Submitted by MARCIA ROVADOSCHI (marciar@unifra.br) on 2018-08-14T13:50:33Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertacao_FrancineLanesMonteiro.pdf: 1907914 bytes, checksum: e70fa1ffe83bde3467796cb62b5c8552 (MD5) / Made available in DSpace on 2018-08-14T13:50:33Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertacao_FrancineLanesMonteiro.pdf: 1907914 bytes, checksum: e70fa1ffe83bde3467796cb62b5c8552 (MD5) Previous issue date: 2014-10-30 / This dissertation presents a research realized an a professional master's degree in teaching of mathematics. It aimed to investigate what contributions can offer an educational workshop to develop visual abilities in geometry by teachers on the early years of elementary school. In order to answer the research problem it was decided to organize it in the following topics: visual abilities can be developed with these teachers about workshops? Construction and use of didactic materials help on the acquisition of visual abilities? Helds activities with puzzles make possible the acquisition of visual activities? The research was characterized as qualitative who subjects were eight teachers. They are teachers in class on a Public School of Basic Education of the City of Júlio de Castillos on the state of Rio Grande do Sul, in Brazil. The instruments to collect data were questionnaires and written records by them and the researcher. The research was conducted in four stages, namely: initial questionnaire, syllabus analysis of the early years, teaching workshops and final questionnaire. profile of the group of teachers who work in the early years of this school, his views on mathematics education. The group researched profile can be regarded as experienced and qualified, therefore, all of them having higher education in Pedagogy and only three of them, do not have graduate. It was noticed was how fragile the mathematical training of these teachers, fear and superficiality to talk about mathematics and geometry. The syllabus of the analysis showed that there are gaps in the second geometry content for four years, since they do not appear in the third. In turn, such content, when they appear, are on the list, or are planned to be developed by the end of the school year. From these two stages of the research, it was planned two workshops with specific activities involving visual skills, which, involved three types of skills: perception of figures in fields, visual discrimination and visual memory. In the workshops there was a need for activities are offered that include the development of visual skills, since some teachers had difficulties in memorizing and compare figures. It was found also that visual skills contribute significantly to the formation of geometric thinking and the importance of manipulatives in developing these skills. It was evidenced by the final questionnaire the group satisfaction studied in relation to the development of the workshops. We conclude that continuing education is a moment of great importance for the expansion and consolidation of knowledge. Justified the use of the term in-service training of teachers in the title of this work because the research was conducted with teachers who work effectively in the early years of elementary school. However, the focus of the dissertation was not the teacher training itself, but the development of visual skills in the teaching of geometry. / Esta dissertação de mestrado profissionalizante em ensino de Matemática desenvolvida no Centro Universitário Franciscano-Rs envolve uma pesquisa, que teve por objetivo principal investigar quais as contribuições que oficinas pedagógicas podem oferecer para ajudar a desenvolver em professores dos anos iniciais habilidades visuais na aquisição de conceitos geométricos. A fim de responder ao problema de pesquisa optou-se por organizá-la nos seguintes tópicos: habilidades visuais podem ser desenvolvidas com professores dos anos iniciais em oficinas pedagógicas? Construção e uso de materiais didáticos auxiliam na aquisição de habilidades visuais? Realizar atividades com quebra-cabeças possibilitam a aquisição de atividades visuais? A pesquisa foi caracterizada como sendo de campo, a qual contemplou o modelo qualitativo, os sujeitos foram oito professoras dos anos iniciais de uma Escola Estadual de Educação Básica do Município de Júlio de Castilhos - Rs. Os instrumentos para coleta de dados foram questionários e diário de bordo. A pesquisa foi desenvolvida em quatro etapas, sendo elas: questionário inicial, análise do plano de estudos dos anos iniciais, oficinas pedagógicas e questionário final. No que diz respeito ao questionário inicial, proporcionou conhecer sobre o perfil do grupo de professoras que atuam nos anos iniciais desta escola, suas concepções sobre ensino de matemática. O perfil do grupo pesquisado pode ser considerado como experiente e qualificado, pois, todas elas possuem curso superior em Pedagogia e, apenas três delas, não possuem pós-graduação. Percebeu-se o quanto foi frágil a formação matemática dessas professoras, o medo e a superficialidade em falar sobre matemática e geometria. A análise do plano de estudos comprovou que existem lacunas em termos de conteúdos de geometria do segundo para o quarto anos, uma vez que no terceiro eles não aparecem. Por sua vez, tais conteúdos, quando aparecem, estão no final da lista, ou seja, são planejados para serem desenvolvidos ao final do ano letivo. A partir dessas duas etapas da pesquisa, planejou-se duas oficinas com atividades específicas envolvendo habilidades visuais, as quais, envolveram três tipos de habilidades: percepção de figuras em campos, discriminação visual e memória visual. Nas oficinas verificou-se a necessidade de que sejam ofertadas atividades que contemplem o desenvolvimento de habilidades visuais, visto que, algumas professoras apresentaram dificuldades em memorizar e comparar figuras. Constatou-se, ainda, que habilidades visuais contribuem de forma significativa para a formação do pensamento geométrico e a importância dos materiais manipuláveis no desenvolvimento dessas habilidades. Evidenciou-se por meio do questionário final a satisfação do grupo pesquisado em relação ao desenvolvimento das oficinas. Conclui-se que a formação continuada é um momento de suma importância para a ampliação e solidificação de conhecimentos. Justifica-se o uso do termo formação em exercício de professores no título desta dissertação pelo fato da pesquisa ter sido realizada com professoras que atuam efetivamente nos anos iniciais do Ensino Fundamental. Entretanto, o foco da dissertação não foi a formação de professores em si, mas o desenvolvimento de habilidades visuais no ensino de Geometria.

