O PTE, as Tic, a Matemática e o GeoGebra

O Plano Tecnológico da Educação veio facilitar o acesso aos recursos tecnológicos (equipamentos e programas) e a utilização, desenvolvimento e partilha de conteúdos. Entre os diversos recursos disponibilizados, encontra-se o quadro interativo, que apresenta várias vantagens em relação ao quadro tradicional: permite a interação entre o aluno/professor e o recurso. Nas aulas de Matemática, a utilização dos quadros interativos com múltiplos recursos aumenta a motivação no processo ensinoaprendizagem. Permite a análise coletiva e a construção colaborativa do saber por parte dos alunos da turma. Possibilita a utilização em conjunto de vários programas relacionados com a Matemática, nomeadamente o Geogebra, que foi utilizado por uma turma na unidade das Isometrias.

A avaliação formativa por meio do feedback escrito no processo de ensino-aprendizagem de alunos de 2.º ciclo em matemática

Relatório final apresentado para a obtenção do grau de mestre em Ensino do 1.º ciclo e do 2.º ciclo do ensino básico

O papel das histórias com matemática na motivação dos alunos na resolução de tarefas matemáticas

Com este trabalho pretendo compreender o papel das histórias com matemática na motivação dos alunos durante a resolução de tarefas matemáticas, partindo das seguintes questões de investigação: a) Qual a relação que os alunos estabelecem com tarefas matemáticas construídas a partir de modelos matemáticos presentes em histórias? b) Que tipo de conhecimentos matemáticos surgem quando os alunos resolvem tarefas construídas a partir de um modelo matemático presente numa história? c) Como se desenvolve a comunicação matemática dos alunos quando se utilizam tarefas construídas a partir de modelos existentes em histórias? O trabalho foi realizado com uma turma de 2º e 3º anos de escolaridade, que têm desenvolvido com a professora cooperante, ao longo do tempo, um excelente trabalho na disciplina de matemática. Para o desenvolvimento deste estudo optei por utilizar uma metodologia de investigação qualitativa, como investigadora participante. Saliento, ainda, que a recolha de dados ocorreu ao longo do estágio da Unidade Curricular: Prática de Ensino Supervisionado. Durante um total de onze aulas, a análise de dados baseou-se em registos de vídeo, produções individuais dos alunos, produções dos alunos em grande grupo, e ainda na observação das interações geradas durante a análise e discussão das estratégias apresentadas pelos alunos, durante a realização das tarefas. As tarefas matemáticas apresentadas aos alunos, para o desenvolvimento deste estudo, surgiram de modelos matemáticos presentes no conto “Ainda não estão contentes?”, inserido no livro Conto Contigo, de António Torrado. Durante a realização das tarefas foi possível desenvolver conceitos que se inserem nos temas matemáticos de Números e Operações e Medida. Os resultados deste trabalho, poderão ser desenvolvidos no futuro, partindo de outros estudos e utilizando diferentes modelos matemáticos, outras histórias, outros contextos educativos, de modo a que seja possível provar que a matemática não tem de ser vista como uma disciplina difícil e angustiante para os alunos, porque existe sempre a hipótese de através de histórias, envolver os alunos nas suas aprendizagens, motivando-os para realizar tarefas matemáticas e desenvolver conhecimento matemático.

A Matemática na sala dos 4 anos: Diferentes contextos da aprendizagem da matemática

O presente estudo situa-se no âmbito da prática de ensino supervisionada e surgiu do questionamento do investigador sobre a metodologia de trabalho aplicada no local da sua prática pedagógica. Assim, pretende perceber e compreender quais os fatores que são promotores da aprendizagem ativa da matemática, nesse local, em crianças com 4 anos de idade. Para tal, no estudo, o investigador analisa os diferentes contextos de aprendizagem, os conceitos/processos matemáticos abordados e dá voz às crianças de forma a compreender como elas explicitam o que fizeram e porque o fizeram. A metodologia de estudo adotada foi no âmbito qualitativo, mais propriamente, um estudo descritivo, exploratório e interpretativo, com componentes de cariz etnográfico. Nos resultados obtidos, após a análise de dados recolhidos através de notas de campo, análise documental e entrevistas, o investigador compreendeu que, neste caso, os contextos de aprendizagem são diferentemente promotores da aprendizagem ativa da matemática pois, as crianças aderem, reagem e explicitam de maneira desigual aos diferentes contextos.

