical and chronostratigraphical scales from P. Choffat, J. Pratsch, C. Palain and from the author are stated. Further correlations are attempted between zonc scales of Carixian-Lower Toarcian and Upper Bajocian-Middle Oxfordian of France, Spain (Asturias, Iberian and Betic Chains), Argel (Orania) and Portugal (northern Tagus basin and Algarve). The study of pyritous fossil assemblages common in Upper Bathonian-Lower Callovian marly levels of the praia da Mareta seems to suggest that these sediments were deposited in a bay or in an almost closed coastal re-entrance virtually without deep water circulation. Although such conditions may occur at any depth one may suppose that these ones actually correspond to an infralittoral neritic environment. The thaphocoenosis collected there are almost entirely composed of nektonic (ammonites, Belemnites) and planktonic (Bositra) faunas. The sedentary (crinoids, brachiopods) or free (sea-urchins, gastropods) epibenthonic forms are very scarce; endobenthonic forms are not known. The palaeontological study of all Nautiloids and Ammonoids of the Liassic and Dogger is presented (except Kosmoceratidae and Perisphinctaceae). Among the thirty one taxa dealt with, one is new (Metaderoceras sp. nov.) and the great majority of the others has been identified for the first time in Algarve. Some others have never been reported before in Portuguese formations. The evolution, during Jurassic times, of the sedimentary basins of the Portuguese plate margin is described. The absence of Cephalopods in the very extensive marly and dolomitic limestones, partly marine, suggests that, during Lower Liassic, palaeogeography underwent no great changes. Dolomitic-limestone with silex nodules from Cabo S. Vicente contain the first ammonites recorded at the base of the Middle Liassic. This facies, although very common in Tethys, is unknown north of the Tagus. The faunal assemblage has a mediterranean to submediterranean character. Comparisons between faunal assemblage" from Algarve with the ones known north of the Tagus show that communications between Boreal Europe and Tethys, virtually non-existent during Lower and Middle Carixian, became very easy during Lower Domerian. In earlier Pliensbachian times two distinct seas were adjacent to the Iberian plate. One, an epicontinental sea with a tethyan fauna, extended southwards from the Meseta margin. Another, was a boreal sea; during its transgressive episodes boreal faunas attained into the basin north of the Tagus. During Middle Carixian and Lower Domerian, owing to simultaneous transgressions, these two seas joined together allowing faunal exchanges along the epicontinental areas which limited the emerging hercynian chains belts. During Liassic, the Algarve belonged undoubtedly to the tethyan submediterranean province. The area north of the Tagus, on the contrary, was a complex realm where subboreal and tethyan affinities alternatively prevailed. In the Algarve the first Middle Jurassic deposits do frequently show lateral thickness reductions as well as unconformities contemporaneous with other generalized disturbances on the sedimentation processes in other parts of Europe. By this time, near Sagres, a barrier reef developed separating lagoonal or ante-reef facies from the transreef pelagic zone. The presence of tethyan fauna, the abundance of Phylloceratidae and the absence of boreal forms allow us to consider the Algarve basin as a submediterranean province. The presence of Callovian pelagic fossiliferous formations in the Loulé area shows that during Middle Jurassic the marl-limestone transreef sedimentation was not confined to the western Algarve. They would extend eastwards where they only can be seen in the core of some anticlines. This is due to the progressive sinking of the meso-cenozoic formations as we proceed towards the South of the Sagres-Algoz-Querença flexure. In the whole of the Peninsule, and as for the Middle Callovian, an important regression can be clearly recognized on the evidence of an erosion surface which strikes obliquely the Middle and Upper Callovian strata. The geographic boundaries of the different faunal provinces are not changed by the presence of many Kosmoceratidae in the phosphate nodules since they are but a minority in comparison with the tethyan forms. An abstract model can be constructed showing that in Western Europe the Kosmoceratidae may have migrated South and westwards through a channel of the sea that linked Paris basin to Poitou and Aquitaine. By migrating between the Iberian meseta and the Armorican massif this fauna reached northern Tagus basin at the beginning of Upper Callovian (Athleta Zone); this south and southwest bound migration would have proceeded, allowing such forms to reach Algarve basin only in latest Callovian times (Lamberti Zone). This migration means that during Middle Jurassic a widely spread North Atlantic sea would exist, flooding the western part of Portugal up to the Poitou.

Professions and inter-disciplinary teamwork in socially embedded bureaucracies: Synthesis and hypotheses on the impact of informal and formal organization

In order to maximize their productivity, inter-disciplinary multi-occupation teams of professionals need to maximize inter-occupational cooperation in team decision making. Cooperation, however, is challenged by status anxiety over organizational careers and identity politics among team members who differ by ethnicity-race, gender, religion, nativity, citizenship status, etc. The purpose of this paper is to develop hypotheses about how informal and formal features of bureaucracy influence the level of inter-occupation cooperation achieved by socially diverse, multi-occupation work teams of professionals in bureaucratic work organizations. The 18 hypotheses, which are developed with the heuristic empirical case of National Science Foundation-sponsored university school partnerships in math and science curriculum innovation in the United States, culminate in the argument that cooperation can be realized as a synthesis of tensions between informal and formal features of bureaucracy in the form of participatory, high performance work systems.

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

Atividade física de mulheres no climatério: comparação entre auto-relato e pedômetro

OBJETIVO Comparar dois métodos de avaliação de atividade física entre mulheres na pré, transição e pós-menopausa. MÉTODOS Estudo transversal aninhado à coorte de mulheres na pré, peri e pós-menopausa em uma cidade do sul do Brasil. As participantes responderam a um questionário com dados sociodemográficos e clínicos. A atividade física foi avaliada utilizando-se o Questionário Internacional de Atividade Física – versão curta e a contagem do número de passos com o uso de pedômetro. As participantes foram classificadas em estratos de atividade física de acordo com o instrumento utilizado. Para análise estatística foram realizados os testes de correlação de Spearman, índice de Kappa, coeficiente de concordância e análise das medidas contínuas de Bland-Altman. RESULTADOS A concordância (k = 0,110; p = 0,007) e a correlação (rho = 0,136; p = 0,02) entre o Questionário Internacional de Atividade Física – versão curta e o pedômetro foram fracas. No gráfico de Bland-Altman, observou-se que as diferenças se afastam do valor zero tanto quanto a atividade física é mínima ou mais intensa. Comparando-se os dois métodos, a frequência de mulheres inativas é maior quando avaliadas pelo pedômetro do que pelo Questionário Internacional de Atividade Física. O oposto ocorre entre as ativas. CONCLUSÕES A concordância entre os métodos foi fraca. Embora de fácil aplicação, o Questionário Internacional de Atividade Física superestima a atividade física em relação à avaliação por pedômetro.