Dissertations / Theses: 'Geometrical knowledge'

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Mak, Ming-wai. "The effects of geometer's sketchpad on mediating students' geometrical knowledge /." View the Table of Contents & Abstract, 2005. http://sunzi.lib.hku.hk/hkuto/record/B35288279.

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Veronese, Paula Cristina de Faria [UNESP]. "O ensino de geometria no ciclo II do ensino fundamental: um estudo analítico." Universidade Estadual Paulista (UNESP), 2009. http://hdl.handle.net/11449/91174.

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Esta pesquisa tem como objeto de análise o Ensino da Geometria no Ciclo II do Ensino Fundamental e algumas implicações políticas pedagógicas que cercam este tema. Trabalho realizado inicialmente em duas salas de 5ª séries de uma Escola Pública Estadual, de um pequeno município às margens do Rio Tietê, na qual um grupo de 20 alunos e seus conhecimentos geométricos, foram o foco inicial desta investigação. Os alunos com idades entre dez e doze anos, pertencentes cada dez, respectivamente, a uma das duas classes de 5ª séries do período da manhã, tendo dois respectivos professores de Matemática, de metodologia e crenças pedagógicas diferentes: a construtivista e a tradicional, que nos levaram a realizar um total de 200 atividades - cada aluno foi avaliado com dez atividades que contemplam fazeres geométricos, pertinentes à Grade Curricular de Matemática. Estas foram analisadas de maneira qualitativa, e independente da crença metodológica do professor, na sua maioria os alunos apresentaram frágil e preocupante desempenho quanto aos conhecimentos geométricos. Tais resultados nos levam a ampliar os questionamentos, assim como os grupos pesquisados, que se completa com 20 professores de Matemática, que respondem a 140 questões sobre o objeto de estudo e seu questionamento principal, o pensamentos dos 2 Professores responsáveis pelas duas 5ª séries envolvidas na pesquisa, e depoimentos de 4 PCOPs – Professores Coordenadores de Matemática de 4 Oficinas Pedagógicas de Diretorias de Ensino do interior paulista. No universo de respostas analisadas, à luz de uma metodologia qualitativa, surgem apontamentos para a situação caótica do Ensino da Geometria. Quanto à categoria docente, as conseqüências de grande carência de conteúdos geométricos na sua Formação Acadêmica e outros que implicam diretamente na produção de conhecimentos matemáticos...
The object of this study is the teaching of Geometry in junior high school and the political and pedagogical implications connected to the theme. I conducted this research in two fifth grade classrooms from a public school of a small town located on the bank of the Tietê River. I initially surveyed a group of 20 students and their knowledge of Geometry. I chose 10 students from each class, ages ranging from 10 to 12 years old, who studied in the morning and had two different teachers whose approaches to the teaching of Geometry was diverse: one followed the traditional model whereas the other adopts Constructivism. With the students, we did 200 activities involving the knowledge of Geometry. Each student performed ten tasks about the syllabus of Geometry. Such tasks were qualitatively analyzed. Throughout the research, both my questionings and the groups enlarged and 20 Math teachers answered 140 questions about my object of study and its main questionings. Also answering the questions, the two teachers responsible for the classes as well as four teachers from different regional Boards of Education. When their answers were analyzed I noticed a lack of geometrical knowledge in their academic formation. Besides this scarce knowledge of the VAN HIELE theoretical bases of the subject they teach, other factors influence performance in class, such as the low salaries they get. These will have damaging effects on the students’ learning process and led me to conclude that we need more solid educational policies, capable of transforming this scenario. The study also shows a documental analysis of more than three decades of syllabuses elaborated by the State Board of Education of the state of São Paulo and ho the teaching of Geometry was carelessly handled.

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Isik, Hakan. "Relationship of college student characteristics and inquiry-based geometrical optics instruction to knowledge of image formation with light-ray tracing." Columbus, Ohio : Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1201718813.

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Veronese, Paula Cristina de Faria. "O ensino de geometria no ciclo II do ensino fundamental : um estudo analítico /." Marília : [s.n.], 2009. http://hdl.handle.net/11449/91174.

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Orientador: José Carlos Miguel
Banca: Nelson Antonio Pirola
Banca: Dagoberto Buim Arena
Resumo: Esta pesquisa tem como objeto de análise o Ensino da Geometria no Ciclo II do Ensino Fundamental e algumas implicações políticas pedagógicas que cercam este tema. Trabalho realizado inicialmente em duas salas de 5ª séries de uma Escola Pública Estadual, de um pequeno município às margens do Rio Tietê, na qual um grupo de 20 alunos e seus conhecimentos geométricos, foram o foco inicial desta investigação. Os alunos com idades entre dez e doze anos, pertencentes cada dez, respectivamente, a uma das duas classes de 5ª séries do período da manhã, tendo dois respectivos professores de Matemática, de metodologia e crenças pedagógicas diferentes: a construtivista e a tradicional, que nos levaram a realizar um total de 200 atividades - cada aluno foi avaliado com dez atividades que contemplam fazeres geométricos, pertinentes à Grade Curricular de Matemática. Estas foram analisadas de maneira qualitativa, e independente da crença metodológica do professor, na sua maioria os alunos apresentaram frágil e preocupante desempenho quanto aos conhecimentos geométricos. Tais resultados nos levam a ampliar os questionamentos, assim como os grupos pesquisados, que se completa com 20 professores de Matemática, que respondem a 140 questões sobre o objeto de estudo e seu questionamento principal, o pensamentos dos 2 Professores responsáveis pelas duas 5ª séries envolvidas na pesquisa, e depoimentos de 4 PCOPs - Professores Coordenadores de Matemática de 4 Oficinas Pedagógicas de Diretorias de Ensino do interior paulista. No universo de respostas analisadas, à luz de uma metodologia qualitativa, surgem apontamentos para a situação caótica do Ensino da Geometria. Quanto à categoria docente, as conseqüências de grande carência de conteúdos geométricos na sua Formação Acadêmica e outros que implicam diretamente na produção de conhecimentos matemáticos... (Resumo completo, clicar acesso eletrônico abaixo)
Abstract: The object of this study is the teaching of Geometry in junior high school and the political and pedagogical implications connected to the theme. I conducted this research in two fifth grade classrooms from a public school of a small town located on the bank of the Tietê River. I initially surveyed a group of 20 students and their knowledge of Geometry. I chose 10 students from each class, ages ranging from 10 to 12 years old, who studied in the morning and had two different teachers whose approaches to the teaching of Geometry was diverse: one followed the traditional model whereas the other adopts Constructivism. With the students, we did 200 activities involving the knowledge of Geometry. Each student performed ten tasks about the syllabus of Geometry. Such tasks were qualitatively analyzed. Throughout the research, both my questionings and the groups enlarged and 20 Math teachers answered 140 questions about my object of study and its main questionings. Also answering the questions, the two teachers responsible for the classes as well as four teachers from different regional Boards of Education. When their answers were analyzed I noticed a lack of geometrical knowledge in their academic formation. Besides this scarce knowledge of the VAN HIELE theoretical bases of the subject they teach, other factors influence performance in class, such as the low salaries they get. These will have damaging effects on the students' learning process and led me to conclude that we need more solid educational policies, capable of transforming this scenario. The study also shows a documental analysis of more than three decades of syllabuses elaborated by the State Board of Education of the state of São Paulo and ho the teaching of Geometry was carelessly handled.
Mestre

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Sönnerhed, Wang Wei. "Mathematics textbooks for teaching : An analysis of content knowledge and pedagogical content knowledge concerning algebra in Swedish upper secondary education." Licentiate thesis, Institutionen för pedagogik, kommunikation och lärande, Göteborgs universitet, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:hj:diva-16949.

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In school algebra, using different methods including factorization to solve quadratic equations is one common teaching and learning topic at upper secondary school level. This study is about analyzing the algebra content related to solving quadratic equations and the method of factorization as presented in Swedish mathematics textbooks with subject matter content knowledge (CK) and pedagogical content knowledge (PCK) as analytical tools. Mathematics textbooks as educational resources and artefacts are widely used in classroom teaching and learning. What is presented in a textbook is often taught by teachers in the classroom. Similarly, what is missing from the textbook may not be presented by the teacher. The study is based on an assumption that pedagogical content knowledge is embedded in the subject content presented in textbooks. Textbooks contain both subject content knowledge and pedagogical content knowledge. The primary aim of the study is to explore what pedagogical content knowledge regarding solving quadratic equations that is embedded in mathematics textbooks. The secondary aim is to analyze the algebra content related to solving quadratic equations from the perspective of mathematics as a discipline in relation to algebra history. It is about what one can find in the textbook rather than how the textbook is used in the classroom. The study concerns a teaching perspective and is intended to contribute to the understanding of the conditions of teaching solving quadratic equations. The theoretical framework is based on Shulman’s concept pedagogical content knowledge and Mishra and Koehler’s concept content knowledge. The general theoretical perspective is based on Wartofsky’s artifact theory. The empirical material used in this study includes twelve mathematics textbooks in the mathematics B course at Swedish upper secondary schools. The study contains four rounds of analyses. The results of the first three rounds have set up a basis for a deep analysis of one selected textbook. The results show that the analyzed Swedish mathematics textbooks reflect the Swedish mathematics syllabus of algebra. It is found that the algebra content related to solving quadratic equations is similar in every investigated textbook. There is an accumulative relationship among all the algebra content with a final goal of presenting how to solve quadratic equations by quadratic formula, which implies that classroom teaching may focus on quadratic formula. Factorization method is presented for solving simple quadratic equations but not the general-formed quadratic equations. The study finds that the presentation of the algebra content related to quadratic equations in the selected textbook is organized by four geometrical models that can be traced back to the history of algebra. These four geometrical models are applied for illustrating algebra rules and construct an overall embedded teaching trajectory with five sub-trajectories. The historically related pedagogy and application of mathematics in both real world and pure mathematics contexts are the pedagogical content knowledge related to quadratic equations.

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Zhang, Kefei. "Geometric model input and feature recognition knowledge base for EXCAP." Thesis, University of Manchester, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.330310.

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Bridge, Steven Frank. "Aspects of the geometric representation of knowledge for computer aided design." Thesis, Imperial College London, 1988. http://hdl.handle.net/10044/1/46974.

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Abbas, Ayman. "A modelling approach to individualised computer aided learning for geometric design." Thesis, University of Strathclyde, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.324096.

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Diligenti, Marcos Pereira. "A geometria da complexidade." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2006. http://hdl.handle.net/10183/8559.

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Esta tese consiste em um estudo sobre a concepção do conhecimento da Geometria nos cursos superiores de Arquitetura. Durante três semestres, desenvolvemos uma proposta de abordagem transdisciplinar no ensino da Geometria Descritiva, junto a seis turmas de estudantes da Pontifícia Universidade Católica do Rio Grande do Sul, que se constituiu no ensino dos conceitos geométricos, compreendidos em suas relações e interdependências com seus entornos histórico / culturais/ filosóficos/ epistemológicos. Aliados a esta postura, introduzimos os conceitos genéricos de solidariedade e criatividade, na forma de migrações conceituais pelos campos geométrico/arquitetônicos, como instrumento instigador do resgate na compreensão da humanidade do conhecimento científico. Discutimos, neste estudo, a receptividade dos estudantes em relação a estas abordagens e às dificuldades verificadas no desenvolvimento destas propostas. Para analisar a concepção de conhecimento advinda destas implementações, utilizamos como referencial teórico o Paradigma da Complexidade, na ótica de Edgar Morin. Finalizando este trabalho, aproximamos as nossas interpretações do conceito de utopia, na perspectiva de Ernst Bloch, na qual encontramos a reafirmação do movimento como componente central dos fenômenos estudados, com a evidência de sua inexorabilidade na compreensão do conhecimento, do ser humano e da vida.
This thesis is a study about the conception of knowledge on Geometry in the graduation programs of Architecture. For three semesters we have developed a proposal of a cross disciplinary approach in the teaching of Descriptive Geometry with six groups of architecture students from the Pontifical Catholic University of Rio Grande do Sul. The proposal involved the teaching of geometric concepts and their relationships and interdependencies with historical, cultural, philosophical and epistemological contours. Along with such approach, we have introduced generic concepts of solidarity and creativity in the form of conceptual migrations through geometric and architectural fields, as an instigating instrument to rescue the understanding of the humanitarian aspect of scientific knowledge. We discussed, in this study, the receptive attitude from the students in terms of these approaches and the difficulties faced in order to develop them. To analyze the concept of knowledge resulting from such implementations, we used as theoretical background the Paradigm of Complexity, in the view of Edgar Morin. We finally approximated our interpretations to the concept of utopia, in the perspective by Ernst Bloch, in which we found the reaffirmation of movement as the central component of the investigated phenomena, with the evidence of its inexorability in the understanding of knowledge, human beings and life.

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Bento, Regina Thaise Ferreira. "Um estudo das geometrias prática e teórica presentes em The Pathewaie to Knowledge de Robert Recorde: possíveis diálogos." Pontifícia Universidade Católica de São Paulo, 2018. https://tede2.pucsp.br/handle/handle/21657.

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In this work we present the English mathematician Robert Record (1512-1558) and his treatise on geometry titled The Pathewaie to Knowledge, written in modern English and whose first edition was printed in the year 1551. We analyze in this treatise the presence and possible dialogue established between the geometric knowledge from ancient traditions linked to practice and the theoretical geometry that is studied in the universities and is based on the geometric treatise written by Euclides. To do so, we analyze the context in which the work and its author were inserted, identify what mathematical knowledge is present in this treatise and how they relate to the mathematical practices and the scholarly knowledge of the time. In addition, we sought indications that would allow us to evidence the presence of other geometric. This analysis was made use of the articulation between three spheres: the historiographical, the contextual and the epistemological. This combination gave us a broader look at the possible motivations that would have led Recorde to write the treatise in question. We find that Record was a man cultivated and attentive to the demands of his people and his time. Sixteenth-century England was at a time of social, political, and religious transformation; there was a great demand for investments in the practical-oriented sciences such as artillery, horology, navigation, and land measurement. Thus, professionals such as land surveyors and navigators assumed a determining role for the development of England and needed greater mathematical knowledge to advance their practices. However, access to education was restricted to most of the population and the little available material was written in Latin. This demand for mathematical knowledge practiced in this period, such as arithmetic, algebra, and geometry, made professionals who mastered their craft begin to produce materials written in the vernacular. Recorde, with his privileged background, was the first to produce a collection of textbooks in English with basic mathematics aimed directly at the interests of these professionals. The Pathewaie to Knowledge was the first treatise on practical geometry written in English. At that time practical and theoretical geometry were independent. With the results of this work it is concluded that in fact Robert Record established a dialogue between practical and theoretical geometries, contributing to the dissemination of speculative mathematical knowledge and the validation of geometry used for centuries by mathematicians. This analysis indicates that the understanding of the process that involves the construction of mathematical knowledge can effectively aid in a more critical learning by mathematical educators
Neste trabalho, apresentamos o matemático inglês Robert Recorde (1512-1558) e seu tratado sobre geometria entitulado The Pathewaie to Knowledge, escrito em inglês moderno e cuja primeira edição foi impressa no ano de 1551. Analisamos neste tratado a presença e possível diálogo estabelecidos entre os conhecimentos geométricos provenientes de antigas tradições ligadas à prática e a geometria teórica que era estudada nas universidades e baseada no tratado geométrico escrito por Euclides. Para tanto, analisamos o contexto no qual a obra e seu autor estavam inseridos, identificamos quais os conhecimentos matemáticos estão presentes nesse tratado e como se relacionam com as práticas matemáticas e o saber erudito da época. Além disso, procuramos indícios que nos permitissem evidenciar a presença de outras tradições geométricas. Esta análise utilizou-se da articulação entre três esferas: a historiográfica, a contextual e a epistemológica. Essa junção permitiu-nos um olhar ampliado sobre as possíveis motivações que teriam levado Recorde a escrever o tratado em questão. Verificamos que Recorde era um homem culto e atento às demandas de seu povo e de seu tempo. A Inglaterra do século XVI estava em um momento de transformação social, política e religiosa, havia uma grande demanda por investimentos nas ciências voltadas às questões práticas, tais como a artilharia, horologia, navegação e medição de terras. Assim, profissionais tais como os agrimensores e navegadores assumiram um papel determinante para o desenvolvimento da Inglaterra e necessitavam de maiores conhecimentos matemáticos para avançarem em suas práticas. Contudo, o acesso ao ensino era restrito para a maioria da população e o pouco material disponível era escrito em latim. Essa demanda por conhecimentos voltados às matemáticas praticadas neste período, tais como aritmética, álgebra e geometria fez com que profissionais que dominavam seus ofícios começassem a produzir materiais escrevendo-os na língua vernacular. Recorde, com sua formação privilegiada, foi o primeiro a elaborar uma coleção de livros textos em inglês com matemática básica voltada diretamente aos interesses desses profissionais. The Pathewaie to Knowledge foi o primeiro tratado sobre geometria prática escrito em inglês. Nesse período a geometria prática e teórica eram independentes. Com os resultados desse trabalho conclui-se que de fato Robert Recorde estabeleceu um diálogo entre as geometrias prática e teórica, contribuindo com a disseminação dos conhecimentos matemáticos especulativos e a validação da geometria utilizada há séculos pelos praticantes das matemáticas. Essa análise indica que a compreensão do processo que envolve a construção de conhecimentos matemáticos pode auxiliar de forma efetiva em uma aprendizagem mais crítica pelos educadores matemáticos

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Malqui, José Luis Sotomayor. "A visual analytics approach for passing strateggies analysis in soccer using geometric features." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2017. http://hdl.handle.net/10183/158188.

