A avaliação da resolução de problemas

Esta investigação teve como objetivo, compreender como é que a avaliação da resolução de problemas contribui para melhorar a aprendizagem da resolução de problemas. A dificuldade na resolução de problemas é de facto um fenómeno mundial com uma extensão considerável em termos cronológicos. Tendo-se escrito muito acerca deste assunto, a verdade é que continua a colocar muitos pontos de interrogação, no que concerne aos métodos e estratégias para ultrapassar este problema. Combinar a avaliação com a resolução de problemas nem sempre é fácil. A resolução de problemas é muito importante para que se cinja a uma visão simplista, temos que perceber que esta se reveste de uma oportunidade para alargar e diversificar os instrumentos de avaliação. Para além disso, permite que os alunos com dificuldades se envolvam ativamente com os seus colegas, numa busca cooperativa pela solução do problema, beneficiando assim ambas as partes. No sentido de verificar o acima referido, os alunos foram colocados em grupos e foi-lhes proposto uma ficha de trabalho de problemas. Os problemas propostos foram os mais diversificados possíveis, no sentido de apelar aos vários tipos de raciocínio e estratégias. Para este estudo foi escolhida uma turma do 5º ano com alunos com bons resultados em matemática e outros com dificuldades. No que concerne à metodologia de investigação, optou-se pela qualitativa e descritiva, com uma pequena nuance quantitativa para consubstanciar o estudo.

A aprendizagem das noções elementares da álgebra e das equações no 7º ano de escolaridade

Esta dissertação é fruto de um processo de reflexão sobre a minha experiência pro fissional de nove anos de serviço, como docente de matemática, bem como do interesse pela análise do processo de aprendizagem que os alunos do sétimo ano de escolaridade fazem das noções elementares da álgebra. Para realizar esta investigação, foi selecionada uma turma de sétimo ano, em que a maioria dos alunos é interessada pelo seu percurso escolar, embora, por vezes, não sejam constantes na sua prestação em sala de aula, bem como na realização do estudo correto em casa. Neste estudo, optou-se por uma metodologia de natureza qualitativa, de caráter interpretativo. O estudo das noções elementares da álgebra no sétimo ano de escolaridade é um marco de suma importância no percurso escolar dos alunos. É no sétimo ano de escolaridade que estes têm o primeiro contacto com noções elementares da álgebra. Por isso as experiências iniciais tornam-se fulcrais para uma aprendizagem significativa da álgebra. Assim, neste estudo, pretende-se estudar o impacte das várias tarefas aplicadas em sala de aula, quer individualmente, quer aos pares, ou em turma, a fim de se perceber o que, efetivamente, o aluno aprendeu das noções elementares da álgebra, mais concretamen te das equações. Com estas tarefas foi possível identificar algumas das dificuldades sentidas pelos alunos, neste ramo da matemática.

Os robots na aprendizagem da trignometria

Este trabalho foi elaborado no âmbito do Mestrado de Ensino de Matemática do 3º Ciclo do Ensino Básico e Secundário da Universidade da Madeira, no ano letivo de 2012/2013. Os grandes objetivos deste estudo são os de analisar qualitativamente uma atividade, para compreender como é que os alunos aprendem trigonometria, utilizando os robots NXT da Lego. De igual modo, se procede também, de forma sucinta, à apresentação do trabalho desenvolvido pelo grupo de estágio, ao longo da Prática de Ensino Supervisionado. Para a realização da investigação, foram recolhidos dados pelo investigador, através de registos audiovisuais do trabalho dos alunos, com câmara e vídeo. Com o fim de melhor estudar o problema aqui apresentado, o mesmo foi dissecado em três questões de investigação: (a) Que aprendizagens os alunos realizam com a montagem, programação e interação com os robots? (b) De que forma é que os alunos aprendem trigonometria, quando utilizam os Robots? (c) Quais as dificuldades manifestadas pelos alunos na resolução de problemas? As questões de investigação iluminaram a análise dos dados. Das conclusões que advêm deste estudo destaca-se o papel essencial da robótica e dos materiais manipuláveis, na construção e concetualização do conhecimento dos alunos.

Corpo, comunicação e educação

O objetivo deste artigo é discutir as dificuldades de comunicação de conteúdos relacionados ao corpo humano, no contexto dos processos de ensino e de aprendizagem na escola fundamental e média. Através da exposição das necessidades dos alunos e das reticências dos professores, apresenta-se algumas teorias sociais como estratégia mediadora e viabilizadora do melhor desempenho da ação pedagógica e da contribuição escolar para a constituição do educando enquanto sujeito social.

