Made available in DSpace on 2014-06-11T19:24:52Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-02-28Bitstream added on 2014-06-13T20:07:57Z : No. of bitstreams: 1 rodrigues_mu_me_rcla.pdf: 2294887 bytes, checksum: e203ccf5f71666cd9e64b5f60c482cbd (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / A presente pesquisa apresenta as possibilidades didático-pedagógicas das narrativas por meio da perspectiva metodológica das Investigações Matemáticas no ensino do conceito de Função. Assim sendo, tecemos algumas considerações a respeito das narrativas no contexto da sala de aula com o intuito de destaca-lás como um meio de viabilizar a comunicação de idéias matemáticas em sala de aula. Com essas perspectivas, buscamos responder a seguinte questão de investigação: Quais são as possibilidades didático-pedagógicas das narrativas no contexto do ensino de funções? Desta maneira, objetivamos investigar e ressaltar as possibilidades didático-pedagógicas das narrativas no processo de ensinar e aprender Funções. Metodologicamente, qualificamos nossa pesquisa como qualitativa interpretativa que utiliza as narrativas como objeto de estudo, a qual propõe que as narrativas são histórias de aprendizagens dos alunos por meio dos seus processos vividos e de suas experiências. A coleta de dados foi realizada junto aos alunos da 8ª série do Ensino Fundamental do Colégio Adventista de Barra do Bugres/MT. Para isso, utilizamos gravações em áudio, entrevistas, diários de bordo do pesquisador, narrativas escritas, questionários e observações diretas como procedimentos metodológicos para a coleta de dados da pesquisa. Destacamos, também, a perspectiva metodológica das Investigações Matemáticas de acordo com Ponte (2003) e Abrantes et al. (1999), com as tarefas de natureza exploratório-investigativas envolvendo o tema Funções. Na análise realizada, evidenciamos indícios de uma cultura diferenciada, a qual valoriza aspectos argumentativos e comunicativos em sala de aula. Esses aspectos se apresentam como potencialidades didático-pedagógicas das narrativas para o processo de ensinar e aprender Funções. / This research presents the didactic and pedagogical possibilities of narratives by means of the methodological perspective of Mathematical Investigation context in the teaching of the function concept. Thus being, we weave some considerações regarding the narratives in the context of the classroom with the intention of detaches-lass as a way to also make possible the communication of mathematical ideas in classroom. With these perspectives, we search to answer to the following problem of inquiry: what are the didactic-pedagogical possibilities of narratives in the functions teaching context? In that way, we aim to investigate and to headlight the didactic-pedagogical possibilities of narratives in the process of teaching and learning functions. Methodologically, we characterize our research as qualitative interpretative that uses the narratives as object of analysis to disclose its didactic-pedagogical potentialities in the education of functions. The data collection was taken with students of a last-middle-school class of School Adventist of Barra do Bugres/MT, for that, we used audio recordings, interviews, researcher s on a board diary, written narratives, questionnaires and direct observations as devices to collect data research. We detach, also, the methodological perspective of the Mathematical Inquiries in accordance with Ponte (2003) and Abrantes et al. (1999), with the exploratório - investigativas tasks of nature involving the subject Functions. In the carried through analysis, we evidence indications of differentiated culture, which values argumentations and communications aspects in classroom. These aspects if present potentialities of the narratives will be the process you teach and you learn functions.

