A geometria do compasso (1797) de Mascheroni (1750 – 1800) em atividades com o GeoGebra

The present work aims to show a possible relationship between the use of the History of Mathematics and Information and Communication Technologies (TIC) in teaching Mathematics through activities that use geometric constructions of the “Geometry of the Compass” (1797) by Lorenzo Mascheroni (1750-1800). For this, it was performed a qualitative research characterized by an historical exploration of bibliographical character followed by an empirical intervention based on use of the History of Mathematics combined with TIC through Mathematical Investigation. Thus, studies were performed in papers dealing with the topic, as well as a survey to highlight problems and /or episodes of the history of mathematics that can be solved with the help of TIC, allowing the production of a notebook of activities addressing the resolution of historical problems in a computer environment. In this search, we came across the problems of geometry that are presented by Mascheroni stated previously in the work that we propose solutions and investigations using GeoGebra software. The research resulted in the elaboration of an educational product, a notebook of activities, which was structure to allow during its implementation, students can conduct historical and/or Mathematics research, therefore, we present the procedures for realization of each construction, followed at some moments by original solution of the work. At the same time, we encourage students to investigate/reflect its construction (GeoGebra), in addition to making comparisons with the solution Mascheroni. This notebook was applied to two classes of the course of Didactics of Mathematics I (MAT0367) Course in Mathematics UFRN in 2014. Knowing the existence of some unfavorable arguments regarding the use of history of mathematics, such as loss of time, it was found that this factor can be mitigated with the aid of computational resource, because we can make checks using only the dynamism of and software without repeating the construction. It is noteworthy that the minimized time does not mean loss of reflection or maturation of ideas, when we adopted the process of historical and/or Mathematics Investigation

Sobre a integração indefinida de funções racionais complexas: teoria e implementação de algoritmos racionais

We present indefinite integration algorithms for rational functions over subfields of the complex numbers, through an algebraic approach. We study the local algorithm of Bernoulli and rational algorithms for the class of functions in concern, namely, the algorithms of Hermite; Horowitz-Ostrogradsky; Rothstein-Trager and Lazard-Rioboo-Trager. We also study the algorithm of Rioboo for conversion of logarithms involving complex extensions into real arctangent functions, when these logarithms arise from the integration of rational functions with real coefficients. We conclude presenting pseudocodes and codes for implementation in the software Maxima concerning the algorithms studied in this work, as well as to algorithms for polynomial gcd computation; partial fraction decomposition; squarefree factorization; subresultant computation, among other side algorithms for the work. We also present the algorithm of Zeilberger-Almkvist for integration of hyperexpontential functions, as well as its pseudocode and code for Maxima. As an alternative for the algorithms of Rothstein-Trager and Lazard-Rioboo-Trager, we yet present a code for Benoulli’s algorithm for square-free denominators; and another for Czichowski’s algorithm, although this one is not studied in detail in the present work, due to the theoretical basis necessary to understand it, which is beyond this work’s scope. Several examples are provided in order to illustrate the working of the integration algorithms in this text

Gráfico de controle modificado para processos com estruturas complexas de autocorrelação

This work proposes a modified control chart incorporating concepts of time series analysis. Specifically, we considerer Gaussian mixed transition distribution (GMTD) models. The GMTD models are a more general class than the autorregressive (AR) family, in the sense that the autocorrelated processes may present flat stretches, bursts or outliers. In this scenario traditional Shewhart charts are no longer appropriate tools to monitoring such processes. Therefore, Vasilopoulos and Stamboulis (1978) proposed a modified version of those charts, considering proper control limits based on autocorrelated processes. In order to evaluate the efficiency of the proposed technique a comparison with a traditional Shewhart chart (which ignores the autocorrelation structure of the process), a AR(1) Shewhart control chart and a GMTD Shewhart control chart was made. An analytical expression for the process variance, as well as control limits were developed for a particular GMTD model. The ARL was used as a criteria to measure the efficiency of control charts. The comparison was made based on a series generated according to a GMTD model. The results point to the direction that the modified Shewhart GMTD charts have a better performance than the AR(1) Shewhart and the traditional Shewhart.

