A metodologia de ensino-aprendizagem de matemática através da resoluçâo de problemas: perspectivas à formaçao docente no contexto da sala de aula

A aprendizagem matemática não ocorre simplesmente pela transmissão de saberes do professor para o aluno, uma vez que é possível aprender matemática com tarefas que incentivem a construção do conhecimento que poderá favorecer o prazer pela descoberta, promover a autonomia e incentivar a comunicação. Além disso, o processo de construção do conhecimento leva o aluno a pensar mais, raciocinar mais, potencializando, dessa forma, um nível de conhecimento bem alicerçado. Nesse sentido, a Resolução de Problemas se apresenta como uma perspectiva metodológica que tem sido reconhecida mundialmente como uma meta fundamental no ensino-aprendizagem da Matemática. Assim, o presente texto pretende apresentar a Metodologia de Ensino- Aprendizagem-Avaliação de Matemática através da Resolução de Problemas como uma proposta didática para se trabalhar em sala de aula.

Ensino médio: un olhar sobre o currículo de matemática na perspectiva de representaçôes semióticas

Essa comunicação apresenta uma pesquisa em desenvolvimento que busca investigar o currículo de Matemática das escolas estaduais de Ensino Médio do Estado do Rio Grande do Sul, sob a ótica das representações semióticas como possibilidade teórica, didática e metodológica para o desenvolvimento dos conhecimentos e procedimentos matemáticos que fazem parte desse nível de escolaridade. No presente momento, a investigação de cunho qualitativo está centrada na análise do currículo de Ensino Médio e nos projetos pedagógicos das escolas pertencentes à área de abrangência da pesquisa. Também fazem parte do estudo as avaliações nacionais propostas para os egressos do Ensino Médio. Resultados preliminares apontam a necessidade de se trabalhar com “outras representações”, principalmente quando os documentos analisados consideram a resolução de problemas como princípio para a organização das atividades escolares, o que, entende-se, indica uma abertura para o trabalho com semiótica na matemática escolar do Ensino Médio.

Exploração matemática de módulos interativos de ciências: um estudo de caso no "Jardim da Ciência" em articulação com a sala de aula com alunos do 1º ciclo do ensino básico

Orientações curriculares portuguesas para o 1.º Ciclo do Ensino Básico [CEB] preconizam o desenvolvimento de capacidades transversais como a resolução de problemas [RP] e a comunicação (em) matemática [CM], o estabelecimento de conexões Matemática–Ciências Físicas e Naturais [CFN] e a articulação de contextos de educação formal [EF] e de educação não formal [ENF]. Em Portugal, professores manifestam querer utilizar recursos didáticos com estes atributos. Contudo, tais recursos escasseiam, assim como investigação que se situa na confluência destas dimensões. Por conseguinte, na presente investigação, foram desenvolvidos recursos didáticos centrados na promoção de conexões Matemática-Ciências Físicas e Naturais e na articulação de contextos de EF e de ENF. Assim, a presente investigação tem por finalidade desenvolver (conceber, produzir, implementar e avaliar) recursos didáticos de exploração matemática de módulos interativos de ciências, articulando contextos de EF e ENF que, nomeadamente, apelem e possam desenvolver capacidades básicas ligadas à RP e à CM de alunos do 1.º CEB. Decorrente desta finalidade, definiram-se as seguintes questões de investigação: 1. Quais as repercussões dos recursos didáticos desenvolvidos na capacidade de RP de alunos do 4.º ano do 1.º CEB?; 2. Quais as repercussões dos recursos didáticos desenvolvidos na capacidade de CM de alunos do 4.º ano do 1.º CEB?. Além disso, procurou-se auscultar a opinião de alunos e professora sobre a exploração dos recursos didáticos desenvolvidos, principalmente, ao nível de conexões Matemática–CFN e articulação de contextos de EF e ENF de Ciências. Para tanto, foi realizado um estudo de caso com uma professora e seus alunos do 4.º ano do 1.º CEB, em sala de aula e num espaço de ENF de Ciências. A recolha de dados envolveu diversas técnicas e vários instrumentos. A técnica de análise documental incidiu nas produções dos alunos registadas em Guiões do Aluno e em Tarefas-Teste. No âmbito da técnica de inquirição foram administrados questionários a todos os alunos da turma – o Questionário Inicial e o Questionário Final – e entrevistas semiestruturadas à professora – a Entrevista Inicial à Professora e a Entrevista Final à Professora – e aos três alunos caso – Entrevista ao aluno caso. No que respeita à técnica de observação foi implementado o instrumento Notas de campo, onde foram efetuados registos de natureza descritiva e reflexiva. Os dados recolhidos foram objeto de análise de conteúdo e de análise estatística. Resultados da investigação apontam para que a exploração dos recursos didáticos desenvolvidos possa ter promovido o desenvolvimento de capacidades matemáticas de RP e, sobretudo, de CM dos alunos. Parecem ainda indicar que, genericamente, os alunos e a professora possam ter considerado que os recursos didáticos promoveram conexões Matemática– CFN e a articulação entre espaços de EF e ENF de Ciências.

