This thesis discusses inquiry-based education in mathematics aimed at the decimal system and large numbers in elementary school environment. Inquiry-based education is a form of education that uses exploration or verification of new findings by the students themselves. The principles and basic characteristics of inquiry-based education are discussed in the theoretical part. The practical section is based on qualitative research. Data collection and analysis of results in 5 experiments in two parallel 5th grade classes are used to determine the characteristics of inquiry-based education and to discover the possible problematic occurrences, which could be encountered with this kind of education. Based on this information, recommendations for practical use are formulated. Results have shown that inquiry-based education in mathematics classes is beneficial to the students. Although greater care in selecting the right exercise and rigorous preparation of the teachers and teaching aids is required, implementation of this education is worth the effort. It represents an untraditional variegation for the students, by which they can calmly educate themselves and consolidate their knowledge.

Submitted by Aelson Maciera (aelsoncm@terra.com.br) on 2017-09-26T19:32:55Z No. of bitstreams: 1 DissDOA.pdf: 5341993 bytes, checksum: 05c9313141d122e090d9e514c16b6287 (MD5) / Approved for entry into archive by Ronildo Prado (bco.producao.intelectual@gmail.com) on 2018-01-30T16:29:52Z (GMT) No. of bitstreams: 1 DissDOA.pdf: 5341993 bytes, checksum: 05c9313141d122e090d9e514c16b6287 (MD5) / Approved for entry into archive by Ronildo Prado (bco.producao.intelectual@gmail.com) on 2018-01-30T16:30:01Z (GMT) No. of bitstreams: 1 DissDOA.pdf: 5341993 bytes, checksum: 05c9313141d122e090d9e514c16b6287 (MD5) / Made available in DSpace on 2018-01-30T16:37:27Z (GMT). No. of bitstreams: 1 DissDOA.pdf: 5341993 bytes, checksum: 05c9313141d122e090d9e514c16b6287 (MD5) Previous issue date: 2017-07-11 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / The present study had as main objective to develop an interactive virtual environment capable of advising the teacher in his pedagogical practices. From this environment we extracted the data that were analyzed and discussed, based on the reports of the students involved. In the course of this work three considerable procedures were carried out: the creation of Blog www.belelite.blogspot.com.br, the management of information that fed the blog and were topics of discussions between the students and the teacher and finally the preparation of The challenge of Virtual Knowledge, a workshop material to be held at the Technical Workshops promoted by the Teaching Board of the city of São Roque in SãoPaulo. / O presente estudo teve como objetivo principal desenvolver um ambiente virtual interativo capaz de assessorar o professor em suas práticas pedagógicas. Deste ambiente extraiu-se os dados que foram analisados e discutidos, baseando-se nos relatos dos alunos envolvidos. No transcorrer deste trabalho foram realizados três procedimentos consideráveis: a criação do Blog www.belelite.blogspot.com.br, o gerenciamento de informações que alimentaram o blog e foram temas de discussões entre os alunos e o professor e, finalmente, a preparação de um material para o Workshop - O desafio do Saber Virtual, a ser realizado nas Oficinas Técnicas promovidas pela Diretoria de Ensino da cidade de São Roque em São Paulo.

