Orientador: Maria Aparecida Viggiani Bicudo / Banca: Geraldo Perez / Banca: Antonio Vicente Marafioti Garnica / Banca: Washington Luiz Pacheco de Carvalho / Banca: Marcos Cesar Danhoni Neves / Resumo: A mudança da prática de ensino do professor é um tema presente na Educação Matemática. Frente a questão do como mudar esta prática entendemos ser necessário, primeiramente, buscar compreender o que é esta mudança. Ao tomarmos a mudança como uma experiência vivida, entendemos que a questão do como mudar é necessariamente antecedida pela interrogação sobre o que é viver essa experiência de mudança. Assim, nosso objetivo é expor o significado da " vivência da experiência da mudança da prática de ensino de Matemática" . Para tanto, tomamos a " vivência da experiência da mudança da prática de ensino da Matemática" como um fenômeno a ser investigado. Baseamo-nos na pesquisa fenomenológica, indo à coisa-mesma, entendida aqui como a experiência vivida pelos professores de Matemática que mudaram a sua prática pedagógica. Entrevistamos sete professores e seus discursos foram fenomenológica e hermeneuticamente analisados. Acreditamos que ao apontar o que nas reduções efetuadas interpretamos como essencial na vivência dessa experiência, estaremos contribuindo com a formação continuada do professor de Matemática, atento à sua prática e à aprendizagem dos seus alunos. Acreditamos, também, que o relato dos procedimentos da pesquisa efetuada, a realização e a interpretação da mesma, podem contribuir com outras investigações sobre o tema enfocado. / Abstract: Change in the teaching practice of the teacher is a theme that is present in mathematics education. Faced with the question of how to change this practice, we believe it is necessary to first seek to understand what this change is. As we consider change to be a lived experience, we understand that the question of how to change is necessarily preceded by the investigation of what it is to live this experience of change. Thus, our objective is to present the meaning of "living the experience of change in the practice of teaching mathematics" . Thus, we take "living the experience of change in the practice of teaching mathematics" as a phenomenon to be investigated. We based ourselves in phenomenological research, going to the "thing-itself" , understood here as the experience lived by mathematics teachers who have changed their pedagogical practice. Seven teachers were interviewed, and their discourses were analyzed phenomenologically and hermeneutically. We believe that, by pointing out what we interpreted at the phenomenological reductions as essential in the descriptions of the living of this experience, we will be contributing to the continuing education of mathematics teachers who are attentive to their practice and to their students' learning. We also believe that the description of the procedures of the research that was carried out, its accomplishment and interpretation, can contribute to other inquiries into the theme. / Doutor

The topic of this half-thesis was conceived after the author had noted with interest, that an alarmingly high number of pupils in the Mdantsane Central District of the Ciskei were registering for Higher Grade (HG) mathematics for their final (Standard 10) year. What mattered most was that the failure rate was abnormally high. As a teacher of the subject for 14 years as at the end of 1988, the author had seen very weak pupils passing through his hands who had nevertheless insisted on registering for the examination in HG mathematics. A look through the Human Sciences Research Council (HSRC) Report of 1971 which recommended the syllabus differentiation, revealed that the intention of the relevant HSRC Committee was to offer a subject at a level in accordance with a pupil's interest, aptitude and ability. In a survey undertaken by the author, samples of teachers, pupils and parents indeed confirmed the existence of a very high number of HG candidates, as suspected. The survey also revealed an aversion to the standard grade (SG) course by some pupils, teachers and even principals. A desire for university education was shown to be in the minds of most pupil respondents. Well sourced registration statistics clearly showed that the Department of Education and Training (DET) in the Republic of South Africa and the Department of Education in the Ciskei had by far the greatest proportion of pupils on the HG in mathematics in comparison with the other race groups.Standard 10 (Std 10) results for two years taken separately confirmed the author's suspicion that aptitude and/or ability were not taken into consideration by most pupils, in the choice of grade. The results were not good at all. In most cases the uninformed pupil was acting alone in taking the important decision, perhaps with only peer group pressure to contend with. Three independent opinions suggested that there was probably a general feeling that Black education was already inferior, even without the syllabus differentiation hence the reluctance to register for the SG option. Furthermore, the investigation indicated that there was no adequate provision for technical education for Blacks in either the RSA or Ciskei which would provide the alternative to a university career for a pupiL Amongst other things, a mild form of pupil screening and a well structured careers guidance programme are suggested in the concluding chapters