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As estrategias de passes têm sido sempre de interesse para a pesquisa de futebol. Desde os inícios do futebol, os técnicos tem usado olheiros, gravações de vídeo, exercícios de treinamento e feeds de dados para coletar informações sobre as táticas e desempenho dos jogadores. No entanto, a natureza dinâmica das estratégias de passes são bastante complexas para refletir o que está acontecendo dentro do campo e torna difícil o entendimento do jogo. Além disso, existe uma demanda crecente pela deteção de padrões e analise de estrategias de passes popularizado pelo tiki-taka utilizado pelo FC. Barcelona. Neste trabalho, propomos uma abordagem para abstrair as sequências de pases e agrupálas baseadas na geometria da trajetória da bola. Para analizar as estratégias de passes, apresentamos um esquema de visualização interátiva para explorar a frequência de uso, a localização espacial e ocorrência temporal das sequências. A visualização Frequency Stripes fornece uma visão geral da frequencia dos grupos achados em tres regiões do campo: defesa, meio e ataque. O heatmap de trajetórias coordenado com a timeline de passes permite a exploração das formas mais recorrentes no espaço e tempo. Os resultados demostram oito trajetórias comunes da bola para sequências de três pases as quais dependem da posição dos jogadores e os ângulos de passe. Demonstramos o potencial da nossa abordagem com utilizando dados de várias partidas do Campeonato Brasileiro sob diferentes casos de estudo, e reportamos os comentários de especialistas em futebol.
Passing strategies analysis has always been of interest for soccer research. Since the beginning of soccer, managers have used scouting, video footage, training drills and data feeds to collect information about tactics and player performance. However, the dynamic nature of passing strategies is complex enough to reflect what is happening in the game and makes it hard to understand its dynamics. Furthermore, there exists a growing demand for pattern detection and passing sequence analysis popularized by FC Barcelona’s tiki-taka. We propose an approach to abstract passing strategies and group them based on the geometry of the ball trajectory. To analyse passing sequences, we introduce a interactive visualization scheme to explore the frequency of usage, spatial location and time occurrence of the sequences. The frequency stripes visualization provide, an overview of passing groups frequency on three pitch regions: defense, middle, attack. A trajectory heatmap coordinated with a passing timeline allow, for the exploration of most recurrent passing shapes in temporal and spatial domains. Results show eight common ball trajectories for three-long passing sequences which depend on players positioning and on the angle of the pass. We demonstrate the potential of our approach with data from the Brazilian league under several case studies, and report feedback from a soccer expert.

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Vemuri, Koteswara Rao. "A knowledge-based approach to automate geometric design with application to design of blockers in the forging process /." The Ohio State University, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487323583622657.

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Camonin, Martine. "Mephisto : un outil de validation de modèles tridimensionnels." Nancy 1, 1987. http://www.theses.fr/1987NAN10149.

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Le système présente a été développé dans le cadre d'un système d'interprétation de scènes tridimentionnelles (Trident). Le modèle choisi permet de décrire des familles d'objets génériques construits par unions de primitives. La tache du système Mephisto est de décider de la cohérence d'un modèle fourni par l'utilisateur avant qu'il ne soit utilisé par trident. Dans le contexte de la représentation choisie, un modèle peut être vu comme un graphe et/ou avec contraintes. Une stratégie de recherche de chemin dans un graphe et/ou, minimisant en moyenne les coûts de construction, à partir d'une évaluation des espérances de succès de cette construction

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Segarra, Escandón Jaime Rodrigo. "Pre-service teachers' mathematics teaching beliefs and mathematical content knowledge." Doctoral thesis, Universitat Rovira i Virgili, 2021. http://hdl.handle.net/10803/671686.

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L’estudi del coneixement matemàtic i les creences de l’eficàcia de l’ensenyament de les matemàtiques en la formació inicial dels futurs mestres és fonamental, ja que influencia el rendiment acadèmic dels seus estudiants. L’objectiu d’aquesta tesi és estudiar tant el coneixement matemàtic inicial dels futurs mestres com també les seves creences sobre l’eficàcia matemàtica i la seva actitud envers les matemàtiques. Per a complir amb l’objectiu, es realitzen vàries investigacions. Primer, s’estudien els coneixements inicials de nombres i geometria dels estudiants del primer curs del Grau d’Educació Primària a la Universitat Rovira i Virgili (URV). En segon lloc, s’estudien les creences de l’eficàcia de l’ensenyament de les matemàtiques dels futurs mestres durant el grau. En tercer lloc, en aquesta Tesi es compara l’autoeficàcia i l’expectativa de resultats de l’ensenyament de les matemàtiques de futurs mestres, mestres novells i mestres experimentats. En quart lloc, s’estudia la relació entre les creences de l’ensenyament de les matemàtiques, l’actitud envers les matemàtiques i el rendiment acadèmic dels futurs mestres. En cinquè lloc, s’estudia la influència dels factors experiència docent, nivell d’educació i nivell d’ensenyament sobre les creences de l’eficàcia de l’ensenyament de les matemàtiques en mestres en actiu. Finalment, es compara l’autoeficàcia de l’ensenyament de les matemàtiques entre els estudiants del quart any del grau de mestres a la Universitat del Azuay i a la URV. Els resultats d’aquesta Tesi ofereixen informació potencialment important sobre el coneixement matemàtic, les creences, l’autoeficàcia de l’ensenyament de les matemàtiques i l’actitud envers les matemàtiques dels futurs mestres i dels mestres en actiu. Aquests resultats poden ajudar a desenvolupar polítiques adients a l’hora de dissenyar plans d’estudis i també assessorar als professors dels graus de mestre en les institucions d’educació superior.
El estudio del conocimiento matemático y las creencias de la eficacia de la enseñanza de las matemáticas en la formación inicial de los futuros maestros es fundamental, ya que influye en el rendimiento académico de los estudiantes. El objetivo de esta tesis es estudiar tanto el conocimiento matemático inicial de los futuros maestros como sus creencias sobre la eficacia matemática y su actitud hacia las matemáticas. Para cumplir con el objetivo se realiza varias investigaciones. Primero, se estudia los conocimientos iniciales de números y geometría de los estudiantes de primer año del Grado de Educación Primaria en la Universidad Rovira y Virgili (URV). En segundo lugar, se estudia las creencias de la eficacia de la enseñanza de las matemáticas de los futuros maestros a lo largo del grado. Tercero, esta Tesis compara la autoeficacia y la expectativa de resultados de la enseñanza de las matemáticas de futuros maestros, maestros novatos y maestros experimentados. Cuarto, se estudia la relación entre las creencias de la enseñanza de las matemáticas, la actitud hacia las matemáticas y su rendimiento académico. Quinto, se estudia la influencia de los factores experiencia docente, nivel de educación y nivel de enseñanza, sobre las creencias de la eficacia de la enseñanza de las matemáticas en maestros en servicio. Finalmente, se compara la autoeficacia de la enseñanza de las matemáticas entre los estudiantes de cuarto año del grado de maestro en la Universidad del Azuay y en la URV. Los resultados de esta Tesis ofrecen información potencialmente importante sobre el conocimiento matemático, las creencias, la autoeficacia de la enseñanza de las matemáticas y la actitud hacia las matemáticas de los futuros maestros y maestros en servicio. Estos resultados pueden ayudar a desarrollar políticas adecuadas para diseñar planes de estudios y también asesorar a los profesores de los grados de maestro en las instituciones de educación superior.
The study of mathematical content knowledge and teachers’ mathematics teaching beliefs of the pre-service teachers is fundamental, since it influences the academic performance of students. The objective of this Thesis is to study the initial mathematical knowledge of pre-service teachers and also their teachers’ mathematics teaching beliefs and their attitude towards mathematics. To meet the objective, various investigations are carried out. First, the initial knowledge of numbers and geometry of first-year students of the primary education degree at the Rovira and Virgili University (URV) is studied. Second, pre-service teachers’ mathematics teaching beliefs are studied throughout the grade. Third, this Thesis compares the self-efficacy and the expectation of results of the teaching of mathematics of pre-service teachers, novice in-service teachers and experienced in-service teachers. Fourth, the relationship between the teachers’ mathematics teaching beliefs, the attitude towards mathematics and their academic performance is studied. Fifth, the influence of the factors teaching level factor and level of training on the teachers’ mathematics teaching beliefs of in-service teachers is studied. Finally, the self-efficacy of mathematics teaching of fourth-year students at the Azuay University and at the URV is compared. The results of this Thesis offer potentially important information on the mathematical knowledge, beliefs, self-efficacy of mathematics teaching and the attitude towards mathematics of pre-service teachers and in-service teachers. These results can help develop policies for curriculum developers and teaching professors at institutes of higher education.

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Vidigal, Sônia Maria Pereira. "Pensamento geométrico: da representação do espaço ao espaço de significações." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/48/48134/tde-19102016-144425/.

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A Geometria relaciona-se, desde as origens mais remotas, com medidas de comprimentos, áreas e volumes, com o estudo das formas e das representações do espaço. Tanto em sentido geométrico quanto em sentido geográfico, no entanto, a ideia de espaço tem sofrido considerável ampliação, conquistando, atualmente, lugar de destaque em terrenos que abrangem desde as tecnologias informáticas, com suas redes de significados e seus lugares virtuais, até as mais recentes caracterizações de espaço em sentido antropológico, como sistemas de proximidades. Paralelamente a tais fatos, a Geometria, que foi o primeiro ramo do conhecimento a ser organizado e apresentado como um sistema dedutivo, por meio do gigantesco trabalho de Euclides(300aC), inspirou sistematizações correlatas, como as realizadas por Newton(séc. XVII) no terreno da Mecânica, e Spinoza(séc. XVII) no terreno da Ética. De modo geral, o estudo da Geometria como representação do espaço serviu de modelo para a organização do conhecimento em todas as áreas. Com a consolidação da ideia de que conhecer algo é compreender o seu significado, construído sempre a partir de representações, um deslocamento das atenções ocorreu do conhecimento geométrico como estudo das representações do espaço para o estudo do conhecimento, em geral, como um estudo de diferentes espaços de representações. Este trabalho tem por objetivo principal explorar o paralelismo entre o espaço geométrico e o espaço de significações. Levando-se em consideração as transformações ocorridas na noção de espaço, bem como o fato de que ideias de distância e proximidade não se limitam mais à distância física, os sentidos epistemológico e antropológico de tais transformações foram examinados em trabalhos seminais como a notável síntese presente na epistemologia de Tung-Sun(1986), os modos de fazer mundos de significações de Goodman(1995), a articulação entre Tecnologia e Antropologia realizada por Lévy(2011), ao vislumbrar os sucessivos espaços Terra, Território, Mercadorias, Saber, e o provocador questionamento sobre o sentido da vida apresentado por Flanagan(2007). Um destaque especial merece o fecundo trabalho de Bruner(2002), com o recurso ao instrumento mais fundamental para a construção simbiótica de significados e valores: as narrativas. Particularmente no caso de Flanagan, sua incursão do terreno da Ética é a principal baliza que orientou a busca das necessárias implicações do que aqui se discutiu no terreno da Educação. Ao propor as seis dimensões que considera invariantes de um Espaço de Significações para o século XXI (Arte, Ciência, Tecnologia, Ética, Política e Espiritualidade), Flanagan abre espaço para a proposta final do trabalho: entre as dimensões, vemos uma como mais fundante que as demais, por ser necessária à construção de uma vida realmente significativa: a Ética. É fundamental, então, voltar as atenções para a possibilidade de articulação do espaço Terra com o espaço do Saber, que é o espaço do conhecimento associado à ideia de valor. Somente uma perspectiva ética pode nos fazer articular o primitivo espaço Terra, que nos acolheu como nômades, com o espaço que resulta da consciência e da sabedoria de que o planeta que habitamos é nosso lar comum.
Geometry relates, from the remotest origins, measures of length, area, and volume to the study of shapes and the representations of space. In both a geometrical and a geographical sense, however, the idea of space has undergone considerable expansion, reaching a prominent place which ranges from information technology, with its network of meanings and its virtual places, to the most recent characterizations of space in an anthropological sense, as proximity systems. Alongside those facts, geometry, the first branch of knowledge to be organized and presented as a deductive system through the colossal work of Euclid (300B.C.), inspired related systematizations as those held by Newton (17th c.) in the field of mechanics, and Spinoza (17th c.) in the field of ethics. In general, the study of geometry as representation of space served as a model for the organization of knowledge in all areas. With the consolidation of the idea that knowing something is to understand its meaning, always constructed from representations, a shift of attention occurred from the geometrical knowledge as the study of the representations of space, to the study of knowledge in general, as a study of different space representations. This work has a main objective to explore the parallels between the geometric space and the space of meaning. Taking into account the changes that occurred in the notion of space as well as the fact that distance and proximity ideas are no longer limited to the physical distance, the epistemological and anthropological senses of such transformations were examined in seminal works, such as the remarkable synthesis present in Tung-Suns epistemology (1986); the making of meaningful worlds by Goodman (1995); the articulation between Technology and Anthropology held by Lévy (2011); to glimpse the successive spaces Earth, Territory, Commodity, Knowledge; and the provocative question about the meaning of life presented by Flanagan (2007). The fruitful work of Bruner (2002) deserves a special mention, for the use of the most fundamental tool for symbiotic construction of meanings and values: the narratives. Particularly in the case of Flanagan, his incursion in the field of ethics was the main goal that guided the search of the necessary implications of what was discussed in the field of education. In proposing the six dimensions to consider the invariants of a Space of Meaning for the twenty-first century (Art, Science, Technology, Ethics, Politics and Spirituality), Flanagan makes room for the final draft of the work: among those dimensions, we see one as being more foundational than the others, because it is necessary to build a truly meaningful life: Ethics. It is essential, then, to turn our attention to the possibility of articulation of the Earth space with the space of Knowledge, which is the area of knowledge associated with the idea of value. Only an ethical perspective can make us connect the primitive Earth space, which welcomed us as nomads, with the space resulting from the awareness and wisdom of realizing that the planet we inhabit is our common home.

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Shahwan, Ahmad. "Processing Geometric Models of Assemblies to Structure and Enrich them with Functional Information." Thesis, Grenoble, 2014. http://www.theses.fr/2014GRENM023/document.

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La maquette numérique d'un produit occupe une position centrale dans le processus de développement de produit. Elle est utilisée comme représentation de référence des produits, en définissant la forme géométrique de chaque composant, ainsi que les représentations simplifiées des liaisons entre composants. Toutefois, les observations montrent que ce modèle géométrique n'est qu'une représentation simplifiée du produit réel. De plus, et grâce à son rôle clé, la maquette numérique est de plus en plus utilisée pour structurer les informations non-géométriques qui sont ensuite utilisées dans diverses étapes du processus de développement de produits. Une demande importante est d'accéder aux informations fonctionnelles à différents niveaux de la représentation géométrique d'un assemblage. Ces informations fonctionnelles s'avèrent essentielles pour préparer des analyses éléments finis. Dans ce travail, nous proposons une méthode automatisée afin d'enrichir le modèle géométrique extrait d'une maquette numérique avec les informations fonctionnelles nécessaires pour la préparation d'un modèle de simulation par éléments finis. Les pratiques industrielles et les représentations géométriques simplifiées sont prises en compte lors de l'interprétation d'un modèle purement géométrique qui constitue le point de départ de la méthode proposée
The digital mock-up (DMU) of a product has taken a central position in the product development process (PDP). It provides the geometric reference of the product assembly, as it defines the shape of each individual component, as well as the way components are put together. However, observations show that this geometric model is no more than a conventional representation of what the real product is. Additionally, and because of its pivotal role, the DMU is more and more required to provide information beyond mere geometry to be used in different stages of the PDP. An increasingly urging demand is functional information at different levels of the geometric representation of the assembly. This information is shown to be essential in phases such as geometric pre-processing for finite element analysis (FEA) purposes. In this work, an automated method is put forward that enriches a geometric model, which is the product DMU, with function information needed for FEA preparations. To this end, the initial geometry is restructured at different levels according to functional annotation needs. Prevailing industrial practices and representation conventions are taken into account in order to functionally interpret the pure geometric model that provides a start point to the proposed method

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Souza, Carolina Zenero de. "O processo vivido por uma professora iniciante na disciplina de desenho geométrico e geometria descritiva em uma licenciatura em matemática /." São José do Rio Preto, 2020. http://hdl.handle.net/11449/192932.

