Matemática na educação Pré-Escolar : esquemas todo-partes

O Singapore Math, método utilizado para o ensino da Matemática em Singapura é, segundo as mais prestigiadas avaliações internacionais, um exemplo bem-sucedido da abordagem «concreto-pictórico-abstrato». Um dos inúmeros procedimentos didáticos são os number bonds (esquemas todo-partes), utilizados no ensino de factos fundamentais relativos à primeira dezena: decomposições, adições e subtrações. Neste artigo, analisaremos o que são, quais as vantagens e a forma de utilização destes esquemas desde a educação pré-escolar.

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.

Diagnosis and treatment of mental disorders: a survey of Singapore mental health professionals

Background: A series of surveys of mental health literacy have been undertaken in Australia, involving members of the general public as well as general practitioners and mental health professionals, whereby respondents consider vignettes of depression and of schizophrenia, offer a diagnosis and rate a series of possible interventions for their judged helpfulness. A similar survey was undertaken in Singapore and is reported in this paper. Methods: The survey was undertaken at a large state psychiatric hospital with staff (psychiatrists, allied health professionals, psychiatrically and generally trained nursing staff) rating a vignette of mania, in addition to the vignettes derived in Australia for depression and schizophrenia, and with the Australian intervention options extended somewhat to respect Singapore facilities. Results: Responses of those in the four professional groups were compared. The psychiatrists were highly accurate in generating diagnoses, other staff somewhat less so for diagnosing depression (with a percentage instead choosing a diagnosis of stress) and mania (with a percentage instead diagnosing a schizophrenic condition). Reported helpfulness ratings identified those interventions judged consensually as likely to be helpful or harmful, as well as establishing some differences across the four professional groups. Conclusions: The consensus decisions of helpful treatments for depression and schizophrenia revealed very similar findings to judgements made by Australian professionals. The treated outcome of schizophrenia was judged as somewhat worse than that for mania and depression. While non-medical staff differed from psychiatrists in judging the comparative utility of some drug interventions and lifestyle issues, there was clear evidence of a relatively dominant 'medical model' to recommended treatments, while traditional healing practices and services were rated as distinctly unhelpful.

A comparative mental health literacy survey of psychiatrists and other mental health professionals in Singapore

Objective: The objectives of this study are, first, to replicate and extend an Australian approach to assessing mental health literacy by studying a sample of Singapore mental health professionals, and to focus on differences between judgements made by the psychiatrists in comparison with the other mental health professionals. Second, to compare the psychiatrists' judgements with those of Australian psychiatrists. Method: The Australian questionnaire, assessing responses in relation to vignettes of major depression and to schizophrenia was extended by adding a third vignette of mania, and by the addition of several region-specific response options. Nearly 500 questionnaires were distributed to representative staff (psychiatrists, nurses and allied health) of a large psychiatric institution in Singapore, with a response rate of 81%. Psychiatrists' judgements were compared with all other hospital staff, and with Australian psychiatrists' judgements. Results: The two principal contrast groups (Singapore psychiatrists and other Singapore mental health professionals) differed slightly in terms of diagnostic accuracy. The psychiatrists differed in favouring a more professionally focused model of intervention, while both professional groups viewed traditional healers and their practices as distinctly unhelpful. Direct comparison of psychiatrist ratings generated in Singapore and in Australia revealed quite similar response profiles. Conclusions: In addition to generating data of some intrinsic importance, comparison with Australian survey data allows the potential impact of regional and cultural differences, as well as of varying psychiatric practices, to be identified. Responses identified more similarities than differences in the judgements of the psychiatrists from the two countries.

Naltrexone in the treatment of male alcoholics - an effectiveness study in Singapore

Naltrexone has been demonstrated in western studies to be a useful pharmacological adjunct within treatment programmes for alcoholic patients. We report the first study of its efficacy and usefulness in an Asian region. This project was designed to allow naltrexone's performance to be assessed under routine clinical conditions but with patients selected on the basis of their being likely to comply. Following in-patient detoxification, 53 male alcohol-dependent patients admitted to the Alcohol Treatment Centre at Woodbridge Hospital, Singapore, were enrolled in a 12-week, placebo-controlled trial of naltrexone hydrochloride (50 mg/day). Subjects were randomized on a 2:1 basis, with 35 receiving naltrexone and 18 receiving placebo. Analyses identified that a higher percentage of naltrexone patients completed the study (40% vs. 22%). In the study non-completers, the dropout rate due to drinking relapse was also lower in the naltrexone group (9% vs. 43%). Of the 39 patients for whom drinking status over the trial could be ascertained, fewer naltrexone-treated patients drank (33% vs. 53%). Alcohol craving scores also showed a selective and distinct reduction in the naltrexone-treated group. Results suggest that naltrexone may be an effective and safe aid to treatment of alcohol dependent patients in Asian patients, for whom the aims are to reduce alcohol craving and drinking reinstatement, but where compliance is likely to be low.

Modelling the control strategies against dengue in Singapore

Notified cases of dengue infections in Singapore reached historical highs in 2004 (9459 cases) and 2005 (13 817 cases) and the reason for such all increase is still to be established. We apply a mathematical model for dengue infection that takes into account the seasonal variation in incidence, characteristic of dengue fever, and which mimics the 2004-2005 epidemics in Singapore. We simulated a set of possible control strategies and confirmed the intuitive belief that killing adult mosquitoes is the most effective strategy to control an ongoing epidemic. On the other hand, the control of immature forms was very efficient ill preventing the resurgence of dengue epidemics. Since the control of immature forms allows the reduction of adulticide, it seems that the best strategy is to combine both adulticide and larvicide control measures during an outbreak, followed by the maintenance of larvicide methods after the epidemic has subsided. In addition, the model showed that the mixed strategy of adulticide and larvicide methods introduced by the government seems to be very effective in reducing the number of cases in the first weeks after the start of control.

FOR DEBATE A hypothesis for the 2007 dengue outbreak in Singapore

A previous mathematical model explaining dengue in Singapore predicted a reasonable outbreak of about 6500 cases for 2006 and a very mild outbreak with about 2000 cases for 2007. However, only 3051 cases were reported in 2006 while more than 7800 were reported in the first 44 weeks of 2007. We hypothesized that the combination of haze with other local sources of particulate matter had a significant impact on mosquito life expectancy, significantly increasing their mortality rate. To test the hypothesis a mathematical model based on the reproduction number of dengue fever and aimed at comparing the impact of several possible alternative control strategies was proposed. This model also aimed at contributing to the understanding of the causes of dengue resurgence in Singapore in the last decade. The model`s simulation demonstrated that an increase in mosquito mortality in 2006 and either a reduction in mortality or an increase in the carrying capacity of mosquitoes in 2007 explained the patterned observed in Singapore. Based on the model`s simulation we concluded that the fewer than expected number of dengue cases in Singapore in 2006 was caused by an increase in mosquito mortality due to the disproportionate haze affecting the country that year and that particularly favourable environmental conditions in 2007 propitiated mosquitoes with a lower mortality rate, which explains the greater than expected number of dengue cases in 2007. Whether our hypothesis is plausible or not should be debated further.