Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-06-09T14:09:14Z No. of bitstreams: 1 thalesdelelismartinspereira.pdf: 3405119 bytes, checksum: b6f2b4bea030a18701a92259f9dd2c73 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-07-13T13:33:50Z (GMT) No. of bitstreams: 1 thalesdelelismartinspereira.pdf: 3405119 bytes, checksum: b6f2b4bea030a18701a92259f9dd2c73 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-07-13T13:34:07Z (GMT) No. of bitstreams: 1 thalesdelelismartinspereira.pdf: 3405119 bytes, checksum: b6f2b4bea030a18701a92259f9dd2c73 (MD5) / Made available in DSpace on 2016-07-13T13:34:07Z (GMT). No. of bitstreams: 1 thalesdelelismartinspereira.pdf: 3405119 bytes, checksum: b6f2b4bea030a18701a92259f9dd2c73 (MD5) Previous issue date: 2012-09-25 / A partir da questão „Como se dá a interação entre professor e alunos em um ambiente colaborativo de geometria para o ensino fundamental e médio a partir da utilização do software geogebra?‟, a pesquisa realizada teve como objetivo analisar as atividades realizadas pelos alunos em sala de aula com o acompanhamento do professor. Foi adotada a pesquisa qualitativa, de modo a verificar o aprendizado do conteúdo relativo à geometria dinâmica, por meio das atividades investigativas entre professor e alunos. Realizaram-se sessões plenárias com os alunos, nas quais demonstraram segurança quanto aos conceitos adotados durante a realização da pesquisa. / From the question „How is the interaction between teacher and students in a colaborative environment of geometry to the primary and secondary levels of teaching by using the geogebra software?‟ the research aimed at analyzing the activities performed by the students inside the classroom with the follow-up of the teacher. The research is qualitative in order to verify the learning of the content on the dynamic geometry, by means of the investigative activities performed. In the plenary sessions the students demonstrated self-security concerning the concepts adopted during the research.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-02-23T11:16:17Z No. of bitstreams: 1 josemiltonlopespinheiro.pdf: 3545415 bytes, checksum: 28d969f5a311f65e5378cc7bdf9acfcc (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-02-23T12:03:40Z (GMT) No. of bitstreams: 1 josemiltonlopespinheiro.pdf: 3545415 bytes, checksum: 28d969f5a311f65e5378cc7bdf9acfcc (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-02-23T12:03:54Z (GMT) No. of bitstreams: 1 josemiltonlopespinheiro.pdf: 3545415 bytes, checksum: 28d969f5a311f65e5378cc7bdf9acfcc (MD5) / Made available in DSpace on 2017-02-23T12:03:54Z (GMT). No. of bitstreams: 1 josemiltonlopespinheiro.pdf: 3545415 bytes, checksum: 28d969f5a311f65e5378cc7bdf9acfcc (MD5) Previous issue date: 2013-12-12 / O presente estudo pretende lançar luz à proposta de trabalho com professores de matemática no empenho sobre atividades exploratórias e investigativas, tematizadas no tratamento de temas de Geometria Analítica Plana. Utilizamos como suporte à pesquisa, a Teoria da Aprendizagem Significativa (TAS) concebida por David Ausubel. Direcionamos olhares qualitativos aos sujeitos ao considerarmos o espaço e a temporariedade de suas experiências vividas. Fizemos convergências da TAS à Fenomenologia e utilizamos das mesmas como suporte metodológico para tratamento de todo o processo que resultou nas análises. Utilizamos das tecnologias informatizadas para subsidiar as interações presenciais e virtuais, oportunizando o dinamismo e a colaboratividade do ambiente Virtual Math Teams with Geogebra (VMTwG) e do software Geogebra. Mediante percepção e descrição dos manifestos explícitos e implícitos dos sujeitos, é colocado em crise o que interroga nossa questão diretriz, buscamos e estruturamos compreensões do que se mostrou nas interações. Lançamos olhares analítico-reflexivos ao todo que tínhamos e intencionamos unidades nucleares: manifestos característicos do empenho dos sujeitos enquanto membros de um grupo colaborativo; manifestos que indicam a postura de sujeitos que exploram e investigam; aplicação de pensamentos em Geometria Dinâmica (GD) e do software de GD, e Manifestos que sugestionam a presença de aspectos tais como os da Teoria da Aprendizagem Significativa. Apoiamo-nos nestas unidades para apresentar o que entendemos serem compreensões do fenômeno interrogado que propiciam argumentos estruturados para tratamento de nossa questão diretriz. / The present study aims to highlight the proposal on mathematics teachers at commitment about investigative and exploratory activities, themed in the treatment of analytic geometry topics. We use as