Matemática se aprende brincando?! Jogos Eletrônicos como uma possibilidade de Ensino

Esta dissertação tem como objetivo analisar a minha ação docente em aulas de matemática, que implicam a utilização de dois tipos de jogos eletrônicos em ambiente informatizado. Para tanto, foram observadas as ações e reações dos educandos ao utilizarem os jogos eletrônicos, a manifestação do pensamento, do raciocínio e de estratégias para a solução dos problemas encontrados. A metodologia desta pesquisa caracterizou-se pela natureza qualitativa - aos moldes da pesquisa-ação - numa modalidade narrativa, desenvolvendo-se pelas pesquisas bibliográficas e de campo. A coleta dos dados foi realizada por meio de entrevista semi-estruturada aplicada a nove sujeitos pertencentes a duas classes de 5ª série do ensino fundamental, em sua segunda fase. A análise dos resultados e das observações em sala de aula possibilitou concluir que os jogos, de uma maneira geral, e os eletrônicos, de forma específica, podem ser utilizados como ferramentas úteis no ensino da Matemática, proporcionando um aprendizado prazeroso, sob a orientação criteriosa do professor.

AVALIAÇÃO EM MATEMÁTICA NA EDUCAÇÃO BÁSICA, DO ESTADO DE SÃO PAULO: PONTOS DE VISTA DOS SUJEITOS ENVOLVIDOS

Este trabalho tem por objetivo levantar e analisar algumas concepções sobre a avaliação escolar em Matemática e sobre a Avaliação em Matemática do Sistema de Avaliação de Rendimento Escolar do Estado de São Paulo (SARESP), procurando desvendar a realidade que é encontrada nas escolas paulistas referente à avaliação dessa disciplina. O intuito é verificar os pontos de vista dos alunos, professores, gestores escolares, família e especialistas para articular uma organização escolar que desenvolva um processo permanente de construção do conhecimento. Para verificar quais as concepções referentes às avaliações já citadas foram adotadas entrevistas, questionários e desenhos realizados pelos alunos, mostrando o que pensam sobre as avaliações previamente aplicadas. As entrevistas somente foram aplicadas aos discentes, pois seus depoimentos são fundamentais para a pesquisa. Para a concretização destas entrevistas foi solicitado aos alunos à produção de desenhos que representassem o que são as avaliações já mencionadas anteriormente. Levantamos uma grande quantidade de informações a partir desses depoimentos e desenhos sobre as avaliações pesquisadas, a opinião que possuem sobre a escola, seus professores de Matemática, de como são ministradas as aulas e também sobre a forma de avaliar dos professores. Os questionários foram dirigidos ao corpo docente de Matemática, diretor, vice-diretor, professor coordenador, supervisor de ensino, família e especialistas em Educação, Psicologia da Educação e Matemática para verificar também sua concepção sobre avaliação escolar em Matemática e sobre a prova de Matemática do SARESP, que fazem parte fundamental de todo o processo de avaliação, pois, direta ou indiretamente, estão ligados a ela e são responsáveis pelos seus resultados. Na análise dos dados obtidos foram destacados, nos depoimentos dos questionários e das entrevistas, as,unidades significativas referentes aos processos de avaliações pesquisadas, para com isso analisarmos e verificarmos quais são as opiniões e fatos que podem ajudar ou atrapalhar todo o processo de Avaliação em Matemática, tanto o escolar quanto o de grande escala como o SARESP. Também foram analisados o que os alunos representaram na produção dos desenhos. As imagens adquiridas demonstraram muitas informações sobre o que os discentes pensam sobre a Avaliação em Matemática ao desenhar monstros, corações, números e até mesmo pontos de exclamação e de interrogação. Este estudo foi desenvolvido em uma escola pública da rede Estadual de ensino do Estado de São Paulo. Essa pesquisa investiga o que realmente está acontecendo em todo o processo de Avaliação em Matemática, possibilitando identificar no que cada sujeito envolvido neste processo pode contribuir ou atrapalhar para sua concretização, evidenciando assim áreas críticas efavoráveis sobre a tão temida e polêmica Avaliação em Matemática.