Prática de ensino supervisionada II: a sequência didática como estratégia para escrita de textos no 1º ano de escolaridade

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

Aprender matemática : tornar-se sujeito da sociedade em rede

A presente dissertação estuda relações entre o processo de aprendizagem de Matemática e o perfil do sujeito da Sociedade em Rede a partir das interações registradas na Lista de Discussão de e-mail da disciplina de Computador na Matemática Elementar do curso de Licenciatura em Matemática da Universidade Federal do Rio Grande do Sul. Os processos sócio-cognitivos dos licenciandos são analisados para investigar a hipótese de que aprender Matemática com o uso das Tecnologias da Informação contribui para a formação do sujeito da Sociedade em Rede. Estão presentes autores como Manuel Castells, Pierre Lévy e Edgar Morin, que participam da configuração dos novos paradigmas da Sociedade em Rede; Jean Piaget, Antonio Battro e Seymour Papert que, dentro da perspectiva da Epistemologia e da Psicologia Genéticas, contribuem para o estudo da aprendizagem; e Jean-Blaise Grize, que analisa os processos de comunicação Seus aportes teóricos nos permitem entrelaçar as áreas de conhecimento de Psicologia Social e Institucional, Educação (Instituição Escolar) e Matemática. A análise de uma proposta didática apoiada na utilização de Tecnologias da Informação (software Super Logo e Lista de Discussão) nos permite observar o movimento de transição de uma postura passiva, receptora de informações, para uma postura ativa, produtora de conhecimento na qual os sujeitos foram desenvolvendo atitudes, habilidades e competências para detectar e formular problemas, pensá-los sob diferentes perspectivas e equacioná-los; buscar e implementar as melhores soluções; testar e avaliar as soluções encontradas; contextualizar e questionar os caminhos escolhidos para solucionar desafios; operar com os conhecimentos, processá-los e integrá-los em novos sistemas de significação; e saber trabalhar em equipe, tendo disposição para ouvir, contribuir e produzir no e para o grupo.

Professores em contexto formativo: um estudo do processo de mudanças de concepções sobre o ensino da matemática