First Year College of Education students who have done and/or passed mathematics at matric level, often lack adequate understanding of basic mathematical concepts and principles. This is due to the fact that formal tests and examinations often fail to assess understanding at anything but a basic level. It is against this background that this study uses alternative and more direct means of assessing the level and nature of the understanding such students have of aspects of basic arithmetic and number theory. More specifically, the goals of the study are: 1. To determine the students' levels of understanding of the following number concepts: Rational numbers; Irrational numbers Real numbers and Imaginary numbers. 2. To determine whether the students understand the rules governing operations with negative numbers and with zero as principles rather than conventions. 3. To determine whether the students understand the rule governing the order of operations as a matter of convention rather than as a matter of principle. A survey of the literature concerning the nature of understanding as well as the nature of assessment is given. The students' understanding in the above areas was assessed by means of a written test followid by interviews. A sample of 50 students participated in the study while a sub-sample of 6 were interviewed. Some of the significant findings of the study were : 1. The students largely failed to draw clear distinctions between Real and Rational numbers as well as between Irrational and Imaginary numbers. 2. Very few of the students could explain the rationale behind the rules governing the. operations with negative numbers and zero. 3. Only half of the students had any knowledge of the rule governing the order of operations. Only one student demonstrated an understanding of the rule as a convention.

Things make us smart. Tools are made by humans aiming not only at solving technical problem but also developing high-order thinking. In a manner different from traditional mathematics lessons involving direct transmission of knowledge from teachers to students, tool-based mathematics classrooms fabricate an interactive teaching and learning environment. This environment fosters teachers' professional guidance based on students' manipulation of tools. The design of tool-based task aims to formulate students' learning experience via their own acquisition of knowledge through tool manipulations. Mathematics concepts can be visualized and manipulated by students through engaging in activities with tools generating tool-based signs and mathematics signs in a semiotic process. The role of mathematics teachers in tool-based mathematics classrooms is to provide well designed tool-based tasks and implement tool-based lessons in order to orchestrate students' learning, coupled with the endeavour of students' manipulating of tools.;Two new ideas, named didactical interactions and Tool-Task dialectics, were proposed in the study to effectively enforce mathematics teachers' instruction through tool-based pedagogy in interactive classrooms. The main objective of this study was to holistically investigate the implementation processes of tool-based lessons by mathematics teachers based on some theoretical perspectives. A multiple-case study, consisting of three cases with similar and different backgrounds, was conducted. Didactical cycle was one of the main theoretical frameworks, which framed analysis of the study. Based on in-depth analysis within and across cases, didactical interactions and Tool-Task dialectics were empirically developed to enrich tool-based education theories allowing teachers to demystify the cognitive development of students in tool-based lessons. The analysis of flows of the lessons uttered transition directions of critical phases ground on the theory; while pragmatic manipulations of tools operated by students and teachers' orchestration provided strong evidence to illustrate interplay between tools and tasks. Thus, the findings of the study potentially contributed to some aspects of tool-based mathematics education research.;Keywords: tool-based task design, tool of semiotic mediation, didactical cycle, didactical interactions, tool-task dialectic, mathematics classroom.

The purpose of this study was to identify preferred learning styles and strategies of secondary school students and to examine the prevailing problems that restrict them to use their own preferences. The study was intended to highlight a number of issues that need to be revealed and addressed in the learning of mathematics. The types of preferred learning styles and strategies students need to employ in learning mathematics, the assistance students require from their teachers, the conduciveness of the design of mathematics curriculum and the challenges they might face to use their own preferred learning styles and strategies in the learning of mathematics were addressed as basic research questions. The study dealt with various elements that were related to environmental, emotional, sociological, physiological and psychological categories of learning in the identification of the types of learning styles and strategies. This study is believed to contribute a lot in addressing the problems of learning styles and strategies, provide feedback to the concerned government bodies to help them improve the teaching learning processes in secondary schools. It is also to reduce the bias or prejudice on mathematics by assisting students to use their own preferred learning styles and strategies, and contribute to further investigations to make the learning of mathematics more enjoyable, participatory and lifelong career. This study was conducted in four secondary schools in West Shoa Zone. A qualitative method that was descriptive in nature was employed in the study while the instruments of the study were questionnaires and an interview. The sample comprised of 249 (128 male and 121 female) secondary school students and 30 (25 male and 5 female) secondary school mathematics teachers selected randomly. The result has shown that students were not learning mathematics on the basis of their preferred learning styles and strategies and the teachers were practicing autocratic teaching styles. Most of the students did not prefer learning mathematics through plasma television; they required brief outlines and concrete presentations, and indicated that there is not enough time to check and recheck the answers they found for the problems. These imply that the organization of secondary school mathematics curriculum requires reform to accommodate the preferred learning styles and strategies of students. / Further Teacher Education / M. Ed. (Mathematics Education)