O laboratório de ensino de matemática temático centrado nos instrumentos de navegação: uma proposta para o IFRN de Mossoró-RN

This work presents a proposal to build a Mathematics Teaching Laboratory (MTL) whose main theme is the study, construction and use of instruments for navigation and location of mathematical content in an interdisciplinary way approach, and develop a notebook of activities focused on navigational instruments. For this it was necessary a literature review to understand the different conceptions of MTL and its pedagogical implications. The methodology used was literature research, construction and handling of instruments, and pedagogical experimentation. Lorenzato (2006) highlights the importance of an environment and suitable for a professional who can do a good job instruments. The implementation of an LEM can find some obstacles. The lack of support from other teachers or the management, the lack of a suitable place to store the materials produced, the lack of time in the workload of the teacher to prepare the lab activity, etc. Even in unfavorable or adverse conditions, according Lorenzato (2006), its implementation will benefit teachers and students. The lack of teacher training in their initial and continuing education, to use materials, and the lack of manuals with lab activities are also mentioned as factors that keep teachers from MTL. With propóposito assist the teacher of elementary or middle school in building a theme MTL prepared and we are providing a notebook of activities that provides a didactic sequence involving History and Mathematics. The book consists of four accompanied by suggestions for teachers activities, however the teacher has full autonomy to adapt the activities to the reality of your school. Among the instruments of navigation presented in this study chose to build the quadrant due to its simplicity, low cost of material and great teaching potential that this instrument has. But a theme lab is always being built and rebuilt as it is a research environment

Produção do mestrado profissional em ensino de ciências naturais e matemática da UFRN (física e química/2005-2012): papel dos documentos oficiais e características dos produtos educacionais

The importance of the Professionals Master in the field of science education is revealed by the recognition that they provide, to practicing teachers, in particular, training spaces for reflection and application of knowledge. This work appears in the context of the project "Research and training in teaching science and mathematics: a cutout of academic production in the northeast and overview of formative action in basic education" on the Centre for Education program, which main objective was to conduct studies description, analysis and evaluation of the academic production of Postgraduate Programs in Science Teaching of UFRPE, UFRN and UEPB and investigate the contribution of continuing education in stricto sensu level, of graduated teachers to improve the quality of basic education . We sought to examine a cut of academic production PPGECNM / UFRN, taking as reference dissertations of Natural Sciences, finished between the years 2005 and 2012, which have developed and applied educational products for high school students. More specifically we sought to conduct a general characterization of the dissertations analyzed for basic descriptors, to understand if and how the official documents governing the Brazilian education, especially science education, subsidized development of dissertations and identify current trends for science teaching are addressed and which ones are used in preparing the product of dissertations. The survey was based on documentary analysis, a type of qualitative approach in which the documents are objects of study in themselves. The results revealed that most of the work was developed in public schools, on subjects of physics and chemistry. During analytical reading of the text of the dissertations was observed that, in its construction, most of them addressed somehow, official documents governing the Brazilian educational system, that the products are basically teaching units and teaching approaches that are more focused on Experimentation and History and Philosophy of Science

História da matemática e teatro nas aulas sobre Teorema de Tales: um script proposto

This study will present the results of an investigation of how the history of mathematics and theater can contribute to the construction of mathematical knowledge of students in the 9th year of elementary school, through the experience, preparation and execution of a play, beyond presentation of the script. This brings a historical approach, defining space and time of events, putting the reader and viewer to do the route in the biography of Thales of Miletus (624-546 a.C), creating situations that led to the study and discussion of the content related to the episode possible to measure the height of the pyramid Khufu and the Theorem of Thales. That said, the pedagogical proposal implemented in this work was based on theoretical and methodological assumptions of the History of Mathematics and Theatre, drawing upon authors such as Mendes (2006), Miguel (1993), Gutierre (2010), Desgrandes (2011), Cabral (2012). Regarding the methodological procedures used qualitative research because it responds to particular issues, analyzing and interpreting the data generated in the research field. As methodological tools we have used participant observation, the questionnaire given to the students, field diary and dissertativos texts produced by students. The processing and analysis of data collected through the questionnaires were organized, classified and quantified in tables and graphs for easy viewing, interpretation, understanding and analysis of data. Data analysis corroborated our hypothesis and contributed to improving the use and display of the play as a motivating activity in mathematics classrooms. Thus, we consider that the script developed, ie the educational product proposed will bring significant contributions to the teaching of Mathematics in Primary Education

A educação básica na região metropolitana de Natal: uma análise da qualidade educativa e sua relação com o contexto familiar dos alunos