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Orientador: Zulind Luzmarina Freitas
Resumo: Este estudo vincula-se à linha de pesquisa “Educação Matemática”, do Programa de Pós-Graduação em Ensino e Processos Formativos da Universidade Estadual Paulista “Júlio de Mesquita Filho”, Campus de Ilha Solteira-SP (FEIS-UNESP). A partir do pressuposto de que analisar a prática de sala de aula contribui para a formação continuada do professor, temos o objetivo de compreender o processo de formação continuada vivido por uma professora iniciante ao ministrar a disciplina de Desenho Geométrico e Geometria Descritiva. A questão norteadora do trabalho foi “Quais as contribuições da prática que vão sendo mobilizadas e incorporadas na formação de uma professora em início de carreira?” A pesquisa desenvolveu-se em ambiente natural, durante os meses de março a junho de 2018, nas aulas de Desenho Geométrico e Geometria Descritiva do Curso de Licenciatura em Matemática na FEIS-UNESP. Como eixo teórico central nos valemos dos estudos de Lee Shulman e seus seguidores e de Paulo Freire. Foram feitos registros através de gravações em vídeos/áudios e de anotações da professora em uma caderneta de campo. Os dados que deram origem ao corpus foram problematizados por meio de Análises de Conteúdo, ancoradas no estudo de Moraes (1999). Foram criadas duas Unidades de análise, a primeira intitulada de Matemática Clássica, foi dividida em duas categorias, sendo elas A Severidade da Matemática, com as subcategorias Utilização dos Conceitos Retirados dos Livros de Euclides e A demonstração Matemática... (Resumo completo, clicar acesso eletrônico abaixo)
Abstract: The present study is encompassed in the research line “Mathematical Education”, from the Postgraduate Program in Teaching and Formative Processes of Sao Paulo State University “Júlio de Mesquita Filho”, at Ilha Solteira Campus (FEIS-UNESP). Based on the assumption that analyzing the teaching practice contributes to the continuing education of a professor, we aim to discuss the process of continuing education of a professor at the beginning of their career by teaching a during the majors of Geometric Design and Descriptive Geometry. The guiding question of the work was “Which are the contributions of the teaching practice that are mobilized and incorporated in the formation of a professor at the beginning of their career?” The research was developed in a natural environment, between March and June 2018, during the majors of Geometric Design and Descriptive Geometry of the Mathematics Undergraduate Course at FEIS-UNESP. As the central theoretical axis, we used the studies of Lee Shulman and his followers, and Paulo Freire. Records were made through video and audio recordings and the professor's notes in a field notebook. Data that originated the corpus were problematized through Content Analysis, anchored at Moraes‟ (1999) work. Two units of analysis were created, the first titled Classical Mathematics, was divided into two categories, namely The Severity of Mathematics, with the subcategories Use of Concepts Taken from Euclid's Books, and The Mathematical Demonstration; as the... (Complete abstract click electronic access below)
Mestre

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Couto, Angela Maria Pinto do. "A formação inicial de professores do Ensino Básico e a geometria: um estudo de dois casos." Doctoral thesis, Universidade Portucalense, 2015. http://hdl.handle.net/11328/1303.

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Tese de Doutoramento em Educação.
Nas últimas décadas a educação tem sofrido mudanças que ainda hoje se estão a tentar perceber. Alguns professores não se encontram preparados para as necessidades de uma sociedade em permanente transformação. Os resultados dos sistemas de avaliação nacionais e internacionais mostram um fraco desempenho dos nossos estudantes particularmente em relação à Geometria. São inúmeras as variáveis que intervêm nestes resultados mas a prática docente é decisiva. Nesta conjuntura a formação inicial e a formação contínua de professores assumem uma importância fundamental. A Geometria tem sido considerada como o conteúdo do currículo de matemática onde os alunos aprendem a raciocinar e a compreender a estrutura axiomática da matemática (NCTM, 2008). Como área favorável ao desenvolvimento do pensamento geométrico, a Geometria é um excelente recurso para representar e dar significado ao mundo que nos envolve (e.g., Abrantes, Serrazina & Oliveira, 1999; Battista, 2007; van Hiele, 1999; Veloso, 2008). E o seu ensino deve proporcionar a experimentação e a descoberta favorecendo o desenvolvimento de uma outra forma de raciocínio – o raciocínio geométrico. Este estudo, realizado no âmbito da unidade curricular (UC) de Geometria do curso de Licenciatura em Educação Básica de uma Escola Superior de Educação, teve como objetivo principal a identificação do conhecimento e do raciocínio geométrico dos futuros professores, num contexto natural de sala de aula, através da realização de testes de diagnóstico e da aplicação de um conjunto diversificado de nove tarefas desafiantes, bem como das suas atitudes em relação à Geometria. Enunciaram-se três questões orientadoras, a saber: (Q1) Como se pode caracterizar o conhecimento geométrico dos estudantes, identificando as principais dificuldades ao longo dos testes e das tarefas?; (Q2) Como se pode caracterizar, de acordo com os níveis de van Hiele, o raciocínio geométrico dos estudantes ao longo dos testes e das tarefas?; e (Q3) Que atitudes manifestam os estudantes em relação às tarefas que realizaram e à UC de Geometria? A investigação seguiu uma abordagem de natureza qualitativa de caráter descritivo e interpretativo. A recolha de dados, realizada numa turma do 2º ano, debruçou-se apenas sobre as quatro alunas que constituíam os dois grupos-caso. Os dados foram recolhidos em ambiente natural, durante as aulas da UC de Geometria que ocorreram no 2º semestre, recorrendo à observação da realização das tarefas propostas, às filmagens e gravações efetuadas, aos documentos produzidos pelos alunos (testes e tarefas) e às várias entrevistas realizadas aos grupos-caso. Antes da UC de Geometria os resultados deste estudo evidenciaram um baixo nível no conhecimento e compreensão de conceitos e de conhecimentos matemáticos exigidos no programa de matemática do ensino básico (ME, 2007). Estas fragilidades relevam a pouca importância que tem sido dada à Geometria no ensino básico e secundário parecendo querer evidenciar que o conhecimento anterior estaria mais memorizado do que compreendido. Após a UC de Geometria houve um nítido progresso no conhecimento e compreensão dos conceitos geométricos, na linguagem matemática utilizada e uma diminuição nos erros cometidos mostrando que os conceitos geométricos evoluem com a instrução. No raciocínio geométrico há a destacar que num dos grupos-caso a evolução foi de mais de um grau no respetivo nível de van Hiele. Este resultado é bem mais otimista pois a investigação mostra que após programas intensivos de Geometria esse progresso é de apenas um grau na aquisição dos níveis de van Hiele. As tarefas utilizadas neste estudo, para além de privilegiarem a componente visual, foram selecionadas de modo a poderem ser implementadas por estes alunos na sua futura atividade docente. O desempenho e a atitude dos grupos indicaram que tarefas que incluam o desafio, a componente visual e a aplicabilidade futura são determinantes para o envolvimento dos grupos e potenciam o desenvolvimento do raciocínio geométrico. Este estudo corroborou que a motivação do estudante para se envolver no processo de ensino e aprendizagem é crucial. A vontade de querer aprender, a pretensão de abraçar a carreira docente, a consciência das dificuldades e a vontade em as superar foram fatores que pesaram na predisposição afetiva positiva para a Geometria. Esta investigação permitiu recolher informação relevante para que se desenvolva uma reflexão aprofundada sobre a UC de Geometria e seu conteúdo, facilitando a sua reformulação e melhoria em aspetos relacionados com os temas a tratar e como os abordar.
In recent decades education has undergone changes that today we are still trying to understand. Some teachers are not prepared for the needs of a society in constant transformation. The results of national and international evaluation systems show a poor performance of our students, particularly in relation to Geometry. There are countless variables involved in these results but the teaching practice is decisive. At this juncture the pre-service and in-service teachers’ development are of fundamental importance. Geometry has been regarded as the mathematics curriculum content where students learn to reason and understand the axiomatic structure of mathematics (NCTM, 2008). As a favourable area for the development of geometric thinking, Geometry is an excellent resource to represent and give meaning to the world around us (e.g. Abrantes, Serrazina & Oliveira, 1999; Battista, 2007; van Hiele, 1999; Veloso, 2008). And its teaching should provide experimentation and discovery favouring the development of another form of reasoning - the geometric reasoning. This study, carried out as part of the Geometry course of the bachelor’s degree course in Basic Education of a School of Education, aimed at identifying the knowledge and geometric reasoning of future teachers, in a natural context of classroom, through diagnostic tests and the application of a diverse set of nine challenging tasks, as well as their attitudes towards Geometry. Three guiding questions were asked, namely: (Q1) How can one characterize the geometrical knowledge of students, identifying the main difficulties during the tests and tasks?; (Q2) How can one characterize, according to Van Hiele’s levels, the geometric reasoning of students during the tests and tasks?; and (Q3) Which attitudes do the students manifest in relation to the tasks carried out and the Geometry course? The research followed a qualitative approach with a descriptive and interpretative character. The data collection, held in a 2nd year class, focused only on four students who made up the two-case groups. The data were collected in natural environment, during the classes of the Geometry course that occurred in the 2nd semester, resorting to the observation of all tasks proposed, the filming and recordings, the documents produced by the students (tests and assignments) and the various interviews to the case groups. Before the Geometry course the results of this study showed a low level of knowledge and understanding of mathematical concepts and knowledge required in the elementary school mathematics programme (ME, 2007). These weaknesses reveal the low priority that has been given to Geometry in primary and secondary education seeming to show that prior knowledge had been more memorized than understood. After the Geometry course, there was a clear improvement in knowledge and understanding of geometrical concepts, in mathematical language used and a decrease in mistakes showing that the geometrical concepts evolve through education. Regarding the geometric reasoning, it should be highlighted that in one case group the evolution was more than one grade within van Hiele’s scale. This result is more optimistic because research shows that after intensive geometry programmes this progress is only one grade in van Hiele’s acquisition levels. The tasks used in this study, besides privileging the visual component, were selected so that they could be implemented by these students in their future teaching activity. The performance and the attitude of the groups indicated that tasks including challenge, a visual component and the future applicability are crucial to the involvement of groups and boost the development of geometric reasoning. This study corroborated that the student's motivation to engage in the process of teaching and learning is crucial. The will to learn, the wish to embrace the teaching profession, the consciousness of the difficulties and the will to overcome them were factors that weighed on the positive emotional predisposition to Geometry. This research allowed to collect relevant information in order to develop an in-depth reflection on the Geometry course and its contents, making easier its redesign and improvement in aspects related to the topics to be addressed and the way to address them.
Orientação: Prof. Doutora Maria Isabel Piteira do Vale.

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Silva, Benedito Cardoso da. "Identificando sinalizações referentes às expectativas de aprendizagem sobre geometria, ao término da educação básica." Pontifícia Universidade Católica de São Paulo, 2004. https://tede2.pucsp.br/handle/handle/11240.

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Made available in DSpace on 2016-04-27T16:58:22Z (GMT). No. of bitstreams: 1 benedito silva.pdf: 1373638 bytes, checksum: 7a60f13ab371ddadb0e5c765db973a05 (MD5) Previous issue date: 2004-08-05
This current paper aims at investigating issues concerning the expectations of Geometry learners after they go through the four years of High School. Thus, its intention is to contribute with the general reflections on the teaching of Geometry throughout that same period. It also tries to approach new curriculum contents (proposals) and their trend, and analyses the questions (tests) proposed in some vestibulares ( College Admission Tests) in the State of São Paulo and in the National Testing System for High Schools (Exame Nacional do Ensino Médio-ENEM).These two major Testing Systems, as we know, are determining factors to define projects for Geometry teaching in High School. This paper also seeks to investigate the characteristics that shape the proposals for Geometry teaching at Elementary School, the directions that vestibulares and ENEM are moving towards and which areas of Geometry have been mostly tested.Our purpose is to examine possible consequences that these recent trends may have on the teaching of Geometry throughout Elementary School. This paper makes use of bibliography and documentation research to offer an evaluation of the most frequent questions (tests) that were presented by ENEM and vestibulares in their 2001-2003 issues. The main results of our study show that vestibulares tend to focus on a limited group of contents and abilities, giving little attention to contextual and interdisciplinary situations, which, nevertheless, are the main characteristic of the tests proposed by ENEM. Therefore, taking into account the trends analyzed, we conclude that the vestibulares fail to meet the expectations of Geometry learners at the end of High School
O presente trabalho tem como objetivo investigar as sinalizações referentes às expectativas de aprendizagem sobre Geometria, ao término da Educação Básica, pretendendo assim contribuir para a reflexão sobre o ensino de Geometria ao final dessa etapa da escolarização. Coteja as orientações de novas propostas curriculares, as questões de alguns vestibulares do Estado de São Paulo e do Exame Nacional do Ensino Médio ENEM, que, como sabemos, são orientadores dos projetos de ensino nas escolas de nível médio. Busca investigar como se caracterizam as propostas para o ensino de Geometria, na Educação Básica, quais as sinalizações dos exames vestibulares e do Exame Nacional do Ensino Médio e que conhecimentos geométricos os exames vestibulares e o ENEM estão priorizando, identificando possíveis conseqüências disso para o ensino de Geometria ao longo da Educação Básica. Utiliza pesquisa bibliográfica e documental e um estudo de questões dessas avaliações, nas edições de 2001 a 2003, destacando os aspectos mais valorizados. Dentre os principais resultados mostra que os exames vestibulares se organizam ao redor de um conjunto restrito de conteúdos e de habilidades, explorando muito pouco as situações contextualizadas ou interdisciplinares que, no entanto, são a maior característica das questões propostas pelo ENEM. Desse modo, revela-se uma forte incoerência entre as expectativas de aprendizagem sobre Geometria, ao término da Educação Básica, levando em conta as sinalizações analisadas

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Reis, Maria Elidia Teixeira. "Formação de professores leigos em serviço : um estudo sobre saberes e praticas docentes em geometria." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/252448.

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Orientador : Dario Fiorentini
Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de EducaÃ§Ã£o
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Resumo: Esta pesquisa analisou um processo de formaÃ§Ã£o de professores leigos, em serviÃ§o, que tinha como objetivo responder Ã seguinte questÃ£o investigativa: Como os professores â?¿ principalmente leigos em serviÃ§o â?¿ percebem, narram e evidenciam as contribuiÃ§Ãµes e as limitaÃ§Ãµes da formaÃ§Ã£o acadÃªmica ocorrida durante um curso emergencial de Licenciatura Plena Parcelada (LPP) em MatemÃ¡tica, especialmente em relaÃ§Ã£o Ã sua prÃ¡tica e aos seus saberes docentes em Geometria? Para respondÃª-la, foi realizado um estudo de caso qualitativo de uma turma de MatemÃ¡tica de LPP da cidade de JataÃ, GoiÃ¡s, envolvendo uma investigaÃ§Ã£o mais aprofundada de dois de seus participantes que possuÃam mais de dez anos de experiÃªncia docente. O material de anÃ¡lise e interpretaÃ§Ã£o foi constituÃdo por questionÃ¡rios aplicados Ã turma, documentos relativos ao projeto de LPP, entrevistas semi-estruturadas realizadas com trÃªs professores-formadores do curso e com os dois professores-alunos que tiveram suas aulas observadas. O processo de anÃ¡lise e interpretaÃ§Ã£o desse material foi desenvolvido em torno de trÃªs eixos: (1) A exploraÃ§Ã£o e a valorizaÃ§Ã£o dos saberes da experiÃªncia e a relaÃ§Ã£o destes com os saberes da formaÃ§Ã£o acadÃªmica no curso de LPP em MatemÃ¡tica. (2) Os problemas, limites e dificuldades enfrentados pelos professores-alunos e professores-formadores no decorrer do curso. (3) O que pensam e relatam os docentes alunos e formadores a respeito das contribuiÃ§Ãµes desse curso. Os resultados mostraram que o curso de LPP em MatemÃ¡tica investigado, de um lado, contribuiu para que os professores leigos obtivessem a qualificaÃ§Ã£o profissional almejada e exigida pela atual legislaÃ§Ã£o, mas, de outro, apresentou poucas evidÃªncias de desenvolvimento profissional de seus participantes. Essa conclusÃ£o apÃ³ia-se no fato de que, embora o projeto de LPP do Estado de GoiÃ¡s tivesse, no papel, o propÃ³sito de articular teoria e prÃ¡tica, na prÃ¡tica, os saberes experienciais e a prÃ¡tica pedagÃ³gica dos professores-alunos nÃ£o foram valorizados/explorados e nem tomados como objeto efetivo de reflexÃ£o e problematizaÃ§Ã£o durante o curso. Talvez essa seja a principal razÃ£o pela qual seus participantes tenham apresentado poucos indÃcios de mudanÃ§a de suas prÃ¡ticas e de seus saberes docentes relativos ao ensino de Geometria
Abstract: This research was aimed at analyzing the educational process of a group of lay teachers during a period of teaching activity, seeking to answer the following investigative question: How do teachers â?¿ especially lay teachers during teaching activity â?¿ perceive, narrate, and elicit the contributions and limitations to academic education acquired during a remedial emergency course of full partitioned licensorship (â?¿Licenciatura Plena Parceladaâ??, or LPP) on mathematics, especially in relation to their practice and their teaching knowledge in geometry? In order to answer this question, a qualitative case study of a mathematics LPP group was carried out in the city of JataÃ, GoiÃ¡s, involving a deeper investigation of two of its participants, who had been through over ten years of teaching experience. The material for analysis and interpretation was composed of questionnaires answered by the group, documents related to the LPP project, semi-structured interviews with three teachers-educators of the course and two teachers-students who had their classes observed. The process of analysis and interpretation of this material was developed on three bases: (1) The exploration and valorization of experience knowledge and its relation to the knowledge from academic education in the mathematics LPP course; (2) the problems, limits and difficulty faced by teachers/students and teachers/educators during the course; and (3) what teachers-students and educators think and tell about the contributions of this course. The results showed that, on the one hand, this LPP mathematics course has made it possible for the lay teachers to have the professional qualification that they desired and that is legally required, but, on the other hand, it has presented little evidence of professional development for its participants. This conclusion is drawn from the fact that, although the LPP project in the state of GoiÃ¡s had been planned to connect theory and practice, the experience knowledge and the teachers-studentsâ?¿ pedogogical practice were not actually valued or explored; neither were they taken as the real object of reflection and questioning throughout the course. Maybe this is the main reason why its participants presented few signs of change in their teaching habits and knowledge regarding geometry teaching
Doutorado
Educação Matematica
Doutor em Educação

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Aragão, Ildema Gomes. "Relações com o saber e o universo explicativo da pessoa com cegueira total sobre a aprendizagem da geometria." Universidade Federal de Sergipe, 2016. https://ri.ufs.br/handle/riufs/5082.