Os anjos podem ferir: um estudo sobre a violência intrafamiliar

This work considers the comprehension of the intrafamiliar violence emphasizing violent mothers relationships with their children. The purpose is to understand the development of these relationships which turn into aggressive behavior of the mothers regarding family education. The research was carried out focusing on two aspects: analysis of the theoretical references and empirical research. The theoretical research was done through a bibliographic survey of subjects related to this study such as: the history of the family, motherhood and children, the intrafamiliar violence practiced by mothers against their children; as well as how those violent relationships emerge from family environment. We point out the Foucault s concept of discipline (FOUCAULT, 1975) and Caldeira s concept of circumscribed body (CALDEIRA, 2000). It was selected a sample of ten women to investigate the relationship between mother and son through a detailed interviews. Five mothers from this sample were denounced to the Tutelary Council and they were set in a so called Denounced Group. Similarly, the other five mothers, who live in the same social and cultural context of the selected families assisted by the Tutelary Council, were set in the Non-Denounced Group. Therefore, we work with representations of the own interviewers about the meaning of the pedagogic socializing discipline in their lives. Our priority was the study of case carried out with the denounced families for physical violence and with the other group in order to develop a comparative analysis of both groups. Such methodological choice is explained by the interest for understanding the violence between mothers and children. It is common to all mothers not to consider aggressive their behavior against their children. We observe that physical punishment is considered a way to discipline children and teenagers, hence that is perceived as necessary to repress, to control, and to adapt them. Thus, it is considered a necessary practice for education. However, the reason that made the community denounced against the mothers of the Denounced Group was due to those did not correspond to an ideal example of what was expected to be a mother (they took drugs, alcohol, and had several sexual partners), that is denounces were not for the physical violence itself. Therefore, those mothers were not denounced because they were not morally able to manage their children s education. The community tolerates the punishment against children, but not the amorality of the women, and they were denounced for disregarding their role as mothers

Ambiente pesqueiro e saúde: representações sociais sobre saúde e doença de pescadores e marisqueiras nos distritos de Diogo Lopes, Barreiras e Sertãozinho Macau RN

According to Brazil s Ministry of Fisheries and Aquaculture, artisanal fishermen are responsible for a significant fish production at national level, highlighting the importance of this activity. In Rio Grande do Norte State, Brazil, fishing has become an important part of economic and social processes. In this context, there are many inland fishing communities such as Barreiras, Diogo Lopes and Sertãozinho, which are part of Ponta do Tubarão State Reserve of Sustainable Development (RDSEPT), located in Macau and Guamaré, Rio Grande do Norte coastline cities. Fishermen and women, the last ones known as marisqueiras who work alongside the menfolk at sea, especially in the shellfish harvest, have been developing narrow relationships with nature, mainly with the sea, from where they extract their families subsistence. However, those communities have been facing several issues related to living conditions, health and diseases. Social representations have been analyzed in the speeches of fishermen/women who were registered active members in a fishermen association named Associação Colônia de Pescadores Z-41, regarding the period from 2008 to 2011. The analysis involved socio-economic profiles verification, identification and analysis of the group s main representative diseases and representations related to health and illness. This study searched for elements in order to provide the comprehension of the relationships among people s social representations and the fishing environment in which they live.. This qualiquantitative study was performed using recordings and transcriptions of structured and open-question interviews. The Collective Subject Speech tecnique proposed by Lefevre & Lefevre (2002) was applied to perform the interviews analysis using QualiQuantiSoft® software. The results showed that health and illness phenomena as well as social representations related to them in the fishing environment are not only abstract states but also physical ones, which interfere in all life extensions, establishing a set of relevant information that indicates that those people realize their own socio-cultural, economic, environmental and political context

Pelos caminhos das idéias e da existência: a propósito das cartografias de J. T. de Moura Filho

The present study aimed to investigate the intellectual, personal and professional tracjetory of José Tavares de Moura Filho. Civil engineer who devoted him self to cartographic cience, though not a cartographer, and to literature. At 65 years old, already with retirement, he devoted his attention to writing his books and see the world, as he said. There were nine books, five of poetry, prose and short stories, and four of cartographic nature. The published his books independently. He wrote and his wife Elza typed. Once ready, he would seek the graphics, later a publisher, to reproduce his writing. He liked to say he would rather to pay for your books than bay a new car, and did so. Died at age of 82 years, leaving a rich material for the young students, those who read, as he always did by dedicating his books. In order to achieve the objectives of this study, we used as a theoretical some authors dealing with historiography, oral history, intellectual intineraries and history of ideas, as Garnica, Nóvoa, Barros, Bosi, Le Goff among others. From this perspective, we constructed an archeology of ideas and the existence of Moura Filho, to point contributions of the teaching of mathematics from his work