This study set out to determine the relationship between assessment practices and teaching methods. I wanted to investigate whether making mathematical investigation assessment tasks available to elementary-school mathematics teachers would have a positive effect on their teaching. Research tells us that standardized tests influence instruction. My research explored whether a national Assessment Task Bank of mathematical investigative tasks could influence teachers.With these aims in mind, the following research questions were formulated:1. Will the teachers' use of mathematical investigation tasks for assessment purposes influence their view of mathematics?2. Will the teachers' use of mathematical investigation tasks for assessment purposes influence the way they teach, and if so, in what ways?3. Will the teachers' use of mathematical investigation tasks for assessment purposes influence the way they assess their students, and if so, in what ways?My research was divided into two parts: 1) a national study involving teachers-leaders throughout the country; and 2) an intensive study in a small Israeli community, called Sharon. The first part examined how the national courses on assessment that I conducted affected the participating teacher-leaders in terms of their concept of mathematics, their teaching methods and their assessment practices. The second part examined the same issues with regard to the mathematics coordinators in the Sharon community. In each case, I have detailed my experiences so that the reader can gain a view of all facets of the study.The research methodology adopted was based on a constructivist paradigm, sometimes referred to as a "naturalistic inquiry", utilizing ethnographic principles wherein the data collection and analysis procedures were eclectic. In the course of the five years of my research, I used many strategies of data collection - ++ / for example, unstructured participant-observations, interviews, questionnaires and content analysis of artifacts (tests and tasks written by teachers).The ideas of reform mathematics (as defined in Ch 2 of this thesis) are based on a broadened vision of mathematics with emphasis on higher-order thinking. My research indicated that the use of mathematical investigation tasks helped the teachers in my study reach the awareness that mathematics, even on the elementary school level, involves generalizations, justifications and even creativity.Prior to my research, and because of my position, I was aware that Israeli teachers were concerned primarily with teaching routine procedures and that their work sheets for the most part involved single-answer exercises. My research indicated that the use of mathematical investigation tasks indeed influenced the way teachers teach. Verbalization-having the students explain "Why"-has become integral to the teaching practices of the participants in my study. Nowadays, the Israeli teachers I worked with use "authentic tasks" in their classrooms: real-life situations that involve some mathematics. Unfortunately, these tasks are not always planned properly.My research demonstrated that teachers attending my professional courses found the mathematical investigation tasks to be useful for assessment purposes, providing them with additional information about their pupils, not obtainable through conventional assessment methods. The additional criteria (I introduced) for evaluating the pupils' work aided in defining these additional areas. I found that while teachers were quite willing to use the mathematical investigation tasks to supplement the conventional tests, they were reluctant to use them as replacements.Exposure to the Assessment Task Bank influenced to a certain degree, the way the teachers in my study assessed their students. The ++ / tests of the teachers who were participants in my study now regularly include elements that were previously absent: questions requiring explanations and questions with more than one possible answer.Although the teachers of my study were increasingly using questions that required higher-order thinking, the tendency was to use the tests in a summative manner, rather than formatively. In other words, many teachers found it difficult to use test results for planning their subsequent lessons. While they were able to analyze their students' work and could report in some detail on each student's performance, they failed to understand how this should affect their teaching. Before they were exposed to the tasks they had administered tests merely in order to provide grades, whereas now the teachers were often trying to understand the students' thinking.While long-term change is still elusive, my research has demonstrated that exposure to reform mathematics through the mathematical investigative tasks of the Assessment Task Bank did have some influence on the teachers' view of mathematics, as well as their teaching and assessment practices.