Made available in DSpace on 2014-06-11T19:24:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2002-12-16Bitstream added on 2014-06-13T18:52:58Z : No. of bitstreams: 1 spina_coc_me_rcla.pdf: 5025570 bytes, checksum: 56148771108d808ad6cd4967943cbaa9 (MD5) / Partindo do pressuposto de que o Cálculo Diferencial e Integral (CDI) é de vital importância para a formação cultural e intelectual do educando no Ensino Médio, o trabalho aborda as razões de não mais se ensinar o CDI neste nível, contemplando e envolvendo a descrição e análise da metodologia do ensino do CDI., procurando demonstrar, por meio de uma experiência prática com abelhas, efetuada com alunos dos 1º, 2º e 3º anos do Ensino Médio, como a Modelagem Matemática pode ser eficiente veículo de transmissão de conceitos do CDI de uma forma atraente e motivadora. Por estas razões, elegemos como proposta central do presente trabalho a inclusão de conceitos (idéias) do Cálculo Diferencial e Integral no Ensino Médio com estratégia que contempla e atende à interdisciplinaridade e facilita a resolução de problemas significativos do mundo real. Nosso problema consiste em apontar uma boa metodologia para transmissão integral e integrada dos conteúdos matemáticos, em sintonia com a realidade em contínua mutação, a fim de criar condições para que o educando possa ampliar sua própria cosmovisão. Este trabalho parte da hipótese de que devemos mudar nossa abordagem, trabalhando os conteúdos vigentes de uma maneira diferente, no contexto do Cálculo Diferencial e Integral e utilizando uma estratégia de ensino interdisciplinar - a Modelagem Matemática. / Leaving of the presupposition that Diferential and Integral Calculus (DIC) is of vital importance for the student's cultural and intellectual formation in the Medium Teaching, the work approaches the reasons of not more to become trained DCI in this level, by the description and analysis of the methodology of the teaching of DCI, trying to demonstrate, through a practical experience with bees, made with students of the 1st, 2nd and 3rd years of the Medium Teaching, as the Mathematical Modelling can be efficient vehicle of transmission of concepts of Diferential and Integral Calculus in an attractive way. For these reasons, we chose as proposal headquarters of the present work the inclusion of concepts of DCI in the Medium Teaching as strategy that assists to the interdisciplinarity and facilitates the resolution of significant problems of the real world. Our problem consists of pointing a good methodology for integral and integrated transmission of the mathematical contents, in syntony with the reality in continuous mutation, in order to create conditions so that the student can enlarge your own world conception. This work part of the hypothesis that we should change our approach, working the effective contents in a different way, in the context of Diferential and Integral Calculus and using a strategy of interdisciplinar teaching - the Mathematical Modelling.