support to research, meaningful learning theory (TAS) designed by David Ausubel. We direct qualitative looks to the subject when we consider the space and the tentativeness of their experiences. We did the convergences of TAS to Phenomenology and use thereof as methodological support for treating the whole process which resulted in the analyses. We use computer technologies to support face-to-face and virtual interactions, enabling the dynamism and the colaboratividade of the environment Virtual Math Teams with Geogebra (VMTwG) and the software Geogebra. By perception and description of explicit and implicit manifests the subjects, that is placed in the crisis that interrogates our question guideline. We seek and structure the understandings that have showed the interactions. Analytical and reflective looks launched altogether, which had and plan nuclear units: characteristic manifests the subject commitment while members of a collaborative group; manifests indicating the posture of subjects that explore and investigate; application of thoughts on Dynamic Geometry (GD) and GD software, and Manifests that suggest the presence of aspects such as the theory of meaningful learning. We support these units to present what we believe to be the understandings phenomenon questioned that provide structured arguments for treating our question guideline.

Denna undersökning syftar till att belysa vad som motiverar gymnasieelever att använda GeoGebra i matematiken. Vidare undersöktes även eventuella skillnader i motivation, både typ och grad, hos gymnasieelever som använder GeoGebra ofta respektive sällan i matematiken. Undersökningen grundar sig i motivationsteori och specifikt förväntan-värde teorin och utfördes med kvantitativa- och kvalitativa metoder. Datainsamlingen skedde med en enkät vilken besvarades av 72 gymnasieelever från fyra skolor i Norrbottens län, Stockholms län och Västra Götalands län. Resultatet från undersökningen visar att gymnasieelever främst motiveras av nytto- och kostnadsvärdet som GeoGebra medför. Med andra ord, att GeoGebra ger dem fördelar i matematiken genom att göra det enklare och mer tidseffektiv att hantera matematikproblem med hjälp av GeoGebra. Vidare så visade även resultatet att gymnasieelever som använder GeoGebra ofta motiverades mer av nyttan som verktyget medförde, än gymnasieelever som använder GeoGebra sällan motiverades av det. / The focus of this research was to enlighten what motivates high school students to make use of GeoGebra in mathematics studies. The research also aimed at finding out if there were any differences in motivation, both type and degree, between high school students who used GeoGebra frequently or rarely in mathematics studies. The study was based on motivational theory and more specific expectancy-value theory and used quantitative- and qualitative methods. The data collection was through a survey in which 72 high school students from four schools in Norrbottens county, Stockholms county and Västra Götalands county participated. The result from this study showed that the main reason why high school students are motivated to use GeoGebra in their mathematics studies is because of the utility and cost value the instrument entails. In other means, high school students use the programme because it's easier and more time efficient to solve mathematical problems with it. The study also showed that high school students who use GeoGebra more frequently in mathematics studies are more motivated by the utility value that the instrument brings, than high school students who only use GeoGebra sometimes were.

For many students, mathematics, traditionally thought to be difficult and dull, is often considered inaccessible, generating a negative attitude towards it. In order to encourage a positive attitude towards mathematics, we propose class practices that, through research activities, will lead the students to experiment a similar path to the one that has given, as a final product, a structured theory, so as to enhance their self-efficacy, give a correct vision of the discipline and stimulate positive emotions. This can be realized, for example, as a “laboratory activity” in which the students compare ideas, intuitions, arguments, and work together to obtain results, using their critical capabilities in a collaborative learning activity. A team of university professors and high school teachers has developed a laboratory activity that focuses on some properties of quadrilaterals. The activity has at any rate been experimented in different first biennium classes of some high schools and has obtained very good results.