Obstáculos superados pelos matemáticos no passado e vivenciados pelos alunos na atualidade : a polêmica multiplicação de números inteiros

In Mathematics literature some records highlight the difficulties encountered in the teaching-learning process of integers. In the past, and for a long time, many mathematicians have experienced and overcome such difficulties, which become epistemological obstacles imposed on the students and teachers nowadays. The present work comprises the results of a research conducted in the city of Natal, Brazil, in the first half of 2010, at a state school and at a federal university. It involved a total of 45 students: 20 middle high, 9 high school and 16 university students. The central aim of this study was to identify, on the one hand, which approach used for the justification of the multiplication between integers is better understood by the students and, on the other hand, the elements present in the justifications which contribute to surmount the epistemological obstacles in the processes of teaching and learning of integers. To that end, we tried to detect to which extent the epistemological obstacles faced by the students in the learning of integers get closer to the difficulties experienced by mathematicians throughout human history. Given the nature of our object of study, we have based the theoretical foundation of our research on works related to the daily life of Mathematics teaching, as well as on theorists who analyze the process of knowledge building. We conceived two research tools with the purpose of apprehending the following information about our subjects: school life; the diagnosis on the knowledge of integers and their operations, particularly the multiplication of two negative integers; the understanding of four different justifications, as elaborated by mathematicians, for the rule of signs in multiplication. Regarding the types of approach used to explain the rule of signs arithmetic, geometric, algebraic and axiomatic , we have identified in the fieldwork that, when multiplying two negative numbers, the students could better understand the arithmetic approach. Our findings indicate that the approach of the rule of signs which is considered by the majority of students to be the easiest one can be used to help understand the notion of unification of the number line, an obstacle widely known nowadays in the process of teaching-learning

Reconceitualização das categorias de skemp de compreensão relacional e compreensão instrumental como critérios globais

The thesis presents a systematic description about the meaning, as Skemp, relational understanding and understanding instrumental, in the context of mathematics learning, being that we had as a guide his understanding of the schema. Especially, we analyze some academic productions, in the area of Mathematics Education, who used the categories of understanding relational and instrumental understanding how evaluative instrument and we see that in most cases the analysis is punctual. Being so, whereas the inherent understanding relational schema has a network of connected ideas and non-insulated, we investigated if the global analysis, where it is the understanding of the diversity of contributory concepts for formation of the concept to be learned, is more appropriate than the punctual, where does the understanding of concepts so isolated. For this, we apply a teaching module, having as main content the Quaternos Pythagoreans using History of Mathematics and the work of Bahier (1916). With the data we obtained the teaching module to use the global analysis and the punctual analysis, using research methodology the Case Study, and consequently we conduct our inferences about the levels of understanding of the subject which has made it possible for us to investigate the ownership of global analysis at the expense of punctual analysis. On the opportunity, we prove the thesis that we espouse in the course of the study and, in addition, we highlight as a contribution of our research evidence of need for a teaching of mathematics that entices the relational understanding and that evaluation should be global, being necessary to consider the notion of schema and therefore know the schematic diagram of the concept that will be evaluated

Os sentidos da autonomia docente no desenvolvimento curricular

Ese estudio se firma en el camino de la formación y del desarrollo profesional de profesores de Matemáticas, objetivando comprender, a partir del discurso de profesores de dicha asignatura, el sentido atribuido a la autonomía profesional y cómo ese sentido es reflejado en la producción y desarrollo curricular de la asignatura de Matemáticas. Para tal, utilizamos la entrevista comprensiva, metodología basada en el supuesto fundamental de la palabra en la construcción del objeto de estudio. A partir del discurso de cinco profesores que imparten la asignatura de Matemáticas en el Centro Federal de Educación Tecnológica de Rio Grande do Norte, percibimos que la autonomía está unida a una posición de soberanía en aula, lo que se traduce en un trabajo volcado al individualismo. Constatamos que las reuniones pedagógicas, espacios por excelencia para discusiones y reflexiones acerca de la enseñanza de Matemáticas y consecuente desarrollo profesional, no contribuyen para la mejora de la enseñaza de dicha disciplina. Percibimos, también, que el libro didáctico es utilizado para estandarizar el trabajo de los profesores y que la selectividad todavía es punto de referencia en lo que concierne al currículum de Matemáticas en la institución, lo que impide la realización de un desarrollo curricular de la asignatura de Matemáticas en que sean considerados conjuntamente todos sus componentes

