Made available in DSpace on 2015-03-26T14:00:07Z (GMT). No. of bitstreams: 1 texto completo.pdf: 2203390 bytes, checksum: 0a577a874e7a6bbc25aebb2008259f10 (MD5) Previous issue date: 2013-03-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In Brazil, one of the main subjects studied in the first year of high school is to function. The calculation of interest, the study of the progression and presentation of statistical data through tables, graphs and averages are also part of the curriculum. The purpose of this paper is to show interesting strategies as a methodology for teaching mathematics in the first year of high school, using the Calc spreadsheet that allows the manipulation of functions, building tables and formulas, exploring themes of daily life for students participatory manner, which enables the development of research skills, encourages creativity and autonomy, as well as provides to educators, educational work stimulating and meaningful learning. / No Brasil, um dos assuntos principais que se estuda no primeiro ano do Ensino Médio é função. O cálculo de juros, o estudo das progressões e a apresentação de dados estatísticos por meio de tabelas, gráficos e médias também fazem parte da grade curricular. A proposta deste trabalho é mostrar estratégias interessantes como metodologia para o ensino de matemática no primeiro ano do Ensino Médio, utilizando-se da planilha eletrônica Calc, que permite a manipulação das funções, construção de tabelas e fórmulas, explorando temas do cotidiano dos estudantes de forma participativa, o que possibilita o desenvolvimento de habilidades de investigação, incentiva a criatividade e autonomia, bem como proporciona aos educadores um trabalho pedagógico estimulante e uma aprendizagem significativa.

Submitted by FERNANDO HENRIQUE LOPES null (prof.fernandohenrique@hotmail.com) on 2017-09-26T12:07:17Z No. of bitstreams: 1 Dissertação FINAL.pdf: 738423 bytes, checksum: 268542ff74b4d1d629da8bc04263c740 (MD5) / Approved for entry into archive by Monique Sasaki (sayumi_sasaki@hotmail.com) on 2017-09-28T12:36:50Z (GMT) No. of bitstreams: 1 lopes_fh_me_sjrp.pdf: 738423 bytes, checksum: 268542ff74b4d1d629da8bc04263c740 (MD5) / Made available in DSpace on 2017-09-28T12:36:50Z (GMT). No. of bitstreams: 1 lopes_fh_me_sjrp.pdf: 738423 bytes, checksum: 268542ff74b4d1d629da8bc04263c740 (MD5) Previous issue date: 2017-08-28 / O presente trabalho tem como objetivo principal apresentar a definição e propriedades de progressões geométricas de 2º grau, geralmente não trabalhadas no estudo de sequências numéricas, que é iniciado no 1º Ano do Ensino Médio. Para isto, é realizado um estudo de casos gerais para sequências e séries de números reais, para posteriormente, exibir aplicações do conceito no Ensino Médio. Inicialmente é apresentado ao aluno as definições e propriedades de sequências e séries, que requer um estudo mais aprofundado uma vez que é um assunto de maior complexidade para aplicação em turmas de ensino médio. Tais propriedades são utilizadas como ferramentas para o desenvolvimento posterior de progressões aritméticas e geométricas, tanto de 1ª como de 2ª ordem. Uma vez definidas as progressões, atividades sobre o assunto são aplicadas aos alunos para que os mesmos dissertem sobre suas facilidades e dificuldades encontradas na resolução. / The present work has as main objective to present the definition and properties of geometric progressions of 2nd degree, usually not worked in the study of numerical sequences, that is initiated in the 1st Year of High School. For this, a study of general cases for sequences and series of real numbers is carried out, later, to show applications of the concept in High School. Initially the definitions and properties of sequences and series are presented to the student, which requires a more in-depth study since it is a subject of greater complexity for application in high school classes. These properties are used as tools for the later development of arithmetic and geometric progressions, both 1st and 2nd order. Once the progressions are defined, activities on the subject are applied to the students so that they tell about their facilities and difficulties found in the resolution.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2016-09-05T12:22:29Z No. of bitstreams: 2 Dissertação - Celmo José dos Reis - 2016.pdf: 3460998 bytes, checksum: c611b6ef55a816f6919e420bf4255a44 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-09-05T12:23:42Z (GMT) No. of bitstreams: 2 Dissertação - Celmo José dos Reis - 2016.pdf: 3460998 bytes, checksum: c611b6ef55a816f6919e420bf4255a44 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-09-05T12:23:42Z (GMT). No. of bitstreams: 2 Dissertação - Celmo José dos Reis - 2016.pdf: 3460998 bytes, checksum: c611b6ef55a816f6919e420bf4255a44 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-07-11 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Given the need for a better interaction between teachers and students in math classes, there is, currently, an increasing search for new educational tools that involve computational resources. This monograph proposes a teaching strategy that makes the study of mathematics more enjoyable and