O papel das representações na resolução de problemas de Matemática: um estudo no 1º ano de escolaridade

Este estudo tem como objectivo investigar o papel que as representações, construídas por alunos do 1.o ano de escolaridade, desempenham na resolução de problemas de Matemática. Mais concretamente, a presente investigação procura responder às seguintes questões: Que representações preferenciais utilizam os alunos para resolver problemas? De que forma é que as diferentes representações são influenciadas pelas estratégias de resolução de problemas utilizadas pelos alunos? Que papéis têm os diferentes tipos de representação na resolução dos problemas? Nesta investigação assume-se que a resolução de problemas constitui uma actividade muito importante na aprendizagem da Matemática no 1.o Ciclo do Ensino Básico. Os problemas devem ser variados, apelar a estratégias diversificadas de resolução e permitir diferentes representações por parte dos alunos. As representações cativas, icónicas e simbólicas constituem importantes ferramentas para os alunos organizarem, registarem e comunicarem as suas ideias matemáticas, nomeadamente no âmbito da resolução de problemas, servindo igualmente de apoio à compreensão de conceitos e relações matemáticas. A metodologia de investigação segue uma abordagem interpretativa tomando por design o estudo de caso. Trata-se simultaneamente de uma investigação sobre a própria prática, correspondendo os quatro estudos de caso a quatro alunos da turma de 1.0 ano de escolaridade da investigadora. A recolha de dados teve lugar durante o ano lectivo 2007/2008 e recorreu à observação, à análise de documentos, a diários, a registos áudio/vídeo e ainda a conversas com os alunos. A análise de dados que, numa primeira fase, acompanhou a recolha de dados, teve como base o problema e as questões da investigação bem como o referencial teórico que serviu de suporte à investigação. Com base no referencial teórico e durante o início do processo de análise, foram definidas as categorias de análise principais, sujeitas posteriormente a um processo de adequação e refinamento no decorrer da análise e tratamento dos dados recolhidos -com vista à construção dos casos em estudo. Os resultados desta investigação apontam as representações do tipo icónico e as do tipo simbólico como as representações preferenciais dos alunos, embora sejam utilizadas de formas diferentes, com funções distintas e em contextos diversos. Os elementos simbólicos apoiam-se frequentemente em elementos icónicos, sendo estes últimos que ajudam os alunos a descompactar o problema e a interpretá-lo. Nas representações icónicas enfatiza-se o papel do diagrama, o qual constitui uma preciosa ferramenta de apoio ao raciocínio matemático. Conclui-se ainda que enquanto as representações activas dão mais apoio a estratégias de resolução que envolvem simulação, as representações icónicas e simbólicas são utilizadas com estratégias diversificadas. As representações construídas, com papéis e funções diferentes entre si, e que desempenham um papel crucial na correcta interpretação e resolução dos problemas, parecem estar directamente relacionadas com as caraterísticas da tarefa proposta no que diz respeito às estruturas matemáticas envolvidas. ABSTRACT; The objective of the present study is to investigate the role of the representations constructed by 1st grade students in mathematical problem solving. More specifically, this research is oriented by the following questions: Which representations are preferably used by students to solve problems? ln which way the strategies adopted by the students in problem solving influence those distinct representations? What is the role of the distinct types of representation in the problems solving process? ln this research it is assumed that the resolution of problems is a very important activity in the Mathematics learning at the first cycle of basic education. The problems must be varied, appealing to diverse strategies of resolution and allow students to construct distinct representations. The active, iconic and symbolic representations are important tools for students to organize, to record and to communicate their mathematical ideas, particularly in problem solving context, as well as supporting the understanding of mathematical concepts and relationships. The adopted research methodology follows an interpretative approach, and was developed in the context of the researcher classroom, originating four case studies corresponding to four 1 st grade students of the researcher's class. Data collection was carried out during the academic year of 2007/2008 and was based on observation, analysis of documents, diaries, audio and video records and informal conversations with students. The initial data analysis was based on the problems and issues of research, as well in the theoretical framework that supports it. The main categories of analysis were defined based on the theoretical framework, and were subjected to a process of adaptation and refining during data processing and analysis aiming the -case studies construction. The results show that student's preferential representations are the iconic and the symbolic, although these types of representations are used in different ways, with different functions and in different contexts. The symbolic elements are often supported by iconic elements, the latter helping students to unpack the problem and interpret it. ln the iconic representations the role of the diagrams is emphasized, consisting in a valuable tool to support the mathematical reasoning. One can also conclude that while the active representations give more support to the resolution strategies involving simulation, the iconic and symbolic representations are preferably used with different strategies. The representations constructed with distinct roles and functions, are crucial in the proper interpretation and resolution of problems, and seem to be directly related to the characteristics of the proposed task with regard to the mathematical structures involved.