The present work was developed in the Postgraduate Program in Mathematics Education and Physics Teaching (PPGEM & EF) of the Federal University of Santa Maria (UFSM) and inserted in the line of research Teaching and Learning of Mathematics and its Philosophical, Historical and Epistemological Foundations. Based on interviews with the pedagogical advisor of the 8ª Regional Education Coordination (8ª CRE), responsible for the Special Education sector, with teachers of Mathematics from state schools of Basic Education and the analysis of official documents of the Brazilian legislation on Special Education and Inclusive Education, curricula and pedagogical projects of undergraduate courses in Mathematics, this research aimed to investigate how these Mathematics teachers organize their classes for teaching in classes that have students included. For the data collection, semi-structured interviews were carried out with five Mathematics teachers from the state public school system who work or have already worked with students included in the regular education and with the pedagogical advisor responsible for the Special Education sector of the 8ª CRE. We used as a theoretical methodological reference for conducting these interviews Oral History, based on the ideas of José Carlos Sebe Bom Meihy (1996) and, mainly, the works developed by the Oral History and Mathematics Education Research Group, coordinated by Antonio Vicente Marafioti Garnica (2005, 2007, 2011, 2013). The analysis of the interviews was performed - according to the work carried out by Maria Edneia Martins-Salandim - in two moments: analysis of singularities and analysis of convergences. In the analysis of singularities we try to record what is characteristic of each deponent in his narrative, its peculiarities and its particularities. In the analysis of convergences we seek to confront the narratives of our deponents with what is written in the official documents of the legislation on Special Education and Inclusive Education and with the grades and pedagogical projects of the degree courses in Mathematics of the institutions where the teachers interviewed concluded the course Training. For this, we list three units of analysis: initial training, continuing training and work with included students. We emphasize, from the analysis carried out, that the Mathematics teachers interviewed consider that the work carried out with students included in regular education is hard work and difficult to be developed, since they did not receive orientation in the initial training course to work with these students. In addition, they have taken part in a few continuing education courses related to this topic, and the 8ª CRE does not provide guidelines for this work that be aimed at teachers in areas other than Special Education. / O presente trabalho foi desenvolvido junto ao Programa de Pós-Graduação em Educação Matemática e Ensino de Física (PPGEM&EF) da Universidade Federal de Santa Maria (UFSM) e inserido á linha de pesquisa Ensino e Aprendizagem da Matemática e seus Fundamentos Filosóficos, Históricos e Epistemológicos. Com base em entrevistas com o assessor pedagógico da 8ª Coordenadoria Regional de Educação (8ª CRE), responsável pelo setor de Educação Especial, com professores de Matemática de escolas estaduais da Educação Básica e na análise de documentos oficiais da legislação brasileira sobre Educação Especial e Educação Inclusiva, de currículos e projetos pedagógicos de cursos de Licenciatura em Matemática, essa pesquisa teve como objetivo investigar como esses professores de Matemática organizam suas aulas para a docência em turmas que possuem alunos incluídos. Para a coleta dos dados foram realizadas entrevistas semiestruturadas com cinco professoras de Matemática da rede pública estadual de ensino que trabalham ou já trabalharam com alunos incluídos no ensino regular e com a assessora pedagógica responsável pelo setor de Educação Especial da 8ª CRE. Utilizamos como referencial teórico metodológico para a realização dessas entrevistas a História Oral, nos fundamentando nas ideias de José Carlos Sebe Bom Meihy (1996) e, principalmente, nos trabalhos desenvolvidos pelo grupo de pesquisa Grupo História Oral e Educação Matemática, coordenado por Antonio Vicente Marafioti Garnica (2005; 2007; 2011; 2013). A análise das entrevistas foi realizada – conforme o trabalho realizado por Maria Edneia Martins-Salandim – em dois momentos: