Submitted by Jean Medeiros (jeanletras@uepb.edu.br) on 2018-04-05T13:20:54Z No. of bitstreams: 2 PDF - Joselito Elias de Araújo.pdf: 25369771 bytes, checksum: 7eefe0bbabb3d67d3ef96a5f039a086e (MD5) Produto - Joselito Elias de Araújo.pdf: 9697110 bytes, checksum: 5c9167e526b9351119be777143870415 (MD5) / Approved for entry into archive by Secta BC (secta.csu.bc@uepb.edu.br) on 2018-04-10T15:08:56Z (GMT) No. of bitstreams: 2 PDF - Joselito Elias de Araújo.pdf: 25369771 bytes, checksum: 7eefe0bbabb3d67d3ef96a5f039a086e (MD5) Produto - Joselito Elias de Araújo.pdf: 9697110 bytes, checksum: 5c9167e526b9351119be777143870415 (MD5) / Made available in DSpace on 2018-04-10T15:08:56Z (GMT). No. of bitstreams: 2 PDF - Joselito Elias de Araújo.pdf: 25369771 bytes, checksum: 7eefe0bbabb3d67d3ef96a5f039a086e (MD5) Produto - Joselito Elias de Araújo.pdf: 9697110 bytes, checksum: 5c9167e526b9351119be777143870415 (MD5) Previous issue date: 2017-11-27 / The discipline of Mathematics is considered to be the most difficult for some students. There are several reasons to justify school failure in learning this content. The difficulty that the students have in understanding Mathematics due to its abstract character deserves, in the present work, a highlight. Thus, we consider the importance of solving mathematical problems, from which we can: use knowledge of the students' daily life as a starting point for the development of their knowledge; Teach mathematics from a meaningful point of view and arouse interest in mathematics. Therefore, in the present work we have as objective: To analyze what are the contributions that Raymond Duval's theory, regarding the study of the Registers of Semiotic Representations, has for a better performance of students in OBMEP. For this, we are resorting to a qualitative research, which until the present moment reveals some results, such as: a higher frequency of the registration of semiotic representation of the natural and symbolic numerical language in the answers of the subjects of the research. / A disciplina de Matemática é tida como a mais difícil para alguns alunos. Vários são os motivos para justificar o fracasso escolar na aprendizagem desse conteúdo. A dificuldade que os alunos têm em compreender a Matemática em função do seu caráter abstrato merece, no presente trabalho, destaque. Assim, consideramos a importância da resolução de problemas matemáticos, a partir dos quais, possamos: utilizar conhecimentos do cotidiano do aluno como ponto de início para o desenvolvimento de seus conhecimentos; ensinar Matemática do ponto de vista significativo e despertar o interesse pela Matemática. Portanto, no presente trabalho temos como objetivo: analisar quais são as contribuições que a teoria de Raymond Duval, relativo ao estudo dos Registros das Representações Semióticas, tem para um melhor desempenho de alunos na OBMEP. Para isso, estamos recorrendo a uma pesquisa de cunho qualitativa, que até o presente momento revela alguns resultados, tais como: uma frequência maior do registro de representação semiótica da linguagem natural e simbólica numérica nas respostas dos sujeitos da pesquisa.

Thesis (Ph. D.)--University of California, Riverside, 2009. / Includes abstract. Includes bibliographical references (leaves 83-98). Issued in print and online. Available via ProQuest Digital Dissertations.