Construção e avaliação de uma unidade de ensino potencialmente significativa para o conteúdo de termoquímica

Nos dias atuais, oferecer uma educação para o exercício da cidadania é função primordial das políticas públicas educacionais, conforme estabelece a constituição brasileira e a legislação de ensino. Essa função vem sendo defendida por muitos professores no Ensino Médio, atribuindo-se a disciplina de Química o papel de proporcionar um ensino crítico, participativo, reflexivo e humano. Segundo os documentos oficiais brasileiros para o Ensino de Química, o estudo do conceito de energia deve favorecer o desenvolvimento de competências para que o aluno compreenda a produção e o seu uso em diferentes fenômenos e possam interpretá-los de acordo com modelos explicativos, além de saber avaliar e julgar os benefícios e riscos da produção e do uso de diferentes formas de energia nos sistemas naturais construídos pelo homem, articulando com outras áreas de conhecimento na procura de promover a interdisciplinaridade. As unidades de ensino potencialmente significativas (UEPS), tomam como base um conjunto de teorias de aprendizagem que tem o intuito de promover um ensino com base na aprendizagem significativa e podem ajudar os estudantes nas diferentes relações que um conceito pode ter. Neste sentido, o estudo do conceito da energia a partir do trabalho com UEPS, pode ser uma importante proposta que favorece um ensino de Química na perspectiva construtivista. Assim, o objetivo deste trabalho é construir e avaliar uma proposta didática para o conteúdo de termoquímica na perspectiva das unidades de ensino potencialmente significativas de Moreira com alunos do Ensino Médio de uma escola pública do Município de Campina Grande-PB. Inicialmente a UEPS foi avaliada por 22 professores em formação inicial de duas instituições públicas de ensino superior. Em seguida, ela foi aplicada para 15 alunos do 2° ano da Escola Estadual de Ensino Médio Prof. Raul Córdula, localizada na cidade de Campina Grande-PB. A coleta dos dados para os professores em formação inicial teve como base um instrumento de validação de elaboração de unidades didáticas baseada na Engenharia Didática proposta por Artigue (1996 apud Guimarães e Giordan, 2011). Já para os alunos do ensino médio, os dados foram coletados no decorrer da UEPS e a avaliação final sobre a proposta didática ocorreu através de um questionário tomando como base a escala de Likert e o uso de mapas conceituais. Para a descrição dos dados, foram utilizados os pressupostos da análise de conteúdo de Bardin. Como produto educacional foi elaborado a Unidade de Ensino Potencialmente Significativa e um DVD contendo orientações de como trabalhar com a proposta. Os resultados deste trabalho apontam uma avaliação positiva quanto à proposta de ensino elaborada para a Educação Básica, onde se observa através do instrumento de validação aplicado, que a maioria das respostas atribuídas pelos professores, ficou entre os itens suficiente e mais que suficiente. Em relação aos momentos de aprendizagem dos alunos do Ensino Médio durante a aplicação da UEPS, foi possível observar que a proposta gerou motivação no processo de ensino e aprendizagem dos conceitos da termoquímica, como também se percebe que os mapas conceituais apresentados pelos alunos apresentaram mais proposições conceituais em uma segunda tentativa de elaboração, logo a proposta de ensino foi aprovada por mais de 90 % dos estudantes do nível médio. Portanto fica evidente que a proposta didática contribuiu no processo de ensino aprendizagem, despertando interesse e motivação nos estudantes pelo conteúdo de Termoquímica.