engaging, showing how math can be used in order to provide the high school student elements to understand the reason to study math and what connection it has with their daily lives. Starting from the observation that the teaching of mathematics in public schools has struggled for acceptance of the students because mathematics is presented mostly in a traditional way, i.e., it presents the student with a pile of ready-made formulas without practical sense for them. This makes it become exhausting and ineffective, leading the student even despise mathematics. Faced with these issues, we propose the use of the program Gnumeric as a tool in teaching Progressions, Functions and Graphics. Currently, interdisciplinarity has been present in education and, following this idea, we use along with the program the mathematical modeling of population dynamics, in particular the dynamics of the Aedes aegypti mosquito as a motivation to work with the proposed contents. It is further proposed to inform and alert students about diseases caused by the mosquito Aedes aegypti. / Tendo em vista a necessidade de uma melhor interação entre docentes e alunos em sala de aula na abordagem de conteúdos matemáticos, atualmente é grande a busca por novas ferramentas didáticas que envolvem recursos computacionais. Propõe-se com este trabalho, fornecer uma ferramenta didática de ensino que torne o estudo da matemática mais prazeroso e envolvente, que seja mais realístico e que forneça ao aluno do ensino médio condições de avaliação do porquê estudar matemática e qual a ligação destes conteúdos com seu dia a dia, partindo da observação de que o ensino da Matemática nas escolas públicas vem enfrentando dificuldades de aceitação e aprendizagem pelos alunos, pois os conteúdos matemáticos são apresentados quase sempre de forma tradicional, ou seja, apresenta-se ao aluno um amontoado de fórmulas prontas sem sentido prático para os mesmos. Dessa forma, o ensino se torna desgastante e ineficaz, levando o aluno a até mesmo, desprezar a Matemática. Frente a essas questões, esse trabalho propõe o uso do aplicativo Gnumeric como ferramenta de apoio no ensino de progressões, funções e construção de gráficos. Atualmente, a interdisciplinaridade tem estado presente na educação e, seguindo essa ideia, usa-se juntamente ao aplicativo a modelagem matemática da dinâmica de populações, em particular do Aedes aegypti como motivação para se trabalhar o conteúdo proposto. Propõe-se ainda, informar e alertar os alunos acerca de doenças causadas pelo mosquito Aedes aegypti.

Este projeto de pesquisa surgiu quando lecionava para alunos do 1º ano do Ensino Médio, quando senti a necessidade de criar um mecanismo para relacionar o conteúdo de progressões e funções afins. Nesse sentido, desenvolvi atividades que se concluem num jogo de cartas que tem por objetivo a abstração desses conteúdos, maior compreensão sobre as características e comportamentos de funções afins, capacitar o aluno nas diferentes formas de leitura de situaçõesproblemas como: funções afins, progressões e maior compreensão de gráficos de funções, com o auxílio do software Geogebra. Esta pesquisa se baseia num conjunto de atividades que transformam uma situaçãoproblema em uma progressão aritmética, em uma função afim e um gráfico com o auxílio do software Geogebra, registrados e apresentados neste trabalho. Durante o processo de ensino aprendizagem, em grupo, os alunos produziram 13 cartões com situações-problema, cada uma relacionando uma progressão aritmética, uma função afim e um gráfico feito com o auxílio do Geogebra, totalizando 52 cartões que são jogados como um simples jogo de memória ou outro jogo que citarei no decorrer da pesquisa. A construção do jogo e sua prática proporcionaram ao aluno uma melhor compreensão do conteúdo abordado, desenvolvimento do senso crítico, melhora nas relações interpessoais e maior estímulo para o aprendizado. / This research project arose when taught to high school students when I felt the need to create a mechanism to relate the content of progressions and linear functions. This way, I developed activities that are completed in a card game that aims abstraction such content, better understanding of the characteristics and behaviors related functions, to enable students in different forms of reading situations-problems such as graphs, functions, progressions and greater understanding of graphing functions, with the aid of the Geogebra software. This research is based on a set of activities that transform a problem situation in an arithmetic progression, in a similar role and a graphic with the help of Geogebra software, recorded and presented in this paper. During the process of teaching and learning in groups, students produced 13 cards with problem situations, each relating an arithmetic progression a similar function and a graphic made with the help of Geogebra, a total of 52 cards that are played as a simple game memory or other game that I will mention during the research. The construction of the game and their practice gave the student a better understanding of the analyzed content, development of critical thinking, improvement in interpersonal relationships and greater stimulus for learning.