Orientador: Rosana Giaretta Sguerra Miskulin / Banca: Miriam Godoy Penteado / Banca: Maria Teresa Menezes Freitas / Resumo: A presente pesquisa apresenta as possibilidades didático-pedagógicas das narrativas por meio da perspectiva metodológica das Investigações Matemáticas no ensino do conceito de Função. Assim sendo, tecemos algumas considerações a respeito das narrativas no contexto da sala de aula com o intuito de destaca-lás como um meio de viabilizar a comunicação de idéias matemáticas em sala de aula. Com essas perspectivas, buscamos responder a seguinte questão de investigação: Quais são as possibilidades didático-pedagógicas das narrativas no contexto do ensino de funções? Desta maneira, objetivamos investigar e ressaltar as possibilidades didático-pedagógicas das narrativas no processo de ensinar e aprender Funções. Metodologicamente, qualificamos nossa pesquisa como qualitativa interpretativa que utiliza as narrativas como objeto de estudo, a qual propõe que as narrativas são histórias de aprendizagens dos alunos por meio dos seus processos vividos e de suas experiências. A coleta de dados foi realizada junto aos alunos da 8ª série do Ensino Fundamental do Colégio Adventista de Barra do Bugres/MT. Para isso, utilizamos gravações em áudio, entrevistas, diários de bordo do pesquisador, narrativas escritas, questionários e observações diretas como procedimentos metodológicos para a coleta de dados da pesquisa. Destacamos, também, a perspectiva metodológica das Investigações Matemáticas de acordo com Ponte (2003) e Abrantes et al. (1999), com as tarefas de natureza exploratório-investigativas envolvendo o tema Funções. Na análise realizada, evidenciamos indícios de uma cultura diferenciada, a qual valoriza aspectos argumentativos e comunicativos em sala de aula. Esses aspectos se apresentam como potencialidades didático-pedagógicas das narrativas para o processo de ensinar e aprender Funções. / Abstract: This research presents the didactic and pedagogical possibilities of narratives by means of the methodological perspective of Mathematical Investigation context in the teaching of the function concept. Thus being, we weave some considerações regarding the narratives in the context of the classroom with the intention of detaches-lass as a way to also make possible the communication of mathematical ideas in classroom. With these perspectives, we search to answer to the following problem of inquiry: what are the didactic-pedagogical possibilities of narratives in the functions teaching context? In that way, we aim to investigate and to headlight the didactic-pedagogical possibilities of narratives in the process of teaching and learning functions. Methodologically, we characterize our research as qualitative interpretative that uses the narratives as object of analysis to disclose its didactic-pedagogical potentialities in the education of functions. The data collection was taken with students of a last-middle-school class of School Adventist of Barra do Bugres/MT, for that, we used audio recordings, interviews, researcher’s on a board diary, written narratives, questionnaires and direct observations as devices to collect data research. We detach, also, the methodological perspective of the Mathematical Inquiries in accordance with Ponte (2003) and Abrantes et al. (1999), with the exploratório - investigativas tasks of nature involving the subject Functions. In the carried through analysis, we evidence indications of differentiated culture, which values argumentations and communications aspects in classroom. These aspects if present potentialities of the narratives will be the process you teach and you learn functions. / Mestre

Neste trabalho são apresentadas duas propostas de sequências didáticas para ensino de logaritmos. A primeira delas é destinada ao aperfeiçoamento de professores de Matemática e a outra, para alunos de Ensino Médio. Tais sequências foram desenvolvidas com base em pesquisas realizadas pelo Prof. João Pedro da Ponte sobre o processo de investigação matemática. A sequência didática para professores foi aplicada no Centro de Aperfeiçoamento do Ensino de Matemática do Instituto de Matemática e Estatística da Universidade de São Paulo (CAEM IME USP). Já a sequência para alunos foi aplicada em uma escola da rede estadual situada no município de São Paulo. Ambas foram analisadas sob os pontos de vista da eficiência e adequação, bem como da clareza das ideias apresentadas. As sequências didáticas têm como ponto de partida a observação das propriedades comuns a várias tabelas, cada uma contendo uma progressão geométrica ao lado de uma progressão aritmética. Tais propriedades caracterizam o que virá a ser definido como logaritmo. Essa introdução ao conceito de logaritmo é diferente da usual, que se baseia na solução de uma equação exponencial. O processo de investigação matemática visa a um aprendizado eficaz por parte do aluno, proporcionado por atividades que conduzam o aluno, de forma gradual, a fazer descobertas, formular conjecturas e buscar validações. Tais investigações são coordenadas e supervisionadas pelo professor, cujo papel é fundamental no processo de construção do conhecimento. / This dissertation presents two didactic sequences for teaching and learning logarithms. One of them aims at Mathematics teachers and is designed for improving their knowledge. The other sequence is meant to be used on high school students. Both didactic sequences were developed based upon research carried out by Professor João Pedro da Ponte on Mathematical Investigations. The didactic sequence for teachers was applied at CAEM IME USP. The one for students was applied at a state school in the city of São Paulo. They were analysed from the points of view of efficiency and of adequacy, as well as of the clarity of the presented ideas. The didactic sequences start with the observation of properties common to multiple tables, each containing a geometric progression side by side with an arithmetic progression. The observed properties characterize what will be later defined as logarithm. Such introduction to the concept of logarithm is different from the usual, which is based on the solution of an exponential equation. The Mathematical Investigation process aims at an effective learning by the students, which is provided by activities that lead the student to gradually make discoveries, formulate conjectures, and search for validations. These investigations are coordinated and supervised by the teacher, whose role in the knowledge construction process is fundamental.

