Children's understanding of fractions

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Understanding risk and uncertainty: the importance of correlations

There is general agreement today that students should leave school with a good grasp of all the basic mathematical ideas about how to deal with uncertainty. As adults, they will have to make important decisions about the probability of certain events and about the risk of a wide range of dangers. The understanding of uncertainty also plays a central role in modern science. Many scientific discoveries of great importance would have been impossible if scientists had only conceived of the world in terms of certainty. In many situations studied by scientists, and most certainly in all situations studied in social sciences, researchers can at best identify and measure imperfect associations between variables. This paper summarises research about understanding correlations, which assess whether, how variables and the degree to which variables show a mutual association. The cognitive demands of understanding these associations are analysed and a brief review of the literature is presented

Can children’s spelling of schwa vowels in stems be improved?

Children in the early grades of primary school do not seem to have much awareness of morphemes. In this study, a priming paradigm was used to try to detect early signs of morphological representation of stems througha spelling task presented to Portuguese children (N= 396; age range 6 to 9 years). Primes shared the stem with the targets and contained well-articulated, stressed vowels; the stems of the target words contained non-stressed schwa vowels, which typically result in spelling difficulties. If priming proved effective, the well-articulated vowels in the prime should lead to improvement in the spelling of the schwa vowels in the targets. Primes were presented in two conditions: in only-oral or in oral-plus-written form. Effectiveness of priming was assessed by comparison with a no-priming condition. There was a significant interaction between priming effects and grade. No priming effects were detected in 6- and 7-year-old children; oral-plus-written priming produced higher rates of correct vowel spelling for 8- and 9-year-olds; only-oral priming was effective in improving the vowel spelling of 9-year-olds. Thus the older children used morphological information under priming conditions but there is no evidence to suggest that younger children did so

Understanding rational numbers

Abstract Rational numbers are important as a foundation for later mathematics learning and particularly for learning algebra. Most researcher agree that students find rational numbers difficult. This article question the traditional use of partitioning as the starting point for the teaching of fractions. It seeks the origin of children's understanding of rational numbers in their understanding of division. A number of empirical studies are presented on children's use of action schemes for division, correspondence and partitioning. At last conclusions and implications for education are drawn. 23 Terezinha Nune

A relação entre a consciência fonológica e as conceptualizações de escrita em crianças dos 4 aos 6 anos

O presente estudo tem como objectivo investigar o desenvolvimento da consciência fonológica e a sua relação com as conceptualizações de escrita em crianças portuguesas dos quatro aos seis anos de idade. A amostra do estudo é constituída por 60 crianças de idade pré-escolar divididas por quatro grupos etários (4 anos – 4 anos e 6 meses.; 4 anos e 7 meses – 5 anos e 1 mês; 5 anos e 2 meses- 5 anos e 8 meses; 5 anos e 9 meses – 6 anos e 3 meses). As crianças foram testadas com uma bateria de seis provas de consciência fonológica e sujeitas a uma entrevista para apreciar as suas conceptualizações de escrita. O teste das Matrizes Progressivas Coloridas de Raven foi aplicado de forma a ser usado como controle na análise de regressão. Os resultados demonstram que existe um crescente desenvolvimento fonológico de acordo com a idade das crianças, mas que a maior parte das crianças ainda não vai além do nível pré-silábico, no que respeita às conceptualizações de escrita. Não foram encontradas correlações significativas entre a consciência fonológica e os níveis de conceptualização sobre a escrita. A hipótese de que a criança desenvolve conceitos de escrita como consequência da sua consciência fonológica não é suportada por este estudo. A falta de correlações significativas sugere que a consciência fonológica não deve ser vista como resultado do desenvolvimento de conceitos de escrita. É possível que a consciência fonológica seja uma condição necessária, mas não suficiente para o desenvolvimento das conceptualizações de escrita silábicas, e consequentemente alfabéticas nas crianças

Uma experiência concreta de planejamento territorial: avaliação do Plano Diretor Municipal (PDM) de Ibiporã/PR

O presente artigo tem como objetivo avaliar o planejamento e a gestão urbanos, bem como os planos diretores produzidos no Brasil nas últimas décadas. Para a análise do tema proposto foi essencial fundamentar a instituição de instrumentos legais para o ordenamento territorial brasileiro. A aprovação do Estatuto da Cidade (EC) gerou expectativa de mudança nos rumos da política e gestão territorial na direção da construção de municípios mais justos, social e ambientalmente. O EC instituiu instrumentos para o cumprimento da função social da propriedade e para institucionalizar a participação da sociedade. Após 15 anos de experiência, discute-se sobre o impacto transformador desta norma, tomando-se como referência a revisão do PDM Participativo de Ibiporã/PR. O planejamento participativo do PDM não conseguiu modificar a trajetória de desenvolvimento desigual nos municípios, contudo, diversificou e ampliou o campo de disputa e instituiu espaços alternativos de representação popular.This article aims to evaluate the planning and urban management, and master plans produced in Brazil in recent decades. For the analysis of the proposed theme was essential reasons for establishing legal instruments for the Brazilian territorial planning. The approval of the City Statute (CS) has generated expectations of change in the direction of policy and land management towards building fairer municipalities, socially and environmentally. The CS has introduced tools for the fulfillment of the social function of property and to institutionalize the participation of society. After 15 years of experience, we discuss about the transformative impact of this standard, taking as reference the review of PDM Participatory Ibiporã / PR. The PDM participatory planning could not modify the unequal development trajectory in the cities, however, diversified and expanded the playing field and set up alternative spaces for popular representation

Transforming research on morphology into teacher practice

Research suggests that the explicit teaching of morphological principles will improve children’s spelling. Despite the fact that reference is made to morphology in English policy documents, teachers make limited use of morphology when teaching spelling, relying more heavily on phonic and visual strategies. After attending a course on role of morphemes in spelling, teachers’ own awareness of morphology increased and this was reflected in their practice. This in turn caused their pupils to make significant gains in spelling, compared to a control group. This reinforces the proposition that explicit instruction about morphemes is helpful to children’s learning. It demonstrates the fact that research can be transformed into teacher practice, but it also illustrates the difficulties. Policy documentation alone is insufficient. Professional development can effect change but this may be hard to sustain. Children’s gains are contingent on teacher’s continuing to dedicate class time to focussed intervention