análise de singularidades e análise de convergências. Na análise de singularidades procuramos registrar o que é característico de cada depoente em sua narrativa, suas peculiaridades e suas particularidades. Na análise de convergências buscamos confrontar as narrativas dos nossos depoentes com o que está escrito nos documentos oficiais da legislação sobre Educação Especial e Educação Inclusiva e com as grades e os projetos pedagógicos dos cursos de Licenciatura em Matemática das instituições onde as professoras entrevistadas concluíram o curso de formação inicial. Para isso, elencamos três unidades de análise: formação inicial, formação continuada e trabalho com alunos incluídos. Destacamos, a partir da análise realizada, que as professoras de Matemática entrevistadas consideram que o trabalho realizado com alunos incluídos no ensino regular é um trabalho árduo e difícil de ser desenvolvido, pois elas não receberam, no curso de formação inicial, orientações para trabalhar com esses alunos. Além disso, participaram de poucos cursos de formação continuada relacionados a esse tema e a 8ª CRE também não fornece orientações para esse trabalho que sejam voltadas aos professores de áreas que não seja a Educação Especial.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The present work has the intention to construct a history of discipline Calculation in the course of Degree in Mathematics of the Federal University of Sergipe, during the period from 1972 to 1990. It examines the historical curse of discipline by means of the workload, of the prerequisite ones, of its contents, its professors and methods of teaching. It analyzes the history of the Calculation in the prism of the history of the disciplines, taking as sources the lesson plans, minutes acts, resolutions, reports, didatic books and verbal stories. We infer that the changes pass the discipline Calculation had went in regards to the workload of great relevance; however, in if treating to prerequisite and summaries, the alterations were smaller. In the case of the movement of contents of each disciplines, we notice that in elapsing of the years the malter of teaching Calculation was configured gradually and before assuming its last formation it pass for different disciplines with reformularizations in its configuration, with distinct signatures, with distinct workload, but with the same contents. We observed although there was renewal of the teaching picture causing significant alterations regarding the profile of the professors of Calculation. We consideed that the method of the lesson was closely connected to the use that the theacher could make of the book and the applications of exercises. / O presente trabalho tem o propósito de construir uma história da disciplina Cálculo no curso de Licenciatura em Matemática da Universidade Federal de Sergipe, durante o período de 1972 a 1990. Examina o percurso histórico da disciplina por meio da carga horária, dos pré-requisitos, de seus conteúdos, seus professores e métodos de ensino. Analisa a história do Cálculo no prisma da história das disciplinas, tomando como fontes os planos de aula, atas, resoluções, relatórios, livros didáticos e relatos orais. Inferimos que as mudanças por que passou a disciplina Cálculo foram no tocante à carga horária de grande relevância; porém, em se tratando de pré-requisitos e ementas, as alterações foram menores. No caso da movimentação dos conteúdos em cada disciplina, notamos que no decorrer dos anos a matéria de ensino Cálculo foi configurada paulatinamente e antes de assumir a sua última formação perpassou por diferentes disciplinas, com reformulações em sua configuração, com assinaturas distintas, com cargas horárias distintas, mas com os mesmos conteúdos. Observamos ainda que o quadro docente ocasionou alterações significativas na disciplina Cálculo. Consideramos que o método da aula estava intimamente ligado ao uso que o professor poderia fazer do livro e das aplicações de exercícios.

We present several possible forms of mathematical competitions for University students. One of them is Blitz Mathematical Olympiad. It is a team competition, when all teams receive the same problem and are allotted 10-15 minutes to come up with a solution. This cycle is repeated 6-8 times with different problems. Modern Internet technologies allow us to organize Blitz Mathematical Olympiads for the teams which are in different cities and even countries.