Submitted by Jean Medeiros (jeanletras@uepb.edu.br) on 2017-02-14T11:59:32Z No. of bitstreams: 1 PDF - Andriely Íris Silva de Araújo.pdf: 3453817 bytes, checksum: b00ec8c89a08b93e7c9d42f674a2973b (MD5) / Approved for entry into archive by Secta BC (secta.csu.bc@uepb.edu.br) on 2017-03-07T16:45:02Z (GMT) No. of bitstreams: 1 PDF - Andriely Íris Silva de Araújo.pdf: 3453817 bytes, checksum: b00ec8c89a08b93e7c9d42f674a2973b (MD5) / Made available in DSpace on 2017-03-07T16:45:02Z (GMT). No. of bitstreams: 1 PDF - Andriely Íris Silva de Araújo.pdf: 3453817 bytes, checksum: b00ec8c89a08b93e7c9d42f674a2973b (MD5) Previous issue date: 2016-12-19 / After a reflection on learning difficulties the basic principles of algebra in the understanding and appropriation of idea and concepts, felt the need to seek a methodology to propose a better learning of students. This is the main objective of this work is to identify how the teaching-learning methodology of Mathematics through Problem Solving and Exploration enables the understanding and concepts ranging from the generalization of the standards to the solving of First Degree Polynomial Equations. Considering that this methodology aims to develop a more focused work for students because the problem generation part for acquiring new mathematical concepts promote a more additive participation of students in the process of knowledge construction. From the moment the student is raised to expose his ideas and thoughts becoming the center of development and construction of knowledge, under the care of teacher who now has the function of mediation, help build a bridge between the student already know what do you want to know. The research methodology used is qualitative on the method of teacher research (LANKSHEAR & KNOBEL, 2008) where the teacher researches mainly his/her own classroom and whose object of research flows from questions, problems or authentic concerns of the teacher–researcher himself/herself. The classroom work was developed in a seventh grade class of elementary school of a public school in the municipality of Itatuba, PB, Brazil. In working with the methodology of problem solving and exploration there is a greater motivation of the students to question the reflection of the discussed idea, the relevance of the adopted methodology, which allowed a greater understanding of Algebra, in order to minimize the difficulties presented by the students. Where the teacher researches, above all, his own classroom and whose object of research flows from questions, problems or authentic concerns of the teacher himself. / Após uma reflexão sobre as dificuldades da aprendizagem dos princípios básicos da Álgebra na compreensão e apropriação de ideias e conceitos, sentiu-se a necessidade de buscar uma metodologia que propusesse uma melhor aprendizagem dos alunos. Desse modo, o objetivo principal deste trabalho é identificar como a metodologia de Ensino- Aprendizagem de Matemática através da Resolução e Exploração de Problemas possibilita o entendimento de ideias e conceitos que vão desde a generalização de padrões até a resolução de Equações Polinomiais do Primeiro Grau. Tendo em vista que essa metodologia visa desenvolver um trabalho mais centrado nos alunos, pois parte de problemas geradores para a aquisição de novos conceitos matemáticos, promovendo assim uma participação mais ativa dos alunos no processo de construção do conhecimento. A partir do momento que o aluno é elevado a expor suas ideias e pensamentos, tornado se o centro do desenvolvimento e da edificação do conhecimento, sob o olhar cuidadoso do professor, que nesse momento tem o papel de mediar, ajudando a construir uma ponte entre o que o aluno já sabe e o que deseja saber. A metodologia de pesquisa usada é de caráter qualitativo na modalidade de pesquisa pedagógica (LANKSHEAR & KNOBEL, 2008) onde o professor pesquisa, sobretudo, sua própria sala de aula e cujo objeto da pesquisa flui de questões, problemas ou preocupações autênticas do próprio professor - pesquisador. O trabalho de sala de aula foi desenvolvido em uma turma do 7º ano do Ensino Fundamental, de uma escola da rede pública do município de Itatuba-PB. Ao trabalhar com a metodologia de Resolução e Exploração de Problemas constatou-se uma maior motivação por parte dos alunos, ao questionarem e refletirem sobre as ideias discutidas, sendo sempre instigados a atuar em fortemente durante o processo de ensino-aprendizagem. Pode-se destacar com a análise dos resultados obtidos a relevância da metodologia adotada, que permitiu uma maior compreensão da Álgebra, de modo a minimizar ou até superar as dificuldades apresentadas constantemente pelos alunos.

