This thesis provides statistical analysis methods and a validation procedure for conducting this statistical analysis, under the common random number (CRN) correlation-induction strategy. The proposed statistical analysis provides estimates for the unknown parameters that are needed for validating the model. While conducting this statistical analysis, we make some key assumptions. Validation comprises of a three-stage statistical procedure. The first stage tests for the multivariate normality,the second stage tests the structure of the covariance matrix between responses, and the third stage tests for the adequacy of the proposed model. The statistical analysis and validation procedures are illustrated with an example of a hospital simulation study. / Master of Science

This thesis focuses on the use of extremal techniques in analyzing problems that historically have been associated with other areas of discrete mathematics. We establish new techniques for analyzing combinatorial problems with two different types of nonlinear orders, and then use them to solve important previously-open problems in mathematics. In addition, we use entropy techniques to establish a variety of bounds in the theory of sumsets. In the second chapter, we examine a problem of Furedi and Hajnal regarding forbidden patterns in (0,1)-matrices. We introduce a new technique that gives an asymptotically tight bound on the number of 1-entries that a (0,1)-matrix can contain while avoiding a fixed permutation matrix. We use this result to solve the Stanley-Wilf conjecture, a well-studied open problem in enumerative combinatorics. We then generalize the technique to give results on d-dimensional matrices. In the third chapter, we examine a problem of Pinchasi and Radoicic on cyclically order sets. To do so, we prove an upper bound on the sizes of such sets, given that their orders have the intersection reverse property. We then use this to give an upper bound on the number of edges that a graph can have, assuming that the graph can be drawn so that no cycle of length four has intersecting edges. This improves the previously best known bound and (up to a log-factor) matches the best known lower bound. This result implies improved bounds on a number of well-studied problems in geometric combinatorics, most notably the complexity of pseudo-circle arrangements. In the final chapter, we use entropy techniques to establish new bounds in the theory of sumsets. We show that such sets behave fractionally submultiplicatively, which in turn provides new Plunecke-type inequalities of the form first introduced by Gyarmati, Matolcsi, and Ruzsa.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In the second year of high school the approach of counting methods is usually done emphasizing the formulas arrangements and combination. In this work we present an alternative to the study of combinatorics using mathematical investigations. Therefore, we used three activities that have been developed with students of the second year of high school to a state school in the interior of Sergipe in the academic year 2015. The activities were done in groups and the textbook was not used. In the analysis of the activities we realize the importance of this type of class that requires an active attitude of the students, because the formulas are not presented as ready and finished and the teacher ceases to be the central figure and becomes a mentor. We also analyze the feasibility of this type of class that has a greater demand on the part of the teacher's planning. The initial plan was modified in the course of activities, but the results, in general, were favorable for significant learning of the students, this was evident in the presentations of the groups on the blackboard and writing the questions. / No segundo ano do Ensino Médio a abordagem dos métodos de contagem geralmente é feita dando ênfase as fórmulas de arranjos e combinação. Nesse trabalho apresentamos como alternativa o estudo da análise combinatória utilizando as investigações matemáticas. Para tanto, fizemos uso de três atividades que foram desenvolvidas com alunos do segundo ano do Ensino Médio de uma escola estadual do interior de Sergipe no ano letivo de 2015. As atividades foram feitas em grupos e o livro didático não foi utilizado. Na análise das atividades percebemos a importância desse tipo de aula que exige uma postura ativa dos discentes, pois, as fórmulas não são apresentadas como prontas e acabadas e o professor deixa de ser a figura central e passa a ser um orientador. Analisamos também a viabilidade desse tipo de aula que possui uma exigência maior por parte do planejamento do professor. O planejamento inicial sofreu modificações no decorrer das atividades, porém os resultados, de maneira geral, foram favoráveis para uma aprendizagem significativa dos alunos, isso ficou evidenciado nas apresentações dos grupos na lousa e na escrita das questões.