Made available in DSpace on 2016-04-27T16:57:53Z (GMT). No. of bitstreams: 1 dissertacao_vania_andrade_luz.pdf: 1642035 bytes, checksum: 179a6afec6f9633eb81f44f31826cdea (MD5) Previous issue date: 2007-04-09 / This dissertation consists of a study focused on the teaching of geometrical transformations based on the analysis of exercises suggested in didactical books published since the 1960s in São Paulo State. The realization of this work is supported by an analysis with the following objectives: to examine the completion of the local mathematical organizations according to the Anthropological Theory of Didactics, by Yves Chevallard; to observe how the students main difficulties were approached, based on research by Jaime and Gutiérrez (1996) and Jahn (1998); to compare the teaching proposals of isometries and homoteties current at the time of the movement of reformation of Modern Mathematics to those which followed the publishing of the Parâmetros Curriculares Nationais (Brazilian National Curricular Standards). Initially, we proceeded to a study of the mathematical organization relative to geometrical transformations, a study in which will be examined the symmetries of elements of nature and the arts, the definitions of the main transformations that are part of the program of Ensino Fundamental (equivalent to an eight-year elementary school), besides the identification of historical elements related to the development of Geometry. After that, we will be moving on to the study of the didactical organization, in which researches about the teaching and learning of isometries were verified, as well as official texts as Curricular Guides, Proposals and Standards, besides a few aspects of the movement of reformation of Modern Mathematics in Brazil, and its relationship with the same movement in the United States and France. The analysis of the books was carried out from the grouping of exercises in types of tasks, a qualification used as much for the identification of the resolution techniques, as for the distinction of the technology appropriate to the justification of the former. Following that, we have performed a study of the set of proposed exercises, in which the above-mentioned was complied with, in the second paragraph of this abstract, as objectives of the analysis that was developed. Departing from the adopted theoretical basis, the conclusions of the research indicate that the orientations observed in each of the analyzed periods would not guarantee, per se, that important problems in the teaching of transformations were resolved. As it is known, the period correspondent to the movement of reformation of Modern Mathematics has emphasized the mathematical structure, whereas the period that followed the publishing of the Parâmetros Curriculares highlighted the relationship of isometries and homoteties with superior levels of mathematical determination. In the first case, the visibility of the mathematical work was not highlighted, while in the second one, the absence of technological elements might have compromised the completion of the mathematical organization / Esta dissertação consiste em um estudo focado no ensino de transformações geométricas e organizado com base na análise de exercícios propostos em livros didáticos publicados, a partir dos anos 60, no Estado de São Paulo. A realização deste trabalho apóia-se em uma análise com os seguintes objetivos: examinar a completude das organizações matemáticas locais conforme a Teoria Antropológica do Didático, de Yves Chevallard; observar como foram abordadas as principais dificuldades dos alunos, com base nas pesquisas de Jaime e Gutiérrez (1996) e de Jahn (1998); comparar as propostas de ensino de isometrias e homotetias vigentes à época do movimento de reforma da Matemática Moderna com aquelas que se seguiram à publicação dos Parâmetros Curriculares Nacionais. Inicialmente, procedemos a um estudo da organização matemática relativa a transformações geométricas, estudo no qual são examinadas as simetrias presentes em elementos da natureza e das artes, as definições das principais transformações que fazem parte do programa do Ensino Fundamental, além da identificação de elementos históricos relacionados ao desenvolvimento da geometria. Em seguida, passamos ao estudo da organização didática, no qual se averiguaram pesquisas sobre ensino e aprendizagem de isometrias, textos oficiais como Guias, Proposta e Parâmetros Curriculares, além de alguns aspectos do movimento de reforma da Matemática Moderna no Brasil, e sua relação com o mesmo