This dissertation aimed to investigate the formal learning process of children and teenagers through elementary education and, mainly, the support of family on domestic school activities as a step in the teaching-learning process. The student's family, with its cultural capital, provides an assistance which was the bias of the essay analyzes presented on this paper, using a spatial area of public elementary schools of the municipalities of the Natal metropolitan region. Such frame of Natal metropolis has been justified by the recent review of their basic education, taken by the Brazilian Ministry of Education, diagnosed in 2011, only 1% of students were in a adequate mathematics learning stage. While 62% were considered in a critical stage in this discipline. Given this issue, this dissertation offers a theoretical analysis about inherited and acquired within the family cultural capital, mainly focusing in the distances between the cultural level of the student's family and the defendant by the school. Then, presents the fundamental aspects of the issue on the urban phenomenon, focusing on social hierarchies and structures of city spaces that express differentiation, segmentation and socio-spatial segregation, and social exclusion. The emphasis on inequalities points to the development of an urban ethos, through formal schooling, which develops from social singularities. To theoretically develop the theme of Cultural Capital Family, this study sought to operationalize the concept through the interpretation of the phenomenon studied by a logical validation work hypotheses. The operation concepts systemically transformed into statistical indicators in order to measure the impact of individual, social and cultural characteristics of students elements. Finally, this dissertation found that the components evaluated, family cultural capital and housing conditions, can influence the development of skills and competencies of students in the educational sphere

Formação docente e conhecimento profissional: desafios para o ensino da matemática na EJA

As for the Education for Youth and Adult (EYA), the challenge of training these teachers is to provide tools to understand and act on the teaching of mathematics. It is realized just how special education in this modality and as such teaching is lacking in an adequate and solid training in the area of knowledge. One of the major problems affecting this type of education is the high dropout and failure rates, and lack of motivation among students. Thus the need to provide differentiated profile with a professional to teach youth and adults students, so that they are able to mobilize didactic-pedagogic knowledge, methodologies and theoretical frameworks that serve as a basis for school-developed teaching practice. This thesis aims to investigate how the math teacher, who acts in adult education from elementary school, has developed its didactic and pedagogical action, and that professional knowledge has been mobilized to teach? It has highlighted the importance of initial and continuing training and professionalization of teachers dedicated to this specific type of education, when teachers should be the protagonists of their professional development. The methodological approach was begun with a literature review, then the research was anchored mainly on the ideas by Gauthier, Nuñez and Ramalho (2004); Imbernon (2011), Garcia (2006); Perrenoud (2000); Tardif (2007 ); Haddad, Di Pierro (2000), D'Ambrosio (2002), Mendes (2006, 2009), Freire (1996, 2011), and other theorists and official documents of field of adult education here and abroad. That work leads us to the understanding of the present moment from a foray into historical and conceptual aspects, as well as educational policies of EYA, as well as training, professionalism, knowledge and skills necessary for professional practice. Then, the subjects and the locus of research and the instrument for data collection were set up and led by the object of study. To consolidate the study was selected a sample of 27 mathematics teachers, working in municipal EYA Network Teaching of Natal. This research is in an investigative nature, within the quantitative and qualitative approaches focused on the responses of study subjects from the content analysis by Bardin (1977). Results from the analyzes have revealed that the initial training of mathematics teachers of adult education needs to be reconfigured in order to formalize the knowledge base of professionals (the mathematical content, didactics and professional knowledge). Thus the study suggests that this base knowledge is embedded in the pedagogical practice of these teachers, so that there is a completion of the teaching and learning process for young people and adults. The study also has pointed out that there is a need for teachers to participate in a continuing education plan that prioritizes learning situations of mathematical content considering the previous knowledge of the students. The final analyses thus indicate that knowledge of mathematics and the didactic and pedagogical strategies to be mobilized by teachers must be able to motivate the students in such a way that they feel need to incorporate in their knowledge, mathematical knowledge capable of making them more likely to have access to social, economic and labor market

Análise wavelet e modelo de manchas em curvas de luz estelares dos telescópios espaciais Kepler e CoRoT