El objetivo en esta tesis consistió en estudiar el proceso de los cambios de los conceptos de profesores de la educación infantil y de los años iníciales de la educación básica referente a la enseñanza de la matemática. La investigación se desenvolvió en la escuela Presidente Kennedy, en la ciudad de Natal, en Rio Grande do Norte, teniendo como participante 05 (cinco) profesores del curso normal superior a través de la educación superior del instituto relacionado. El trabajo asocia el programa a él Programa de Pós-Graduação em Educação da Universidade Federal do Rio Grande do Norte, en la base de pesquisa Formação e Profissionalização Docente coordinada de los doctores Betânia Leite Ramalho e Isauro Beltran Núñez. El referencial teórico-metodológico en quien si apoya el trabajo se inserta en la señal conceptual usada por Giordan y de Vecchi (1996), de Carrillo y Contreras (1994), Ramalho; Núñez y Gauthier (2003), Ponte (1998), Guimarães (1988), Ernest (1989). En esta investigación, los conceptos de los profesores habían sido estudiados en el contexto educativo de la formación del nivel superior, usándola reflexiva crítico práctico como estrategia formativa. Estos conceptos se entienden como estructuras subyacentes al pensamiento del profesor. Dado la naturaleza del objeto del estudio, la información, para las intenciones de esta investigación, habían sido cosechados a través de los instrumentos siguientes: cuestionario, plan de la lección, entrevista diaria y del campo. El cuestionario fue constituido de preguntas abiertas y de las entrevistas de la mitad-structuralized. La organización de los datos permitió a La inferencia de los conceptos, usando la técnica de la triangulación de datos. La investigación divulgó que los conceptos de los profesores, a través del proceso formativo, se habían desarrollado de una plataforma para otra, yéndose puesto que los modelos didácticos tradicionales para otros modelos dirigidos a una tendencia didáctica de espontaneísta/investigativa. La reflexión crítica era considerada como elemento catalítico de los cambios de los conceptos de los profesores en la educación de las matemáticas, sin embargo déjenos verifican que estos cambios son difíciles de ocurrir para la naturaleza compleja de estos conceptos. Como facilitadores de los factores de estos cambios, encontramos y el investigativo el trabajo, la dinámica y la naturaleza de las actividades se convirtió en el colaborativo de proceso formativo, entre otros. Como obstáculos a los cambios, identificamos el contexto del trabajo de los profesores, de la cultura de los individualistas prácticos de sus profesores de los colegas, del concepto linear, estático y de los mecánicos de los procesos para enseñar, el conocimiento profesional construído durante la formación inicial, alineación con los modelos didácticos de sus viejos profesores, entre otros

Ateliês de história e pedagogia da matemática: contribuições para a formação de professores que ensinam matemática nos anos iniciais

This paper presents a discussion about the use of the History of Mathematics as an educational resource and conceptual mediator in the formation of teachers who teach mathematics in the years of elementary school. It was a qualitative action method, in order to show the importance of holding workshops of History and Pedagogy of Mathematics as contribution to overcome the conceptual difficulties of teaching and teachers regarding the content covered in the course of education and afterwards they have to teach in the early of elementary school. We assume that understanding the historical, social and cultural comprehension as a conceptual and didactic focus effectively nurture the pursuit of a teaching and learning of mathematics students safe and justified in order to contribute to overcoming the difficulties of teaching and learning usually occurred in the classroom of the early years. In this sense, we organized a study group formed by students of Bachelors in Education and Mathematics at the University of Piauí. We developed five training workshops in History and Pedagogy of Mathematics, with a workload of 20 hours each and four follow-up sessions and advicement, totalizing 180 hours. The purpose of workshops was to develop studies on the History of Mathematics that could support the formation of a conceptual and didactic group with a view to prepare teaching materials and activities based on information drawn from undertaken historical studies .The products designed were used in formation of the group itself and will later be used in training teachers of public school in Teresina, in the form of workshop of History and Pedagogy of Mathematics in order to overcome problems arising from teaching and conceptual this education degree in Education Based on the obtained informations it was possible to suggest new referrals procedural level of education and university extension that may contribute to the reorientation of initial and continuing training of teachers in the early years elementary school

Física no cotidiano: da cozinha para a sala de aula relato de uma experiência didática no município de Limoeiro do Norte (CE)

Brazilian high school teaching has passing through important changes. Based on current legislation and other official documents this research focus on the notion of contextualization, discussing the possibilities of a Physics teaching contextualized at a kitchen environment. Given the difficulties presented by students in establishing the relation between the contents discussed in classroom and their own daily lives, we propose the elaboration and application of a didactic unity. This started after the analyses of an initial questionnaire answered by the students. The didactic unity was elaborated based on an earlier proposal made by GREF (Physics Teaching Reelaboration Group) for a Thermal Physics course, and involved situations on students daily lives, in particular, those activities tried to relate formal contents discussed in classrooms to the kitchen environment. The didactic unity was applied to a public high school classroom at Limoeiro do Norte (CE). After evaluation of this experience it is possible to state that contextualization is a challenge that shall be faced, so that students may have a more critical look at physics, understanding that this subject is of relevance to all of us and is present in all world around us