Formação docente para a inserção da história e filosofia da ciência no ensino: textos histórico-pedagógicos em discussão

The present dissertation focuses on specific problems in the educational context: challenges in the construction of historical narratives for pedagogical use as well as the difficult task of using them in the classroom. In this context, we seek to work in teacher training for insertion of History and Philosophy of Science (HPS) in classroom, and historical narratives become mediation elements to advance the dialogue with this specific audience. This initiative is in line with a recurring concern: one of the main challenges related to the didactic transposition of HFC would be the lack of teacher preparation. Historical contents and Nature of Science are still absent in classrooms. Insecurity and lack of knowledge by teachers are often mentioned as factors that contribute to this situation. It is important, therefore, that teachers (active and in training) take part in discussions concerning the inclusion of HPS in classroom. It is relevant that they know examples of historic-philosophical didactic proposals to address science and contents on science, develop skills to adapt them to their specific contexts and to develop their own proposals. It is believed that these issues are significant to undertake conscious initiatives to insert HPS in classrooms. It is considered that adapting educational proposals to particular educational contexts depends on understanding what these proposals indeed mean and how flexible they can be. In order to address these objectives, we elaborated an educational product, a didactic material focused on teacher training, which was used in an extension course at UFRN. The didactic material discusses the role of HPS in Education, Nature of Science and historiographical issues. It presents a series of dialogical activities on aspects of didactic transposition of HPS, especially those regarding historical narratives. A set of historicpedagogical texts on the History of Vacuum and Atmospheric Pressure is used as a mediation element in discussions. We address potential, possibilities and limitations historical narratives. To carry out the course, it was taken into account methodological concerns of so-called action research. There have been expected changes, modifications and effective actions in the own teacher training material in face of the experience of the researcher-lecturer in interactions with the participants of the course as well as in face of impressions reported by the participants. Developments in this direction have been incorporated into the teacher training material.

Aprendizagem significativa: uma proposta de ensino e aprendizagem da geometria euclidiana espacial no ensino médio

This dissertation is a research based on the Meaningful Learning Theory, with students from the second year of High School, in the city named Capinzal do Norte, state of Maranhão. The pedagogic approach of this research focuses on what to do and how to do so students can better grasp knowledge inherent to the Euclidean Special Geometry in a more meaningful and changing way, also that information may be kept longer in their brain, so it can last longer in the present and future. The methodological strategy adopted was the research-action, followed by the constant observance of a researcher on the matter with the purpose to ensure consistent results, which come from the use of a variety of data collector instruments, such as: Concept Maps, manipulatives, educational softwares and application of evaluative tests, besides the observations made throughout the process of investigation and the diagnosis itself. It is all due to the fact that we rely on the premise that knowledge is assimilated in particular and idiosyncratic ways, which means each and every student learns in different ways and in different periods of time. That is why it is so important to develop diversified methodologies to the same subject. This research adds to the other ones related to the theoretical frameworks of the Meaningful Learning Theory, of Concept Maps, of the use of technology on the educational process and of manipulatives, which purpose is to connect their common dots. This pedagogical intervention also focuses on the construction of the educational orientations with applicability directly on class, directed specially by the Mathematics teacher of the basic education, who might use them during your teaching practice. Such guidelines established here as an educational product aim to follow the Theory's assumptions that serves as basis to this research, thus becoming an educational element with a relevant significance. The results, with which we are faced, proved overwhelming to the proposed objectives in terms of learning, which were evident in the construction of Conceptual Maps, as well as in the use of Concrete Materials, in addition to serving as a motivational element to participating students of research. The results obtained are indeed reliable in terms of learning, considered the expected goals, and made us certain that the way we have approached the subject is consistent with a holistic education and that at the same time values the tiniest details, which are fundamental to all the learning-teaching process.

