Explorando a matemática dentro da calculadora

This dissertation aims to suggest the teacher of high school mathematics a way of teaching logic to students. For this uses up a teaching sequence that explores the mathematical concepts that are involved in the operation of a calculator one of the greatest symbols of mathematics.

Explorando a matemática dentro da calculadora

This dissertation aims to suggest the teacher of high school mathematics a way of teaching logic to students. For this uses up a teaching sequence that explores the mathematical concepts that are involved in the operation of a calculator one of the greatest symbols of mathematics.

Lousa digital no ensino de matemática

Using the digital whiteboard and its resources , classes become much more motivating and interesting than those that only require the chalk or whiteboard. In the face of still images , or moving, this technology has caused a broader interaction between the student, the content taught and the teacher bringing positive and significant changes to education. In this work, we discuss the technological evolution of education, new educational technologies, the digital blackboard and your pedagogical applications inmath classes and howthe teacher can mount it using resources available at the school and other relatively low cost. Finally, we will address the concept of homography and how it is applied in its operation.

Lousa digital no ensino de matemática

Using the digital whiteboard and its resources , classes become much more motivating and interesting than those that only require the chalk or whiteboard. In the face of still images , or moving, this technology has caused a broader interaction between the student, the content taught and the teacher bringing positive and significant changes to education. In this work, we discuss the technological evolution of education, new educational technologies, the digital blackboard and your pedagogical applications inmath classes and howthe teacher can mount it using resources available at the school and other relatively low cost. Finally, we will address the concept of homography and how it is applied in its operation.

O jogo dos discos: o uso da experimentação como suporte para o ensino da probabilidade

In this paper we propose a class for introducing the probability teaching using the game discs which is based on the concept of geometric probability and which is supposed to determine the probability of a disc randomly thrown does not intercept the lines of a gridded surface. The problem was posed to a group of 3nd year of the Federal Institute of Education, Science and Technology of Rio Grande do Norte - Jo~ao C^amara. Therefore, the students were supposed to build a grid board in which the success percentage of the players had been previously de ned for them. Once the grid board was built, the students should check whether that theoretically predetermined percentage corresponded to reality obtained through experimentation. The results and attitude of the students in further classes suggested greater involvement of them with discipline, making the environment conducive for learning.

O jogo dos discos: o uso da experimentação como suporte para o ensino da probabilidade

In this paper we propose a class for introducing the probability teaching using the game discs which is based on the concept of geometric probability and which is supposed to determine the probability of a disc randomly thrown does not intercept the lines of a gridded surface. The problem was posed to a group of 3nd year of the Federal Institute of Education, Science and Technology of Rio Grande do Norte - Jo~ao C^amara. Therefore, the students were supposed to build a grid board in which the success percentage of the players had been previously de ned for them. Once the grid board was built, the students should check whether that theoretically predetermined percentage corresponded to reality obtained through experimentation. The results and attitude of the students in further classes suggested greater involvement of them with discipline, making the environment conducive for learning.

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.

Um estudo sobre polinômios matriciais

This research work aims to make a study of the algebraic theory of matrix monic polynomials, as well as the definitions, concepts and properties with respect to block eigenvalues, block eigenvectors and solvents of P(X). We investigte the main relations between the matrix polynomial and the Companion and Vandermonde matrices. We study the construction of matrix polynomials with certain solvents and the extention of the Power Method, to calculate block eigenvalues and solvents of P(X). Through the relationship between the dominant block eigenvalue of the Companion matrix and the dominant solvent of P(X) it is possible to obtain the convergence of the algorithm for the dominant solvent of the matrix polynomial. We illustrate with numerical examples for diferent cases of convergence.