We follow a research paper that J. Elstrodt published in 1998 to prove the Prime Number Theorem for arithmetic progressions. We will review basic results from Dirichlet characters and L-functions. Furthermore, we establish a weak version of the Wiener-Ikehara Tauberian Theorem, which is an essential tool for the proof of our main result.

History has proved that too much power, in any form, is detrimental to the greater good of the society concerned. People at the hands of the power-hungry face discrimination and are often subjected to extreme violence and abuse. Society has undergone several changes and progressions through time, including economic, political and social changes. One thing that has remained unchanged however, is man‟s power over woman. Patriarchal power is present in all sectors and scenarios of society, from the home to the international legal system. My study focuses on the notion that an abundance of power leads to fear, violence and total disarray at the micro and macro levels of society. I argue that the essential problem in the relationship between man and woman is not a man‟s abuse of power, but rather that he has too much power in the first place. A culture of entitlement breeds among men, enabling them to treat women as inferior, sub-human objects. Definitions of male and female prove to be concreted into specific roles and gendered identities within the home and the greater society. People fall automatically into these roles, blindly and unquestioningly. It is for this reason that I maintain all members of society ensure the survival of patriarchy – even if they do so unconsciously. While the difference in the understanding of rape and sexual intercourse should be stark, it is blurred because they are defined according to male terms. Man‟s entitlement allows him to think it his right to take sex from a woman, even if she does not offer it willingly. Culture and tradition serve as major obstacles in any possibility of society‟s progression. Culture has proved such an undisputed order in society that it even trumps the international legal system of human rights. Culture justifies, or at least trivialises, the abuse of women. The social stigmatisation of sexual abuse silences women, providing further endorsement for men to continue asserting their power. A woman‟s life, as determined by male hierarchy, gender bias, culture and social stigmas, is therefore fated. It is with this in mind that I strongly question the progression of society into a true form of liberality and equality. In order for society to attain such a transcended state, it will have to disregard everything that it knows and deconstruct everything that has defined it up to that point. Until this is achieved, women will continue to live their lives in fear of the silent weapon in war and peace. / Dissertation (MPhil)--University of Pretoria, 2012. / gm2014 / Centre for Human Rights / unrestricted

Various researchers have indicated the importance of graphs in physical sciences and the difficulties that learners may experience with graphs. More specifically, learners’ problems with motion graphs have been reported in literature. Learners’ difficulty in the application of basic concepts in graphs to solve kinematics graphs problems leads to underperformance in physical sciences. Their ability to handle problems in kinematics graphs is enhanced if they have an effective knowledge base or conceptual resources on graphs. In South Africa there seems to be a gap between the GET [General Education and Training] and FET [Further Education and Training] band’s requirements on graphs. A smooth learning progression is needed. For this reason this study selected to investigate the conceptual resources acquired by grade 10 learners from grade 9 that can be used productively for the learning of kinematics graphs in grade 10. The primary aim of the study was to determine and analyse grade 10 learners’ conceptual resources for learning kinematics graphs in physical sciences. The use of a mixed method approach was considered appropriate for this study. The mixed method depended on the quantitative method to produce precise and measurable data, while a qualitative method was to enhance the understanding of the data produced by the quantitative method. Data obtained by quantitative methods was drawn into tables and graphs, and the consistency in responses determined. Patterns and trends in learners’ reasoning were probed with the aid of qualitative method. In the study it was reported that the quantitative data in the form of a questionnaire was completed by 201 learners. Qualitative data was also obtained by interviewing three learners with varying abilities. The results showed that many learners could answer mathematics questions, but struggled with similar questions in kinematics. The results further showed that the learners did not answer the questionnaire consistently, but their responses depended on the context of the questions. In the interviews learners used everyday applications to explain scientific concepts, instead of using scientific principles. Still, some of the everyday applications may be used as resources for teaching the science concepts. From the results it can be deduced that learners’ conceptual resources can influence their understanding of kinematics graphs in physics. These resources are gained from everyday experiences and previous learning in mathematics and the natural sciences. A constraint is that many learners do not efficiently integrate their mathematics and physics knowledge. iv In the study some learners did not transfer their mathematics knowledge to physics, while others could not transfer their physics knowledge to mathematics. From the results recommendations can be made for the teaching of graphs in the GET band for easier progress into the FET band. The strategy to improve understanding of kinematics graphs is to progressively integrate mathematics and physics from grade nine. Line graphs should be treated in more detail in grade 9 to form proper conceptual resources for kinematics graphs in grade ten. / MEd (Natural Sciences Education), North-West University, Potchefstroom Campus, 2014