Läroboken utgör en stor roll i gymnasielärares undervisning både då det handlar om planering och genomförande. Studien syftar till att besvara hur läroboken används av gymnasielärare och hur lärarna frångår den. Det handlar både om när läroboken används samt vilket innehåll i den som används. Frångående av läroboken innebär att läraren avviker från det matematiska innehåll som presenteras i läroboken. Det kan exempelvis handla om att en lärare anpassar sin kommunikation till ett vardagligt och enkelt språk som inte uttrycks i läroboken. Studien är av kvalitativ karaktär och är en fallstudie. Resultatet är baserat i empiri av två informanter, där tillvägagångssätten är intervju, observation av lektion samt granskning av planeringsdokument och läromedel. Resultatet har analyserats utifrån ett antal teorier och begrepp, där de mest betydelsefulla för studien är orkestreringsteorin samt ett relationellt perspektiv mellan läraren och läroboken. Analysen visar att läroboken är synlig och används under alla studerade aktiviteter, både i lärarnas planering, genomgång på skrivtavlan samt under elevernas individuella räknande. Det framkommer även att lärarna inte alltid använder lärobokens innehåll i en kronologisk ordning och att lärarna hjälper eleverna att sålla bland mängden av uppgifter i läroboken. / The textbooks are an important foundation in the education of mathematics. The aim of this study is to examine how teachers in the upper secondary school actually use the textbook and to study when the textbook is absence in their teaching. The study aims to investigate, from a teacher’s perspective, when the textbook is being used and what content in the textbook that the teacher uses. The absence of the textbook implicates when and how the teachers deviate from the content and how the content is presented in the textbook. An example of absence of the textbook is when the teacher adapts the explanations of a mathematical content to an everyday language or to an informal way, which the textbook does not. The study is a qualitative case study and the results are founded in interviews with two informants and by an observation of their practice as teachers in mathematics. The teacher’s textbook and document that are used as planning materials are also reviewed and presented. The result of the study is analyzed by some theoretical concepts, where the theory of orchestration and the relation between the teacher and the textbook are of importance in this study. The analysis of the study implicates that the textbook in mathematics is visible in every moment that were investigated. This means that the textbook is visible in the planning of the course and lessons, in the instructions on the whiteboard lead by the teacher and when the pupils independently use the textbook. The analysis also showed that the use of the textbook was not always presented in a chronological order and that the teachers helped the pupils to organize the tasks in the textbook.

Made available in DSpace on 2016-04-27T16:57:35Z (GMT). No. of bitstreams: 1 Agnaldo Da Conceicao Esquincalha.pdf: 2760765 bytes, checksum: 4b98025a110f8c095d5e0d5b8d626829 (MD5) Previous issue date: 2015-03-09 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work aims at investigating the knowledge revealed by tutors of a distance continuing education course for mathematics teachers. The context of the research was the tutoring system of the Improvement Course in Mathematics, offered by the State Government of Rio de Janeiro from 2011 onwards. Initially we follow the work of 32 tutors over a year between 2011 and 2012 in order to list and classify the types of interventions in discussion forums among the course participants. After considering the results, we offer initial training to freshman tutors in 2012, to promote an improvement in the actions that we consider to be below expectations. Between August 2012 and July 2013 six tutors, the subjects of this research, were followed and participated in a training program in service. For the training of tutors, beyond the specifics of the Improvement Course in Mathematics, we grounded our work on the TPACK (Technological Pedagogical Content Knowledge) theoretical framework, assuming that technological, pedagogical and mathematical knowledge skills are fundamental for the exercise of their functions. The research, qualitative in nature, made use of questionnaires and conducting focus groups to collect data, which were interpreted under the light of thematic content analysis. For the triangulation of data, we used the discursive types found in interventions by tutors in the course s discussion forums. Our analysis indicated that affective and attitudinal components play a key role in the exercise of mentoring in this context and, therefore, we concluded the research by proposing the expansion of TPACK theoretical