Thesis (MEd (Curriculum Studies))--University of Stellenbosch, 2007. / This thesis deals with my practice as a mathematics teacher at a post-matric programme at the University of Stellenbosch. I use aspects of three different approaches to social science research, namely phenomenology, narrative inquiry and the discipline of noticing, to research my personal experiences. These experiences include learning mathematics at school and university as well as teaching mathematics in a post-matric programme. These experiences are presented by means of briefbut- vivid descriptions, journal entries and records of classroom conversations and are reflected on in the light of relevant literature. The reflections and readings lead to alternative ways of thinking about learning, teaching and researching as found in the cognitive theory of enactivism. These new ways of thinking are used to reflect on my current practice by focusing particularly on knowing, listening and noticing and are used to imagine what my practice could look like in the future. My approach, framework, focus areas and imagined practice all emerge during the research process. This process is presented through ‘behind-the-scene’ reflections on my own experiences of doing research. By presenting these experiences, this thesis also deals with the process of doing research – in particular it deals with the process of using an emergent design.

Submitted by Sandra Pereira (srpereira@ufrrj.br) on 2018-03-22T12:57:35Z No. of bitstreams: 1 2017 - Daniela Mendes Vieira da Silva.pdf: 5871201 bytes, checksum: 81245529f779a84c8bcfd0d67fef3424 (MD5) / Made available in DSpace on 2018-03-22T12:57:35Z (GMT). No. of bitstreams: 1 2017 - Daniela Mendes Vieira da Silva.pdf: 5871201 bytes, checksum: 81245529f779a84c8bcfd0d67fef3424 (MD5) Previous issue date: 2017-01-27 / This research discusses written productions of high school students about logarithmic properties in an investigative environment. For the development of this work, we rely on the Design Experiment. Within this theoretical contribution: we make the Theoretical Methodological basis of this research and establish the teaching framework learning logarithms from the analysis of a reference book on the theme for teacher training, two collections of textbooks adopted by the school that hosts this research And dissertations on the teaching of the subject and a conceptual study of the logarithm mathematical object. Second, we used the research scenarios associated with classroom research to elaborate a set of tasks that facilitated the introduction of the logarithms theme. This set we tested and reworked in a cycle of applications and applied as a tool for collecting the textual productions of the research participants in a second cycle. The data analyzed with the support of Theory of Registers of Semiotic Representation - TRRS indicate the scope of several properties of the logarithms from the tasks proposed to the participants as well as their adherence to the proposed research. The resulting product of this dissertation is a didactic guide for teachers containing reflections on the theoretical contribution of this research together with a set of tasks for the learning of logarithms elaborated from the data analysis of the present work / Esta pesquisa discute produ??es escritas de estudantes do Ensino M?dio acerca de propriedades de logaritmos em um ambiente investigativo. Para o desenvolvimento deste trabalho apoiamo-nos no Experimento de design. Dentro deste aporte te?rico fazemos a fundamenta??o Te?rico Metodol?gica desta pesquisa e estabelecemos o quadro de ensino aprendizagem de logaritmos a partir da an?lise de um livro de refer?ncia no tema para a forma??o de professores, duas cole??es de livros did?ticos adotadas pela escola que sedia esta pesquisa e disserta??es sobre o ensino do tema e um estudo conceitual do objeto matem?tico logaritmo. Em um segundo momento, utilizamos os cen?rios para investiga??o aliados ? investiga??o em sala de aula para elaborar um conjunto de tarefas que facilitasse a introdu??o do tema logaritmos. Conjunto esse que testamos e reelaboramos em um ciclo de aplica??es e aplicamos como instrumento de coleta das produ??es textuais dos participantes da pesquisa em um segundo ciclo. Os dados analisados com o apoio da Teoria dos Registros de Representa??o Semi?tica -TRRS indicam o alcance de diversas propriedades dos logaritmos a partir das tarefas propostas aos participantes assim como a ades?o dos mesmos ? investiga??o proposta. O produto resultante desta disserta??o ? um guia did?tico para professores contendo reflex?es sobre o aporte te?rico desta pesquisa em conjunto com um conjunto de tarefas para o aprendizado de logaritmos elaborado a partir da an?lise dos dados do presente trabalho.