movimento nos Estados Unidos e na França. A análise dos livros foi feita a partir do agrupamento dos exercícios em tipos de tarefas, qualificação essa utilizada tanto para a identificação da técnica de resolução, como para a distinção da tecnologia apropriada à justificação da primeira. Em seguida, efetuamos um estudo do conjunto dos exercícios propostos, no qual se encaminhou o cumprimento do acima exposto, no segundo parágrafo deste resumo, como objetivos da análise desenvolvida. A partir da base teórica adotada, as conclusões da pesquisa indicam que as orientações observadas em cada um dos períodos analisados não garantiriam, por si, que importantes problemas no ensino de transformações fossem resolvidos. Como sabido, a época correspondente ao movimento de reforma da Matemática Moderna enfatizou a estrutura matemática, ao passo que o período que se seguiu à publicação dos Parâmetros Curriculares destacou a relação de isometrias e homotetias com níveis superiores de determinação matemática. No primeiro caso, a visibilidade da obra matemática não foi destacada, enquanto, no segundo, a ausência de elementos tecnológicos pode ter comprometido a completude da organização matemática

Made available in DSpace on 2016-04-27T16:58:40Z (GMT). No. of bitstreams: 1 Idalise Bernardo Bage.pdf: 11341963 bytes, checksum: dbdb18882c985b58259417d04c99b744 (MD5) Previous issue date: 2008-05-29 / Secretaria da Educação do Estado de São Paulo / This paper is part of the Informational Technologies and Mathematical Education survey line and aims at verifying the possible contributions that a Teachers Development Course , so called Curso de Formação Continuada , bring to the professional practice of teaching Geometry in the initial series of our elementary school, that is, Ensino Fundamental I . In that intent the survey question formulated was: to what extent can a workshop, with the use of technological resources, contribute to the practices of the professionals teaching the basic Geometry concepts in the initial series of our Ensino Fundamental I ? In order to answer that question, we firstly elaborated a workshop proposition with ten activities using the Building Perspective and Cabri-Géomètre softwares and applied it to a group of 30 (thirty) teachers who worked on the fourth year of Ensino Fundamental I . Such proposition is based on the theoretical presuppositions of the geometrical thought development in Van Hiele s pattern, for the elaboration of the activities, and the teachers development with the use of technology. At a second moment, the referred teachers applied the activities to their students. Design Experiments was adopted as the survey methodology, aiming at the refinement of the workshop proposition for future groups of teachers participating in it. As data collectors this survey relied on: an initial questionnaire for checking the teachers traits, the protocol of the activities developed by the teachers, a semi-structured interview to collect information about the application of the workshop with the students and a final questionnaire intended to evaluate the workshop. Analyzed all the data, the conclusion was that the proposition allowed the teachers to notice the importance of the teaching of Geometry at the initial series of Ensino Fundamental I and the possibilities the software Cabri- Géomètre offer in enriching the development of the geometric concepts. At the end, based on the analyses done throughout this job, as well as on the suggestions from the participant teachers, there s the proposition of a new, enhanced workshop / Este trabalho está inserido na linha de pesquisa Tecnologias da Informação e Educação Matemática, e tem como objetivo verificar quais as possíveis contribuições que um curso de formação continuada, com a utilização da tecnologia, traz para a prática do professor no ensino da Geometria nas séries iniciais do Ensino Fundamental I. Para isso, formulou-se como questão de pesquisa: em que medida uma oficina, com a utilização dos recursos da tecnologia, poderá contribuir para a prática dos professores das séries iniciais no ensino dos conceitos básicos da Geometria? Primeiramente se elaborou uma proposta de oficina com dez atividades utilizando os softwares Building Perspective e Cabri-Géomètre, e se aplicou a trinta professores que lecionam na 4ª série do ensino fundamental. Essa proposta tem como base os pressupostos teóricos do desenvolvimento do pensamento geométrico do modelo Van Hiele, para a elaboração das atividades, e a formação de professores com o uso da tecnologia. Em