Various researchers have indicated the importance of graphs in physical sciences and the difficulties that learners may experience with graphs. More specifically, learners’ problems with motion graphs have been reported in literature. Learners’ difficulty in the application of basic concepts in graphs to solve kinematics graphs problems leads to underperformance in physical sciences. Their ability to handle problems in kinematics graphs is enhanced if they have an effective knowledge base or conceptual resources on graphs. In South Africa there seems to be a gap between the GET [General Education and Training] and FET [Further Education and Training] band’s requirements on graphs. A smooth learning progression is needed. For this reason this study selected to investigate the conceptual resources acquired by grade 10 learners from grade 9 that can be used productively for the learning of kinematics graphs in grade 10. The primary aim of the study was to determine and analyse grade 10 learners’ conceptual resources for learning kinematics graphs in physical sciences. The use of a mixed method approach was considered appropriate for this study. The mixed method depended on the quantitative method to produce precise and measurable data, while a qualitative method was to enhance the understanding of the data produced by the quantitative method. Data obtained by quantitative methods was drawn into tables and graphs, and the consistency in responses determined. Patterns and trends in learners’ reasoning were probed with the aid of qualitative method. In the study it was reported that the quantitative data in the form of a questionnaire was completed by 201 learners. Qualitative data was also obtained by interviewing three learners with varying abilities. The results showed that many learners could answer mathematics questions, but struggled with similar questions in kinematics. The results further showed that the learners did not answer the questionnaire consistently, but their responses depended on the context of the questions. In the interviews learners used everyday applications to explain scientific concepts, instead of using scientific principles. Still, some of the everyday applications may be used as resources for teaching the science concepts. From the results it can be deduced that learners’ conceptual resources can influence their understanding of kinematics graphs in physics. These resources are gained from everyday experiences and previous learning in mathematics and the natural sciences. A constraint is that many learners do not efficiently integrate their mathematics and physics knowledge. iv In the study some learners did not transfer their mathematics knowledge to physics, while others could not transfer their physics knowledge to mathematics. From the results recommendations can be made for the teaching of graphs in the GET band for easier progress into the FET band. The strategy to improve understanding of kinematics graphs is to progressively integrate mathematics and physics from grade nine. Line graphs should be treated in more detail in grade 9 to form proper conceptual resources for kinematics graphs in grade ten. / MEd (Natural Sciences Education), North-West University, Potchefstroom Campus, 2014

Cette thèse concerne quelques problèmes liés à la répartition des entiers sans facteur carré dansles progressions arithmétiques. Ces problèmes s’expriment en termes de majorations du terme d’erreurassocié à cette répartition.Les premier, deuxième et quatrième chapitres sont concentrés sur l’étude statistique des termesd’erreur quand on fait varier la progression arithmétique modulo q. En particulier on obtient une formuleasymptotique pour la variance et des majorations non triviales pour les moments d’ordre supérieur. Onfait appel à plusieurs techniques de théorie analytique des nombres comme les méthodes de crible et lessommes d’exponentielles, notamment une majoration récente pour les sommes d’exponentielles courtesdue à Bourgain dans le deuxième chapitre.Dans le troisième chapitre on s’intéresse à estimer le terme d’erreur pour une progression fixée. Onaméliore un résultat de Hooley de 1975 dans deux directions différentes. On utilise ici des majorationsrécentes de sommes d’exponentielles courtes de Bourgain-Garaev et de sommes d’exponentielles torduespar la fonction de Möbius dues à Bourgain et Fouvry-Kowalski-Michel. / This thesis concerns a few problems linked with the distribution of squarefree integers in arithmeticprogressions. Such problems are usually phrased in terms of upper bounds for the error term relatedto this distribution.The first, second and fourth chapter focus on the satistical study of the error terms as the progres-sions varies modulo q. In particular we obtain an asymptotic formula for the variance and non-trivialupper bounds for the higher moments. We make use of many technics from analytic number theorysuch as sieve methods and exponential sums. In particular, in the second chapter we make use of arecent upper bound for short exponential sums by Bourgain.In the third chapter we give estimates for the error term for a fixed arithmetic progression. Weimprove on a result of Hooley from 1975 in two different directions. Here we use recent upper boundsfor short exponential sums by Bourgain-Garaev and exponential sums twisted by the Möbius functionby Bourgain et Fouvry-Kowalski-Michel.