Made available in DSpace on 2014-12-17T15:05:03Z (GMT). No. of bitstreams: 1 AnnaKSN_DISSERT.pdf: 2228892 bytes, checksum: fc6b8553824d405981f02c90c321636a (MD5) Previous issue date: 2013-07-25 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / This present research the aim to show to the reader the Geometry non-Euclidean while anomaly indicating the pedagogical implications and then propose a sequence of activities, divided into three blocks which show the relationship of Euclidean geometry with non-Euclidean, taking the Euclidean with respect to analysis of the anomaly in non-Euclidean. PPGECNM is tied to the line of research of History, Philosophy and Sociology of Science in the Teaching of Natural Sciences and Mathematics. Treat so on Euclid of Alexandria, his most famous work The Elements and moreover, emphasize the Fifth Postulate of Euclid, particularly the difficulties (which lasted several centuries) that mathematicians have to understand him. Until the eighteenth century, three mathematicians: Lobachevsky (1793 - 1856), Bolyai (1775 - 1856) and Gauss (1777-1855) was convinced that this axiom was correct and that there was another geometry (anomalous) as consistent as the Euclid, but that did not adapt into their parameters. It is attributed to the emergence of these three non-Euclidean geometry. For the course methodology we started with some bibliographical definitions about anomalies, after we ve featured so that our definition are better understood by the readers and then only deal geometries non-Euclidean (Hyperbolic Geometry, Spherical Geometry and Taxicab Geometry) confronting them with the Euclidean to analyze the anomalies existing in non-Euclidean geometries and observe its importance to the teaching. After this characterization follows the empirical part of the proposal which consisted the application of three blocks of activities in search of pedagogical implications of anomaly. The first on parallel lines, the second on study of triangles and the third on the shortest distance between two points. These blocks offer a work with basic elements of geometry from a historical and investigative study of geometries non-Euclidean while anomaly so the concept is understood along with it s properties without necessarily be linked to the image of the geometric elements and thus expanding or adapting to other references. For example, the block applied on the second day of activities that provides extend the result of the sum of the internal angles of any triangle, to realize that is not always 180? (only when Euclid is a reference that this conclusion can be drawn) / A presente pesquisa tem como objetivo mostrar ao leitor a Geometria n?o-euclidiana enquanto anomalia indicando as implica??es pedag?gicas e em seguida propor uma sequ?ncia de atividades distribu?das em tr?s blocos, as quais mostram a rela??o da geometria euclidiana com a n?o-euclidiana, tomando a euclidiana com refer?ncia para an?lise da anomalia na n?o-euclidiana. Est? vinculada ao Programa de P?s-Gradua??o em Ensino de Ci?ncias Naturais e Matem?tica da Universidade Federal do Rio Grande do Norte na linha de pesquisa de Hist?ria, Filosofia e Sociologia da Ci?ncia no Ensino de Ci?ncias Naturais e da Matem?tica. Aborda aspectos relativos a Euclides de Alexandria, bem como sobre a sua obra mais famosa Os Elementos e, al?m disso, enfatiza o Quinto Postulado de Euclides, sobretudo ?s dificuldades (que perduraram v?rios s?culos) que os matem?ticos tinham em compreend?-lo. At? que, no s?culo XVIII, tr?s matem?ticos: Lobachevsky (1793 1856), Bolyai (1775 1856) e Gauss (1777-1855) foram convencidos que tal axioma era correto e que existia uma outra geometria (an?mala) t?o consistente quanto a de Euclides, mas que n?o se enquadrava em seus par?metros. ? atribu?da a esses tr?s o advento da geometria n?o-euclidiana. Para o percurso metodol?gico s?o pontuadas algumas defini??es de car?ter bibliogr?fico sobre as anomalias, depois elas s?o caracterizadas, para que a defini??o seja melhor compreendida pelo leitor e, em seguida,s?o destacadas as geometrias n?o-euclidianas (Geometria Hiperb?lica, Geometria