framework, including these components in a fourth type of knowledge, featuring TPACK-OTE (Technological Pedagogical Content Knowledge-Online Teacher Education) / Neste trabalho, teve-se o intuito de investigar os conhecimentos revelados por tutores de um curso de formação continuada para professores de Matemática, oferecido na modalidade a distância. O contexto da investigação foi o sistema de tutoria do Curso de Aperfeiçoamento em Matemática, oferecido pela Rede Estadual do Rio de Janeiro a partir de 2011. Inicialmente, acompanhou-se o trabalho de 32 tutores ao longo de um ano, entre 2011 e 2012, a fim de elencar e tipificar suas intervenções realizadas em fóruns de discussão junto aos cursistas. A partir dos resultados, foi oferecida uma formação inicial aos tutores ingressantes em 2012, a fim de promover melhoria nas ações consideradas aquém do esperado. Entre agosto de 2012 e julho de 2013, foram acompanhados, e participaram de um programa de formação em serviço, seis tutores, que constituem os sujeitos desta pesquisa. Para a formação desses tutores, além das especificidades do Curso de Aperfeiçoamento, houve inspiração no quadro teórico TPACK (Technological Pedagogical Content Knowledge), assumindo que os conhecimentos tecnológicos, pedagógicos e de conhecimento matemático são fundamentais para o exercício de suas funções. A pesquisa, de natureza qualitativa, utilizou-se de questionários e de grupos focais para coleta de dados, que foram interpretados à luz da análise temática de conteúdo. As tipologias discursivas encontradas nas intervenções realizadas pelos tutores nos fóruns de discussão permitiram a triangulação dos dados. As análises indicaram que componentes afetivo-atitudinais têm papel fundamental no exercício da tutoria no contexto da formação continuada de professores a distância e, por isso, a pesquisa é concluída com uma proposta de expansão do quadro teórico TPACK, incluindo esses componentes em um quarto tipo de conhecimento, caracterizando o TPACK-OTE (Technological Pedagogical Content Knowledge-Online Teacher Education)

Submitted by Vanessa Cerignoni Benites Bonetti (vanessa.benites@gmail.com) on 2018-07-05T12:53:07Z No. of bitstreams: 1 Versão Final Tese Vanessa Benites-Bonetti.pdf: 7277152 bytes, checksum: 6822e2ba0a8899ff247a810dbb0425b8 (MD5) / Approved for entry into archive by Ana Paula Santulo Custódio de Medeiros null (asantulo@rc.unesp.br) on 2018-07-05T13:49:22Z (GMT) No. of bitstreams: 1 benitesbonetti_vc_dr_rcla.pdf: 4688048 bytes, checksum: 3cf920d62e44d1ebc0fcfb22bc848726 (MD5) / Made available in DSpace on 2018-07-05T13:49:22Z (GMT). No. of bitstreams: 1 benitesbonetti_vc_dr_rcla.pdf: 4688048 bytes, checksum: 3cf920d62e44d1ebc0fcfb22bc848726 (MD5) Previous issue date: 2018-05-22 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Inserida no contexto da formação de professores de Matemática, a presente pesquisa objetiva – analisar e compreender a identidade docente de egressos de cursos de Licenciatura em Matemática de Instituições Públicas de Ensino Superior (IPES) do Estado de São Paulo. Para alcançar o objetivo, tomamos como eixo norteador a seguinte questão: Como se constitui a identidade docente de egressos de cursos de Licenciatura em Matemática? Balizadas por essa interrogação, realizamos uma pesquisa qualitativa, que foi desenvolvida em dois movimentos. No 1º Movimento, utilizamos dois procedimentos metodológicos: Análise Documental e Questionário, os quais foram utilizados como recurso/instrumento para obtenção dos dados. Realizamos a Análise Documental dos Projetos Pedagógicos de Cursos (PPC) de três cursos de Licenciatura em Matemática do estado de São Paulo (UNESP/Rio Claro; UNESP/Bauru; e USP/São Carlos). Ainda no 1º Movimento, aplicamos um Questionário com egressos desses três cursos, que os haviam concluído entre os anos de 2004 e 2009. O 1º Movimento foi importante para caracterizarmos o cenário investigado, e subsidiar a elaboração das Entrevistas (2º Movimento), que se mostrou como o corpus de análise. Dessa forma, o 2º Movimento foi marcado pela realização de Entrevistas com seis egressos dos cursos de Licenciatura em Matemática (UNESP/Rio Claro; UNESP/Bauru; e USP/São Carlos), três coordenadores dessas instituições e cinco pesquisadores envolvidos com Políticas Públicas de formação de professores. O momento da sistematização, baseada em alguns conceitos de Análise de Conteúdo, foi realizado a partir do delineamento do corpus de análise, as Entrevistas. Elencamos, por meio de sentido e significado, Unidades de Contexto, Unidades de Registro, Eixos Temáticos, até findarmos em cinco Categorias de Análise: Trabalho Docente e Conhecimento do Professor: caminhando para a profissionalidade; Cursos de Licenciatura: aspectos estruturais e conceituais; Profissionalização como Espaço Próprio à Profissionalidade; Comprometimento e Engajamento do Professor: um