"Os Conflitos ambientais em Portugal (1974-2015): uma breve retrospectiva"

In this chapter, the authors made a survey of the research undertaken by social scientists and their reflections on environmental conflicts in Portugal. In these, a critical discourse has emerged concerning, on the one hand, the weak public environmental awareness, and, on the other, the progressive obliteration of environmental movements and their institutionalization throughout the creation of different environmental groups and the incorporation of the “environment” in legislation and in political discourse. In a brief retrospective, we review several conflicts taking into account different relevant factors: level of mobilization, media attention received, organization, impact, and ideological reference they have had in Portugal since the seventies. We have particularly highlighted the movement against nuclear energy and the construction of dams, the pollution caused by intensive breeding, the expansion of eucalyptus plantations, the conflicts against “wild” forms of mining, the business of toxic waste, the expansion of the economy of the concrete, the installation of landfills, and the defense of the natural heritage. This survey has considered three periods: the 1970s, marked by the emergence and performance of ecological movements of different ideological extraction; the second half of the 1980s, marked by the institutionalization of the environment and the imposition of a new legal framework with impact on environmental policies resulting from the integration into the European Economic Community; and finally, a third period, from the 1990s to present, marked by increasing environmental media coverage, with a particular emphasis on environmental conflicts in a context of an increasing liberalization of economic activities and the expansion of extraction and of the concrete economy. This is also the period where the environment emerges in disputes over the uses of the territory as economic and asset value. Most of these conflicts arise from the activities of local agents or national environmental groups that quickly gain strong local roots and sometimes even have some success. However, their impact on the national and Community legislation seems to be less relevant.

Conflitos ambientais e progresso técnico na indústria mineira e metalúrgica em Portugal (1858-1938)

This chapter explores the relationship between environmental conflicts and technical progress, trying to understand, in the case of large mines of the Iberian Pyrite Belt, in Alentejo, how emerging environmental problems conditioned the performance or led to the search for alternative technical solutions, taking as chronological limit for this observation the beginning of World War II. In the absence of the archives of the companies, the research was based on existing administrative documents in the state archives (mining engineers reports, the licensing of mining activities), on reports and documents published in specialized mining press, in particular, the Bulletin of the Ministry of Public Works, Trade and Industry, the Journal of Public Works, Trade and Industry (both in Portuguese), and finally in the local press. Despite that limitation, the information available shows that in global competition markets, the success of the British enterprise in Santo Domingo had the active search for new technical solutions for the creation and adaptation of existing knowledge to local problems in order to maximize the mineral resources available. The early development of the hydrometallurgical processes for the treatment of poor ores, named ‘natural cementation’, can be explained as the way these companies tried to solve problems of competitiveness, boosting economies of scale. Thus, they transferred the environmental costs previously limited to agriculture to more fragile social groups, the poor fishermen of Guadiana River and of Vila Real de Santo António. Therefore, the hydrometallurgy of pyrites was developed locally, pioneered in Santo Domingo that allowed the survival and expansion of the British company from the late 1870s, that is, at a time when most small mines shut since they were not able to compete globally. Through different consented and regulated processes (judicial), through conflict or parliamentary mediation, the State imposed exceptionally additional costs to companies, either for compensation, the imposing the application of remediation measures to reduce the environmental damage in some cases, thus contributing to derail some projects. These cases suggest that the interaction between local conflicts, corporate behavior and technological progress proves to be complex. This article aims to contribute to the debate on economic and social history between the environment and technological progress, arguing that the fixed costs and economic imponderable social risks were factors that encouraged the companies to search for new solutions and to introduce innovations since that would allow the expansion of their activity. In this process the companies sometimes faced environmental dilemmas and unforeseen costs with consequences on the economy of firms. The nature of the knowledge needed to address the environmental problems they created, however, is of a very different nature from that knowledge needed to face the environmental burdens that were inherent to the development of its activity.