um segundo momento, os professores aplicaram as atividades aos seus alunos. Adotou-se como metodologia de pesquisa o Design Experiments, visando ao aprimoramento da proposta da oficina para futuros professores participantes. A pesquisa possui como instrumentos de coleta de dados: um questionário inicial para o levantamento das características dos professores, o protocolo das atividades desenvolvidas pelos professores, uma entrevista semiestruturada para colher informações sobre a aplicação da oficina aos alunos e um questionário final de avaliação da oficina. Após a análise dos dados, concluiu-se que a proposta permitiu que os professores percebessem a importância do ensino da Geometria nas séries iniciais e as possibilidades do software Cabri-Géomètre no desenvolvimento de conceitos geométricos. O final do trabalho apresenta uma nova proposta de oficina aprimorada com base nas análises feitas e sugestões dos professores participantes

Made available in DSpace on 2016-06-02T20:02:53Z (GMT). No. of bitstreams: 1 5649.pdf: 10966324 bytes, checksum: f6b3c2eb22b9165966dab0fa4763fada (MD5) Previous issue date: 2013-11-05 / The objective of this research is to analyze and evaluate methodological developments proposed for the teaching of geometry, in public school in the State of São Paulo in the high school level in recent decades. We elaborate a proposal of a didactic sequence using manipulative objects, assisting the teacher of mathematics at the construction of concepts of areas and volumes. / O objetivo desta pesquisa é analisar e avaliar as evoluções metodológicas propostas para o Ensino de Geometria, na Escola Pública do Estado de São Paulo no nível do Ensino Médio, nas últimas décadas. Elaboramos uma proposta de uma sequência didática utilizando objetos manipulativos, auxiliando o professor de matemática na construção dos conceitos de áreas e volumes.

Dem Erwerb geometrischer Kompetenzen wird in der Primarstufe im Allgemeinen eine wichtige Bedeutung zugemessen. Geometrische Inhalte finden sich in Deutschland sowohl in den nationalen Bildungsstandards als auch in den Lehrplänen der Bundesländer wieder. An einer strukturierten empirischen Aufarbeitung der Kompetenzentwicklung, der Fähigkeiten sowie der Schwierigkeiten der Schülerinnen und Schüler in der Auseinandersetzung mit diesen Inhalten mangelt es dennoch in einigen dieser Bereiche. Damit einhergehend fehlen auch erforderliche Grundlagen, die es Lehrkräften ermöglichen, Unterricht planen zu können und somit ein anschlussfähiges Verständnis bei den Schülerinnen und Schülern aufzubauen. Aus der Lehrerprofessionsforschung liegen Modelle vor, welche zentrale Wissensfacetten, die eine Rolle bei der unterrichtlichen Vermittlung fachlicher Inhalte spielen, beschreiben (u.a. Weinert, Schrader & Helmke 1990; Shulman 1986; Bromme 1992, 1997; Baumert & Kunter 2006, 2011; Ball, Thames & Phelps 2008). Insbesondere dem fachlichen sowie dem fachdidaktischen Wissen der Lehrperson wird eine entscheidende Rolle bezüglich des Lernerfolgs der Schülerinnen und Schüler zugeschrieben (u.a. Kunter et al. 2013). Ein geometrischer Inhaltsbereich, in dem bereits Wissen vorliegt, auf das Lehrerinnen und Lehrer zurückgreifen können, ist die Achsenspiegelung und -symmetrie. Dieses Wissen bezieht sich jedoch überwiegend auf die Sekundarstufe und ist wenig systematisch angelegt bzw. lückenhaft. Diese Arbeit verfolgt daher das Ziel, systematisch Wissen herauszuarbeiten, auf das Lehrkräfte zurückgreifen können, um im Geometrieunterricht der Grundschule fachlich fundierte Entscheidungen treffen zu können und im Bereich der Achsenspiegelung und Achsensymmetrie mit Bezug auf die individuellen Fähigkeiten der Schülerinnen und Schüler ein anschlussfähiges und tragfähiges Verständnis aufzubauen. Basierend auf einer integrativen Betrachtung der Facetten professionellen Wissens werden inhaltsspezifisch relevante Facetten des Wissens von Lehrkräften herausgearbeitet. Diese Perspektiven der Lehr-Lern-Forschung werden aufgegriffen und bieten eine Rahmung zur fachlichen und fachdidaktischen Einordnung der einzelnen Forschungsarbeiten dieser Dissertation. Die Forschungsschwerpunkte dieser Arbeit werden daraufhin ebenfalls in der Rahmung verankert, anschließend vorgestellt und ihre Ergebnisse zusammengefasst. • Der erste Forschungsschwerpunkt setzt sich mit wichtigen Grundlagen zu spezifischen Anforderungen von Aufgabenstellungen sowie typischen schwierigkeitsgenerierenden Merkmalen bei der Achsenspiegelung und Achsensymmetrie auseinander (vgl. Götz & Gasteiger 2019; Götz et al. 2020; Götz 