Submitted by Jean Medeiros (jeanletras@uepb.edu.br) on 2017-02-14T12:18:10Z No. of bitstreams: 1 PDF - Joseane Mirtis de Queiroz Pinheiro.pdf: 1869239 bytes, checksum: f9ccd4d1ae52b6cbe4266b9b38f6e09b (MD5) / Approved for entry into archive by Secta BC (secta.csu.bc@uepb.edu.br) on 2017-03-07T16:45:31Z (GMT) No. of bitstreams: 1 PDF - Joseane Mirtis de Queiroz Pinheiro.pdf: 1869239 bytes, checksum: f9ccd4d1ae52b6cbe4266b9b38f6e09b (MD5) / Made available in DSpace on 2017-03-07T16:45:31Z (GMT). No. of bitstreams: 1 PDF - Joseane Mirtis de Queiroz Pinheiro.pdf: 1869239 bytes, checksum: f9ccd4d1ae52b6cbe4266b9b38f6e09b (MD5) Previous issue date: 2016-12-14 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The aim of the present research was to investigate how questions can promote the development of strategies to solve an algebraic problem in the 3rd Grade of High School. It was carried out with students of the 3rd Grade of High School of a Public School from the State Educational System of the city Afogados da Ingazeira - PE, from June/2015 to December/2016. The Methodology uses qualitative research. These are case studies, two case studies were carried out, whose participating students were indicated by the teacher. It was used as data collection instruments the application of semi-structured interviews to the teacher in charge of the class and to the students who were part of the case studies, and the execution of a problem solving task with the students. The results suggest that the teacher in charge values the Problem Solving Methodology and uses exercises, although she thinks that she is using problems. Therefore, the question in her classes seems to be reduced to the IRE standard. Beatriz understands that solving problems is different from doing exercises. For Beatriz, the act of asking functions basically to clear up doubts and remind about previously studied subjects. Actual questions and examination questions allowed us to obtain information and a survey of previous knowledge from the student. The didactic questions, on the other hand, explored her way of thinking about Mathematics, interpretation, search for solutions, reflections and conjectures, besides favoring the written calculations. Beatriz developed basically two solving strategies for the algebraic problem. In the first one she used arithmetic, specifically the operations of addition, subtraction, multiplication and division. In the second she used the System of Linear First Degree Equations. The questions helped her to make decisions and to proceed with the development of the System satisfactorily. For Julia, a problem is a question that brings a challenge that needs to be understood and then solved. Her conception about a question is that it is important to remember subjects previously studied, to clarify and to complete something that you already know or even about content when you do not understand something. The actual questions, the exam questions and the didactic questions made her expose her previous knowledge and provide information about them to the researcher teacher, what helped her in other actions regarding the problem. With the didactic questions, Julia reflected more about what is in the problem, like the information and the graphical representation, which helped her in the reflections to search for solutions. She developed basically two strategies to solve the algebraic problem. In the first one, she used the arithmetic fundamental operations, specifically addition, subtraction and division, without presenting any difficulty. In the second one, she used the Algebra and she elaborated three equations with the weights using the algorithm of Systems of Linear First Degree Equations, without presenting any difficulty. The algebraic language and its representation do not seem to have been a problem for her. The questions made her broaden her algebraic thinking, considering the way how she demonstrates the organization of the problem. / A presente pesquisa teve como objetivo investigar como as perguntas podem promover o desenvolvimento de estratégias de resolução de problema algébrico no 3º Ano do Ensino Médio. Foi realizada com alunos do 3º Ano do Ensino Médio de uma Escola pública da Rede Estadual de ensino da cidade de Afogados da Ingazeira – PE, no período de junho/2015 a dezembro/2016. A Metodologia utiliza uma pesquisa qualitativa. Trata-se de estudos de caso, foram realizados dois estudos de caso, cujas alunas participantes foram indicadas pela professora. Utilizamos como instrumentos de coleta de dados entrevistas (semiestruturadas) com as alunas constituintes dos estudos de caso e a realização de uma tarefa de resolução de problema com as alunas. Os resultados sugerem que Beatriz entende que a ação de resolver problemas é diferente de fazer exercícios. Para Beatriz o ato de perguntar serve, basicamente, para tirar dúvidas e relembrar assuntos passados. Perguntas do tipo real e de exame nos permitiram obter da aluna uma informação ou um levantamento de conhecimentos prévios. Já as perguntas didáticas, exploraram seu modo de pensar sobre a Matemática, interpretação, a busca por soluções, reflexões e conjecturas, além de favorecer os cálculos escritos. Beatriz desenvolveu basicamente duas estratégias de