O passado e o presente nos conflitos ambientais na indústria mineira e metalúrgica

This chapter reflects on several forthcoming key topics on environmental social conflits in historical perspective, namely, the relationship between the expansion of extractivism and the reactive and preemptive conflicts, the role of scientists and scientific discourses on social mobilization, the environmental movements and the empowerment of the poor, the strategic response behavior of large mining corporations. The conclusive analysis looks for continuities and contrasts between contemporary environmental conflicts and the conflicts of the past, often identified as 'peasant conflicts' over industrial polution.

Os direitos humanos em tempos de paz negativa. A Síria e a Somália como estudos de caso

A questão dos Direitos Humanos e as suas violações continuam a passar despercebidas a nível mundial. Perante uma Paz negativa, é o dever da comunidade internacional interferir na construção de Paz em Estados dominados pela violência e fazer esforços na prevenção de conflitos. Os confrontos que se alastram em diferentes regiões da Somália, sob controlo de grupos rebeldes e a escalada de violência que levou a uma crise humanitária na Síria, com habitantes de ambos os países a terem de se deslocar e a refugiarem-se em países vizinhos por não se sentirem seguros no próprio país, são os estudos de caso escolhidos para analisar o que tem falhado na sua resolução. É também necessário realçar a emergência dos Estudos da Paz, presentes na ordem do dia da política mundial na mediação de conflitos, na gestão de crises e cooperação nas sociedades afetadas pela violência; Abstract: Human Rights in times of negative peace. Syria and Somalia as case studies The human rights subject and their violations continue unnoticed in a global level. Faced with a negative peace, it is the duty of the internacional community to assist in building peace in states where violence dominates and make efforts in preventing conflicts. The deadly confrontations that spread through diferentes regions in Somalia, under the control of rebels groups, and the escalation of violence that led to a humanitarian crisis in Syria, with the population of both countries moving around and taking shelters in neighbor countries because they don’t feel safe in their own, are the case studies chosen to analyze what has failed in their solution. It is also necessary to enhance the emergency of Peace Studies, which comes in the agenda of world politics in conflict mediation, in crisis management and cooperation in societies affected by violence.

Relatório de prática de ensino supervisionada realizada na Escola de Música do Conservatório Nacional: a embocadura do clarinete: caracterização, deteção e resolução de problemas

O presente relatório surge no seguimento da Prática de Ensino Supervisionada, realizada na Escola de Música do Conservatório Nacional sob a orientação da Professora Doutora Ana Telles Béreau (orientadora interna) e do orientador cooperante Professor Luís Miguel Gomes. A primeira secção deste trabalho pretende fazer o enquadramento histórico e organizacional da instituição, bem como descrever os alunos e as práticas metodológicas utilizadas pelo orientador cooperante nos domínios da psicologia educacional e do ensino especializado do clarinete. A segunda e última secção deste relatório aborda a noção de embocadura, definindo as suas principais conceções, função, formação, erros comuns associados e respetivas causas, apresentando finalmente propostas de vários autores para o desenvolvimento das componentes diretamente relacionadas com a embocadura, como meio de prevenção de problemas e desenvolvimento desta componente, tão importante para a prática do clarinete e de qualquer instrumento de sopro; Abstract: Supervised Teaching Report held at Escola de Música do Conservatório Nacional: The embouchure of the clarinetist – characterization, detection and problem resolution This report follows the Supervised Teaching Practice held at Escola de Música do Conservatório Nacional under the inner guidance of PhD Professor Ana Telles Béreau and having had, as cooperating advisor, Professor Luís Miguel Gomes. A first section is intended to provide the historical and organizational framework of the institution, describe students and methodological practices used by the cooperating advisor about educational psychology and specialized clarinet education. The second and final section of this report deals with the notion of embouchure, defining its main conceptions, function training, common errors and their causes, finally presenting the proposals of various authors aiming at the development of components directly related to embouchure, as a way for preventing problems and develop this specific issue, so important to the practice of the clarinet and, indeed, of any wind instrument.