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This dissertation presents a qualitative study, whose main research question, analyze how it develops the explanatory universe of two people with total blindness on learning of geometry, from the relations with the knowledge that these individuals established to build knowledge geometric during their school lives. The research is inserted in the line of research: Science, scientific knowledge and techniques in contemporary societies of the Master in Science and Mathematics Teaching, Federal University of Sergipe. Falls into the area of Special Education and Mathematics Education in inclusive perspective. The route chosen in this work was determined by the voices of the two participants, so that through the speech, feelings and actions could explain how to build explanatory universe, which senses and relations with the knowledge established with the mathematical knowledge of geometry. The theoretical references pervade the ways of Inclusive Education (MANTOAN (2006), MANSINI (1994), SASSAKI (1999), SOUZA E SILVA (2005), SOUZA et al. (2005), STAINBACK & STAINBACK (1999), among others; and the relationship of theory and knowledge (CHARLOT 1999, 2000 , 2001 , 2005 and 2009), among others. As data collection instrument was used text production based on technical "balance of knowledge" - developed by the team ESCOL (Paris VIII), organized by Charlot (1999) - and three interview stages, one of which is based on interview technique developed by Pierre explicitness Vermersh (1994). This study was a qualitative approach involving the analysis of the content of the interviews to establish possible situations of similarities or differences between subject’s research participants. The results showed us that the person with total blindness, that does not have the involvement of other organs than sight, has the capacity to build an explanatory universe, with constructions of thought and objects of any geometric mathematical object, provided it has been prepared considering its features. The Relations with the knowledge of these people were based on the need for self-affirmation, considering them able to become independent subjects and citizens of the world.
Esta dissertação apresenta um estudo de natureza qualitativa, que teve como questão norteadora principal, analisar como se desenvolve o universo explicativo de duas pessoas com cegueira total sobre a aprendizagem da geometria, a partir das relações com o saber que esses sujeitos estabeleceram ao construir o conhecimento geométrico durante suas vidas escolar. A pesquisa está inserida na linha de pesquisa: Ciências, saberes científicos e técnicas nas sociedades contemporâneas do Mestrado em Ensino de Ciências e Matemática da Universidade Federal de Sergipe. Se enquadra na área da Educação Especial e Educação Matemática na perspectiva inclusiva. O percurso escolhido neste trabalho foi determinado pelas vozes das duas pessoas participantes da pesquisa, para que, através das falas, sentimentos e ações pudessem explicitar como se constrói o universo explicativo, quais os sentidos e as relações com o saber estabelecidas com o conhecimento matemático de geometria. Os referenciais teóricos perpassam os caminhos da Educação Inclusiva (MANTOAN (2006), MANSINI (1994), SASSAKI (1999), SOUZA E SILVA (2005), SOUZA et al. (2005), STAINBACK & STAINBACK (1999), dentre outros; e da teoria da Relação com o saber (CHARLOT 1999, 2000, 2001, 2005 e 2009), dentre outros. Como instrumento de coleta de dados foram utilizados produção de texto baseado na técnica “balanço do saber” – desenvolvida pela equipe ESCOL (Paris VIII), organizada por Charlot (1999) – e três etapas de entrevista, sendo uma delas baseada na entrevista de explicitação técnica desenvolvida por Pierre Vermersh (1994). Este trabalho teve uma abordagem qualitativa envolvendo a análise dos conteúdos das entrevistas para estabelecer possíveis situações de semelhanças ou diferenças entre os sujeitos participantes da pesquisa. Os resultados nos mostraram que a pessoa com cegueira total, que não possui o comprometimento de outros órgãos que não seja a visão, possui capacidade de construir um universo explicativo, com construções de objetos de pensamento e de qualquer objeto matemático geométrico, desde que tenha sido elaborado considerando suas particularidades. As Relações com o saber dessas pessoas basearam-se na necessidade de auto afirmação, considerando-as capazes de tornarem-se sujeitos independentes e cidadãos do mundo.

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Pinto, Rodrigo Hayasi. "A noção de perspectivismo na filosofia de Blaise Pascal." Universidade Federal de São Carlos, 2006. https://repositorio.ufscar.br/handle/ufscar/4757.

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Financiadora de Estudos e Projetos
The aim of this thesis is to understand Blaise Pascal's philosophical conception of science and morality on the basis of a more fundamental notion the notion of perspectivism. By not basing knowledge on ultimate and absolute terms, the French philosopher pointed the way to a new kind of knowledge, no longer guided by metaphysics, but by a hypotheticaldeductive ideal. This new kind of knowledge was to have provisional principles as points of departure, their rôle being that of epistemological perspectives in the sphere of science and practice.
O objetivo da presente tese é compreender a concepção filosófica de Blaise Pascal, tanto em sentido epistemológico, quanto moral, a partir de uma noção fundamental, a noção de perspectivismo . No nosso entender, ao não fundamentar o conhecimento em termos últimos e absolutos, o filósofo francês teria apontado para um novo tipo de conhecimento, não mais orientado pela metafísica, mas guiado por um ideal hipotético-dedutivo. Esse novo tipo de conhecimento, por sua vez, estaria relacionado à adoção de princípios provisórios como pontos de partida, os quais desempenhariam o papel de perspectivas epistemológicas, na esfera científica e prática.

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Moreno, Heliete Martins Castilho. "A geometria no curso de Pedagogia a distância do acordo Brasil-Japão : conhecimentos para a docência mobilizados na formação inicial." Universidade Federal de Mato Grosso, 2014. http://ri.ufmt.br/handle/1/296.

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O trabalho intitulado “A Geometria no Curso de Pedagogia a distância do acordo Brasil-Japão: conhecimentos para a docência mobilizados na formação inicial” resultou da pesquisa realizada no Programa de Pós Graduação em Educação, na linha de Educação em Ciências e Educação Matemática da Universidade Federal de Mato Grosso (UFMT), junto ao Grupo de Estudos e Pesquisas em Educação Matemática (GRUEPEM). O interesse em saber quais as contribuições que a realização da área de Matemática oferece aos acadêmicos para o exercício de suas funções docentes nos anos iniciais do ensino fundamental surge desde a primeira participação como professora formadora do Curso de Pedagogia a distância da UFMT nas oito ofertas realizadas. Tendo como objetivo geral “Investigar os conhecimentos para docência em Geometria, mobilizados pelos acadêmicos do Curso de Pedagogia na modalidade a distância do acordo Brasil-Japão”, elegeu-se a abordagem qualitativa, com base em Bogdan e Biklen (1994) e a análise interpretativa com método da análise de conteúdo de acordo com Bardin (2011) e Laville (1999) para responder o problema de pesquisa: Quais conhecimentos para a docência foram mobilizados com a Geometria apresentada no curso de formação inicial de Pedagogia a distância do acordo Brasil-Japão? Para a produção de informações utilizou-se os registros das acadêmicas nos fóruns que discutiram assuntos de geometria no decorrer da área, nos relatórios do estágio realizado em Geometria depois de concluída a área de Matemática e nos Trabalhos de Conclusão de Curso. Os dados foram analisados utilizando a teoria de García (1999) sobre a formação de professores, com apoio de Tardif (2002) e Shulman (1986). Freitas e Bittar (2004), Nacarato (2001), Nacarato e Passos (2003) e Lorenzato (2006) contribuíram com os temas sobre ensino de Matemática. Foram utilizadas como categorias de análise, os componentes do conhecimento profissional propostos por García (1999): psicopedagógico, do conteúdo, didático do conteúdo e do contexto. Os sujeitos foram selecionados a partir da classificação dos relatórios de estágio, que resultou em cinco acadêmicas que realizaram o estágio em Geometria, em Escolas Brasileiras no Japão, no Ensino Fundamental I, que têm a Pedagogia como primeira formação superior e que contribuíram pelo menos uma vez em cada um dos fóruns analisados. A análise realizada aponta a mobilização, pelas acadêmicas, durante o desenvolvimento da área de matemática no Curso de Pedagogia a distância do acordo Brasil-Japão, dos quatro componentes do conhecimento para a docência apontados por García (1999). Acreditamos que pela natureza dos próprios documentos analisados, a categoria mais presente nos fóruns foi o Conhecimento de Conteúdo, enquanto que nos relatórios de estágio foi o Conhecimento Didático do Conteúdo e nos Trabalhos de Conclusão de Curso foi o Conhecimento Psicopedagógico. O Conhecimento do Contexto aparece muito pouco nos TCC, não aparece nos fóruns, mas é mobilizado nos relatórios de estágio de uma forma considerável.
The paper entitled "The Geometry in Pedagogy Course of distance the Agreement Brazil - Japan: knowledge for teaching mobilized in the initial training" resulted from research conducted in the post-Graduation Program in Education, in line de Science Education and Mathematics Education of University Federal de Mato Grosso (UFMT) with the Group of Studies and Research in Mathematics Education (GRUEPEM). The interest in knowing what are the contributions that holding the area of Mathematics offers academics to carry out their teaching duties in the early years of elementary school arises from the first participation as a trainer currently teaching pedagogy of distance at UFMT the eight offerings made. Having the general objective "to investigate the knowledge in teaching Geometry, mobilized by academics of the Education Course of distance the Agreement Brazil-Japan", chose a qualitative approach, based on Bogdan and Biklen (1994) and interpretive analysis method with content analysis according to Bardin (2011) and Laville (1999) to answer the research problem: What skills for teaching were mobilized with the geometry shown in the initial course of Pedagogy distance of the agreement Brazil-Japan? To produce information were used remarks from the academic foruns boards that discussed matters of geometry throughout the area, on the reports of internship in geometry after the completion in Mathematics area and Course Conclusion Paper (CCP). Data were analyzed using the theory of Garcia (1999) on teacher training, supported by Tardif (2003) and Shulman (1986). Freitas and Bittar (2004), Nacarato (2001), Nacarato and Passos (2003) and Lorenzato (2006) contributed to the topics on teaching mathematics. Psycho pedagogic, content, didactic content and context: the components of professional knowledge proposed by García (1999) were used as categories of analysis. The subjects were selected from the classification of internship reports, which resulted in five academics who were trainee in Geometry in Brazilian Schools in Japan, in elementary school, who have Pedagogy as superior first training and who contributed at least once in each of the analyzed forums. The analysis points to the mobilization by academics, during the development of the area of mathematics at the Pedagogy Course of distance of Brazil-Japan agreement, the four components of knowledge for teaching pointed out by García (1999). We believe that by the nature of the documents themselves analyzed, the most current category on the forums was the Knowledge Content, while the reports of internship was Didactic Content Knowledge and on course conclusion paper was the Psycho pedagogic Knowledge. The Knowledge Context appears very little in the CCP, doesn’t appear on the forums, but it is mobilized in internship reports with an appreciable extent.

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Brito, Dejildo Roque de. "Saberes matem?ticos produzidos por agricultores: uma vis?o Etnomtem?tica na Educa??o Agr?cola." Universidade Federal Rural do Rio de Janeiro, 2016. https://tede.ufrrj.br/jspui/handle/jspui/2214.

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This dissertation is a research work in a agricultural community in the municipality of Porto Grande, in the state of Amap? in Brazil. The research aimed to investigate the produced knowledge and practices and practiced by farmers in their working practice and the relationship of these with the educated knowledge. We propose the use of Ethnomathematics as a form of reflection on the activities of this social group. Data collected from visits in loci surveyed treat the mathematical methods used by these groups of workers and the application possibilities of these in the classroom. The methodology used for this research is a qualitative approach. We discuss the work of the farmers in that community. We interviewed farm workers in their working environment and analyzed the existing mathematical knowledge in their work activities. We present two schools of Macap? some of the problems dealt with farmers to analyze the content or not schooled students facing such problems. We realize that students have difficulties to solve problems because they can not relate them to the everyday agricultural activities.
Esta disserta??o ? um trabalho de pesquisa desenvolvido em uma Comunidade Agr?cola localizada no munic?pio de Porto Grande, no Estado do Amap?, no Brasil. A pesquisa teve como objetivo principal investigar os saberes e fazeres produzidos e praticados por agricultores em sua pr?tica laboral e a rela??o desses com os conhecimentos escolarizados. Propomos a utiliza??o da Etnomatem?tica como uma forma de reflex?o sobre as atividades desse grupo social. Os dados coletados nas visitas realizadas nos l?cus pesquisados tratam dos m?todos matem?ticos utilizados por esses grupos de trabalhadores e as possibilidades de aplica??o desses em sala de aula. A metodologia utilizada para a realiza??o desta pesquisa tem uma abordagem qualitativa. Discorremos sobre o trabalho desenvolvido pelos agricultores na referida comunidade. Entrevistamos trabalhadores agr?colas em seu ambiente de trabalho e analisamos os conhecimentos matem?ticos existentes em suas atividades laborais. Apresentamos em duas escolas de Macap? alguns dos problemas tratados com os agricultores para analisarmos os conte?dos escolarizados ou n?o dos alunos diante de tais problemas. Percebemos que os alunos t?m dificuldades para solucionar os problemas por n?o conseguirem relacionar os mesmos com as atividades agr?colas cotidianas

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Hörberg, Thomas. "Influences of Form and Function on Spatial Relations : Establishing functional and geometric influences on projective prepositions in Swedish." Thesis, Stockholm University, Department of Linguistics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-6867.

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The present work is concerned with projective prepositions, which express the relation between two objects by referring to a direction in three-dimensional space. The projective prepositions have been regarded as expressing simple schematic relations of a geometric nature. A theory of the apprehension of projective relations can account for their meanings when they express strictly geometric relations. However, many studies have shown that the appropriateness of the prepositions also depends on the functional relation between the objects and that a number of functional factors influence the comprehension of English prepositions. This experimental study investigates if the acceptability of the Swedish prepositions över, under, ovanför and nedanför are influenced by functional factors as well, and whether acceptability judgments about över and under are more sensitive to functional influences than judgments about ovanför and nedanför, as has been shown for the corresponding English prepositions over and under, and above and below, respectively. It also investigates how the shapes and the parts of the related objects influence their functional interaction, and how the acceptability of the prepositions is in consequence influenced by the shapes of the objects. It was found that the theory of apprehension can indeed account for the acceptability of the prepositions when the relation between the objects is strictly geometric. It was further found that acceptability judgments about them are influenced by functional factors in a similar manner to the corresponding English prepositions when the objects are functionally related, although judgments about under and nedanför are not differentially influenced by these factors. Furthermore, the shapes and the parts of both of the related objects influence acceptability judgments about the prepositions in predictable manners. An extension of the theory of apprehension is suggested which can account for the functional influences indicated in the present study.

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Cavalcante, Cristiane de Oliveira. "A orientaÃÃo espacial na prÃ-escola: analisando saberes docentes." Universidade Federal do CearÃ, 2015. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=16860.

