The purpose of this study was to investigate plane geometry problem solving strategies of pre-service elementary mathematics teachers in technology and paper-and-pencil environments after receiving an instruction with GeoGebra. Qualitative research strategies were used to investigate teacher candidates&lsquo / solution strategies. The data was collected and analyzed by means of a multiple case study design. The study was carried out with 7 pre-service elementary mathematics teachers. The main data sources were classroom observations and interviews. After receiving a three-week instructional period, the participants experienced data collection sessions during a week. The data was analyzed by using records of the interviews, answers to the instrument, and transcribing and examining observation records. Results revealed that the participants developed three solution strategies: algebraic, geometric and harmonic. They used mostly algebraic solutions in paper-and-pencil environment and v geometric ones in technology environment. It means that different environments contribute separately pre-service teachers&lsquo / mathematical problem solving abilities. Different from traditional environments, technology contributed students&lsquo / mathematical understanding by means of dynamic features. In addition, pre-service teachers saved time, developed alternative strategies, constructed the figures precisely, visualized them easily, and measured accurately and quickly. The participants faced some technical difficulties in using the software at the beginning of the study but they overcome most of them at the end of instructional period. The results of this study has useful implications for mathematics teachers to use technology during their problem solving activities as educational community encourages to use technology in teaching and learning of mathematics.

Submitted by Milena Rubi (milenarubi@ufscar.br) on 2017-09-27T12:21:25Z No. of bitstreams: 1 CARMO_Rodrigo_2017.pdf: 2234714 bytes, checksum: 3ab51ffaa79e5c6edf2ddbde9dd2ae46 (MD5) / Approved for entry into archive by Milena Rubi (milenarubi@ufscar.br) on 2017-09-27T12:21:37Z (GMT) No. of bitstreams: 1 CARMO_Rodrigo_2017.pdf: 2234714 bytes, checksum: 3ab51ffaa79e5c6edf2ddbde9dd2ae46 (MD5) / Approved for entry into archive by Milena Rubi (milenarubi@ufscar.br) on 2017-09-27T12:21:43Z (GMT) No. of bitstreams: 1 CARMO_Rodrigo_2017.pdf: 2234714 bytes, checksum: 3ab51ffaa79e5c6edf2ddbde9dd2ae46 (MD5) / Made available in DSpace on 2017-09-27T12:21:49Z (GMT). No. of bitstreams: 1 CARMO_Rodrigo_2017.pdf: 2234714 bytes, checksum: 3ab51ffaa79e5c6edf2ddbde9dd2ae46 (MD5) Previous issue date: 2017-03-15 / Não recebi financiamento / In this work we discuss two important movements that are part of the curriculum of the physical discipline of physics in high school, wich are classified as part of a set of phenomena that constitute as an Simple Harmonic Motion (SHM). Namely, the pendulum movement and the projection of uniform circular motion on one of the cartesian axes. In both situations we have a SHM. We have developed dynamic simulations of these phenomena using GeoGebra software. This approach allows user’s, teacher and student, the establish a visual connection between geometry, algebra and the physical concepts present in the studied subjects, it allows interactions that go beyond the conventional simulators, such as having full access to the programming used, allowing user’s to control it at will. We also elaborated two routes of usage, one for each simulator. We applied the simulators in the environment a suggestion of didactic application of our simulators. / Neste trabalho abordamos dois importantes movimentos que fazem parte do currículo da disciplina de Física no ensino médio e são classificados como parte do conjunto de fenômenos que se constituem como um Movimento Harmônico Simples (MHS) . A saber, o movimento pendular e a projeção do movimento circular uniforme sobre um dos eixos cartesianos. Nas duas situações temos um MHS. Desenvolvemos simulações dinâmicas desses fenômenos utilizando o software GeoGebra. Tal abordagem permite ao usuário, professor e estudante, uma conexão visual entre a geometria, a álgebra e os conceitos físicos presentes nos temas estudados, possibilitando interações que vão além dos simuladores convencionais como, por exemplo, ter acesso total à programação utilizada, permitindo ao usuário adaptações e alterações que julgar pertinente. Elaboramos também dois roteiros de utilização, um para cada simulador. Realizamos a aplicação dos simuladores em sala de aula e aqui apresentamos uma sugestão de aplicação didática dos nossos simuladores.