O uso pedagógico de uma seqüência didática para a aquisição de algumas idéias relacionadas ao conceito de números complexos

The aim of the present work is to contribute to the teaching-learning process in Mathematics through an alternative which tries to motivate the student so that he/she will learn the basic concepts of Complex Numbers and realize that they are not pointless. Therefore, this work s general objective is to construct a didactic sequence which contains structured activities that intends to build up, in each student s thought, the concept of Complex Numbers. The didactic sequence is initially based on a review of the main historical aspects which begot the construction of those numbers. Based on these aspects, and the theories of Richard Skemp, was elaborated a sequence of structured activities linked with Maths history, having the solution of quadratic equations as a main starting point. This should make learning more accessible, because this concept permeates the students previous work and, thus, they should be more familiar with it. The methodological intervention began with the application of that sequence of activities with grade students in public schools who did not yet know the concept of Complex Numbers. It was performed in three phases: a draft study, a draft study II and the final study. Each phase was applied in a different institution, where the classes were randomly divided into groups and each group would discuss and write down the concepts they had developed about Complex Numbers. We also use of another instrument of analysis which consisted of a recorded interview of a semi-structured type, trying to find out the ways the students thought in order to construct their own concepts, i.e. the solutions of the previous activity. Their ideas about Complex Numbers were categorized according to their similarities and then analyzed. The results of the analysis show that the concepts constructed by the students were pertinent and that they complemented each other this supports the conclusion that the use of structured activities is an efficient alternative for the teaching of mathematics

Controvérsias sobre a natureza da luz: uma aplicação didática

Researches in the field of Science Teaching have shown, in recent decades, that students from high school level have difficulties in understanding basic concepts of science, in general, and physics, in particular. The specific literature indicates, as a priority for a scientific education of better quality, a more structured understanding about science. This work proposes the introduction of elements of History and Philosophy of Science in high school as an aid to learning the concepts of optics, in general, and of aspects concerning the nature of science, specifically. Making use of historical episodes regarding the controversy on the nature of light, especially during the seventeenth and eighteenth centuries, as well as clippings of the history of optics in relation to the development of models that explain the process of vision, we formulated a teaching unit and implemented it on two night high school classes of a public school in the city of Parnamirim (RN). The unit involved, primarily, the reading of three historical texts containing written questions followed by a collective debate ("moot"). The results indicated some difficulties in overcoming the misconceptions related to the process of vision and the nature of light. Nevertheless, we believe that the teaching unit has succeeded in relation to the learning of most students, both in relation to a better understanding of science as well as concepts of optics

A estratégia didática de resolução de problemas na formação de professores de química

In this work it is presented a research developed in the initial training of teachers of the chemistry graduation course at the Universidade Federal do Rio Grande do Norte (UFRN). The intervention was realized in two classes in the context of a discipline in the curricular structure with nineteen undergraduate students of chemistry. The study utilizes characteristics of the qualitative approach and uses observation, questionnaires, interviews and examination papers. The experiment involved a sequence of activities fundamented on the Problem Solving (PS) teaching strategy to approach chemical concepts. The proposal was planned and organized according to the theoretical presupposition of the work developed by the authors of the Science Education in PS, of teaching experience and from the initial hypotheses of the research. The goal was that the future teachers could experience the strategy and advance to the new meanings. The themes addressed in the activities were the difference between exercises and problems, exercises turning into problems, the steps of problem solving and some implications of the teaching strategy for the work of the teacher. The results showed evidence that through a process of collective reflection, and from the difficulties experienced in the strategy practice, the undergraduates are introduced to new perspectives of reflection and action of teaching practice, and understanding some benefits of innovative proposals for the teaching of chemistry. It also showed that, although this theme is approached, in some moments of the graduation, the future teachers don‟t know when or how to realize activities in this perspective. From the aspects that rose in research we highlighted the difficulties in the problem solving steps, the use of the strategy in school and the knowledge and skills of the teacher for planning activities in Problem Solving