Esf?rica e a Geometria do Motorista de T?xi) confrontando-as com a euclidiana para que sejam analisadas as anomalias existentes nas geometrias n?o-euclidianas e observemos sua import?ncia ao ensino. Ap?s tal caracteriza??o segue-se a parte emp?rica da proposta que consistiu na aplica??o de tr?s blocos de atividades em busca de implica??es pedag?gicas de anomalia. O primeiro sobre as retas paralelas, o segundo sobre o estudo dos tri?ngulos e o terceiro sobre a menor dist?ncia entre dois pontos. Esses blocos oferecem um trabalho com elementos b?sicos da geometria a partir de um estudo hist?rico e investigativo das geometrias n?o-euclidianas enquanto anomalia de modo que o conceito seja compreendido juntamente com suas propriedades sem necessariamente estar vinculada a imagem dos elementos geom?tricos e, consequentemente, ampliando ou adaptando para outros referenciais. Por exemplo, o bloco aplicado no segundo dia de atividades proporciona que se amplie o resultado de soma dos ?ngulos internos de um tri?ngulo qualquer, passando a constatar que n?o ? sempre 180? (somente quando Euclides ? refer?ncia que esta conclus?o pode ser tirada)

Made available in DSpace on 2018-06-27T19:13:04Z (GMT). No. of bitstreams: 2 Lucilene Oenning Saraiva.pdf: 1871833 bytes, checksum: 1d1ab13bc56881ecec548e19f20fe542 (MD5) Lucilene Oenning Saraiva.pdf.jpg: 3610 bytes, checksum: f7234f5fa942fc34645d9e1b2b9188b7 (MD5) Previous issue date: 2012-04-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O presente trabalho teve como objetivo analisar as possibilidades que a metodologia de investigação matemática pode proporcionar ao ensino e aprendizagem dos conceitos e propriedades de sucessões numéricas. O trabalho foi desenvolvido com 28 estudantes do quarto ano de um curso de Licenciatura em Matemática de uma universidade privada do oeste do Paraná. A revisão de literatura baseou-se em livros, artigos, dissertações e teses que tratam dos aspectos teóricos da investigação Matemática, do papel do professor e da investigação no currículo escolar. A pesquisa é de caráter qualitativo e nela empregaram-se, como instrumentos, anotações de observações de sala de aula, os trabalhos realizados pelos alunos e um questionário aplicado ao final da experiência. O questionário forneceu dados das opiniões dos alunos sobre a experiência realizada. Os resultados obtidos permitiram constatar as dificuldades do grupo de formular hipóteses, argumentar e formalizar ideias matemáticas. Além disso, foi possível constatar que atividades investigativas desenvolvidas na etapa de formação inicial podem incentivar seu uso na futura prática docente e permitir uma mudança de concepção sobre o ensino de matemática e da postura do professor no trabalho de sala de aula.

In this workshop, we present a model of problem that we call Research Situation for the Classroom (RSC). The aim of a RSC is to put students in a role close to a mathematical researcher in order to make them work on mathematical thinking/skills. A RSC has some characteristics : the problem is close to a research one, the statement is an easy understandable question, school knowledge are elementary, there is no end, a solved question postponed to new questions... The most important characteristic of a RSC is that students can manage their research by fixing themselves some variable of the problem. So, a RSC is completely different from a problem that students usually do in France. For short : there is no final answer, students can try to resolve their own questions : a RSC is a large open field where many sub-problems exist; the goal for the students is not to apply a technique: the goal is, as for a researcher, to search. These type of situations are particularly interesting to develop problem solving skills and mathematical thinking. They can also let students discover that mathematics are “alive” and “realistic”. This workshop will be split into two parts. First, we propose to put people in the situation of solving a RSC to make them discover practically what is it. After, we present the model of a RSC and some results of our experimentations.