Made available in DSpace on 2016-04-27T17:13:00Z (GMT). No. of bitstreams: 1 Andrea Gomes Nazuto Goncalves.pdf: 11389774 bytes, checksum: af30b407d8ab80be3ce67b30707b85ed (MD5) Previous issue date: 2007-05-29 / Made available in DSpace on 2016-08-25T17:25:36Z (GMT). No. of bitstreams: 2 Andrea Gomes Nazuto Goncalves.pdf.jpg: 2104 bytes, checksum: c4715912a635b5fbde63d2a9b070733f (MD5) Andrea Gomes Nazuto Goncalves.pdf: 11389774 bytes, checksum: af30b407d8ab80be3ce67b30707b85ed (MD5) Previous issue date: 2007-05-29 / Secretaria da Educação do Estado de São Paulo / The objective of this research is to investigate the learning of Geometric Progressions by fractals and their influences on the construction of the knowledge of this subject. Starting from this objective our research questions emerge: How the use of the fractals motivate can be in the perception of the solemnity-similarity? How can the solemnity-similarity contribute in the process of generalization of the formulas of the geometric progression to High School students? So, we developed a teaching sequence, using some elements of the methodology of research denominated engineering didacticism. The conceived sequence is constituted by three blocks, and in the first, we worked the fractals construction; in the second we used the Dynamic Geometry to represent them; and in the third party we focused the generalizations. We used in our research the theoretical presuppositions of Parzysz for the geometry teaching, in what it concerns at their four levels of development of the geometric thought; Machado's ideas that suggest in the construction of a geometric object an articulation among four processes: perception, physical construction, representation and conceptual organization; the situations of resolutions of problems for development of significant concepts proposed by Vergnaud; and also the Dynamic Geometry to motivate the student to investigate. The analysis of the results obtained in the application of the didactic sequence showed that the construction, the manipulation and the observation take to the perception of the solemnity-similarity this, has the aim to facilitate the process of generalization of the mathematical elements that compound the study of Geometric Progressions. In spite of, the number of students used in the sequence (22 couples) brought us great difficulties in the application of the activities, however, it reflected an atmosphere similar to the found at classroom / O objetivo desta pesquisa é investigar o aprendizado de Progressões Geométricas via fractais e as suas influências sobre a construção do conhecimento deste assunto. A partir deste objetivo emergem as nossas questões de pesquisa: Como a utilização dos fractais pode ser motivadora na percepção da autosemelhança? Como a auto-semelhança pode contribuir no processo de generalização das fórmulas da progressão geométrica para alunos do Ensino Médio? Para isto, desenvolvemos uma seqüência de ensino, utilizando alguns elementos da metodologia de pesquisa denominada engenharia didática. A seqüência concebida é constituída por três blocos, sendo que no primeiro, trabalhamos a construção de fractais; no segundo utilizamos a Geometria Dinâmica para representá-los; e no terceiro enfocamos as generalizações. Empregamos em nossa pesquisa os pressupostos teóricos de Parzysz para o ensino de geometria, no que concerne aos seus quatro níveis de desenvolvimento do pensamento geométrico; as idéias de Machado que sugere na construção de um objeto geométrico uma articulação entre quatro processos: percepção, construção física, representação e organização conceitual; as situações de resoluções de problemas para desenvolvimento de conceitos significativos propostas por Vergnaud; e também a Geometria Dinâmica para incentivar o espírito investigativo do aluno. A análise dos resultados obtidos na aplicação da seqüência didática mostrou que a construção, a manipulação e a observação levam à percepção da auto-semelhança, esta, por sua vez, facilita o processo de generalização dos elementos matemáticos que compõem o estudo de Progressões Geométricas. Não obstante, o número de alunos utilizado na seqüência (22 duplas) nos trouxe grandes dificuldades na aplicação das atividades, porém, refletiu um ambiente semelhante ao encontrado em sala de aula