Neste trabalho são apresentadas duas propostas de sequências didáticas para ensino de logaritmos. A primeira delas é destinada ao aperfeiçoamento de professores de Matemática e a outra, para alunos de Ensino Médio. Tais sequências foram desenvolvidas com base em pesquisas realizadas pelo Prof. João Pedro da Ponte sobre o processo de investigação matemática. A sequência didática para professores foi aplicada no Centro de Aperfeiçoamento do Ensino de Matemática do Instituto de Matemática e Estatística da Universidade de São Paulo (CAEM IME USP). Já a sequência para alunos foi aplicada em uma escola da rede estadual situada no município de São Paulo. Ambas foram analisadas sob os pontos de vista da eficiência e adequação, bem como da clareza das ideias apresentadas. As sequências didáticas têm como ponto de partida a observação das propriedades comuns a várias tabelas, cada uma contendo uma progressão geométrica ao lado de uma progressão aritmética. Tais propriedades caracterizam o que virá a ser definido como logaritmo. Essa introdução ao conceito de logaritmo é diferente da usual, que se baseia na solução de uma equação exponencial. O processo de investigação matemática visa a um aprendizado eficaz por parte do aluno, proporcionado por atividades que conduzam o aluno, de forma gradual, a fazer descobertas, formular conjecturas e buscar validações. Tais investigações são coordenadas e supervisionadas pelo professor, cujo papel é fundamental no processo de construção do conhecimento. / This dissertation presents two didactic sequences for teaching and learning logarithms. One of them aims at Mathematics teachers and is designed for improving their knowledge. The other sequence is meant to be used on high school students. Both didactic sequences were developed based upon research carried out by Professor João Pedro da Ponte on Mathematical Investigations. The didactic sequence for teachers was applied at CAEM IME USP. The one for students was applied at a state school in the city of São Paulo. They were analysed from the points of view of efficiency and of adequacy, as well as of the clarity of the presented ideas. The didactic sequences start with the observation of properties common to multiple tables, each containing a geometric progression side by side with an arithmetic progression. The observed properties characterize what will be later defined as logarithm. Such introduction to the concept of logarithm is different from the usual, which is based on the solution of an exponential equation. The Mathematical Investigation process aims at an effective learning by the students, which is provided by activities that lead the student to gradually make discoveries, formulate conjectures, and search for validations. These investigations are coordinated and supervised by the teacher, whose role in the knowledge construction process is fundamental.

Submitted by VINÍCIUS DOS SANTOS HONORATO (honoratovinicius@hotmail.com) on 2018-07-16T13:37:03Z No. of bitstreams: 1 DISSERTAÇÃO_FINAL_VINÍCIUS_HONORATO.pdf: 5049898 bytes, checksum: d897c5f9e9a8ce1fe397a1cea0fbd795 (MD5) / Approved for entry into archive by Ana Paula Santulo Custódio de Medeiros null (asantulo@rc.unesp.br) on 2018-07-16T16:15:19Z (GMT) No. of bitstreams: 1 honorato_vs_me_rcla.pdf: 4917728 bytes, checksum: 6f822e844993d744732fc0be6ff0bb46 (MD5) / Made available in DSpace on 2018-07-16T16:15:19Z (GMT). No. of bitstreams: 1 honorato_vs_me_rcla.pdf: 4917728 bytes, checksum: 6f822e844993d744732fc0be6ff0bb46 (MD5) Previous issue date: 2018-06-11 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O objetivo da pesquisa foi investigar como ocorre o processo de elaboração de atividades matemáticas com a utilização do software GeoGebra por parte de um grupo de pesquisadores em Educação Matemática. As perspectivas teóricas denominadas experimentação-com-tecnologias e investigação matemática foram utilizadas para elaborar e analisar as atividades criadas. Tais perspectivas também embasaram a análise das discussões ocorridas. Do ponto de vista metodológico, a pesquisa possui um caráter qualitativo pois visa compreensões específicas acerca do fenômeno investigado. Nesse sentido, foram registradas em vídeo reuniões nas quais um grupo de pesquisadores dialogou sobre a elaboração e aprimoramento de diferentes versões de cada tarefa, visando sua utilização em um curso de extensão universitária destinado a professores e alunos de licenciatura em Matemática. As tarefas eram baseadas na Geometria Espacial. Parte das discussões ocorreu também por meio de postagens e comentários em um grupo fechado do Facebook, no qual as versões das atividades eram inicialmente compartilhadas. As diferentes versões de cada atividade foram documentadas assim como os comentários de cada postagem. Este material foi analisado visando a compreensão do processo de aprimoramento do caráter investigativo