Made available in DSpace on 2016-04-27T16:58:46Z (GMT). No. of bitstreams: 1 Antonio Jose Fernandes de Melo.pdf: 715944 bytes, checksum: 2022fafd68b9f1300db8bb3db10c99be (MD5) Previous issue date: 2008-10-17 / Technology of information is more and more present in our environment, but most of times it s set aside. This job searched, with the use of the calculator, provide a dynamic and investigative education through the reflection and development of conjuctures. There for, it developed activities in a classroom of a High School in a public network of the State of São Paulo and showed it s possible a new way of teaching Mathematics contents. Our analysis was divided in four areas: handling a calculator, committed errors, investigative attitudes and dynamics in the classroom. In relations to the area of handling a calculator we analyzed the difficulties and the facilities found with its use in the classroom, offering the teachers a material for study, if they want to insert new technologies in the classrooms with an investigative broach. In case of analysis area of the committed errors we searched to analyze the difficulties found in relation to power and roots contents, trying to justify the errors found, as well as offer ways to solve some of these difficulties. We also analyzed the amount of the students errors in each activity. The area of the investigative attitudes in classroom, one of the greatest important point of our work, intend to become the students into reflexive an active citizens in the learning process. The process followed the evolution of this reflexive practice from the analysis of the beginning difficulties. The dynamic area of the classroom had it analysis centralized on the teacher s role as a mediator in investigative classes / A tecnologia de informação cada vez mais se faz presente em nosso meio, mas muitas vezes, em nossas escolas, é deixada de lado. Este trabalho buscou, com o uso da calculadora, proporcionar um ensino dinâmico e investigativo por meio da reflexão e da elaboração de conjecturas. Para isso, desenvolveu atividades em uma sala de aula do Ensino Médio da rede pública de ensino do Estado de São Paulo e demonstrou ser possível uma nova forma de tratar conteúdos matemáticos. Nossa análise foi dividida em quatro eixos: manuseio da calculadora, erros cometidos, atitude investigativa e dinâmica da sala de aula. Em relação ao eixo do manuseio da calculadora, analisaram-se as dificuldades e as facilidades encontradas com sua utilização em sala de aula, oferecendo aos professores um material de estudo, caso queiram inserir novas tecnologias em suas aulas, com uma abordagem investigativa. No caso do eixo de análise dos erros cometidos buscou-se analisar as dificuldades encontradas em relação aos conteúdos de potências e raízes, tentando justificar os erros encontrados, assim como propor meios que possam solucionar algumas dessas dificuldades. Analisou-se também a quantidade de erros dos alunos em cada atividade. O eixo da atitude investigativa em sala de aula, um dos pontos de maior importância neste trabalho, pretende fazer dos alunos cidadãos reflexivos e atuantes no processo de aprendizagem. O processo acompanhou a evolução dessa prática reflexiva, a partir da análise das dificuldades iniciais. O eixo da dinâmica da sala de aula teve análise centralizada no papel do professor como mediador em aulas investigativas

CAPES / Este trabalho traz um relato a respeito da Hipótese de Riemann, com o objetivo de tornar os conceitos referentes a esse problema acessíveis ao professor da educação básica, que pretenda abordá-los em sala de aula quando tratar de conteúdos a ele relacionados. A pesquisa foi inteira bibliográfica, apoiada em sua grande parte em textos de História da Matemática, tornando este trabalho divulgador dos problemas que ocupam parte das pesquisas matemáticas deste século, em especial da Hipótese de Riemann. / This study presents a report about the Riemann Hypothesis, leaving the underlying concepts behind this problem more accessible to a high school teacher. The literature review was based mainly on History of Mathematics texts. This research aims to study significant topics of mathematical research throughout this century, particularly to popularize the Riemann Hypothesis.