The subject of teacher competencies or knowledge has been a key issue in mathematics education reform. This study attempts to identify and analyze teacher competencies necessary in the orchestration of a problem-centred approach to dynamic geometry teaching and learning. The advent of dynamic geometry environments into classrooms has placed new demands and expectations on mathematics teachers. In this study the Teacher Development Experiment was used as the main method of investigation. Twenty third-year mathematics major teachers participated in workshop and microteaching sessions involving the use of the Geometer's Sketchpad dynamic geometry software in the teaching and learning of the geometry of triangles and quadrilaterals. Five intersecting categories of teacher competencies were identified: mathematical/geometrical competencies. pedagogical competencies. computer and software competences, language and assessment competencies. / Mathematical Sciences / M. Ed. (Mathematical Education)

The subject of teacher competences or knowledge has been a key issue in mathematics education reform. This study attempts to identify and analyze teacher competences necessary in the orchestration of a problem-centred approach to dynamic geometry teaching and learning. The advent of dynamic geometry environments into classrooms has placed new demands and expectations on mathematics teachers. In this study the Teacher Development Experiment was used as the main method of investigation. Twenty third-year mathematics major teachers participated in workshop and microteaching sessions involving the use of the Geometer’s Sketchpad dynamic geometry software in the teaching and learning of the geometry of triangles and quadrilaterals. Five intersecting categories of teacher competences were identified: mathematical/geometrical competences, pedagogical competences, computer and software competences, language and assessment competencies. / Mathematics Education / M. Ed. (Mathematics Education)

Text in Afrikaans / Real empowerment of school learners requires preparing them for the age of technology. This empowerment can be achieved by developing their higher-order thinking skills. This is clearly the intention of the proposed South African FET National Curriculum Statements Grades 10 to 12 (Schools). This research shows that one method of developing higher-order thinking skills is to adopt an integrated curriculum approach. The research is based on the assumption that an integrated curriculum approach will produce learners with a more integrated knowledge structure which will help them to solve problems requiring higher-order thinking skills. These assumptions are realistic because the empirical results of several comparative research studies show that an integrated curriculum helps to improve learners' ability to use higher-order thinking skills in solving nonroutine problems. The curriculum mentions four kinds of integration, namely integration across different subject areas, integration of mathematics with the real world, integration of algebraic and geometric concepts, and integration into and the use of dynamic geometry software in the learning and teaching of geometry. This research shows that from a psychological, pedagogical, mathematical and historical perspective, the theme conic sections can be used as an integrating factor in the new proposed FET mathematics curriculum. Conics are a powerful tool for making the new proposed curriculum more integrated. Conics can be used as an integrating factor in the FET band by means of mathematical exploration, visualisation, relating learners' experiences of various parts of mathematics to one another, relating mathematics to the rest of the learners' experiences and also applying conics to solve real-life problems. / Mathematical Sciences / D.Phil. (Wiskundeonderwys)

La géométrie à l'école primaire consiste en une familiarisation avec des formes géométriques et leurs propriétés, à travers l'utilisation d'instruments de géométrie. Les objets géométriques reposent sur les représentations graphiques, les relations géométriques sont souvent implicites. L'introduction d'un logiciel de géométrie dynamique (TracenPoche) est vu comme un moyen de les expliciter, conduisant ainsi à voir le dessin comme une figure. Nous avons proposé à des professeurs une série de cinq situations, que nous avons conçues à partir des modes d'intégration de Assude (2007). Nous en proposons une analyse a priori en trois temps (Assude et Mercier, 2007), une analyse a priori du point de vue des savoirs mathématiques, une analyse a priori ascendante du point de vue des actions des élèves modélisée en terme de praxéologie (Chevallard, 1998) et une analyse a priori du point de vue de l'enseignant. Les situations mises en oeuvre dans les classes sont