Submitted by Automação e Estatística (sst@bczm.ufrn.br) on 2018-06-05T23:00:29Z No. of bitstreams: 1 EduardoLeandroPeresNogueira_DISSERT.pdf: 1184770 bytes, checksum: 8e017e4e51244b11d253a36bde8dccfb (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2018-06-12T21:58:33Z (GMT) No. of bitstreams: 1 EduardoLeandroPeresNogueira_DISSERT.pdf: 1184770 bytes, checksum: 8e017e4e51244b11d253a36bde8dccfb (MD5) / Made available in DSpace on 2018-06-12T21:58:33Z (GMT). No. of bitstreams: 1 EduardoLeandroPeresNogueira_DISSERT.pdf: 1184770 bytes, checksum: 8e017e4e51244b11d253a36bde8dccfb (MD5) Previous issue date: 2018-04-27 / Este trabalho tem como objetivo analisar o uso da Calculadora Gráfica GeoGebra no Smartphone para o ensino das Funções Exponencial e Logarítmica, verificando a capacidade do aplicativo em conduzir o aluno às definições e algumas propriedades dessas funções e a reflexão, translação vertical e função inversa através da visualização do comportamento dos seus gráficos. Para analisar o aplicativo, foram elaboradas duas atividades com questões discursivas que verificavam a influência de cada parâmetro nos gráficos das funções Exponencial e Logarítmica e foram aplicadas à cinco turmas de 1º ano do Ensino Médio da Escola Estadual Prof. Anísio Teixeira. As respostas obtidas nas atividades e as opiniões dos alunos nos levaram a verificar que a Calculadora Gráfica GeoGebra realmente foi capaz de facilitar a compreensão do conteúdo trabalhado, além de aumentar o interesse dos alunos, sendo uma ferramenta de grande potencial que serve de benefício para o trabalho do docente e para o aprendizado do aluno. / This work aims to analyze the use of the Graphing Calculator GeoGebra on Smartphone in the teaching the Exponential and Logarithmic Functions, verifying the application's ability to lead the student to the definitions of these functions and to the idea of reflection, vertical translation and inverse function by viewing the behavior of their graphs. In order to analyze the application, two activities were elaborated with discursive questions that verified the influence of each parameter on the Exponential and Logarithmic function graphs and were applied to the five classes of the 1st year of High School of the Escola Estudal Prof. Anísio Teixeira. The answers obtained in the activities and the opinions of the students led us to verify that the GeoGebra Graphing Calculator was really able to facilitate the students' comprehension of the worked content, besides increasing the interest of the students, being a tool of great potential that benefits the work of the teacher and the student's learning.

Orientador: Ermínia de Lourdes Campello Fanti / Banca: Evelin Meneguesso Barbaresco / Banca: Ana Paula Tremura Galves / Resumo: O estudo das cônicas (não degeneradas) Elipse, Hipérbole e Parábola é de grande importância não apenas na Matemática mas também em outras áreas afins, como Astronomia e Física. As cônicas estão presentes no nosso cotidiano, podemos encontrá-las, por exemplo, na arquitetura, na natureza, em alguns aparelhos utilizados na medicina e odontologia, em antenas de televisão, em faróis de automóveis, etc. As órbitas dos planetas ao redor do Sol têm formato de Elipses. Este trabalho aborda um estudo das cônicas, incluindo a classificação e uma análise de como esse assunto é tratado no Ensino Médio. Apresenta-se também propostas de atividades experimentais para serem desenvolvidas utilizando o software GeoGebra no estudo das mesmas, bem como o resultado da aplicação para uma turma de alunos da 3ª Série do Ensino Médio de uma escola pública estadual. Espera-se que as atividades aqui propostas possam contribuir para o estudo das cônicas no Ensino Médio, podendo ser utilizadas e adaptadas pelos professores da Educação Básica para serem desenvolvidas com os alunos, no Laboratório de Informática, de acordo com o nível de ensino e o conhecimento dos seus alunos / Abstract: The study of the conics (not degenerated) Ellipse, Hyperbole and Parabola is of great importance not only in mathematics but also in other related areas, such as Astronomy and Physics. Conics are present in the our everyday life, we can find them, for example, in architecture, in some apparatus used in medicine and dentistry, television antennas, Car headlights, etc. The orbits of the planets around the Sun are shaped like Ellipses. This work approaches a study of the conics, including classification and an analysis of how this subject is treated in High School. It also presents proposals for experimental activities to be developed using software GeoGebra in their study, as well as the result of the application for a class of students in the 3 rd Grade of High School of one public school of the state. It is hoped that the activities proposed here may contribute in the study of conics in High School, and may be used and adapted by teachers of Basic Education to be developed with the students, in the Laboratory of Informatics, according to the level of education and the knowledge of its students / Mestre