A linguagem audiovisual do cinema como elemento integrador da arte e ciência na formação cultural dos professores de ciências e matemática

This work aims to study about the importance of cinema for cultural and professional training of teachers of Natural Sciences and Mathematics. The educational potential of cinema is emphasizing by different authors, which also reveal the teachers' training gap in this issue (media). In this study, we defend the audiovisual language of cinema as an integrating element of Arts and Science for cultural and professional training of teachers. This subject has been developed by different authors, in which the emphasis has been the importance of intelligent dialogue with the world. Specifically, the training of science teachers and mathematics, by the approach of Cinema in its formation, It envisions the possibility of minimizing the dichotomy between humanistic and scientific training, already much discussed by some researchers. Educational products contribute to an effective experience and reflection on the cultural and educational role of the Seventh Art. Considering the Cinema as a possible "bridge" between the two cultures (scientific culture and humanistic culture) and promoting ownership of audiovisual language in teacher training It was accomplished the I Exhibition - Cultural Spring: Cinema and Science Education in UFRN. The production of the booklet "Topics of History, Language and Art of Cinema for Science and Mathematics Teachers," and its application in a short course in the XXI National Symposium on Physics Teaching also aimed to contribute to the approximation of Science and Art in training teachers.

Estimação e previsão no processo INARCH(2)

In the last decades the study of integer-valued time series has gained notoriety due to its broad applicability (modeling the number of car accidents in a given highway, or the number of people infected by a virus are two examples). One of the main interests of this area of study is to make forecasts, and for this reason it is very important to propose methods to make such forecasts, which consist of nonnegative integer values, due to the discrete nature of the data. In this work, we focus on the study and proposal of forecasts one, two and h steps ahead for integer-valued second-order autoregressive conditional heteroskedasticity processes [INARCH (2)], and in determining some theoretical properties of this model, such as the ordinary moments of its marginal distribution and the asymptotic distribution of its conditional least squares estimators. In addition, we study, via Monte Carlo simulation, the behavior of the estimators for the parameters of INARCH(2) processes obtained using three di erent methods (Yule- Walker, conditional least squares, and conditional maximum likelihood), in terms of mean squared error, mean absolute error and bias. We present some forecast proposals for INARCH(2) processes, which are compared again via Monte Carlo simulation. As an application of this proposed theory, we model a dataset related to the number of live male births of mothers living at Riachuelo city, in the state of Rio Grande do Norte, Brazil.

Estimação e previsão no processo INARCH(2)

In the last decades the study of integer-valued time series has gained notoriety due to its broad applicability (modeling the number of car accidents in a given highway, or the number of people infected by a virus are two examples). One of the main interests of this area of study is to make forecasts, and for this reason it is very important to propose methods to make such forecasts, which consist of nonnegative integer values, due to the discrete nature of the data. In this work, we focus on the study and proposal of forecasts one, two and h steps ahead for integer-valued second-order autoregressive conditional heteroskedasticity processes [INARCH (2)], and in determining some theoretical properties of this model, such as the ordinary moments of its marginal distribution and the asymptotic distribution of its conditional least squares estimators. In addition, we study, via Monte Carlo simulation, the behavior of the estimators for the parameters of INARCH(2) processes obtained using three di erent methods (Yule- Walker, conditional least squares, and conditional maximum likelihood), in terms of mean squared error, mean absolute error and bias. We present some forecast proposals for INARCH(2) processes, which are compared again via Monte Carlo simulation. As an application of this proposed theory, we model a dataset related to the number of live male births of mothers living at Riachuelo city, in the state of Rio Grande do Norte, Brazil.

Classificador máquina de suporte vetorial com análise de Fourier aplicada em dados de EEG e EMG

The classifier support vector machine is used in several problems in various areas of knowledge. Basically the method used in this classier is to end the hyperplane that maximizes the distance between the groups, to increase the generalization of the classifier. In this work, we treated some problems of binary classification of data obtained by electroencephalography (EEG) and electromyography (EMG) using Support Vector Machine with some complementary techniques, such as: Principal Component Analysis to identify the active regions of the brain, the periodogram method which is obtained by Fourier analysis to help discriminate between groups and Simple Moving Average to eliminate some of the existing noise in the data. It was developed two functions in the software R, for the realization of training tasks and classification. Also, it was proposed two weights systems and a summarized measure to help on deciding in classification of groups. The application of these techniques, weights and the summarized measure in the classier, showed quite satisfactory results, where the best results were an average rate of 95.31% to visual stimuli data, 100% of correct classification for epilepsy data and rates of 91.22% and 96.89% to object motion data for two subjects.