décrites et analysées à l'aide d'éléments de la théorie de l'action conjointe en didactique (TACD, Sensevy, 2011). Nous décrivons l'action conjointe du professeur et des élèves comme un jeu du professeur sur l'élève, permettant ainsi de rendre compte de la dynamique du travail didactique et de l'évolution du « voir un dessin comme une figure ». Les résultats de la thèse, dans le cadre de cette ingénierie exploratoire (Perrin-Glorian, 2009), montrent comment les objets géométriques peuvent être travaillés conjointement dans l'environnement papier-crayon et dans l'environnement tracenpoche, mettant en évidence des caractéristiques de l'action conjointe du professeur et des élèves dans l'explicitation des relations géométriques. / Geometry in primary school is a familiarization with geometric shapes and their properties through the use of geometrical instruments. Geometric objects are based on diagrams and the geometric relationships are often implicit. The introduction of a dynamic geometry software (here TracenPoche) is thus a way to explain how to see « the diagram » as « a figure ». Five situations are given to three teachers. We have built them with « integration modes » from Assude (2007). We proposed an a priori analysis in three stages (Assude and Mercier, 2007), the first a priori analysis - the viewpoint of mathematical knowledge - , the second a priori analysis - students action modelized by the praxeology (Chevallard, 1998) - and the third a priori analysis - the teacher's point of view - . The Situations established in classrooms are described and analyzed using elements of the joint action theory (Sensevy, 2011). We describe the joint action of the teacher and students as a game of the teacher on the student, thereby enabling an analysis of the dynamic of the teaching work and of the evolution of the "seeing a diagram as a figure." The results of this thesis, as part of the exploratory engineering (Perrin-Glorian, 2009), show how geometrical objects can be worked jointly in a paper-and-pencil environment and in a Tracenpoche environment, highlighting the characteristics of the joint action of the teacher and students in the explanation of geometric relationships. The teachers demonstrate initiatives that prove particularly interesting with regard to mathematical issues, and which could be the basis for further research in cooperative engineering (Sensevy & al., 2013).

Made available in DSpace on 2016-04-27T16:58:22Z (GMT). No. of bitstreams: 1 ivanildo desp.pdf: 6867880 bytes, checksum: f543f759303d555b6a8c5534e0ec35bd (MD5) Previous issue date: 2007-06-04 / This study, inserted in the theme of the use of digital teachnologies within Mathematics Education, discusses the teaching and learning of proof. It aims to investigate an approach to proof in geometry with its basis in geometrical constructions using the software Cabri-Géomètre. With this aim in mind, a teaching experiment involving students from the 7th grade of school from the public school system of the state of São Paulo was conducted. The experiment was carried out in two phases: the design phase and the analysis phase. In the design phase, three sets of activities were created and tested, two involved use of the dynamic geometry software, will the thirds was paper and pencil based. The dynamic geometry activities were inspired by Mascheroni´s geometry of the compass. During the analysis phase, Balacheff´s notions related to types of proof produced by students (pragmatic and conceptual) were employed (BALACHEFF, 1987, 1988). Through the medium of the dynamic geometry activities, the study sought to explore not only the impact of the dynamism but also how the availability of different tools for the solution of the same problem influenced students´ strategies and thinking. The activities drew from the possibilities associated with geometrical constructions, in terms of aspects inductive and deductive proofs as well as movements between these two poles. Results points to how the use of Cabri encouraged students to at least give attention to empirical verifications of geometrical proprieties within the constructed figures, but may also have contributed to the tendency to focus more on constructions and descriptions than on justifications. Another notable result relates to students´ difficulties with the notion of robust construction, indicating that the screen of Cabri is frequently confused with the paper and pencil environment / Este trabalho, inserido na temática do uso de tecnologias digitais, discute o ensino e aprendizagem da prova. O objetivo é investigar uma abordagem para a prova em geometria, tomando por objeto de estudo as construções geométricas no ambiente do Cabri-Géomètre. A fim de alcançar o objetivo proposto, foi elaborado um experimento de ensino envolvendo estudantes