percurso de seu profissionalismo; e Formação de Professores na Atualidade: desafios e perspectivas das políticas educacionais e da colaboração. Posteriormente realizamos um diálogo entre o referencial teórico e os dados coletados, por meio de inferências e interpretações a partir dos núcleos de sentido. A identidade docente foi revelada nas inter-relações entre os aspectos pessoais e sociais, e influenciada diretamente pelos aspectos relacionados à profissionalidade e à profissionalização docente. / Inserted in the context of Mathematics Teachers Education, the present research aims to analyze and understand the teaching identity of graduates of Mathematics Degree courses’ graduates of Higher Education Public Institutions in the State of São Paulo. To reach this objective, we took as a guiding axis the following question: How is the teaching identity of graduates in Mathematics undergraduate courses constituted? Based on this question, we performed a qualitative research, which was developed in two movements. In the first movement, we used two methodological procedures: Documentary Analysis and Questionnaires, which were used as a resource/instrument to obtain the data. We carried out the Documentary Analysis of the Pedagogical Projects of Courses of three Mathematics courses in the state of São Paulo (UNESP/Rio Claro, UNESP/Bauru, and USP/São Carlos). Still in the first movement, we applied a Questionnaire with graduates of these three courses, which had concluded the course between the years of 2004 and 2009. The first movement was important to characterize the scenario investigated, and to subsidize the elaboration of the Interviews (second movement), which was shown as the corpus of analysis. Thus, the second movement was marked by the conduction of Interviews with six graduates of the Mathematics degree courses (UNESP/Rio Claro, UNESP/Bauru, and USP/São Carlos), three coordinators of these institutions and five researchers involved with public policies for teacher education. The moment of systematization, based on some concepts of Content Analysis, was carried out from the delineation of the corpus of analysis, that is, the Interviews. We listed, through sense and meaning, Context Units, Registration Units, Thematic Axes, until we finished in five Categories of Analysis: Teaching Work and Teacher Knowledge: moving towards professionality; Degree courses: structural and conceptual aspects; Professionalization as a Private Space for Professionality; Commitment and Engagement of the Teacher: a course of his professionalism and; Teacher Education in the Present: challenges and perspectives of educational policies and collaboration. Subsequently, we conducted a dialogue between the theoretical data collected through inferences and interpretations from the sense cores. The teaching identity was revealed in the interrelationships between the personal and social aspects, and directly influenced by the aspects related to the professionality and the teacher’s professionalization.

Mathematics learning seems to be a demanding and time-consuming task for many learners. Information and communication technology (ICT) is an attractive tool of learning for students at any level and it can provide an effective atmosphere for understanding mathematics. The question is how to combine mathematics teaching contents, approaches, curricula, and syllabus with new media. The key issue in European educational policy (and other countries as well) is exchange and sharing digital learning resources (learning objects) among countries. In order to accumulate the practice of various countries and use the best digital resources created by different countries, it is necessary to localize learning objects (LO). The paper deals with some problems connected with localization of LO, developed for mathematics education, and presents some solution. Software localization is mainly referred to as language translation (e.g., translation of user interface texts and help documents). However, there are many other important elements depending on the country and people who will use the localized software. In this paper, the main attention is paid to localization of learning objects used for teaching and learning mathematics.

The major aims of this paper are to: present the background of the mathematics education problem in the Stamford Public School (SPS) district which is common is most U.S cities; explain the need for change in mathematics education; describe the process to systemically transform both the curriculum and instruction of mathematics thereby ensuring that each and every students is prepared for the 21st century, for higher education, and for success in a global society; and provide ways to measure these changes. The K-12 mathematics education reform model presented can be replicated in other cities and for other academic areas.