2018). Dabei führt der Abgleich psychometrisch erfasster Aufgabenschwierigkeiten mit inhaltlich fachdidaktischen Analysen der Fehler und theoretischen Erkenntnissen zur Achsenspiegelung zu einem Kategorienschema mit unterschiedlichen schwierigkeitsgenerierenden Merkmalen bei Aufgaben zur Achsenspiegelung und deren Ausprägungen. • Der zweite Forschungsschwerpunkt nimmt das Wissen über das mathematische Denken von Schülerinnen und Schülern bei der Achsenspiegelung in den Fokus. Um dieser Frage nachzugehen, wurden in dieser Studie Äußerungen der Schülerinnen und Schüler während ihrer Lösungsprozesse bei Aufgaben zur Achsenspiegelung beobachtet und analysiert (vgl. Götz & Gasteiger 2022). Der Mehrwert dieser Arbeit liegt insbesondere in den Erkenntnissen zu fachdidaktischem Wissen bezüglich des Unterrichtens der Achsensymmetrie und Achsenspiegelung in der Grundschule. Ein Kategorienschema zu den schwierigkeitsgenerierenden Merkmalen bei der Achsenspiegelung, ein Überblick über Fehlerarten bei Aufgaben zur Achsensymmetrie sowie Zusammenstellungen, die Rückschlüsse auf das Verständnis von Schülerinnen und Schülern bei der Achsenspiegelung ermöglichen, bieten eine wertvolle Wissensbasis für Lehrkräfte in der Grundschule. Für die Unterrichtspraxis sind die Ergebnisse dieser Arbeit an unterschiedlichen Stellen relevant. Zum einen stellen die Ergebnisse dieser Arbeit ein Handlungsgerüst zur Erstellung adäquater Aufgaben, zum anderen liefern sie eine wertvolle Unterstützung bei der Kompetenzdiagnostik. Gleichzeitig geht aus den Ergebnissen dieser Arbeit die hohe Bedeutung adäquater Unterrichtsmaterialien hervor – wobei diesbezüglich wertvolle Hinweise zur Auswahl geeigneter Arbeitsmittel gegeben werden.

This study was carried out to investigate the effect of using animated computer 3-D figures illustration (ACTDFI) in the learning of polyhedron in geometry. By random sampling, intact group of four grade 9 classes in four different schools from a cluster of four educational district schools of Limpopo province in South Africa were selected. The study involved quasi-experimental and inquiry research approaches, the quasi-experimental approach involved pre and posttest design while the inquiry research approach involve classroom observation. There were three experimental groups and a control group with a total of 174 study participants. ACTDFI was used as an intervention for two weeks in the three experimental groups while in the control group, chalk-talk traditional teaching approach was used. Pre-test and post-test was used to collect quantitative data while classroom observation was used to collect qualitative data. This study was carried out to investigate the effect of using animated computer 3-D figures illustration (ACTDFI) in the learning of polyhedron in geometry. By random sampling, intact group of four grade 9 classes in four different schools from a cluster of four educational district schools of Limpopo province in South Africa were selected. The study involved quasi-experimental and inquiry research approaches, the quasi-experimental approach involved pre and posttest design while the inquiry research approach involve classroom observation. There were three experimental groups and a control group with a total of 174 study participants. ACTDFI was used as an intervention for two weeks in the three experimental groups while in the control group, chalk-talk traditional teaching approach was used. Pre-test and post-test was used to collect quantitative data while classroom observation was used to collect qualitative data. The findings from the quantitative Classroom observations were carried out to collect relevant data on how the study participants were taught stationary points in differential calculus, especially with the use of the constructivist pedagogical approach. A suitable observation checklist was developed for this purpose (Appendix 6 refers). Classroom observation checklist is a list of factors to be considered while observing a class. It gives a structure and framework for the observation. suggested that the use of ACTDFI might have improved academic achievement in learning of polyhedron during the intervention, while the qualitative data analysis indicated that the use of ACTDFI in the experimental groups might have facilitated the learning of the concepts of polyhedron. It is therefore recommended that further research is necessary on the application of ACTDFI in the teaching of 3-dimensional shapes at the primary schools / Mathematics Education / M. Sc. (Mathematics Education)