e experimental de cada tarefa matemática elaborada. A análise foi dividida em três categorias, sendo elas: design e investigação, experimentação no processo de elaboração e visualização. Tal análise sugere que o processo de elaboração está sujeito a reflexões a respeito do público alvo e seu conhecimento a respeito do GeoGebra e também de Matemática. A participação do grupo de pesquisa GPIMEM no processo também se mostrou significativa para a concepção das tarefas. Repensar as atividades após e durante sua utilização didático-pedagógica também surge como parte fundamental deste processo, assim como mudanças recursivas de enunciado mediante as considerações levantadas colaborativamente. Esta pesquisa visou contribuir para os estudos que envolvem a Matemática ensinada em conjunto com recursos tecnológicos. Conhecer o processo de elaboração proporciona à comunidade da Educação Matemática perceber a gênese do desenvolvimento de materiais didáticos construídos colaborativamente, assim como a riqueza de ideias desenvolvidas em meio a este progresso. / The aim of this research was investigate how the process of elaboration of mathematical tasks using the computational software GeoGebra by researchers in Mathematics Education takes place. The theoretical perspectives called experimentation-and-technologies and mathematical investigation theories were used to elaborate and analyze the tasks created. Such perspectives also have brought the analysis of the discussions that took place. From the methodological point of view, the research has a qualitative character because it aims specific understanding of the investigated phenomenon. In this scenario, video meetings were recorded in which a group of researchers dialogged on the elaboration and improvement of different versions of each task, aiming at its use in a university extension course for teachers and students of licencatory in mathematics. The tasks presented are based on spatial geometry. Part of the discussions also occurred through posts and comments in a closed group of Facebook, in which the versions of the activities were initially shared. The different versions and the comments of each activity were documented. This material was analyzed aimed at understanding the process of improving the investigative and experimental character of each elaborate mathematical task. Moreover, the participation of the GPIMEM research group was important for the process of creation of the tasks. Rethinking the activities after their didactic-pedagogy use is also a fundamental part of these processes, such as recursive changes of statements through the considerations raised collaboratively. The analysis was divided into three categories, are they design and research, experimentation in the process of preparation and visualization. Such an analysis suggests that the process of preparation is subject to reflections regarding the target pubic and his knowledge about Geogebra and also of mathematics. Also the participation of the GPIMEM research group in the process was significant for the design of the tasks. Rethinking activities after their didactic-pedagogical use also arises as a key part of this process, as well as recursive changes in the statement of collaboratively. This research aimed to contribute to the studies involving Mathematics taught in conjunction with technological resources. Knowing the process of elaboration provides the Community of Mathematical Education to realize the genesis of the development of didactic materials constructed collaboratively, as well as the wealth of ideas developed in the midst of this progress. / CAPES: 130128/2017-1

Made available in DSpace on 2017-07-21T20:56:29Z (GMT). No. of bitstreams: 1 Jefferson Gomes de Moraes.pdf: 12025632 bytes, checksum: 8edfb208fa4ea0bd57379b0f607d4645 (MD5) Previous issue date: 2016-07-06 / The main objective of this work is to present and research a teaching-learning methodology that leads to the classroom a more favorable environment for the assimilation of mathematical concepts, providing an education with greater potential for encouragement of learner autonomy. Initially we present a historic review ofmathematics education, their prospects for education and his trajectory in Brazil. We approach as central and fundamental point of the constructivist methodology, this is characterized by enhancing and valorizing the knowledge constructions made by the learners themselves, and in this sense, we are engaged in defending it as a feasible alternative to the math education. In order to provide a constructivist environment, we described some investigation scenarios where the teacher goes to address mathematical content in order to stimulate students to think, analyze and investigate.This process of encouragement for the student’s autonomy in building his knowledge was corroborated through a proposal of investigative