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CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior
De acordo com documentos oficiais brasileiros, a Ãrea da MatemÃtica escolar Ã dividida em quatro blocos ou eixos: NÃmeros e OperaÃÃes, EspaÃo e Forma (Geometria), Grandezas e Medidas, e Tratamento da InformaÃÃo (EstatÃstica). O ensino da MatemÃtica, entretanto, ainda Ã muito focado no primeiro, em detrimento dos outros blocos. HÃ duas dÃcadas, vÃrios pesquisadores (PAVANELLO, 1993; ARAÃJO, 1994; LORENZATO, 1995; FAINGUELERNT, 1995) denunciaram o abandono da Geometria, a qual contempla conteÃdos referentes a forma e espaÃo, na EducaÃÃo BÃsica e defenderam a sua valorizaÃÃo. Na dÃcada passada, dispositivos legais determinaram a inclusÃo da PrÃ-Escola na EducaÃÃo BÃsica obrigatÃria. No que se refere ao trabalho pedagÃgico com a Geometria nesta fase da EducaÃÃo Infantil, muitas vezes o educador aborda apenas o (re)conhecimento de figuras geomÃtricas planas â cÃrculo, triÃngulo, retÃngulo, quadrado â em atividades de pintura e nomeaÃÃo. O ensino e a aprendizagem de Geometria, no entanto, precisa oportunizar, tal como propÃem vÃrios pesquisadores â (GRANDE, 1994), (CERQUETTI-ABERKNE; BERDONNEAU, 1997), (DUHALDE; CUBERES, 1998), (SMOLE; DINIZ; CÃNDIDO, 2003), (LORENZATO, 2006) â o desenvolvimento de conceitos referentes a espaÃo e forma, oferecendo Ãs crianÃas oportunidades de perceberem e conhecerem os espaÃos em que vivem, se locomovem, nos quais elas aprendem a explorar, conquistar, ordenar e representar. Este estudo teve como objetivo identificar os saberes docentes de pedagogos que lecionam na PrÃ-Escola sobre orientaÃÃo espacial. A pesquisa de natureza qualitativa, do tipo estudo de caso, foi realizada numa instituiÃÃo de EducaÃÃo Infantil e Ensino Fundamental do sistema municipal de Fortaleza. Participaram do estudo duas professoras, sendo uma do Infantil IV e uma do Infantil V, e uma formadora da EducaÃÃo Infantil. Ao longo de nove encontros, foram realizadas visitas periÃdicas para a realizaÃÃo das observaÃÃes em campo das aulas ministradas pelas professoras participantes da pesquisa e entrevistas (iniciais e reflexivas), que foram gravadas, e, posteriormente, transcritas, gerando textos e reflexÃes. A partir dos resultados, constatou-se que, apesar de possuÃrem algum conhecimento de Geometria, os saberes docentes das professoras e formadora referentes Ã orientaÃÃo espacial, um conteÃdo importante no desenvolvimento e na aprendizagem das crianÃas da PrÃ-Escola, sÃo fragmentados, sendo necessÃrio proporcionar, com urgÃncia, oportunidades de formaÃÃo que ampliem e articulem tais saberes.
According to Brazilian official documents, the area of school mathematics is divided into four blocks or axes: Numbers and Operations, Space and Shape (Geometry), Quantities and Measurements, and Treatment Information (Statistics). The teaching of mathematics, however, is still very focused on the first, at the expense of other blocks. Two decades ago, several researchers (PAVANELLO, 1993; ARAÃJO, 1994; LORENZATO, 1995; FAINGUELERNT, 1995) denounced the abandonment of geometry, which includes content related to form and space, in Basic Education and defended their appreciation. In the past decade, legal provisions determined the inclusion of Pre-School in compulsory basic education. With regard to the pedagogical work with the geometry at this stage of early childhood education, often the educator addresses only the (re) knowledge of plane geometric figures - circle, triangle, rectangle, square - in painting and appointment activities. Teaching and Geometry learning, however, need to create opportunities, as proposed by several researchers - (GRANDE, 1994) (CERQUETTI-ABERKNE; BERDONNEAU, 1997) (DUHALDE; Cuberes, 1998) (Smole; DINIZ; CANDID , 2003), (Lorenzato, 2006) - the development of concepts for space and form, giving children opportunities to realize and know the areas in which they live, they move, where they learn to explore, conquer, order and represent. This study aimed to identify the teachersÂs knowledge of teachers who teach the spatial orientation on Pre-School. The qualitative research, case study type, was carried out in an institution of Early Childhood Education and Elementary Education municipal fortress system. Study participants were two teachers, one of child IV and of child V, and a trainer of early childhood education. Over nine meetings were held periodic visits to the realization of field observations of classes taught by teachers participating research and interviews (initial and reflective), which were recorded and later transcribed, generating texts and reflections. From the results, it was found that, despite having some geometry knowledge, the teacherÂs knowledge of teachers and trainer regarding the spatial orientation, an important content in the development and learning of children from pre-school, are fragmented, requiring provide urgently training opportunities that enhance and articulate such knowledge.

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Barbariz, Taís Alves Moreira [UNESP]. "A constituição do conhecimento matemático em um curso de Matemática à distância." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/150212.

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Esta pesquisa tem por meta compreender a constituição de conhecimento matemático, tomando como foco a experiência vivenciada no mundo-vida da Educação a Distância. O desdobramento dos estudos persegue a questão, objetivo da investigação: Como se constitui o conhecimento matemático quando se está junto à Matemática, ao computador e aos cossujeitos? A pesquisadora assume, para isso, a postura filosófica-fenomenológica, entendendo que a Fenomenologia busca a ir-às-coisas-mesmas, não deduzindo consequências de pressupostos teóricos. Assim, a pesquisadora foca sua análise nas vivências em que o sentido vai se fazendo para ela. Para a constituição dos dados foi projetado um curso na modalidade à distância sobre Geometria, tomando como inspiração o tratado em dois capítulos de duas obras de Hans Freudenthal que tratam dessa parte da Matemática. Os procedimentos que conduzem a investigação tomam como dados, constituídos para esse fim, dois momentos distintos. O primeiro momento se deu na temporalidade da preparação do curso, quando se constituíram os dados que tiveram como solo os registros da pesquisadora, sujeito da investigação, que buscou, de modo atentivo, dar-se conta do por ela percebido nesse movimento, descrevendo essa percepção tal como a ela aparece no fluxo de sua lembrança. O segundo momento selecionado para análise e interpretação se constituiu de um dos diálogos, destacado entre todos os que ocorreram durante a realização do curso. Este diálogo mostrou-se exemplar pelo fato de apresentar diferentes maneiras de participações nas atividades do curso, como a apresentação de outros autores, que não os indicados no curso, para dialogar e auxiliar nas compreensões dos assuntos tratados, e, também por trazer outros alunos no movimento do diálogo em que um comenta a fala do outro, ratificando-a ou trazendo-a em sua própria reflexão. Todos os registros, do primeiro e do segundo momento, foram interpretados como um único movimento, à luz da interrogação que conduz esta pesquisa. A esta interpretação seguiu-se o movimento de metainterpretação, onde a pesquisadora busca transcender às compreensões constituídas por meio da pesquisa. Nesse momento, a pesquisadora compreendeu, ainda, abranger a busca de sentido que isso que está em constituição faz para o sujeito que indaga pelo que diz para ele. Ao explicitar o como se constitui o conhecimento matemático, estando junto a cossujeitos, na realidade do ciberespaço, a pesquisadora deu-se conta de que sua pesquisa se dá em uma direção que aprofunda compreensões a respeito dos modos pelos quais se dá a produção de conhecimento pelos seres humanos com mídias.
This research aims to understand the constitution of mathematical knowledge, focusing on the experience lived in the Distance Education life-world. The studies unfolding pursues the question which is the aim of the investigation: How is mathematical knowledge constituted when one is close to Mathematics, the computer and co-subjects? The researcher assumes, for this, the philosophical-phenomenological position, understanding that Phenomenology aims to go-to-things-themselves, without deducing consequences of theoretical presuppositions. The researcher thus focuses her analysis on her living experiences in which it is making sense to her. For the constitution of data, a Geometry distance learning course was projected, inspired in two chapters of two Hans Freudenthal works that deals with this branch of Mathematics. The investigation procedures took two distinct moments as data, which was constituted specifically for this purpose. The first moment occurred in the temporality of the preparation of the course, when the constituted data had the researcher, the investigations subject, own records as its soil. She has attentively sought of her perceptions in the movement to describe this as it shows in her remembrance flow. The second moment selected for analysis and interpretation consisted of one of the dialogues, highlighted among all occurred during the realization of the course. This dialogue showed itself exemplary because it presented different ways of participating in the course activities, such as the presentation of authors other than those indicated in the course, dialoguing and helping in understanding some matters discussed, and also to bring other students into the dialogue movement in which one comments the speech of the other, ratifying it or bringing it in his/her own reflection. All records, from the first and second moments, were interpreted as a single movement, in the light of the interrogation which drives this research. This interpretation was followed by the meta-interpretation movement, where the researcher seeks to transcend the understandings constituted through the research. The researcher further understood that it encompasses the search for sense that what is in constitution makes for the subject who inquires what it tells her. In explaining how mathematical knowledge is constituted, being close to co-subjects, in the reality of cyberspace, the researcher realized that she understood that her research takes place in a direction that deepens understandings about the ways in which knowledge production takes place by humans with media.

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Almeida, Janaína Xavier de. "AS CONCEPÇÕES DE PROFESSORES AO ENSINAR QUADRILÁTEROS NOS ANOS INCIAIS DO ENSINO FUNDAMENTAL E AS POSSIBILIDADES DE CONTRIBUIÇÕES DAS TIC." Universidade Federal de Santa Maria, 2015. http://repositorio.ufsm.br/handle/1/6761.

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With the proposed study aimed to analyze and understand the mathematical conceptions of teachers, seeking to provide opportunities to introduce the use of Information and Communication Technologies (TIC) as an important tool of teaching practice, teaching geometry, in basic education, especially from 1st to 5th grade of elementary school. This understanding used as theoretical support the Knowledge Teachers seconds Tardif (2014), knowledge of the specific content, general educational, pedagogical content Shulman (1986, 1987) and the technological and pedagogical content knowledge seconds Palis (2010). To develop this elaborate research, execute and evaluate two distinct stages, the first conducted interviews and applied questionnaires to teachers of the Municipal Public School Network Tingling / RS active from 1st to 5th year of teaching in the second stage, from the analysis of the interviews and answers to questionnaires prepared and implemented a training workshop entitled Continuing: "The Geogebra software in Teacher Continuing Education in Teaching and Learning Quads", which was offered to all teachers of the Municipal Public School Network that city. From, analysis and discussion of the completion of these two steps we find that the teachers from 1st to 5th grade of elementary school proved to be aware of the importance of the teaching of mathematics and geometry in the early years of elementary school, however this coming up awareness in trouble arising from its initial and continuing education, lack of infrastructure and multisseriação in most schools. In addition, we realized through the implementation of the workshop, TIC, particularly the software Geogebra can contribute effectively to the organization and development of teaching practice, providing alternative techniques that enrich the Quads teaching in the early years of elementary school. It is believed that the objective was achieved, since the end of the workshop the teachers managed mediated technologies, consolidate knowledge teachers need to learn the minimum properties of outstanding quads, thus contributing, even if indirectly, to improve of student learning.
Com o estudo proposto objetivamos analisar e compreender as concepções matemáticas dos professores, buscando proporcionar oportunidades de introduzir a utilização das Tecnologias de Informação e Comunicação (TIC) como ferramentas auxiliares da prática docente, no ensino de Geometria, em particular quadriláteros, na educação básica, em especial do 1º ao 5º ano do Ensino Fundamental. Essa compreensão utilizou como subsídios teóricos os Saberes Docentes segundo Tardif (2014), os conhecimentos do conteúdo específico, pedagógico geral, pedagógico do conteúdo de Shulman (1986, 1987) e o conhecimento tecnológico e pedagógico do conteúdo segundo Palis (2010). Para desenvolvermos essa pesquisa elaboramos, executamos e avaliamos duas etapas distintas, na primeira realizamos entrevistas e aplicamos questionários aos professores da Rede Escolar Pública Municipal de Formigueiro/RS atuantes do 1º ao 5º ano do ensino. Na segunda etapa, a partir da análise das entrevistas e respostas aos questionários elaboramos e implementamos uma Oficina de formação Continuada intitulada: O Software Geogebra na Formação Continuada de Professores no Ensino e Aprendizagem de Quadriláteros , que foi oferecida a todos os professores da Rede Escolar Pública Municipal daquela cidade. A partir da análise e discussão da realização dessas duas etapas constatamos que as professoras do 1º ao 5º ano do ensino fundamental mostraramse conscientes da importância do ensino da matemática e da Geometria nos anos iniciais do ensino fundamental, entretanto essa consciência esbarra em dificuldades decorrentes da sua formação inicial e continuada, da falta de infra-estrutura e da multisseriação na maioria das escolas. Além disso, percebemos por meio da realização da Oficina, que as TIC, em particular o Software Geogebra, podem contribuir de maneira efetiva para organização e desenvolvimento da prática docente, oferecendo técnicas alternativas que enriquecem o ensino de Quadriláteros nos anos iniciais do Ensino Fundamental. Acreditamos que o objetivo da pesquisa foi atingido, uma vez que ao final da oficina as professoras conseguiram mediadas pelas tecnologias, consolidar os saberes docentes necessários ao aprendizado das propriedades mínimas dos quadriláteros notáveis, contribuindo assim, mesmo que de forma indireta, para a melhoria da aprendizagem dos alunos.

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Fonseca, Simone Silva da. "Aproximações e distanciamento sobre os saberes elementares geométrico no ensino primário entre Sergipe e São Paulo." Universidade Federal de Sergipe, 2015. https://ri.ufs.br/handle/riufs/5181.

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This paper presents the results of a survey that aimed to identify the similarities and differences on the geometric basic knowledge in primary education between Sergipe and São Paulo, in the period 1911-1930, from the content (s), method (s) and feature (s.). To achieve this purpose, sources were located and examined as, regulations, decrees, laws and education programs, and referred to as the reference Lessons Manual of Things Calkins (1950). As theoretical support, authors have been adopted as, Valente (2007) for the understanding of the history of mathematics education, Valente and Leme da Silva (2013) on the work of the historian of mathematics education, Valente (2011), Nunes (1998) and Souza (2013) for comparative studies and historical Chartier (2002) on representations. Based on the examination conducted in the sources, it is clear that the approaches elements are: the subjects / materials that refer to geometric elementary knowledge of São Paulo are Shapes, Geometry, Design and Crafts and Sergipe Design and Crafts. Regarding the contents, were set gradually, exploring the contents to be taught successively and in progression of difficulty levels for each year. The model was incorporated into the manual work as content. The Crafts in both states directed to "do", and use objects of everyday life that remind solids and geometric figures. We noticed the presence of natural drawing by copying and invention in the discipline / field design for Sergipe and São Paulo. We found that the minimum programs of both states were formed in the 1930s with the principles of the New School, from the recommendation that the contents should be developed by the teacher, by the method of projects or interests centers. In the methods, São Paulo had most of their methodologies and requirements appropriate to Calkins method. Have Sergipe, despite being shown the recommendation for teaching through Calkins method, since 1891, the requirements and methodologies are presented implicitly in educational programs. We note as distancing elements the presence of Forms and Geometry in São Paulo and Sergipe the contents related to embedded geometry in the drawing. Regarding the resources identified indications of rules and compasses in Regulations of Sergipe and the recommendation for the use of books of Olavo Freire Collection, composed of seven books and the use of the Teacher´s guide: Linear Design Abilio Cezar Borges, the Program education. In São Paulo, we found the use of the rule, the square, the protractor and compass in different materials: Forms, Geometry and Crafts.
O presente trabalho apresenta os resultados de uma pesquisa que teve por objetivo identificar as aproximações e distanciamentos sobre os saberes elementares geométricos no ensino primário entre Sergipe e São Paulo, no período de 1911 a 1930, a partir dos conteúdo(s), método(s) e recurso(s.). Para atingir esse propósito, foram localizadas e examinadas fontes como, Regulamentos, Decretos, Leis e Programas de ensino, além de consultado como referência o Manual de Lições de Coisas de Calkins (1950). Como sustentação teórica, foram adotados autores como, Valente (2007) para o entendimento sobre história da educação matemática, Valente e Leme da Silva (2013) sobre o trabalho do historiador da educação matemática, Valente (2011), Nunes (1998) e Souza (2013) para os estudos históricos comparativos e Chartier (2002) sobre representações. Com base no exame efetuado nas fontes, é possível afirmar que os elementos de aproximações entre os estados de Sergipe e São Paulo são: as disciplinas/matérias que remetem aos saberes elementares geométricos de São Paulo são Formas, Geometria, Desenho e Trabalhos manuais e para Sergipe Desenho e Trabalhos manuais. Em relação aos conteúdos, estavam postos de forma gradual, explorando os conteúdos a serem ministrados de forma sucessiva e em progressão de graus de dificuldade para cada ano, nos dois estados. A modelagem foi incorporada aos Trabalhos manuais como conteúdo em Sergipe e São Paulo. Os Trabalhos manuais em ambos estados orientavam para o fazer , além de usar objetos do dia a dia que lembram os sólidos e figuras geométricas. Constatamos a presença do desenho natural por meio da cópia e invenção na disciplina/matéria Desenho para Sergipe e São Paulo. Verificamos que os Programas mínimos de ambos estados se constituíram na década de 1930 com os princípios da Escola Nova, a partir da recomendação que os conteúdos deveriam ser desenvolvidos pelo professor, por meio do método de projetos ou centros de interesses. Em relação aos métodos, São Paulo teve grande parte de suas metodologias e prescrições apropriadas ao método de Calkins. Já Sergipe, apesar de ser evidenciado a recomendação para o ensino por meio do método de Calkins, desde 1891, as prescrições e as metodologias se apresentam de forma implícita nos Programas de ensino. Constatamos como elementos de distanciamentos a presença das Formas e da Geometria em São Paulo e em Sergipe os conteúdos referentes a Geometria incorporados no Desenho. Em relação aos recursos identificamos indicações de réguas e compassos nos Regulamentos de Sergipe e a recomendação para o uso de Cadernos da Coleção de Olavo Freire, composta por sete cadernos e o uso do Guia do professor: Desenho linear de Abílio Cezar Borges, nos Programas de ensino. No caso de São Paulo, identificamos o uso da régua, do esquadro, do transferidor, e do compasso nas diferentes matérias: Formas, Geometria e Trabalhos manuais.

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Moniz, Carmen Machemer de Vasconcelos. "Visualização espacial na perspectiva da epistemologia genética." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2013. http://hdl.handle.net/10183/71275.

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Este trabalho analisa a aplicação da proposta de uma nova sequência didática para a disciplina de Geometria Descritiva, que trata do ensino da visualização espacial. A proposta foi desenvolvida a partir da construção das noções de espaço e questões gerais sobre aprendizagem, conhecimento e desenvolvimento possibilitados pelo apoio teórico da Epistemologia Genética de Jean Piaget. A pesquisa, de tipo longitudinal, foi realizada em 4 (quatro) turmas de Curso Técnico em Edificações, sendo utilizado o método Dialético-Didático para o desenvolvimento das aulas. Os dados foram coletados por meio de registros em diários de campo, fotografias e produções gráficas dos alunos. São feitas comparações entre a nova sequência didática e a antiga e apresentadas as possíveis vantagens da utilização da nova sequência, fundamentada no princípio que a construção das noções espaciais se constitui a partir de noções topológicas, na direção de noções projetivas e depois euclidianas. Este trabalho não encerra as pesquisas sobre a melhor sequência didática para a visualização espacial, mas alerta pela busca de uma aprendizagem duradoura e significativa para a vida profissional dos alunos.
This work analyzes the application of the proposed of a new didatic sequence for the discipline of Descriptive Geometry, which deals with the teaching of the spacial visualization. The proposal was developed from the construction of the notions of space and general questions about learning, knowledge and development made possible by the theorical support of Jean Piaget’s Genetic Epistemology. The research, of longitudinal type, was performed in 4 (four) class sizes of Technical Course in Edifications, having been used the Dialectic-Didatic method for the development of the classes. Data were collected through registries in field diaries, photographs and graphic productions of the students. Comparisons are made between the new and the old didatic sequence and the possible advantages of using the new sequence are presented, based on the principle that the construction of spacial concepts is founded upon topological notions toward notions of projective and afterwards Euclideans. This work does not end the researches on the best didatic sequence for spacial visualization, but we believe it is on the right track to provide more chances to develop a lasting and significant learning for the professional life of the students.