Um estudo sobre a aprendizagem de alguns conceitos algébricos e geométricos

The objective of the present work was develop a study about the writing and the algebraic manipulation of symbolical expressions for perimeter and area of some convex polygons, approaching the properties of the operations and equality, extending to the obtaining of the formulas of length and area of the circle, this one starting on the formula of the perimeter and area of the regular hexagon. To do so, a module with teaching activities was elaborated based on constructive teaching. The study consisted of a methodological intervention, done by the researcher, and had as subjects students of the 8th grade of the State School Desembargador Floriano Cavalcanti, located on the city of Natal, Rio Grande do Norte. The methodological intervention was done in three stages: applying of a initial diagnostic evaluation, developing of the teaching module, and applying of the final evaluation based on the Mathematics teaching using Constructivist references. The data collected in the evaluations was presented as descriptive statistics. The results of the final diagnostic evaluation were analyzed in the qualitative point of view, using the criteria established by Richard Skemp s second theory about the comprehension of mathematical concepts. The general results about the data from the evaluations and the applying of the teaching module showed a qualitative difference in the learning of the students who participated of the intervention

Trajetória de mulheres e a participação masculina no processo de aborto provocado

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Aprendendo e ensinando o sistema de numeração decimal: uma contribuição à prática pedagógica do professor

The central question of the present study is to identify the epistemological knowledge that the teachers-trainees possess regarding the characteristics (properties) of the decimal numbering system; its purpose is to offer a contribution to the pedagogic practice of the teachers who work within the Basic Literacy Cycle, in terms of what concerns both the acquisition of contents and the development of the knowledge that helps them in the elaboration of adequate strategies to working with the Decimal Numbering System in the classroom. The study is based on the constructivist sociointeractionist approach to teaching Mathematics and it constitutes, in itself, a methodological intervention with the teachers-trainees engaged in the Professional Qualification Program in Basic Education of the Federal University of Rio Grande do Norte. The foundations of the study were found in investigations of researchers who had carried out studies on the construction of numerical writing, showing, for instance, that the construction process of ideas and procedures involved in groupings and changes to base 10 take a lot longer to be accomplished than one can imagine. A set of activities was then elaborated which could not only contribute to the acquisition of contents but that could also make the teachers-trainees reflect upon their teaching practices in the classroom so that in this way they will be able to elaborate more consistent didactic approaches, taking into consideration the previous knowledge of the students and also some obstacles that often appear along the way. Even when teachers have access to the most appropriate dicactic resources, the lack of knowledge of the content and of the real meaning of that content make the Decimal Numbering System, a subject of fundamental importance, be taught most times in a mechanical way. The analisys of the discussions and behaviours of the teachers-trainees during the activities reavealed that they made them reflect upon their current practices in the classroom and that, as a whole, the aims of each of the activities carried out with the teachers-trainers were reached

Uma análise dos questionamentos dos alunos nas aulas de números complexos

This work presents a contribution for the studies reffering to the use of the History of Mathematics focusing on the improvement of the Teaching and Learning Process. It considers that the History of Matematics, as a way of giving meaning to the discipline and improve the quality of the Teaching and Learning Process. This research focuses on the questions of the students, classified in three categories of whys: the chronological, the logical and the pedagogical ones. Therefore, it is investigated the teaching of the Complex Numbers, from the questions of the students of the Centro Federal de Educação Tecnológica do Rio Grande do Norte (Educational Institution of Professional and Technology Education from Rio Grande do Norte). The work has the following goals: To classify and to analyse the questions of the students about the Complex Numbers in the classes of second grade of the High School, and to collate with the pointed categories used by Jones; To disccus what are the possible guidings that teachers of Mathematics can give to these questions; To present the resources needed to give support to the teacher in all things involving the History of Mathematics. Finally, to present a bibliographic research, trying to reveal supporting material to the teacher, with contents that articulate the Teaching of Mathematics with the History of Mathematics. It was found that the questionings of the pupils reffers more to the pedagogical whys, and the didatic books little contemplate other aspects of the history and little say about the sprouting and the evolution of methods of calculations used by us as well

Aplicações das atividades estruturadas de Skemp para a construção do conhecimento matemático

The present study constitutes a discussion about the application of Structured Activities to the construction of the mathematical knowledge, proposed by Richard Skemp. The discussion is based on the research that the author carried out in a public school of the state education chain buy using procedures of the research-action. It investigates the possibility of adoption of the proposal of Skemp in a new reality. It utilizes explanations from several theorists to understand the necessity and, at the same time, to enhance the efficiency of the referred activities in first grades of elementary school when students have their first mathematics teachings. It emphasizes the important rule of the teacher, as mediator to the mental constructions of the child. It presents considerations about the results achieved by the research, noticing the possibility of adoption of the studied proposal even though it is necessary an adjustment of the procedures to appropriate didactic-pedagogic requirements to the educational reality in which this project was done