resolução para o problema algébrico. Na primeira se utilizou da Aritmética, especificamente das operações de adição, subtração, multiplicação e divisão. Na segunda, utilizou-se do Sistema de Equações Lineares do 1º Grau. As perguntas lhe ajudaram a tomar decisões e proceder com o desenvolvimento do Sistema de modo satisfatório. Para Júlia o problema é uma questão que traz um desafio que precisa ser entendido para depois poder resolver. Sua concepção sobre a pergunta é que esta é importante para relembrar assuntos passados, tirar dúvidas ou esclarecer e completar algo que já sabe ou mesmo sobre o conteúdo, quando não entende algo. As perguntas real, de exame e as didáticas fizeram-na expor seus conhecimentos prévios e fornecer informações destes à professora pesquisadora a ajudando em outras ações, diante do problema. Com as perguntas didáticas Júlia refletiu mais sobre o que está posto no problema, como as informações e a representação gráfica, que lhe ajudaram nas reflexões em busca de soluções. Ela desenvolveu basicamente duas estratégias de resolução do problema algébrico. Na primeira utilizou as operações fundamentais da Aritmética especificamente à adição, subtração, divisão sem nenhuma dificuldade. Na segunda, ela utilizou a Álgebra, elaborando três equações com os pesos, utilizando o algoritmo de Sistemas de Equações Lineares do 1º grau, sem dificuldade. A linguagem algébrica e sua representação não parecem ter sido problema para ela. As perguntas fizeram-na ampliar seu raciocínio algébrico, considerando o modo como demonstra a organização do problema.

The purpose of this study was to determine the relationship between High School learners‟ mathematics-related belief systems and their approaches to mathematics non-routine problem-solving. A mixed methods approach was employed in the study. Survey questionnaires, mathematics problem solving test and interview schedules were the basic instruments used for data collection. The data was presented in form of tables, diagrams, figures, direct and indirect quotes of participants‟ responses and descriptions of learners‟ mathematics related belief systems and their approaches to mathematics problem solving. The basic methods used to analyze the data were thematic analysis (coding, organizing data into descriptive themes, and noting relations between variables), cluster analysis, factor analysis, regression analysis and methodological triangulation. Learners‟ mathematics-related beliefs were grouped into three Learners‟ mathematics-related beliefs were grouped into three categories, according to Daskalogianni and Simpson (2001a)‟s macro-belief systems: utilitarian, systematic and exploratory. A number of learners‟ problem solving strategies were identified, that include unsystematic guess, check and revise; systematic guess, check and revise; trial-and-error; logical reasoning; non-logical reasoning; systematic listing; looking for a pattern; making a model; considering a simple case; using a formula; numeric approach; piece-wise and holistic approaches. A weak positive linear relationship between learners‟ mathematics-related belief systems and their approaches to non-routine problem solving was discovered. It was, also, discovered that learners‟ mathematics-related belief systems could explain their approach to non-routine mathematics problem solving (and vice versa). / Mathematics Education / D.Phil. (Mathematics Education)

The purpose of this study was to determine the relationship between High School learners‟ mathematics-related belief systems and their approaches to mathematics non-routine problem-solving. A mixed methods approach was employed in the study. Survey questionnaires, mathematics problem solving test and interview schedules were the basic instruments used for data collection. The data was presented in form of tables, diagrams, figures, direct and indirect quotes of participants‟ responses and descriptions of learners‟ mathematics related belief systems and their approaches to mathematics problem solving. The basic methods used to analyze the data were thematic analysis (coding, organizing data into descriptive themes, and noting relations between variables), cluster analysis, factor analysis, regression analysis and methodological triangulation. Learners‟ mathematics-related beliefs were grouped into three Learners‟ mathematics-related beliefs were grouped into three categories, according to Daskalogianni and Simpson (2001a)‟s macro-belief systems: utilitarian, systematic and exploratory. A number of learners‟ problem solving strategies were identified, that include unsystematic guess, check and revise; systematic guess, check and revise; trial-and-error; logical reasoning; non-logical reasoning; systematic listing; looking for a pattern; making a model; considering a simple case; using a formula; numeric approach; piece-wise and holistic approaches. A weak positive linear relationship between learners‟ mathematics-related belief systems and their approaches to non-routine problem solving was discovered. It was, also, discovered that learners‟ mathematics-related belief systems could explain their approach to non-routine mathematics problem solving (and vice versa). / Mathematics Education / D.Phil. (Mathematics Education)