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Morais, Junior Eduardo. "Por trás do currículo oficial, que Geometria acontece?: um estudo sobre os saberes anunciados nas narrativas de professoras dos anos iniciais do ensino fundamental." Universidade Federal de São Carlos, 2015. https://repositorio.ufscar.br/handle/ufscar/8453.

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This research aims to identify the teacher's knowledge announced by a group of teachers Initial Years of elementary school (1st to 3rd grade), linked to PNAIC (National Pact for Literacy Certain Age) in 2014 in the city of Sumaré - SP, through the detailed planning by a collective reflection and realization of a geometry activity developed in the classroom. This study, of qualitative nature, are based on participatory research, specifically action research, in view of the proposal for an intervention in the group studied. For the analysis of data produced by the teachers, the content analysis by the very nature of such data was used, the main landmarks references Bardin (1977) and Franco (2005) and for reasons of narrative, which constitute the data from this survey, we rely on Cunha (1997), Souza (2006) and Galvão (2005). The issue of teaching knowledge which is another aspect discussed in this work is grounded by the studies of Tardif (2011), Gauthier (1998) and other researchers dealing with the subject. The perspective is adopted in this research is an investigative work and that does not close at the time of analysis, and opening to the continuity of the reflections that now will be brought here. The object of study is seated in the triad: teaching knowledge, curriculum and teaching of geometry, with the theoretical foundation Silva (2010) in the curriculum conceptions, Leme da Silva and Valente (2014), Lorenzato (2011) and Fainguelernt (1999) in thinking about the geometry of education as well as the theoretical development of Piaget and Inhelder (1993) and Van Hiele (1990). Presented with this dissertation contributions to the continued discussion of teaching knowledge in the educational context, valuing the voice of the teacher of Primary Education Years Initials. As conclusions, we have the teaching knowledge arising announced by the teachers of vocational training, as well as disciplinary, curricular and experiential knowledge in the analyzed narratives. We bring to this indicative study for teacher continuing education concerning the reflective professional attitude and also to learn experiential as knowledge important to be considered in academic research as well as in their own continuing education of teachers.
A presente pesquisa tem como objetivo identificar os saberes docentes anunciados por um grupo de professoras dos Anos Iniciais do Ensino Fundamental (1º ao 3º ano), vinculadas ao PNAIC (Pacto Nacional pela Alfabetização na Idade Certa) no ano de 2014, na cidade de Sumaré – SP, por meio do planejamento circunstanciado por uma reflexão coletiva e realização de uma atividade de geometria desenvolvida em sala de aula. Este estudo, de cunho qualitativo, se assenta na pesquisa participante, especificamente a pesquisa-ação, tendo em vista a proposta de uma intervenção no grupo pesquisado. Para a análise dos dados, produzidos pelas professoras, foi utilizada a análise de conteúdo pela própria natureza desses dados, tendo como principais marcos referenciais Bardin (1977) e Franco (2005) e para fundamentação das narrativas, que se constituem os dados desta pesquisa, nos apoiamos em Cunha (1997), Souza (2006) e Galvão (2005). A questão dos saberes docentes, que é outra vertente discutida neste trabalho, é fundamentada pelos estudos de Tardif (2011), Gauthier (1998) e demais pesquisadores que tratam da temática. A perspectiva que se adota nessa pesquisa é de um trabalho investigativo e que não se fecha no momento de análise, tendo abertura para a continuidade das reflexões que ora serão trazidas aqui. O objeto de estudo está assentado na tríade: saberes docentes, currículo e ensino de geometria, tendo como fundamentação teórica Silva (2010) nas concepções de currículo, Leme da Silva e Valente (2014), Lorenzato (2011) e Fainguelernt (1999) na reflexão sobre o ensino de geometria, bem como o desenvolvimento teórico de Piaget e Inhelder (1993) e Van Hiele (1990). Apresentamos com esta dissertação contribuições para a continuidade da discussão dos saberes docentes no contexto educacional, valorizando a voz do professor dos Anos Iniciais do Ensino Fundamental. Como conclusões, temos os saberes docentes anunciados pelas professoras decorrentes da formação profissional, bem como saberes disciplinares, curriculares e experienciais nas narrativas analisadas. Trazemos com esse estudo indicativos para formação continuada docente que dizem respeito à postura reflexiva do profissional e também o saber experiencial como um saber importante a ser considerado nas pesquisas acadêmicas e também nas próprias formações continuadas de professores.

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Resende, Maria José de. "Saberes geométricos para a formação de professores primários em Sergipe : uma investigação sobre o período de 1890 a 1944." Pós-Graduação em Ensino de Ciências e Matemática, 2018. http://ri.ufs.br/jspui/handle/riufs/8309.

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This work presents the result of a research that had as objective to examine how were prescribed the geometric knowledge for the formation of primary teachers in Sergipe in the period from 1890 to 1944. For this, the sources used were official documents like Decrees, Laws, Regulations, Teaching programs and pedagogical journals in order to identify and characterize geometric knowledge in the training of primary teachers. They were consulted as reference: Valente (2005, 2013) regarding the understanding about the production in history of mathematical education; Leme da Silva (2015) on the understanding of geometric knowledge; Chervel (1990) on the constituents and purposes of a discipline, among other authors. Initially, the research used the documentary study, examining sources from the period from 1890 to 1931, with the purpose of understanding and identifying the geometric knowledge in the formation of normalists in the period before the 1930s. made it possible to compare the geometric knowledge that was proposed for the Normal Course and the Primary Course. According to the Teaching Programs, the geometric knowledge in the Primary Course constituted the subject / discipline Drawing (Linear Design), being recommended in some moments by means of the free drawing, the drawing of geometric figures and, in Arithmetica, approaching "surface , perimeter, area evaluation, relation between diameter and circumference "; for the Normal Course, the geometric knowledge had a more specific treatment with a level of deepening, for example, in relation to the treatment of theories like: "theory of perpendiculars"; "Theory of parallels"; "Polygonos theory". With regard to the teaching method proposed, at the time in Sergipe, we can highlight two moments: the first in the period of 1890 - 1930, whose teaching method recommended in the official documents were intuitive; and the period 1930-1940, with indications of the change of method, going to the active method. The latter can be identified in the guidelines proposed to teachers, under two scopes: in the pedagogical magazines located in the collection of the Epifânio Dórea Library (which probably circulated in this State) and in the organization of geometric knowledge, from the Teaching Programs.
Este trabalho apresenta o resultado de uma pesquisa que teve por objetivo examinar como eram prescritos os saberes geométricos para a formação de professores primários em Sergipe no período de 1890 a 1944. Para isso, as fontes utilizadas foram documentos oficiais como Decretos, Leis, Regulamentos, Programas de Ensino e revistas pedagógicas a fim de identificar e caracterizar os saberes geométricos na formação dos professores primários. Foram consultados como referência: Valente (2005, 2013) quanto ao entendimento sobre a produção em história da educação matemática; Leme da Silva (2015) acerca do entendimento de saberes geométricos; Chervel (1990) sobre as constituintes e finalidades de uma disciplina, dentre outros autores. Inicialmente, a pesquisa recorreu ao estudo documental, examinando fontes do período de 1890 a 1931, com o intuito de compreender e identificar quais e como se apresentavam os saberes geométricos na formação de normalistas no período anterior à década 1930. O exame das fontes desse período possibilitou tecer uma comparação entre os saberes geométricos que eram propostos para o Curso Normal e Curso Primário. De acordo com os Programas de Ensino, os saberes geométricos no Curso Primário constituíam a matéria/disciplina Desenho (Desenho Linear), sendo recomendado, em alguns momentos por meio do desenho livre, o traçado de figuras geométricas e, em Arithmetica, abordando “superfície, perímetro, avaliação das áreas, relação entre diâmetro e circunferência”; para o Curso Normal, os saberes geométricos tinham um tratamento mais específico com um nível de aprofundamento, por exemplo, em relação ao tratamento de teorias como: “theoria das perpendiculares”; “teoria das paralelas”; “teoria dos polygonos”. Com relação ao método de ensino proposto, à época em Sergipe, pode-se destacar dois momentos: o primeiro no período de 1890 – 1930, cujo método de ensino recomendado nos documentos oficiais eram o intuitivo; e o período de 1930 – 1940, com indícios da mudança de método, passando ao método ativo. Esse último, pode ser identificado nas orientações propostas aos professores, sob dois âmbitos: nas revistas pedagógicas localizadas no acervo da Biblioteca Epifânio Dórea (as quais, provavelmente circularam neste Estado) e na organização dos saberes geométricos, a partir dos Programas de Ensino.
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Santana, Ivanilde da Conceição. "Professores de matemática na educação de jovens e adultos: o pensamento geométrico no centro das atenções." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/48/48134/tde-11062010-135442/.

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A presente pesquisa de cunho qualitativo tem como propósito responder à seguinte questão: quais as tensões e re-ações dos professores de matemática que atuam na Educação de Jovens e Adultos, frente a situações de ensino-aprendizagem da geometria que ocorrem a partir do conhecimento construído pelo aluno ao longo de sua vida/trabalho? Desse modo, nos aproximamos dos professores que atuam na Educação de Jovens e Adultos de escolas públicas de São Paulo, tanto pela via de questionários como pelo diálogo sobre suas expectativas e postura pedagógica a partir de questões reflexivas sobre a Educação de Jovens e Adultos (EJA) e o ensino da geometria. Os resultados da pesquisa indicaram, entre outros aspectos que, embora o ensino da geometria seja pouco delineado nos planos de trabalho da EJA, ainda assim, os professores participantes do estudo mostraram-se conscientes de sua importância e das possíveis contribuições do seu ensino. Nessa perspectiva, a pouca experiência com a prática pedagógica da geometria aliada à dominância da matemática escolar parecem levar a obstáculo quando os professores procuram elaborar atividades relacionando a geometria com a vida cotidiana do educando. A análise das manifestações aponta que os esforços empreendidos pelos professores na busca de reconhecer/respeitar os conhecimentos prévios dos alunos estão repletos de tensão e ansiedade dada a expectativa da necessidade de contextualizar/problematizar o ensino da geometria a partir da realidade do educando adulto.
The current qualitative research aims at answering the following question: what are the tensions and reactions of the mathematics teachers who dwell in the Education of Youngsters and Adults, in light of situations of teaching-learning geometry from the knowledge built by the student along his life/work? Therefore, we approached the teachers who work with Education of Youngsters and Adults in public schools from São Paulo, both, through questionnaires and dialogue, talking about their expectations and pedagogical posture from reflexive questions about the Education of Youngsters and Adults and the teaching of geometry. The results of the research indicated, among other aspects, that although the teaching of geometry is not adequately outlined in the working plans of Education of Youngsters and Adults, still the teachers participating in the study demonstrated that they were aware of their importance and of the possible contributions of their teachings. In this perspective, the little experience with the pedagogical practice of geometry combined with the dominance of school mathematics seem to lead to an obstacle when the teachers try to elaborate activities relating geometry with the daily life of the student. The analysis of the manifestations indicates that the efforts of the teachers in the search to recognize/respect the previous knowledge of the students are full of tension and anxiety given the expectation of the necessity to contextualize/problematize the teaching of geometry from the reality of the adult student.

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Santos, Joana Kelly Souza dos. "Apropriações do método intuitivo de Clakins nas orientações para o ensino de saberes geométricos em revistas pedagógicas brasileiras (1890-1930)." Pós-Graduação em Ensino de Ciências e Matemática, 2017. http://ri.ufs.br/jspui/handle/riufs/7110.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this text are presented results of a research whose objective was to characterize appropriations about the Calkins’ intuitive method in orientations to teaching geometric knowledge in primary school, present in Brazilian pedagogical journals of period between 1890 and 1930, finded in UFSC’s repository. The contribution came from the use of Chartier (2003) to talk about appropriation, Calkins (1886/1950) about intuitive method and Leme da Silva (2005) about geometric knowledge. The choice to examine the intuitive method from Calkins (1886/1950) can be justified because he was identified as reference in the intuitive method in Brazilian works. After exam, it was identified that the orientations for geometrics knowledge followed two paths: implicit and explicit. In the first case, when the authors used expression such as “lições de coisas” and “Calkins” in the text. In the second case, implicit when it was possible identified the uses of the principles of Calkins. Based on theses paths it was possible to characterize the appropriations from how of the geometric knowledge was related to teaching of lines, points, angles, geometric forms, geometrics figures and geometric solids, with the objective of stimulating the child’s senses, especially from the sight. The authors used principles of Calkins’ intuitive method starting from the dialogue, instigating the students to see the draws or objects and to do sentences about it. The comparison, association and classification were also identified in the treatment of sight education. From this, it was possible to affirm that the author appropriations were related to two uses: use of objects or from the imagination of children. Thus, it was possible to affirm that there was appropriation of Calkins’ intuitive method to teaching geometric knowledge, mainly of the principle of educating of sight, because in the recommendations the observation was highlighted.
Neste texto é apresentado o resultado de uma pesquisa com o objetivo de caracterizar apropriações do método intuitivo de Calkins nas orientações para o ensino de saberes geométricos do curso primário, presente em exemplares de revistas pedagógicas brasileiras do período de 1890 a 1930, localizadas no repositório alocado no sítio da UFSC. Foram adotados os entendimentos de Chartier (2003) para apropriação, Calkins (1886/1950) para a compreensão de princípios do método intuitivo e Leme da Silva (2015) para saberes geométricos. A opção por examinar o método intuitivo a partir de Calkins (1886/1950) pode ser justificada por ser identificado em pesquisas brasileiras, como uma referência para o método intuitivo. Após exame das fontes, foi identificado que as orientações para os saberes geométricos perpassavam por dois caminhos: explícito e implícito. No primeiro caso, quando os autores utilizavam expressões como “lições de coisas” ou “Calkins” no texto e implícito quando foi possível identificar usos dos princípios do método como defendido por Calkins. Com base nesses caminhos foi possível caracterizar apropriações a partir da forma como os saberes geométricos estavam relacionados ao ensino das linhas, pontos, ângulos, formas geométricas, figuras geométricas e sólidos geométricos, que tinha o objetivo de estimular os sentidos da criança, principalmente a partir da vista. Os autores adotavam princípios do método intuitivo de Calkins (1886/1950) partindo, principalmente, do diálogo, instigando os alunos a ver os desenhos ou objetos e formar sentenças sobre os mesmos. A comparação, associação e classificação também foram identificadas no tratamento da educação da vista. A partir dessa constatação, é possível afirmar que as apropriações dos autores estavam relacionadas ao uso dos princípios de duas formas diferentes: com ênfase no uso de objetos ou a partir da imaginação da criança. Dessa forma, os autores que tratavam do método intuitivo de Calkins (1886/1950) tanto explícito quanto implicitamente para o ensino de saberes geométricos se apropriaram do princípio de educar a vista, uma vez que nas recomendações para o ensino a observação ganhava destaque.
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Silva, Nicolly Peçanha do Nascimento. "Saberes geométricos na Revista do Ensino de Minas Gerais no período de 1925 a 1932." Universidade Federal de Juiz de Fora (UFJF), 2018. https://repositorio.ufjf.br/jspui/handle/ufjf/7891.