Modelagem multiescala de fenômenos eletrocinéticos em meios porosos carregados eletricamente: aplicação a meios porosos argilosos

In this master thesis, we propose a multiscale mathematical and computational model for electrokinetic phenomena in porous media electrically charged. We consider a porous medium rigid and incompressible saturated by an electrolyte solution containing four monovalent ionic solutes completely diluted in the aqueous solvent. Initially we developed the modeling electrical double layer how objective to compute the electrical potential, surface density of electrical charges and considering two chemical reactions, we propose a 2-pK model for calculating the chemical adsorption occurring in the domain of electrical double layer. Having the nanoscopic model, we deduce a model in the microscale, where the electrochemical adsorption of ions, protonation/ deprotonation reactions and zeta potential obtained in the nanoscale, are incorporated through the conditions of interface uid/solid of the Stokes problem and transportation of ions, modeled by equations of Nernst-Planck. Using the homogenization technique of periodic structures, we develop a model in macroscopic scale with respective cells problems for the e ective macroscopic parameters of equations. Finally, we propose several numerical simulations of the multiscale model for uid ow and transport of reactive ionic solute in a saturated aqueous solution of kaolinite. Using nanoscopic model we propose some numerical simulations of electrochemical adsorption phenomena in the electrical double layer. Making use of the nite element method discretize the macroscopic model and propose some numerical simulations in basic and acid system aiming to quantify the transport of ionic solutes in porous media electrically charged.

Modelagem multiescala de fenômenos eletrocinéticos em meios porosos carregados eletricamente: aplicação a meios porosos argilosos

In this master thesis, we propose a multiscale mathematical and computational model for electrokinetic phenomena in porous media electrically charged. We consider a porous medium rigid and incompressible saturated by an electrolyte solution containing four monovalent ionic solutes completely diluted in the aqueous solvent. Initially we developed the modeling electrical double layer how objective to compute the electrical potential, surface density of electrical charges and considering two chemical reactions, we propose a 2-pK model for calculating the chemical adsorption occurring in the domain of electrical double layer. Having the nanoscopic model, we deduce a model in the microscale, where the electrochemical adsorption of ions, protonation/ deprotonation reactions and zeta potential obtained in the nanoscale, are incorporated through the conditions of interface uid/solid of the Stokes problem and transportation of ions, modeled by equations of Nernst-Planck. Using the homogenization technique of periodic structures, we develop a model in macroscopic scale with respective cells problems for the e ective macroscopic parameters of equations. Finally, we propose several numerical simulations of the multiscale model for uid ow and transport of reactive ionic solute in a saturated aqueous solution of kaolinite. Using nanoscopic model we propose some numerical simulations of electrochemical adsorption phenomena in the electrical double layer. Making use of the nite element method discretize the macroscopic model and propose some numerical simulations in basic and acid system aiming to quantify the transport of ionic solutes in porous media electrically charged.

O ensino por investigação: construindo possibilidades na formação continuada do professor de ciências a partir da ação-reflexão