Analogous to sunspots and solar photospheric faculae, which visibility is modulated by stellar rotation, stellar active regions consist of cool spots and bright faculae caused by the magnetic field of the star. Such starspots are now well established as major tracers used to estimate the stellar rotation period, but their dynamic behavior may also be used to analyze other relevant phenomena such as the presence of magnetic activity and its cycles. To calculate the stellar rotation period, identify the presence of active regions and investigate if the star exhibits or not differential rotation, we apply two methods: a wavelet analysis and a spot model. The wavelet procedure is also applied here to study pulsation in order to identify specific signatures of this particular stellar variability for different types of pulsating variable stars. The wavelet transform has been used as a powerful tool for treating several problems in astrophysics. In this work, we show that the time-frequency analysis of stellar light curves using the wavelet transform is a practical tool for identifying rotation, magnetic activity, and pulsation signatures. We present the wavelet spectral composition and multiscale variations of the time series for four classes of stars: targets dominated by magnetic activity, stars with transiting planets, those with binary transits, and pulsating stars. We applied the Morlet wavelet (6th order), which offers high time and frequency resolution. By applying the wavelet transform to the signal, we obtain the wavelet local and global power spectra. The first is interpreted as energy distribution of the signal in time-frequency space, and the second is obtained by time integration of the local map. Since the wavelet transform is a useful mathematical tool for nonstationary signals, this technique applied to Kepler and CoRoT light curves allows us to clearly identify particular signatures for different phenomena. In particular, patterns were identified for the temporal evolution of the rotation period and other periodicity due to active regions affecting these light curves. In addition, a beat-pattern vii signature in the local wavelet map of pulsating stars over the entire time span was also detected. The second method is based on starspots detection during transits of an extrasolar planet orbiting its host star. As a planet eclipses its parent star, we can detect physical phenomena on the surface of the star. If a dark spot on the disk of the star is partially or totally eclipsed, the integrated stellar luminosity will increase slightly. By analyzing the transit light curve it is possible to infer the physical properties of starspots, such as size, intensity, position and temperature. By detecting the same spot on consecutive transits, it is possible to obtain additional information such as the stellar rotation period in the planetary transit latitude, differential rotation, and magnetic activity cycles. Transit observations of CoRoT-18 and Kepler-17 were used to implement this model.

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 e análise dinâmica de um sistema de conversão de energia eólica dotado de gerador síncrono de imã permanente utilizando a plataforma ATP

Human development requires a broad balance between ecological, social and economic factors in order to ensure its own sustainability. In this sense, the search for new sources of energy generation, with low deployment and operation costs, which cause the least possible impact to the environment, has been the focus of attention of all society segments. To do so, the reduction in exploration of fossil fuels and the encouragement of using renewable energy resources for distributed generation have proved interesting alternatives to the expansion of the energy matrix of various countries in the world. In this sense, the wind energy has acquired an increasingly significant role, presenting increasing rates of power grid penetration and highlighting technological innovations such as the use of permanent magnet synchronous generators (PMSG). In Brazil, this fact has also been noted and, as a result, the impact of the inclusion of this source in the distribution and sub-transmission power grid has been a major concern of utilities and agents connected to Brazilian electrical sector. Thus, it is relevant the development of appropriate computational tools that allow detailed predictive studies about the dynamic behavior of wind farms, either operating with isolated load, either connected to the main grid, taking also into account the implementation of control strategies for active/reactive power generation and the keeping of adequate levels of voltage and frequency. This work fits in this context since it comprises mathematical and computational developments of a complete wind energy conversion system (WECS) endowed with PMSG using time domain techniques of Alternative Transients Program (ATP), which prides itself a recognized reputation by scientific and academic communities as well as by electricity professionals in Brazil and elsewhere. The modeling procedures performed allowed the elaboration of blocks representing each of the elements of a real WECS, comprising the primary source (the wind), the wind turbine, the PMSG, the frequency converter, the step up transformer, the load composition and the power grid equivalent. Special attention is also given to the implementation of wind turbine control techniques, mainly the pitch control responsible for keeping the generator under the maximum power operation point, and the vector theory that aims at adjusting the active/reactive power flow between the wind turbine and the power grid. Several simulations are performed to investigate the dynamic behavior of the wind farm when subjected to different operating conditions and/or on the occurrence of wind intensity variations. The results have shown the effectiveness of both mathematical and computational modeling developed for the wind turbine and the associated controls.

O programa institucional de bolsa de iniciação à docência PIBID na formação inicial de professores de matemática

This research sought to understand the space training provided by Institutional Scholarship Program Initiation of Teaching to a group of students of Degree in Mathematics that had activities developed in the same public school. The goal is to qualify them for teaching practice for these basic institutions. We decided to conduct a qualitative study of type ethnographic case study. For a year and a half while we were at the meetings and activities of the Group, we did what we call as a participant observation. To obtain the data, we used different survey instruments: the researcher\'s field notes through his observation of everyday life of the group, photographs and filming of the activities, document analysis and database produced, physically and digitally, in addition to questionnaires and interviews with records written, which complemented each other and helped establish a triangulation of information collected. We analyze the trajectory of the group on three axes: on the first, we present and understand the paths taken by the Group in the process of setting up training spaces, and production of their professional training, in the second, we analyze how the space of PIBID is being integrated with others spaces of formations in the educational institution of the degree course in mathematics and, in the third axis, we understand the process of knowledge production of that group. The trajectory taken by the group was marked by a process of reflection and discussion systematic and collective, which favored the pursuit for be a better professional and also confirmed a possible path to be followed in initial teacher education.