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A presente pesquisa investiga historicamente o ensino dos saberes geométricos no ensino primário em Minas Gerais, no período de 1925 a 1932, tendo como fonte de pesquisa a Revista do Ensino de Minas Gerais. Utilizamos como referencial teórico-metodológico de investigação para este estudo a História Cultural. Duas questões norteiam o estudo: como o ensino dos saberes geométricos se mostrava em relação às concepções de elemento e/ou de rudimento? E quais as profissionalidades identificadas em relação ao ensino de saberes geométricos no período pesquisado? Para concepções de elemento consideramos o conhecimento mais abstrato, racional, o saber pelo saber, tendo como caminho a razão e, de rudimento, consideramos o conhecimento mais concreto, prático, reverenciado pela experiência, o ensino essencial à vida. E o conjunto de saberes, conteúdos, orientações para o professor ensinar são os elementos da profissionalidade. O recorte temporal desta pesquisa se deu de 1925 a 1932, pois 1925 foi um ano de reativação, com número considerável de publicações, e 1932 sendo o limite, já que foi um ano marcado pela aprovação de um novo programa de metodologia para as Escolas Normais de 1º grau e 2º graus, apresentado pelo decreto de 10.392, de 30 de junho de 1932, pelo estado de Minas Gerais. Neste período de 1925 a 1932, a partir das análises feitas nesses impressos pedagógicos, totalizados em 78 Revistas, foi possível destacar para o ensino primário o surgimento de novas tendências, como o escolanovismo, que propunha reformas educacionais deslocando o centro da aprendizagem do conteúdo para o aluno, como também a forte presença de raízes no passado, no caso o método intuitivo, que se baseava na observação de coisas. Foi observado que o ensino dos saberes geométricos mostrava traços de caráter ora elementar, como o trabalho com as formas espaciais de maneira intuitiva, utilizando a observação de modelos para a comparação dos diferentes sólidos e obter sua memorização, e ao ensinar as noções de espaço e corpo, ao utilizar os objetos da classe para observação dos alunos, trabalhando cada saber em favor do próximo conteúdo, valorizando o rigor das definições. Ora rudimentar, ao aproximar o ensino para a vida profissional do aluno, como trabalhar formas planas com o intuito voltado à confecção de toalhinhas, ou explorar os conceitos de perímetro e área de forma livre, sem se prender ao rigor dos conceitos, mas de maneira prática para que o aluno consiga utilizar para sua vida cotidiana. E foram identificados diferentes elementos da profissionalidade para o ensino dos saberes geométricos, como o manuseio de argila e cartolina para trabalhar os conceitos de sólidos (inclusive sua planificação), dobraduras de papel e desenhos, para as formas planas, a observação de objetos de madeira e arame para desenvolver os quadriláteros, visitações com a classe à casa em construção, para as noções de perímetro e, entre outros.
The present investigation investigates historically the teaching of the means of communication in primary education in Minas Gerais, from 1925 to 1932, having as a research source the Revista de Ensino de Minas Gerais. He used as a theoretical-methodological reference of research for this study the Cultural History. The basic questions of teaching: how do the teaching of geometric knowledge show in relation to the conceptions of element and / or rudiment? And how about their skills in relation to the teaching of geometric knowledge in the period studied? The conceptions of element considered the knowledge more abstract, the knowledge by the knowledge, the tendency of reasoning, the rudiment, the more concrete knowledge, practical, the recovery of the experience, the essential teaching for the life. And the set of knowledges, contents, guidelines for the teacher are the elements of professionalism. The time cut of this research was 1925, 1932, because 1925 was a year of reactivation, with a considerable number of publications, and 1932 being the limit, since it was a year marked by the help of a new methodology program such as Normal Schools of 1º grade and 2nd degree, presented by the decree of 10,392, of June 30, 1932, by the state of Minas Gerais. This is a year from 1925 to 1932, from the solutions of printing companies, having reached a universe of 78 revolutions, being possible to emphasize for the primary education the emergence of new tendencies, such as Escolanovismo, which proposed educational reforms and the learning center of the student, as well as a strong presence of roots in the past, in the case of the intuitive method, which was based on the observation of things. This study is an instruction of geometrical patterns features ora elementary, or how to work with spatial forms in an intuitive way, using a notification to models from the soil and have their memorization and, and teaching and the teaches in The objectives of the lesson are the objectives of the student, learning each of the following objectives, valuing the rigor of the definitions. Nowadays it is rudimentary, when approaching teaching for the student's professional life, such as working flat shapes with the intention of making wipes, or exploring the concepts of perimeter and free-form area, without being attached to the rigor of concepts, but in a way practice for the student to use for their daily lives. And different elements of professionalism were identified for the teaching of geometric knowledge, such as the handling of clay and paperboard to work on the concepts of solids (including their planning), paper folding and drawing, for flat shapes, the observation of wooden objects and wire to develop the quadrilaterals, class visits to the house under construction, notions of perimeter and, among others.

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Silva, Cleusiane Vieira. "A prática docente e sua influência na construção de conceitos geométricos: um estudo sobre o ensino e a aprendizagem da Simetria Ortogonal." Pontifícia Universidade Católica de São Paulo, 2015. https://tede2.pucsp.br/handle/handle/11051.

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This thesis aimed to investigate how an environment of action and reflection that involves the pre-analysis , reflections on the pre-analysis , experimentation with students from Elementary School II , post-analysis and reflections on the post-analysis that is related to a didactic sequence on orthogonal symmetric , interferes in the Mathematics teachers knowledge , in the mentioned level. Nevertheless, this research aimed to answer the following question: how can an environment of action and reflection that is constituted in the times for the Complementary Activities, influence the Mathematics teachers (from Elementary School II) knowledge on orthogonal symmetric? The methodology that was used in this study was based on the presupposition of Didactical Engineering according to Artigue (1995) and on the contributions by Schön (1995; 2000). The theoretical referential had its basis on the Theory of Didactical Situations - Brousseau (1997) - to do a study on the influence of the didactical variables that were chosen in the Math teachers (Elementary School II) procedures and answers, as well as their students , and Margolinas (2002; 2004) to hold an analysis on the teacher s activity, in view of understanding how he/she develops the teaching practice and how it can influence students learning. Yet, the theoretical referential was based in Parzysz Picture of Geometric Paradigms (2001; 2006), in the analysis of the nature of the geometric work that is developed by teachers in the moments of construction and analysis of problem situations, and by students in the moments of interaction with these problems. The studies by Grenier (1988) were used as a reference in order to observe the students conceptions of Elementary School II according to orthogonal symmetric. The analysis of the registers that had been provided by the students made it possible the identification of conceptions that are related to the orthogonal symmetric some of them corroborate with the results from studies done by Grenier (1988); other ones seem to be specific in the group of investigated students. The analysis of registers of Math teachers also showed some concepts about orthogonal symmetric, and these conceptions seem to be related to the way this concept is presented in the course books. During the investigation, teachers had the opportunity to evaluate their own practice and reflected on the teaching methods they were using, to really know if they were working or not with their students. It was noted that an environment of action and reflection that is constituted at school, have influence on Math teachers knowledge, but this influence is limited
Esta tese teve por objetivo investigar como um ambiente de ação e reflexão, que envolve a pré-análise, reflexões sobre a pré-análise, experimentação com alunos do Ensino Fundamental II, pós-análise e reflexões sobre a pós-análise relacionadas a uma sequência didática sobre a simetria ortogonal, interfere nos saberes docentes de professores de Matemática desse mesmo nível de ensino. Portanto, foi pretensão desta pesquisa responder à seguinte questão: como um ambiente de ação e reflexão constituído nos horários destinados às Atividades Complementares (A.C.) pode influenciar os saberes docentes de professores de Matemática do Ensino Fundamental II, sobre a simetria ortogonal? A metodologia utilizada para este estudo apoiou-se nos pressupostos da Engenharia Didática, segundo Artigue (1995) e nas contribuições de Schön (1995; 2000). O referencial teórico baseou-se na Teoria das Situações Didáticas de Brousseau (1997), para fazer um estudo sobre a influência das variáveis didáticas escolhidas nos procedimentos e respostas de professores de Matemática do Ensino Fundamental II e de seus alunos, e Margolinas (2002; 2004), para realizar a análise da atividade do professor no sentido de compreender como esse profissional desenvolve sua prática docente e como esta influência na aprendizagem dos alunos. O referencial teórico baseou-se ainda no quadro dos Paradigmas Geométricos de Parzysz (2001; 2006) na análise da natureza do trabalho geométrico desenvolvido por professores nos momentos de resolução e análise das situações-problema e por alunos nos momentos de interação com essas mesmas situações-problema. Foram utilizados, como trabalho de referência, os estudos de Grenier (1988) para observar as concepções de alunos do Ensino Fundamental II quanto à simetria ortogonal. A análise nos registros fornecidos pelos alunos propiciou a identificação de concepções relativas à simetria ortogonal, algumas corroboram os resultados obtidos nos estudos realizados por Grenier (1988), outras parecem específicas do grupo de alunos investigado. A análise nos registros de professores de Matemática também expôs algumas concepções acerca da simetria ortogonal, cujas concepções parecem estar relacionadas à forma como esse conceito é apresentado nos livros didáticos. Durante a investigação, os professores avaliaram a própria prática e ponderaram sobre os métodos de ensino adotados por eles, no sentido de observar se tais métodos estão ou não surtindo efeito na aprendizagem de seus alunos. Constatou-se que um ambiente de ação e reflexão, constituído na escola, influencia nos saberes docentes de professores de Matemática, embora sua influência seja limitada

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Ben, marzouka Wissal. "Traitement possibiliste d'images, application au recalage d'images." Thesis, Ecole nationale supérieure Mines-Télécom Atlantique Bretagne Pays de la Loire, 2022. http://www.theses.fr/2022IMTA0271.

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Dans ce travail, nous proposons un système de recalage géométrique possibiliste qui fusionne les connaissances sémantiques et les connaissances au niveau du gris des images à recaler. Les méthodes de recalage géométrique existantes se reposent sur une analyse des connaissances au niveau des capteurs lors de la détection des primitives ainsi que lors de la mise en correspondance. L'évaluation des résultats de ces méthodes de recalage géométrique présente des limites au niveau de la perfection de la précision causées par le nombre important de faux amers. L’idée principale de notre approche proposée est de transformer les deux images à recaler en un ensemble de projections issues des images originales (source et cible). Cet ensemble est composé des images nommées « cartes de possibilité », dont chaque carte comporte un seul contenu et présente une distribution possibiliste d’une classe sémantique des deux images originales. Le système de recalage géométrique basé sur la théorie de possibilités proposé présente deux contextes : un contexte supervisé et un contexte non supervisé. Pour le premier cas de figure nous proposons une méthode de classification supervisée basée sur la théorie des possibilités utilisant les modèles d'apprentissage. Pour le contexte non supervisé, nous proposons une méthode de clustering possibiliste utilisant la méthode FCM-multicentroide. Les deux méthodes proposées fournissent en résultat les ensembles de classes sémantiques des deux images à recaler. Nous créons par la suite, les bases de connaissances pour le système de recalage possibiliste proposé. Nous avons amélioré la qualité du recalage géométrique existant en termes de perfection de précision, de diminution du nombre de faux amers et d'optimisation de la complexité temporelle
In this work, we propose a possibilistic geometric registration system that merges the semantic knowledge and the gray level knowledge of the images to be registered. The existing geometric registration methods are based on an analysis of the knowledge at the level of the sensors during the detection of the primitives as well as during the matching. The evaluation of the results of these geometric registration methods has limits in terms of the perfection of the precision caused by the large number of outliers. The main idea of our proposed approach is to transform the two images to be registered into a set of projections from the original images (source and target). This set is composed of images called “possibility maps”, each map of which has a single content and presents a possibilistic distribution of a semantic class of the two original images. The proposed geometric registration system based on the possibility theory presents two contexts: a supervised context and an unsupervised context. For the first case, we propose a supervised classification method based on the theory of possibilities using learning models. For the unsupervised context, we propose a possibilistic clustering method using the FCM-multicentroid method. The two proposed methods provide as a result the sets of semantic classes of the two images to be registered. We then create the knowledge bases for the proposed possibilistic registration system. We have improved the quality of the existing geometric registration in terms of precision perfection, reductionin the number of false landmarks and optimization of time complexity

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Kaheru, Sam James Murungi. "The use of computer simulations for cognitive load change and acquisition of knowledge and skills in geometrical optics." Thesis, 2014. http://hdl.handle.net/10500/18609.

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The aim of the study was to compare the effects of the use of interactive computer simulations for cognitive load change of grade 11 learners in the acquisition of knowledge and a science process skill in geometrical optics. Both the use of computer simulations and traditional teaching was teacher centred. The study was done in a rural area in South Africa, in the Limpopo Province in the district of Vhembe. The theoretical framework was based on the information processing model. Within the non-equivalent quasi experimental design a switching replications design study was used whereby 105 learners in four schools took part. This study found that in terms of the acquisition of knowledge, female learners gained more by the use of simulations than their male counterparts. No significant effect was found in the acquisition of the skill when computer simulations were used. Initial reduction of cognitive load was found when simulations were used and with time this increased. Experienced educators reduced the cognitive load through use of their knowledge and expertise and their role needs to be highlighted. Further studies are suggested to study the effect of a learner centred approach on decreasing the cognitive load and its effect on the acquisition of knowledge and skills.
Mathematics, Science and Technology Education
D. Phil. (Mathematics, Science and Technology Education with specialisation in Physics Education)

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Brodie, John Hector, University of Western Sydney, College of Arts, and School of Education. "Background factors affecting success in geometry." 2004. http://handle.uws.edu.au:8081/1959.7/12566.

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Mathematics plays a key role in bolstering a country’s knowledge economy. Australia’s knowledge economy is negatively affected by the underachievement of Australian school students in geometry. Research indicates a continuing decline in student performance in geometry and a distinct lack of geometrical knowledge and understanding on the part of students and teachers. To address this issue a theory of success in geometry that focussed on background variables and attitude, was developed. In the theory it was hypothesised that success in geometry can be understood in terms of predictor variables and that attitude mediates the effects of the variables on success in geometry. A model of success in geometry was developed to systematically determine the relationships of the variables. Trainee teachers from the University of Western Sydney (n = 224) participated in the survey. Using Confirmatory Factor Analysis the use of one or two attitude scales was determined as were the items in the scales. Using Structural Equation Modeling (SEM) the relationships between the background factors (age, education, gender, left/right brain preference) on success in geometry (van Hiele level) mediated by attitude were determined. The evidence, however, suggests that attitude is not only correlated with the measures of success in geometry (van Hiele levels) but that it may also be a predictor of success in geometry. It was also hypothesised that attitude was composed of three analytically distinct factors (affective, cognitive and behavioural). The evidence suggests that this hypothesis cannot be rejected. This is an important finding as previous research has not been empirically able to distinguish these factors. In order to improve the success of Australian school students in geometry and assist teachers to succeed and consequently improve Australia’s knowledge economy, the present research indicates that: all trainee teachers should have their van Hiele level of geometry understanding determined; appropriate geometry courses should be a mandatory part of the curriculum for all pre-service teachers whose van Hiele level is less than three; all trainee teachers should have a van Hiele level of three or four before they commence teaching; appropriate changes to the curriculum of trainee teachers should be made so that their stored general evaluative process produces a positive attitude to geometry, especially in female students; school students who intend to pursue a teaching career should complete mathematics courses with a geometry content.
Doctor of Philosophy (PhD)

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40

Brodie, John Hector. "Background factors affecting success in geometry." Thesis, 2004. http://handle.uws.edu.au:8081/1959.7/12566.

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Mathematics plays a key role in bolstering a country’s knowledge economy. Australia’s knowledge economy is negatively affected by the underachievement of Australian school students in geometry. Research indicates a continuing decline in student performance in geometry and a distinct lack of geometrical knowledge and understanding on the part of students and teachers. To address this issue a theory of success in geometry that focussed on background variables and attitude, was developed. In the theory it was hypothesised that success in geometry can be understood in terms of predictor variables and that attitude mediates the effects of the variables on success in geometry. A model of success in geometry was developed to systematically determine the relationships of the variables. Trainee teachers from the University of Western Sydney (n = 224) participated in the survey. Using Confirmatory Factor Analysis the use of one or two attitude scales was determined as were the items in the scales. Using Structural Equation Modeling (SEM) the relationships between the background factors (age, education, gender, left/right brain preference) on success in geometry (van Hiele level) mediated by attitude were determined. The evidence, however, suggests that attitude is not only correlated with the measures of success in geometry (van Hiele levels) but that it may also be a predictor of success in geometry. It was also hypothesised that attitude was composed of three analytically distinct factors (affective, cognitive and behavioural). The evidence suggests that this hypothesis cannot be rejected. This is an important finding as previous research has not been empirically able to distinguish these factors. In order to improve the success of Australian school students in geometry and assist teachers to succeed and consequently improve Australia’s knowledge economy, the present research indicates that: all trainee teachers should have their van Hiele level of geometry understanding determined; appropriate geometry courses should be a mandatory part of the curriculum for all pre-service teachers whose van Hiele level is less than three; all trainee teachers should have a van Hiele level of three or four before they commence teaching; appropriate changes to the curriculum of trainee teachers should be made so that their stored general evaluative process produces a positive attitude to geometry, especially in female students; school students who intend to pursue a teaching career should complete mathematics courses with a geometry content.

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41

Brandão, Susana Isabel Pereira de Azevedo. "Geometria descritiva : didática em prol do pensamento espacial e geométrico." Master's thesis, 2013. http://hdl.handle.net/10400.14/13713.

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A Geometria Descritiva tem sido profundamente desprezada nas escolas, tanto pela classe docente, como pela discente. Em tempos de inovação informática e tecnológica, questiona-se o seu interesse e atualidade. Porém, não se questionam os métodos pedagógicos praticados por um grande número de professores. Apesar do programa curricular da Geometria Descritiva e as suas sugestões metodológicas apontarem para a construção do conhecimento, a lecionação da disciplina está assente no dogmatismo e transmissão de fórmulas de resolução de problemas-tipo. O resultado é escassez de pensamento geométrico, praticamente irreversível, que se prolonga para além dos ciclos de estudos. Perceção, Construção, Representação e Conceção são as quatro faces do tetraedro que serve de metáfora para reativar a dinâmica do pensamento geométrico. Articuladas de forma sólida e equilibrada, estas atividades permitem valorizar a forma como o sujeito se relaciona com o espaço, tanto pessoal, como profissionalmente. Fundamentado na História, na Arte, na Psicologia e na Pedagogia, o presente documento configura-se sob a forma de uma proposta para uma didática da Geometria Descritiva que enaltece a comunicação entre a mão e o cérebro, no desenvolvimento recíproco de ideias e representações gráficas. O professor deve usar e construir consistentemente a sua distinção profissional para uma meta: ensinar para a autonomia e criatividade.
Descriptive Geometry has been deeply neglected in schools, not only by teachers, but also by students. In times of computer innovation and technological wonders, its interest and contemporaneity are questioned. However, pedagogue methods adopted by a large number of teachers are not. Although descriptive geometry’s curricular program and its methodology suggestions tend to point to the construction of knowledge, the manner the subject is taught is based on dogmatism and the transmission of problemsolving formulas. The result is the geometric reasoning scarcity, almost irreversible, that is extended beyond the study cycles. Perception, Construction, Representation and Conception are the four faces of the tetrahedron that serves as a metaphor to reactivate the dynamic of geometric reasoning. Aligned in a solid and balanced form, these activities allow the enhancement in which the subject relates to space, both personally and professionally. Based in History, in Art, in Psychology and in Pedagogy, the present document is set under the form of a proposal for a Descriptive Geometry didactic, which improves the communication between hand and brain, in the reciprocal development of ideas and graphic representations. The teacher must consistently use and construct its professional distinction aiming at a target: teaching autonomy and creativity.