Studies and reflections about the current trends on teaching Science show us the importance of include in the teaching practice, activities with a investigative and problematic approach, that allow to the learners to understand and to apply concepts and phenomena scientifics. On this perspective, the teacher continuing education is essential to effect the practice of this approach in the classroom. Therefore, this research has as an objective to contribute with Science teacher continuing formation in the basic education, in the use of the investigative approach, with a view to overcoming obstacles and making change in pedagogical practice using this research elements. For this, a qualitative research with science teachers of basic schools in the city of Natal/ RN/ Brazil was held, who attended the training course on teaching by investigation in 2012, through the project entitled "Em Busca de Novos Talentos para a Ciência: uma intervenção no ensino público" (Searching New Talents for Science: an intervention in public education).The research was conducted in four stages: Diagnosis of the conceptions of education for research and incorporation into practice after the New Talents course; projection of the intervention, intervention and evaluation. To obtain the data it was made a questionnaire, semi-structured interviews, group studies, written records and participant observation. It was analyzed that the course had significant contributions to the participating teachers to promote the approach and the motivation for incorporation of the investigative approach in practice. The permanence of weaknesses related to the theoretical basis was found, the wear resistance, difficulty in planning activities and the change in practice, diagnosed the previous course of this research. It was also noticed certain lack of domain of teaching principles of investigation by the teachers, who despite being well understood in theory, reveal gaps in practice. Despite not having been exploited the full potential of investigative activity is apparent that the inclusion of activities with an investigative approach to science and biology classes is essential for an active, critical and reflective posture of the students as well as the interest in learning about science. It was demonstrated that intervention with moments of reflection, engagement, knowledge exchange, it was effective in overcoming difficulties identified at baseline as well as providing greater motivation to face the innovations and changes in education, suggesting an important format to considered in the course of continuing education. This is because the planning and replanning allow teachers to reflect and evaluate their practice, contributing to overcoming difficulties of teachers on a daily basis.

O ensino por investigação: construindo possibilidades na formação continuada do professor de ciências a partir da ação-reflexão

Studies and reflections about the current trends on teaching Science show us the importance of include in the teaching practice, activities with a investigative and problematic approach, that allow to the learners to understand and to apply concepts and phenomena scientifics. On this perspective, the teacher continuing education is essential to effect the practice of this approach in the classroom. Therefore, this research has as an objective to contribute with Science teacher continuing formation in the basic education, in the use of the investigative approach, with a view to overcoming obstacles and making change in pedagogical practice using this research elements. For this, a qualitative research with science teachers of basic schools in the city of Natal/ RN/ Brazil was held, who attended the training course on teaching by investigation in 2012, through the project entitled "Em Busca de Novos Talentos para a Ciência: uma intervenção no ensino público" (Searching New Talents for Science: an intervention in public education).The research was conducted in four stages: Diagnosis of the conceptions of education for research and incorporation into practice after the New Talents course; projection of the intervention, intervention and evaluation. To obtain the data it was made a questionnaire, semi-structured interviews, group studies, written records and participant observation. It was analyzed that the course had significant contributions to the participating teachers to promote the approach and the motivation for incorporation of the investigative approach in practice. The permanence of weaknesses related to the theoretical basis was found, the wear resistance, difficulty in planning activities and the change in practice, diagnosed the previous course of this research. It was also noticed certain lack of domain of teaching principles of investigation by the teachers, who despite being well understood in theory, reveal gaps in practice. Despite not having been exploited the full potential of investigative activity is apparent that the inclusion of activities with an investigative approach to science and biology classes is essential for an active, critical and reflective posture of the students as well as the interest in learning about science. It was demonstrated that intervention with moments of reflection, engagement, knowledge exchange, it was effective in overcoming difficulties identified at baseline as well as providing greater motivation to face the innovations and changes in education, suggesting an important format to considered in the course of continuing education. This is because the planning and replanning allow teachers to reflect and evaluate their practice, contributing to overcoming difficulties of teachers on a daily basis.

Avaliação e correções de testes de hipóteses em modelos de sobrevivência com fração de cura

Survival models deals with the modelling of time to event data. In certain situations, a share of the population can no longer be subjected to the event occurrence. In this context, the cure fraction models emerged. Among the models that incorporate a fraction of cured one of the most known is the promotion time model. In the present study we discuss hypothesis testing in the promotion time model with Weibull distribution for the failure times of susceptible individuals. Hypothesis testing in this model may be performed based on likelihood ratio, gradient, score or Wald statistics. The critical values are obtained from asymptotic approximations, which may result in size distortions in nite sample sizes. This study proposes bootstrap corrections to the aforementioned tests and Bartlett bootstrap to the likelihood ratio statistic in Weibull promotion time model. Using Monte Carlo simulations we compared the nite sample performances of the proposed corrections in contrast with the usual tests. The numerical evidence favors the proposed corrected tests. At the end of the work an empirical application is presented.