de uma 7ª série da rede pública estadual de São Paulo. Este experimento foi formado por duas fases, o design e a análise das atividades. Na fase de design, foram criados e aplicados três conjuntos de atividades, sendo um deles fora do ambiente do Cabri. As atividades tinham como uma inspiração a geometria do compasso (MASCHERONI, 1980). Para a fase de análise, buscou-se apoio na teoria de Balacheff (1987,1988) sobre as categorias de provas produzidas pelos aprendizes: pragmáticas e conceituais. Por meio das atividades desenvolvidas com o Cabri, além dos aspectos dinâmicos deste software, procurou-se explorar os diferentes tipos de ferramentas para a resolução de um mesmo problema proposto. Enfatizou-se, em grande parte das tarefas com construções geométricas, não apenas os aspectos indutivo e dedutivo das provas, mas também possíveis movimentos do primeiro rumo ao segundo. Um dos principais resultados obtidos aponta que o Cabri é bastante sugestivo aos aprendizes no sentido de que tende a facilitar as verificações empíricas de propriedades geométricas nas figuras e, além disso, em grande medida, se centram mais nas tarefas de construções e descrição que nas de justificativas. Outro resultado importante diz respeito às dificuldades dos aprendizes com a noção de construção robusta, indicando que a tela do Cabri é confundida, muitas vezes com o ambiente do lápis e papel

Made available in DSpace on 2016-04-27T16:58:49Z (GMT). No. of bitstreams: 1 ADRIANA MARIA COZZOLINO.pdf: 4568146 bytes, checksum: 0e32b55df54f9d137d6bfb0530e21ca9 (MD5) Previous issue date: 2008-12-19 / Secretaria da Educação do Estado de São Paulo / This work is inserted in the context of teaching-learning Spatial Geometry in Basic Education, in particular, teaching Perspective by High School students and the relations between three-dimensional objects and their representations in the plain. We have used the dynamic geometry environment, CABRI 3D, considering the limitations existing of the paper and pencil environment. The difficulties of students in relation to three-dimensional representations into two-dimensional environment, were researched by Parzysz (1988, 1989, 1991, 2001), and our work was basis in his theoretical Geometry presuppositions. Our aim is verify how the education of the perspective can help students to change or to articulate different points of view of three-dimensional geometric object. Besides, to notice how CABRI 3D can contribute with them, so that they will articulate the real image and its representations. Design Experiments was adopted as the methodology of this work. It was developed by Steffe and Thompson (2000), Doerr and Wood (2000), Cobb et al (2003) and Collins et al (2004). High School students of a private school of the state of São Paulo participated in this work. Their productions showed that the changes between the paper and pencil (static) environment and the dynamic geometry environment CABRI 3D, contributed so that the students mobilize and articulate knowledge between the image and its representations. Finally, we pretend that this work was used as a tool to enlarge the visualization capacity and to sensitize the look of the students for the representations perspective of three-dimensional objects / A presente pesquisa está inserida no contexto do ensino-aprendizagem da Geometria Espacial na Educação Básica, referindo-se, em particular, ao ensino da Perspectiva para alunos do Ensino Médio e as relações entre os objetos tridimensionais e suas representações no plano. Optamos por utilizar o ambiente de geometria dinâmica CABRI 3D, considerando as limitações no ambiente convencional papel e lápis. As dificuldades dos alunos com relação à representação plana de objetos espaciais são tratados por Parzysz (1988, 1989, 1991, 2001) e estes estudos serviram como referencial teórico para a nossa pesquisa. Procuramos verificar em que medida o ensino da perspectiva pode auxiliar o aluno a mudar ou articular diferentes pontos de vista sobre um objeto geométrico tridimensional e de que forma o CABRI 3D pode contribuir para que articulem a imagem real e suas representações. A metodologia utilizada foi o Design Experiments, fundamentada nos autores Steffe e Thompson (2000), Doerr e Wood (2000), Cobb et al (2003) e Collins et al (2004). Participaram do estudo alunos do Ensino Médio de uma escola particular da cidade de São Paulo. As produções dos alunos mostraram que as variações entre o ambiente papel e lápis (estático) e ambiente de geometria dinâmica CABRI 3D, contribuíram para que eles mobilizassem seus conhecimentos e articulassem entre a imagem e suas representações. Este trabalho foi utilizado como uma ferramenta para ampliar a capacidade de visualização e sensibilizar o olhar dos alunos para as representações em perspectiva, de objetos espaciais