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Yang, Chung-Hsuan, and 楊忠璇. "The effect of knowledge and reasoning ability on geometric conceptual change for senior elementary children." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/26846951480837013988.

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碩士
國立臺灣師範大學
教育心理與輔導學系
101
This study is to understand the results and the cognitive processes of geometric conceptual change from the 5th grade elementary pupils who face counter-examples of quadrilaterals, especially to focus on the roles that geometric knowledge and reasoning ability play in the conceptual change. The inclusion relationship, square included in rectangle, was discussed further. 131 grade 3rd to 5th elementary pupils were selected for the pilot study to examine two self - designed tests of the geometric knowledge and reasoning ability. In addition, grade 5th elementary pupils were selected simultaneously to confirm the accuracy of the experimental procedure. The formal study contained two experiments: the conceptual change experiment and the definition-changed experiment. The former aimed to change the children’s performance of under-extension and to adjust the performance of conceptual intension; the latter aimed to refine the performance of conceptual intension when children were able to change the performance of performance of conceptual extension. As far as materials were concerned, positive instances and counter-examples were involved in the former; except for the materials mentioned above, the negative instances were added in the latter. The subjects were divided via the 2(geometric knowledge)*2(reasoning ability) way; then, three groups were formed, exclusive of the group with those had the worst geometric knowledge and reasoning ability. The valid samples for each group were 16, 17 and 16. All the subjects were with under-extension. The results of the conceptual change experiments were addressed as follows. First, the “worse geometric knowledge and better reasoning ability” group performed significantly better than the “better geometric knowledge and reasoning ability” group in accepting the counterexample and changing the performance of conceptual extension. It reveals that the poor geometric knowledge subjects have, the more difficult is for them to accept the counter-example and adjustment conceptual extension. Secondly, nearly half of the children are progressive in understanding the conceptual intension, and nearly 70% of the subjects found that the necessary attribute is “four angles are right angles.” Finally, the performance of inducting common attributes for positive instances and counter-examples of all subjects are shown as follows. the “better geometric knowledge and reasoning ability” group and the “better geometric knowledge and worse reasoning ability” group described more rectangular properties than the “worse geometric knowledge and better reasoning ability” group. Moreover, the “better geometric knowledge and reasoning ability” group could come up with more geometric properties, which can be regarded as effective reasoning concerning why square can be included in rectangular. It demonstrates that the performance of inducting common attributes is affected through the geometric knowledge and the reasoning ability. The result of the definition-changed experiment was that quarter of subjects turned their wrong conceptual intension correct after the experimental treatment. However, very few of the “better geometric knowledge and reasoning ability” group were able to refine the performance of conceptual intension, so the researcher speculated working memory limits subjects to refine the performance of conceptual intension. The researcher found that the role of the geometric knowledge in geometry conceptual change is to provide background knowledge for reasoning. Eventually, the school children rely on the reasoning ability to manipulate background knowledge and obtain the correct concepts.

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Chen, Yuan, and 陳沅. "The Development of a Gifted Students' Knowledge Transfer Model using a Geometric Reasoning Learning System." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/28965959179360158618.

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博士
國立高雄師範大學
工業科技教育學系
96
This study investigated how gifted students transferred knowledge in the subject area of Mathematics and how this system was effectively applied in order to help them construct a supportive learning system. The study involved two phases, the first being how the investigator helped the students perform in problem-solving situations and how knowledge transfer was performed in a GSP environment, and how the students successfully experienced this transfer process that produced a hierarchical Mindtool that developed into a transference model. The second phase of the study utilized the aforementioned model to establish a systematic e-learning source that assisted the 5th and 6th grade students in geometry. Based on quasi-experiment research, the researcher objectively assisted how effectively the scaffolding system of the students’ geometric reasoning could be incorporated into the elementary school’s Math curriculum. This three-year study involved observing two gifted students solve difficult math problems and how they later passed their problem-solving methods onto 11 other general students. In the first phase of the research, the records indicated that the students’ Zone of Proximal Development (ZPD) in geometric reasoning helped shape their scaffolding system for later geometry learning. Overall, the transference modes among the gifted students were carried out in three stages. The first stage involved categorizing their knowledge into various modules, the second involved systemizing the transference, and the final stage involved making the transference become a technical and automatic one. The results for the first phase of the research showed that GSP could effectively help the students to discover problem-solving methods in the initial stages, become aware of the distinctive natures of geometric segmentation, to draw a conclusion using common logic from varied problems, categorize their geometric knowledge into different modules, and expand their knowledge from the field of linear relationships to non-linear relationships. These problem-solving procedures involved setting up quantitative relationships, and using realistic information to create geometric shapes. Quantity relationships, again, according to the degree of abstractness inherent in the students’ learning, were divided into four different levels that included correspondence, recursion, function and conclusion. In general, it can be said that the acquired empirical data fitted the scaffolding SEM (Structural Equation Model) of this study. The second phase researched issues that included the following: (1) differences in both the experimental group and control groups’ growth slope rates in the respect to their reasoning abilities; (2) the characteristic features exhibited by elementary students while they were learning the geometric reasoning process; (3) different geometric reasoning abilities that existed among students who had different traits and who came from different districts; (4) students who had different traits in respect to geometric design creation and misconceptions. To assess the effectiveness of the scaffolding system, the study adopted evaluation by the Dynamic Assessment Model to observe the student growth slope rates. There were 328 students in the dynamic assessment experimental group, including 30 gifted members. There were another 192 students who made up the control group. The experiments consisted of 10 classes held over a two month period. The study adopted the Hierarchical Linear Model (HLM) to analyze the supporting effects of the scaffolding system. The results showed that both the general student experimental group and the gifted student experimental group gained substantially higher growth rates in pattern reasoning and geometric reasoning than the control group. The general student experimental group accounted for 35％ of the total variance of growth rates. And the gifted student experimental group accounted for 85％ of the total variance of growth rates. The hierarchical design of the scaffolding system had also effectively elevated the weaker students’ reasoning abilities. In the experimental group, both the gifted students and the general students’ creativity in geometric design had advanced dramatically, while the incorrect types reflected the students’ geometric deductive reasoning misconceptions, which was of significant value for reference in instruction design. The study kept detailed, in-depth observation records on the quick learning characteristics of the gifted students and how they shared these experiences with the other general students. Using information technology to fully integrate an automatic feedback and the communication feedback, the researchers developed the scaffolding Mindtool. Using a minimum cost, an efficient, highly abstract learning method was incorporated into the selected groups’ curriculum. It was expected to be effectively incorporated into all the 5th and 6th graders’ general learning curriculum. The results of this research proved that the scaffolding model of the gifted students’ knowledge transfer would be great value to both schools and enterprises that could aim to empower human strengths.

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盧信彰. "The Application of the Social Presence Theory and Dynamic Geometric Knowledge Map to Computer-mediated Learning." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/59199849862029525036.

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博士
國立高雄師範大學
工業科技教育學系
98
Due to the paradigm shift in education, development and application of new technology give rise to new perspectives of learning. Educational technology alters the scope, content, and presentation of knowledge. As a result, changes in the learning process create changes in the approaches to learning. Students acquire new knowledge in a multi-perspective and multi-layered manner by interacting in virtual reality. This new web-based learning support system incorporates the “social presence theory” into the online community and introduces the “knowledge map” computer-mediated learning tools. Students manipulate computer-mediated tools freely to analyze knowledge. This new learning model helps the student not only to construct a comprehensive knowledge framework but to learn basic concepts by providing new learning methods and strategies. In addition, it permits students flexibility in applying what they have learned to situations in life.

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Bovell, Carlos R. "Rhetoric More Geometrico in Proclus' Elements of Theology and Boethius' De Hebdomadibus." Thesis, 2007. http://hdl.handle.net/10756/285232.

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My thesis inquires into the reasons behind Proclus' and Boethius' adaptation of discussion more geometrico in their metaphysical works, Elements of Theology and De Hebdomadibus, respectively. My argument is that each philosopher is engaged in a spiritual exercise to the effect that each sought, in his own way, to predispose readers to the anagogical acceptance of profound matters of faith.

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Chen, Hui-Yi, and 陳惠怡. "The influence of knowledge activation and the proposition sequence on geometric argument for sixth-grade elementary school students." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/79kc6j.

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碩士
國立臺北教育大學
數學暨資訊教育學系(含數學教育碩士班)
98
This research investigates the possible ways of developing a geometric argument on the part of sixth-grade elementary school students, through a semi-structural interview pilot study and an experiment. The pilot study included nine students from Taipei for one-on-one interviews through three procedures. 　It was found that elementary school students can manage simple geometric arguments. However, arguments related to congruent triangles were not deemed to be suitable as topics for questions. Also, hands-on operation proved helpful for students to understand the questions and derive relevant arguments. However, if students got used to the paper-folding discourse at the beginning of the activity, perseveration would occur, and would not produce better argument quality. The performance of students’ arguments can be classified into the following categories: “acceptable”, “incomplete”, “inappropriate”, or “stuck”. Having summarized the results, two key points were derived regarding the possible argument- developing paths of students: 1) the ability to bridge knowledge; and 2) the logical arrangement ability. Thus, in the official experiment, “knowledge activation” and “logical arrangement” were both manipulated. The official experiment aimed to determine the influence of language activation and logical arrangement for bridging knowledge on elementary students’ argument performance. The researcher selected 354 students who demonstrated bridging knowledge from the 531 students of four elementary schools in northern Taiwan who had taken the paper tests. Then the teacher further picked 55 talkative students for one-on-one interview. The researcher then conducted One-way ANOVA on the two groups of students’ absorption of knowledge during three stages: before the experiment, in the middle of the experiment and after the experiment. The results revealed that language knowledge activation can successfully help students to absorb bridging knowledge. Students who developed arguments through the use of paper also demonstrated bridging of knowledge, but not as well as the language group did. According to Bowker's test of symmetry, the finding shows that knowledge activation can increase students’ ability to develop a geometric argument, especially in regard to questions which only need bridging knowledge without logical arrangement. If the questions also need logical arrangement, knowledge activation does not help very much. Logical arrangement of bridging knowledge on paper does not help to improve students in developing arguments. The reason is that students need relevant bridging knowledge to help them with logical arrangement. For those students who have bridging knowledge but lack logic, logical arrangement activities can help them to make acceptable arguments.

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Wang, Chien-Chih, and 王建智. "Tracking DNA route on protein structure by knowledge-based learning considering geometric propensity between side chains and bases." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/73386643507864036734.

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碩士
國立臺灣大學
生物產業機電工程學研究所
97
DNA-binding proteins reveal their functions through specific or non-specific protein-DNA recognition. Identifying DNA-binding residues with computational tools facilitates predicting or validating protein functions at a high-throughput rate. The protein-DNA complexes available in Protein Data Bank (PDB) further unveils how a DNA-binding protein recognizes its partners. Such information greatly helps biologists to determine or predict the binding elements in DNA sequences such as transcription factor binding sites (TFBSs). In this way, accurate regulatory networks in whole-genome scale can be constructed more efficiently in the near future. While it remains a challenging task to understand the mechanism of protein-DNA interactions without crystal complex structures, this thesis proposes an algorithm to predict the binding position and direction of DNA when given a known protein structure. First, potential DNA-binding regions of a query protein is predicted by a sequential pattern mining software, MAGIIC-PRO, which identifies functional regions of a protein by discovering concurrent conserved regions among its related protein sequences. After functional regions are predicted, we extract the residues in the protein surface and use hierarchical clustering algorithm to derive potential DNA-binding units, compact conserved regions with high DNA-binding propensity. Afterward, principal component analysis (PCA) is applied on the collected atoms to predict the orientation of DNA grooves. In order to derive the positions where the DNA bases like to be present, we propose a knowledge-based learning procedure to construct a predicting model that considers geometric propensity between protein side chains and DNA bases. The experiments conducted in the thesis reveal that we can predict the orientation of the DNA grooves around the selected conserved regions with satisfied errors. Furthermore, with a well-designed scoring function that incorporates radius basis function (RBF) as the kernel, we build spatial distributions of the positions where DNA bases likes to be present. The computational outputs are expected to provide useful information for many of the next-step analyses such as protein-DNA docking and TFBS predictions.

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YANG, SHUN-HSING, and 楊順興. "Explore the ability of the Students of an University to solve a geometric problem through available information and knowledge." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/56414391401187101086.

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Σοφοτάσιος, Δημήτριος. "Δενδρικές δομές διαχείρισης πληροφορίας και βιομηχανικές εφαρμογές." Thesis, 2007. http://nemertes.lis.upatras.gr/jspui/handle/10889/683.

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H διατριβή διερευνά προβλήματα αποδοτικής οργάνωσης χωροταξικών δεδομένων, προτείνει συγκεκριμένες δενδρικές δομές για τη διαχείρισή τους και, τέλος, δίνει παραδείγματα χρήσης τους σε ειδικές περιοχές εφαρμογών. Το πρώτο κεφάλαιο ασχολείται με το γεωμετρικό πρόβλημα της εύρεσης των ισo-προσανατολισμένων ορθογωνίων που περικλείουν ένα query αντικείμενο που μπορεί να είναι ένα ισο-προσανατολισμένο ορθογώνιο είτε σημείο ή κάθετο / οριζόντιο ευθύγραμμο τμήμα. Για την επίλυσή του προτείνεται μια πολυεπίπεδη δενδρική δομή που βελτιώνει τις πολυπλοκότητες των προηγούμενων καλύτερων λύσεων. Το δεύτερο κεφάλαιο εξετάζει το πρόβλημα της ανάκτησης σημείων σε πολύγωνα. H προτεινόμενη γεωμετρική δομή είναι επίσης πολυεπίπεδη και αποδοτική όταν το query πολύγωνο έχει συγκεκριμένες ιδιότητες. Το τρίτο κεφάλαιο ασχολείται με την εφαρμογή δενδρικών δομών σε δύο βιομηχανικά προβλήματα. Το πρώτο αφορά στη μείωση της πολυπλοκότητας ανίχνευσης συγκρούσεων κατά την κίνηση ενός ρομποτικού βραχίονα σε μια επίπεδη σκηνή με εμπόδια. Ο αλγόριθμος επίλυσης κάνει χρήση μιας ουράς προτεραιότητας και μιας UNION-FIND δομής ενώ αξιοποιεί γνωστές δομές και αλγόριθμους της Υπολογιστικής Γεωμετρίας όπως υπολογισμός κυρτών καλυμμάτων, έλεγχος polygon inclusion, κλπ. Το δεύτερο πρόβλημα ασχολείται με το σχεδιασμό απαιτήσεων υλικών (MRP) σε ένα βιομηχανικό σύστημα παραγωγής. Για το σκοπό αυτό αναπτύχθηκε ένας MRP επεξεργαστής που χρησιμοποιεί διασυνδεμένες λίστες και εκτελείται στην κύρια μνήμη για να είναι αποδοτικός. Το τελευταίο κεφάλαιο εξετάζει το πρόβλημα του ελέγχου της παραγωγής και συγκεκριμένα της δρομολόγησης εργασιών. Στο πλαίσιο αυτό σχεδιάστηκε και υλοποιήθηκε ένα ευφυές σύστημα δρομολόγησης σε περιβάλλον ροής που συνδυάζει γνωσιακή τεχνολογία και προσομοίωση με on-line έλεγχο προκειμένου να υποστηρίξει το διευθυντή παραγωγής στη λήψη αποφάσεων.
Τhe dissertation examines problems of efficient organization of spatial data, proposes specific tree structures for their management, and finally, gives examples of their use in specific application areas. The first chapter is about the problem of finding the iso-oriented rectangles that enclose a query object which can be an iso-oriented rectangle either a point or a vertical / horizontal line segment. A multilevel tree structure is proposed to solve the problem which improves the complexities of the best previous known solutions. The second chapter examines the problem of point retrieval on polygons. The proposed geometric structure is also multileveled and efficient when the query polygon has specific properties. The third chapter is about the application of tree structures in two manufacturing problems. The first one concerns the reduction in the complexity of collision detection as a robotic arm moves on a planar scene with obstacles. For the solution a priority queue and a UNION-FIND structure are used, whereas known data structures and algorithms of Computational Geometry such as construction of convex hulls, polygon inclusion testing, etc. are applied. The second problem is about material requirements planning (MRP) in a manufacturing production system. To this end an MRP processor was developed, which uses linked lists and runs in main memory to retain efficiency. The last chapter examines the production control problem, and more specifically the job scheduling problem. In this context, an intelligent scheduling system was designed and developed for flow shop production control which combines knowledge-based technology and simulation with on-line control in order to support the production manager in decision making.

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Dissertations / Theses on the topic 'Geometrical knowledge'

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