Made available in DSpace on 2014-06-11T19:24:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2003-02-12Bitstream added on 2014-06-13T19:11:47Z : No. of bitstreams: 1 martins_ra_me_rcla.pdf: 5124566 bytes, checksum: 7439f5f4948cdcd2f5c5fd4a783ba6da (MD5) / O objetivo desta pesquisa foi o de apresentar uma proposta alternativa para o ensino-aprendizagem da Geometria utilizando caleidoscópios, sólidos geométricos, jogos e softwares educacionais. A utilização conjunta desses instrumentos permitiu explorar temas como tesselações do plano (por polígonos regulares) e do espaço (por poliedros regulares com bases caleidoscópicas em suas faces). As construções geométricas (bases e planificações dos sólidos) feitas graficamente e depois no computador resultaram numa integração entre o laboratório de ensino e o de informática. São relatadas experiências com alunos da 8ª série do Ensino Fundamental, para os quais foram aplicadas atividades usando a Resolução de Problemas, observando-se grande interesse e participação. / The purpose of this research was to present an alternate proposal to the teaching and learning process in Geometry using kaleidoscopes, building blocks, games and educational softwares. With a parallel use of all these devices, we could explore themes as tesselations of the plan (by regular polygons) and of the space (by regular polyhedrons with kaleidoscopical bases in their sides). Firstly, the geometrical constructions (base and flat surfaces of the solids) were made graphically and after in the computer resulting in an integration between the teaching and computer labs. Activities, with eighth grade students, using solving problems, were applied and these experiments were reported. A great interest and participation among the students could be noticed.

Made available in DSpace on 2014-06-11T19:26:00Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-11-29Bitstream added on 2014-06-13T18:29:18Z : No. of bitstreams: 1 patricio_mfgmk_me_prud.pdf: 642086 bytes, checksum: 9a3face8bed26cec66b023faa2f068f3 (MD5) / Este trabalho apresenta uma pesquisa de mestrado, desenvolvida junto à linha de pesquisa “Práticas e Processos Formativos em Educação”, do Programa de Pós-graduação em Educação – Mestrado Interinstitucional entre a Faculdade de Ciências e Tecnologia da Universidade Estadual Paulista, campus de Presidente Prudente e a Universidade Federal de Juiz de Fora. Trata-se de uma pesquisa qualitativa, de natureza analítico-descritiva, cujo objetivo é investigar e analisar as percepções dos tutores – professores formadores – sobre o Programa Pró-Letramento em Matemática, desenvolvido na rede municipal de ensino de Juiz de Fora. O interesse por esta pesquisa surgiu de nossa preocupação com a formação continuada dos professores que ensinam Matemática nos anos iniciais do Ensino Fundamental, segmento em que atuamos como professora no Colégio de Aplicação João XXIII/UFJF. A coleta de dados se deu por meio de entrevista com a Coordenadora do Programa da rede municipal de ensino, abordando a implantação deste projeto, da aplicação de questionário e de entrevistas com três tutores, a fim de identificar seus perfis, bem como as suas percepções sobre o Programa. Um dos tutores é licenciado em Matemática e preocupa-se de forma mais expressiva com o ensino do conteúdo da Matemática. Os dois outros tutores são formados em Pedagogia e dão maior relevância à formação integral do aluno. Acreditamos que esta diferença de “olhar” para o ensino e aprendizagem da Matemática possa estar associada à formação da graduação. Os três possuem Pós-graduação e mais de dez anos de experiência no exercício do magistério. De acordo com o Guia do Curso de Matemática, a formação continuada deve desenvolver... / This study introduces a research for a Master‟s Degree, developed together with the “Practices and Formative Processes in Education” line of study, from the Post-Graduation in Education Program – from the Universidade Federal de Juiz de Fora (UFJF, acronym in Portuguese) together with the Universidade Estadual Paulista (UNESP – University from the State of São Paulo, acronym in Portuguese). It is a qualitative research, of a analytical-descriptive nature, whose goal is to investigate and analyze the perceptions from the tutors – Teacher Trainers – about the Pro-Literacy Program in Mathematics developed by the public schools from the city of Juiz de Fora. The interest in this research was brought about our concern with the continuous improvement of Mathematics teachers in the first years of Elementary School, segment in which we work as teachers, at the Colégio de Aplicação João XXIII, which belongs to the Federal University of Juiz de Fora (UFJF). The gathering of data was carried out through interview with the coordinator of the Program of the city, approaching the implementation of the project; through questionnaires and interviews with three tutors so as to identify their profiles, as well as their perceptions of the Program. 0ne tutor is licensed to teach Mathematics and is more concerned with teaching mathematic contents. Two tutors are graduated in Education and focus on the development of the student as a whole. All of the tutors are post-graduated, and have been teaching for over ten years. According to the official guide of Mathematics, the development of the student has to entice an investigative and reflexive attitude, bearing in mind that the professional activity is a field of production of knowledge, involving learning processes that go beyond the mere use of what has been learned. However... (Complete abstract click electronic access below)