Formação continuada de professores que ensinam matemática: o papel do ábaco na ressignificação da prática pedagógica

The present dissertation performs a study about abacus part on the continuous education of Elementary School s Mathematic teachers on what concerns the basic operations of addition and subtraction with (re)unification by using the manipulative and/or informatical abacus. Therefore, the research intends to answer the following question: How does a teacher reframe the pedagogical practice while teaching the Decimal Numeral System and the conventional operations of addition and subtraction with (re)unification through manipulative and informatical abacus? In order to do so, we rely ourselves on the Guy Brousseau s Theory of Didactic Situations (TDS) from 1996 that affirms the necessity to trace a way in accordance with the teaching situations that lead the student s learning; and on the work of Pierre Lévy (1993), in which the poles of communication oral, written and virtual create three ways of communication through which the learning process happens. The methodology of this paper was based on the Strategic Research-Action of Franco (2005). The didactic sequence was elaborated in accordance with TDS and used the manipulative and informatical abacus as didactic resource. With the application of the didactic sequence, it was verified that the continued formation of Elementary School s teachers concerning the operations of addition and subtraction on the initial years/levels is pertinent once it has been observed some difficulties of the teachers concerning this mathematical subject. Besides, the analysis of the didactic sequence has allowed one to realize that teachers had some difficulties concerning the numeric representation with order zero, the resolution of operations of addition and subtraction using the manipulative and informatical abacus and the realization of (re)unification on the subtraction with meaning. These observations has been discussed with the teachers and, after that, it has been done some didactic-methodological routings of the operations of addition and subtraction with re(unification) that contributes with the teaching and learning process.

Uma sequencia didática para o ensino da resolução da equação do 2. grau : adequação para o uso com professores

The present study aims to check whether the use of activities mediated by the History of Mathematics can contribute to improve the understanding of resolution the 2nd degree equation for teachers and undergraduates that reproduce methods of solving such equations, uncritically, without domain of the justifications for their actions. For this, we adapted a didactic sequence with activities that aims to cause a rediscovery of resolutive formula of 2nd degree equation through the method known as cut and paste. Finally, we presented the activity module containing the didactic sequence used during the study, as suggestion for use in the classroom, by the math teacher

Elaboração de uma sequência didática sobre os conceitos geométricos preliminares ao estudo da trigonometria

This study is qualitative, including literature search and preparation of teaching materials. Your goal is to report the study of geometric problems of character presented in the application of trigonometry and work on the preparation of detailed activities that help in overcoming these difficulties. For this, we read some papers on teaching and learning of trigonometry in order to identify the difficulties encountered during their journey. Then separate the geometric difficulties of character and prepare a list of geometric content and procedures associated with them. Thus, we can organize a notebook with activities that would address most of these concepts. Finally we present the specification of activities called Activity on introductory concepts to the study of trigonometry

Uma sequência didática a partir da temática terremotos com ênfase em CTS

Throughout its history the population of the region of Mato Grande, which includes the city of João Câmara, in Rio Grande do Norte, was subject to earthquakes. These events are caused by a geological fault, known as fault Samambaia. In the 1980s there was an intensification of this phenomenon culminating in an earthquake 5.1 on the Richter scale in the early hours of November 30, 1986, causing researchers from Brazil and other countries to shift to the region to conduct research in Seismology. During this period there was a strong interaction between scientists and local people. With the aim of studying how people experienced that moment that marked the history of the city of João Câmara, from interviews with some individuals who witnessed the incident, is that this research was developed. Taking as a theoretical approach to Science, Technology and Society (STS), aimed to thus carry the theme in a systematic way to the classroom, promoting ways to help teachers with the scientific training and guidance to students in case of occurrence of earthquakes