activity applied in the teaching of proportionality and rule of three, which proved a viable and effective strategy for a more meaningful learning of mathematical concepts. / O presente trabalho tem como principal objetivo apresentar e pesquisar uma metodologia de ensino e aprendizagem que leva para a sala de aula uma ambiente mais favorável a assimilação de conceitos matemáticos, propiciando um ensino com maior potencial de estímulo a autonomia do estudante. Inicialmente apresentamos um resgate teórico sobre a educação matemática, suas perspectivas de ensino e sua trajetória no Brasil. Abordamos como ponto central e fundamental a metodologia construtivista, caracterizada por valorizar a construção do conhecimento efetuada pelo próprio estudante, e nesse sentido defendemos ser uma alternativa facilitadora para o ensino de matemática. Com o intuito de favorecer um ambiente construtivista descrevemos alguns cenários de investigação, onde o professor passa a abordar conteúdos matemáticos de forma a estimular o aluno a pensar, analisar e investigar.Esse processo de encorajamento para autonomia do estudante na construção de seu conhecimento foi analisado por meio de uma proposta de atividade investigativa aplicada no ensino de proporcionalidade e regra de três, o qual se mostrou uma estratégia viável e efetiva para uma aprendizagem mais significativa dos conceitos matemáticos.

Dans cette thèse, nous nous sommes intéressé aux très bons élèves et à leur façon d'étudier les mathématiques, en tenant compte du fait que tout ce qu'il y a à étudier mathématiquement n'est pas désigné par les professeurs. Partant de l'hypothèse que leur façon d'étudier leur permet de mieux réussir, nous avons suivi pendant deux années scolaires de très bons élèves de cinq établissements différents. Par une enquête anthropologique et ethnologique de terrain, nous les avons observés après les séances de cours en classe, sur leur lieu de travail (le bureau, la chambre ou un coin spécialement aménagé); en train de faire des exercices, des enquêtes, des recherches mathématiques sur les objets d'études des grands chapitres de la classe terminale scientifique (l'analyse, lois de probabilités continues, la géométrie, les similitudes...) ; chacun à sa manière, avec des supports didactiques de son choix. Cette forme d'observation particulière que nous appelons avec Mercier la méthode des épisodes biographiques, nous a permis de constituer des épisodes de leur biographie en mathématique, c'est-à-dire des moments où l'on peut attester qu'une question nouvelle se pose à eux, qu'ils apprennent quelque chose de nouveau en cherchant la réponse à la question donnée, et qu'ils identifient ce qu'ils ont appris en l'interrogeant depuis ce qu'ils savaient déjà. Nous montrons ainsi, comment les très bons élèves de terminales scientifiques fabriquent un répertoire de savoirs efficaces: leur répertoire épistémologique et heuristique. Pour construire ce répertoire, ils ont besoin d'aller enquêter loin de la classe, dans l'espace ou dans le temps (dans de nombreux manuels, scolaires ou non, dans des anciens livres, sur internet, quelques fois avec l'aide d'un membre de la famille ou d'un copain). C'est cette manière d'enquêter que nous appelons la transhumance didactique. / In this thesis, we were interested in the very good students and their way studying mathematics taking account of the fact that what there is to study mathematically is not always indicated by the professor in the courses of the various school grades. Based on the hypothesis that their way of studying enables them to succeed better in mathematics, we followed very good students from five different schools for two school years. Thus, using anthropological and ethnological field study methods, we observed the students after classroom hour, in their individual workplace settings (office, room or an especially arranged corner) doing exercises, investigations, mathematical research studies, each one in different way, with different didactic supports. This particular kind of observation, that we are calling the biographic episode method, enabled us to constitute episodes of their cognitive biography in mathematics, in other words moments of independent study where one can observe that they are faced with a news question, they learn something new by seeking the answer to a given problem, and they identify what they learned by questioning it in what they knew already. Thus we show how last year secondary school science students manufacture or build a directory of effective knowledge: the epistemological and heuristic directory. To build this directory, they need to seek learning away from the classroom, physically or temporally (using many textbooks or not, old textbooks, the Internet, or with the help of a family member or friend). It is this need for investigation which we call didactic transhumance.