Made available in DSpace on 2014-06-11T19:31:40Z (GMT). No. of bitstreams: 0 Previous issue date: 2003-02-21Bitstream added on 2014-06-13T19:42:07Z : No. of bitstreams: 1 hiratsuka_pi_dr_rcla.pdf: 1108738 bytes, checksum: 03f34efb5db83a1f23f0bec3e3e410b2 (MD5) / A mudança da prática de ensino do professor é um tema presente na Educação Matemática. Frente a questão do como mudar esta prática entendemos ser necessário, primeiramente, buscar compreender o que é esta mudança. Ao tomarmos a mudança como uma experiência vivida, entendemos que a questão do como mudar é necessariamente antecedida pela interrogação sobre o que é viver essa experiência de mudança. Assim, nosso objetivo é expor o significado da vivência da experiência da mudança da prática de ensino de Matemática . Para tanto, tomamos a vivência da experiência da mudança da prática de ensino da Matemática como um fenômeno a ser investigado. Baseamo-nos na pesquisa fenomenológica, indo à coisa-mesma, entendida aqui como a experiência vivida pelos professores de Matemática que mudaram a sua prática pedagógica. Entrevistamos sete professores e seus discursos foram fenomenológica e hermeneuticamente analisados. Acreditamos que ao apontar o que nas reduções efetuadas interpretamos como essencial na vivência dessa experiência, estaremos contribuindo com a formação continuada do professor de Matemática, atento à sua prática e à aprendizagem dos seus alunos. Acreditamos, também, que o relato dos procedimentos da pesquisa efetuada, a realização e a interpretação da mesma, podem contribuir com outras investigações sobre o tema enfocado. / Change in the teaching practice of the teacher is a theme that is present in mathematics education. Faced with the question of how to change this practice, we believe it is necessary to first seek to understand what this change is. As we consider change to be a lived experience, we understand that the question of how to change is necessarily preceded by the investigation of what it is to live this experience of change. Thus, our objective is to present the meaning of living the experience of change in the practice of teaching mathematics . Thus, we take living the experience of change in the practice of teaching mathematics as a phenomenon to be investigated. We based ourselves in phenomenological research, going to the thing-itself , understood here as the experience lived by mathematics teachers who have changed their pedagogical practice. Seven teachers were interviewed, and their discourses were analyzed phenomenologically and hermeneutically. We believe that, by pointing out what we interpreted at the phenomenological reductions as essential in the descriptions of the living of this experience, we will be contributing to the continuing education of mathematics teachers who are attentive to their practice and to their students' learning. We also believe that the description of the procedures of the research that was carried out, its accomplishment and interpretation, can contribute to other inquiries into the theme.

Orientador: Roberto Ribeiro Baldino / Banca: Dione Lucchesi de Carvalho / Banca: Antonio Carlos Carrera de Souza / Resumo: Nesta dissertação, viso a apresentar a investigação que realizei junto ao Grupo de Pesquisa-Ação em Educação Matemática, na Universidade Paulista, campus de Rio Claro (GPA-RC). Na investigação, trato o fracasso do ensino e da aprendizagem em Matemática, por meio de ação diferencial auto-regulada, própria da linha de investigação adotada pelo GPA-RC: análise dos condicionantes da sala de aula e intervenção pedagógica. Tomo minha prática como objeto de pesquisa e busco as conseqüências de uma tentativa de combate ao fracasso escolar de alunos universitários através da estratégia de Grupo de Estudos. A descoberta, realizada no GPA-RC, provoca mudança em meu olhar e adoção de aporte teórico sobre grupos operativos. / Abstract: This dissertation aims at presenting the research made within the Group of Action Research in Mathematical Education at the Universidade Paulista on the Rio Claro campus (GPA-RC). This project investigates the failure of the teaching and learning of Mathematics through the self-regulated differential action approach, which is adopted by the GPA- RC, and includes the analysis of the conditioning factors in the classroom and of pedagogical intervention. My research is based on my own teaching practice and I look at the consequences of an attempt to combat the failure of university students using the Group-Work strategy. The findings, which took place at the GPA-RC, have brought about changes in my perception and the adoption of the operative group-work theoretical framework. / Mestre