Submitted by Raniere Barreto (raniere.barros@ufvjm.edu.br) on 2018-04-11T19:02:13Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) lincoln_ferreira_nunes.pdf: 15147355 bytes, checksum: 2fa1f34defc7c2b96c3429455de8add1 (MD5) / Approved for entry into archive by Rodrigo Martins Cruz (rodrigo.cruz@ufvjm.edu.br) on 2018-04-20T14:19:37Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) lincoln_ferreira_nunes.pdf: 15147355 bytes, checksum: 2fa1f34defc7c2b96c3429455de8add1 (MD5) / Made available in DSpace on 2018-04-20T14:19:37Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) lincoln_ferreira_nunes.pdf: 15147355 bytes, checksum: 2fa1f34defc7c2b96c3429455de8add1 (MD5) Previous issue date: 2017 / Este trabalho relaciona a utiliza??o da Modelagem Matem?tica no processo de ensino-aprendizagem das fun??es exponenciais e logar?tmicas nos primeiros anos do Ensino Superior, com possibilidades de aplica??o no Ensino M?dio. Inicialmente, relacionou-se a import?ncia das fun??es supracitadas na descri??o de fen?menos das ci?ncias em geral. Em seguida, ap?s an?lise sobre os livros did?ticos, detectou-se defici?ncias em rela??o ? contextualiza??o do estudo das referidas fun??es nestes livros. Para propor sequ?ncias did?ticas que auxiliassem a suprir as lacunas desta contextualiza??o utilizou-se a Modelagem Matem?tica, com aux?lio do software GeoGebra. Para analisar a utiliza??o das sequ?ncias did?ticas propostas, foi escolhida a Engenharia Did?tica como metodologia de pesquisa. Finalmente, ap?s planejadas as sequ?ncias did?ticas, as interven??es did?ticas foram realizadas, tendo como p?blico-alvo um grupo de estudantes do curso de Bacharelado em Ci?ncia e Tecnologia do Campus Mucuri da Universidade Federal dos Vales do Jequitinhonha e Mucuri. Ao final das interven??es, question?rios e relatos produzidos foram analisados, em rela??o ao cumprimento do objetivo inicial da pesquisa. Constatou-se ao final das an?lises dos resultados obtidos, um progresso expressivo dos estudantes em rela??o ? compreens?o da utiliza??o das fun??es supracitadas nas ci?ncias. / Disserta??o (Mestrado Profissional) ? Programa de P?s-Gradua??o Matem?tica, Universidade Federal dos Vales do Jequitinhonha e Mucuri, 2017. / This work relates the use of Mathematical Modeling in the teaching-learning process of exponential and logarithmic functions in College Education, With possibilities of application in High School. The importance of the above-mentioned functions in phenomenas description in general was initially related. Then, after analyzing the textbooks, deficiencies were detected in relation to the contextualization of the study of these functions in these books. In order to propose didactic sequences that helps to fulfil the gaps of this contextualization, Mathematical Modelling with the help of software GeoGebra was used. In order to analyze the use of the proposed didactic sequences, Didactic Engineering was chosen as a research methodology. Finally, after the didactic sequences were planned, the didactic interventions were carried out targeting a group of students from the Bachelor?s Degree in Science and Technology of the Mucuri Campus of the Federal University of the Jequitinhonha and Mucuri Valleys. At the end of the interventions, the questionnaires and reports produced were analyzed in relation to the accomplishment of the initial objective of the research. At the end of the analysis of the reports and questionnaires, a very significant progress was made by the students in understanding the use of these functions in the sciences.

Modern information technologies accompany all of us in our daily life. They not only use to serve to our work and for the entertainment, they even have got a great potential to be used in the education. The submitted thesis deals with the appropriate utilization of the special IT application in the pedagogic process, especially in teaching of maths, the topic of trigonometric functions. The aim of this thesis is to create structures with a high potential of the modern technology handling. To tackle this task the graphical program GeoGebra was chosen due to its qualities for creating dynamic structures and the other advantages presented further in the thesis. To the created constructions the detailed instructions how they can be constructed are added. The thesis is also accompanied by worksheets with solved tasks, focusing on the application of trigonometric functions in real situations.

Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-11-12T20:05:27Z No. of bitstreams: 1 EDSON BERNARDO DE OLIVEIRA – DISSERTAÇÃO (PPGMat) 2014.pdf: 20218452 bytes, checksum: c593530a3d5fc5bf24210de8f9a493e2 (MD5) / Made available in DSpace on 2018-11-12T20:05:27Z (GMT). No. of bitstreams: 1 EDSON BERNARDO DE OLIVEIRA – DISSERTAÇÃO (PPGMat) 2014.pdf: 20218452 bytes, checksum: c593530a3d5fc5bf24210de8f9a493e2 (MD5) Previous issue date: 2014-03 / Capes / No âmbito do ensino de geometria as possibilidades do uso de recursos tecnológicos no processo de ensino são imensas. Os softwares de geometria dinâmica surgem como um instrumento propício para auxiliar o professor em sua prática pedagógica e contribuir com o processo de aprendizagem dos alunos, apresentando novos meios para o entendimento de conceitos e propriedades geométricas. Além disso, cabe observar que na educação básica pública existe certa dificuldade em se ensinar todos os tópicos de geometria pelo fato de o currículo escolar ser bastante abrangente (não condizendo com o tempo dedicado à disciplina de matemática) e a parte dedicada à geometria aparecer nos últimos capítulos na maioria dos livros didáticos. Observando estes aspectos, realizamos um estudo do círculo e suas propriedades planas utilizando o software GeoGebra, oferecendo aos alunos a possibilidade de investigar problemas, levantar hipóteses e propor soluções, proporcionando a eles meios para a realização de um aprendizado significativo da matemática, tornando-os agentes do processo de construção do próprio conhecimento. Por fim, apresentamos um relato de experiência das atividades didáticas propostas aplicadas em uma turma da segunda série do ensino médio. / In the context of geometry teaching the possibility of the use of technological resources in the teaching process is immense. The dynamic geometry software emerge as an enabling tool to assist teachers in their teaching practice and contribute to students learning process,presenting new ways for understanding concepts and geometrical properties. Furthermore, it is worth noting that in the public basic education there is some difficulty in teaching all topics in geometry because the school curriculum is very comprehensive (not befitting the time devoted to the discipline of mathematics) and the part dedicated to geometry appears in the last chapters in most textbooks. Observing these aspects, we conducted a study circle and its flat properties using the software GeoGebra, offering students the opportunity to investigate problems, raise hypotheses and propose solutions, giving them the means to achieve a meaningful learning of mathematics, making them actors of the construction process of their own knowledge. Finally, we present an experience report of the educational activities implemented in a second grade class of high school.

Este estudo descreve momentos da investigação de um trabalho aplicado em uma turma de uma escola da rede privada de ensino de Florianópolis. Aborda o estudo dos Sistemas de Equações Lineares de Duas Variáveis no Ensino Fundamental. Apresenta uma revisão do conteúdo na forma como se encontra nos livros didáticos, seguido da aplicação de uma sequência didática que inverte a forma de se trabalhar o conteúdo, dando enfoque geométrico para a solução dos sistemas de equações. A fundamentação teórica foi baseada nas Representações Semióticas e no uso de Tecnologias na Educação, acreditando, por meio da teoria de Duval, que a chave para o aprendizado do objeto matemático está nas conversões. Para o desenvolvimento dessa sequência, fez-se uso do software livre Geogebra. Finaliza com as considerações sobre os resultados obtidos com a aplicação da sequência didática proposta nesse trabalho. Apresenta Apêndice com o produto final, sugerindo que outros professores façam uso da mesma para o ensino desse conteúdo. / This study describes the stages of the research work applied to a class in a private school education in Florianopolis. Approaches the study of Systems of Linear Equations in Two Variables in Elementary Education. Presents a review of the content in the way it is in textbooks, followed by the application of an instructional sequence that reverses the way to work content, giving geometric approach to solving systems of equations. The theoretical framework was based on representations Semiotics and the use of technology in education, believing, through the theory of Duval, the key to learning the mathematical object is in conversions. For the development of this sequence, made use of free software Geogebra. Concludes with considerations about the results obtained from the application of instructional sequence proposed in this work. Appendix presents with the final product, suggesting that other teachers make use of it for teaching that content.

This work thesis is dealing with planar mechanisms. It?s concentrated on definition the topic, enumeration methods of mathematical description of mechanisms and occasion of simulation with usage information technology. It?s going mainly on GeoGebra program, in which were created most of schemes and models mechanisms. Created models are recorded on attached CD. Important charter of this theses are mechanisms used to draving planar curves, ending with mechanisms used to drawing straight line.

This diploma thesis is due to its theme within the reach of two scientific branches mathematics and geography. Particularly, it deals with possibilities of unusual application of dynamic geometry during lessons of geography in elementary schools. From the theoretical point of view, the thesis is grounded in the crucial document for czech schooling Framework Education Programme for Elementary Education. The theoretical part of the thesis is followed by practical part, whose content is influenced by analysis of Geography as an educational area, which can be found in this very document. The particular contents of the practical part consist applets describing selected geographic phenomenons and problems.