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

Um estudo sobre o ensino de evaporação no contexto ciência, tecnologia e sociedade

The scope of this Dissertation is propose the teaching of the evaporation based on the approach Science, Technology and Society (STS) because we believe that this type of approach is able to provide students with a more critical and conscious learning about science. Moreover, with this search, it´s possible to show for students the importance of role to play for them as citizens in decision making aimed to benefit all who are part of the community to which they belong. From this perspective, broached the theme evaporation in a region characterized by constant lack of water for consumption, the municipality of Santa Cruz/RN because, despite the creation of dams to regulate the flow of rivers and increase the availability of water during periods of scarcity, we know that these reservoirs have a large free liquid surface allowing high water loss by evaporation. Thus, evaporation affects the performance of reservoirs for water supply and irrigation, being a phenomenon of particular interest to study. To this end, a questionnaire in order to identify students' preconceptions on the subject was applied. Was then prepared and conducted a workshop geared toward students majoring in Physics Campus Santa Cruz, Federal Institute of Education, Science and Technology of Rio Grande do Norte (IFRN). The completion of the workshop served as a space for discussion of the topic within the context of the municipality of Santa Cruz/RN. As a product, we suggest to physics teachers a guide with recommendations to be taken into account when they teach this subject

Inércia e Natureza da Ciência no Ensino de Física: uma sequência didática centrada no desenvolvimento histórico do conceito de inércia

During the last decades the area of science education has discussed issues related to the inclusion of the History and Philosophy of Science (HFS) in the practice of science teaching. Among the arguments put forward in favour of this approach, it is pointed out the possible enhancement of scientific content learning and the understanding of the nature of Science (NoS). In spite of such considerations, we still have a very small number of research papers reporting results of practical interventions that utilize the historical approach, moreover, there is a lack of teaching materials in this perspective. Our work has sought to contribute to this area with regard to two aspects: on the one hand, with the production of didactic material, by drawing up texts on the history of inertia for graduate students. On the other hand, we investigate whether the arguments mentioned above in relation to the didactic use of HFS sustain themselves, in a particular context. We developed and applied a didactic sequence, using the texts that we built, to teach the concept of inertia and discuss selected contents of NoS. The didactic sequence was applied in two graduate classes, one from a course of Geophysics (BSc.) and another from the Physics (teaching formation), both from the Federal University of Rio Grande do Norte (UFRN). An initial survey exposed that students, even having approached the concept of inertia in basic education, presented conceptions of common sense regarding the relationship between force and motion. The questionnaire also allowed us to identify the existence of elements of concepts considered inadequate as regards to NoS. At the end of our research, our data indicated a greater number of positive hits on the issues concerning the concept of inertia. Regarding the aspects of NoS, we were able to identify, in a few cases, a move towards a more appropriate understanding, however, certain distortions persisted, highlighting the limitations of the approach used

Física do meio ambiente como disciplina nas licenciaturas em física: proposta de uma unidade didática para ensinar efeito estufa e aquecimento global

In this dissertation we propose a Teaching Unit of Physics to teach content through environmental discussions of the greenhouse effect and global warming. This teaching unit is based on a problem-methodological intervention from the application of the method of the Arch of Charles Maguerez. The methodological foundations of the thesis are embedded in action research and this is structured in five chapters: the first chapter deals with the Physical Environment (FMA) as a subject in Degree Courses in Physics in Brazil, bringing the concern of how this discipline has been taught. We started the first chapter explaining the reasons behind the inclusion of the discipline of Physical Environment in a Physics Degree Courses. Then we did a search on the websites of Institutions of Higher Education, to know of the existence or not of this discipline on curricular. We then analyzed the menus to see what bibliographies are being adopted and what content of Physics are being worked, and how it has been done. The courses surveyed were those of Federal and Federal Institutes Universities. Thus ended the first chapter. Given the inseparability between studies in Physics Teaching and studies on competencies, skills and significant learning, wrote the second chapter. In this chapter we discuss the challenge of converting information into knowledge. Initially on initial teacher training, because even if this is not our focus, the study is a discipline on the upper reaches, therefore, offered to future teachers. Then we talked about the culture of knowledge, where we emphasize the use of a teaching approach that promotes meanings taught by content and make sense to the student. We finished the third chapter, making some considerations on skills and abilities, in order to identify what skills and competencies were developed and worked during and after the implementation of Curriculum Unit. The third chapter is the result of a literature review and study of the radioactive EarthSun interaction. The subjects researched approach from the generation of energy in the sun to topics stain solar coronal mass ejections, solar wind, black body radiation, Wien displacement law, Stefan-Boltzmann Law, greenhouse effect and global warming. This chapter deals with material support for the teacher of the aforementioned discipline. The fourth chapter talks about the arc method of Charles Maguerez; Here we explain the structure of each of the five steps of the Arc and how to use them in teaching. We also show another version of this method adapted by Bordenave. In the fifth and final chapter brought a description of how the method of Arc was used in physics classes of Environment, with students majoring in Physics IFRN Campus Santa Cruz. Here, in this chapter, a transcript of classes to show how was the application of a problem-based methodology in the teaching of content proposed for Physics Teaching Unit from the environmental discussion about the greenhouse effect and global warming phenomena

O uso de modelos ocultos de Markov no estudo do fluxo de rios intermitentes

In this work, we present our understanding about the article of Aksoy [1], which uses Markov chains to model the flow of intermittent rivers. Then, we executed an application of his model in order to generate data for intermittent streamflows, based on a data set of Brazilian streams. After that, we build a hidden Markov model as a proposed new approach to the problem of simulation of such flows. We used the Gamma distribution to simulate the increases and decreases in river flows, along with a two-state Markov chain. The motivation for us to use a hidden Markov model comes from the possibility of obtaining the same information that the Aksoy’s model provides, but using a single tool capable of treating the problem as a whole, and not through multiple independent processes

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

Teorema de Tales e suas aplicações

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES

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.

Conteúdos de matemática do ensino médio com abordagem de raciocínio recursivo e questões do ENEM e OBMEP

In this work, we have the purpose of reminding the math teacher of High School the recursive process so that he/she can use this tool to introduce contents, using recursion as an alternative to the teaching of mathematics. For this, we used questions taken from the Exame Nacional do Ensino M´edio (ENEM) [National Examination of High School] and from the Olimp´ıada Brasileira de Matem´atica das Escolas P´ublicas (OBMEP) [Brazilian Mathematics Olympiad of Public Schools], in addition to present some contents of mathematics that are defined by recursion. In this dissertation, we also showed some activities that involved the recursive reasoning and were applied in a 3rd grade class of high school in a public school in Natal / RN.

Funções e algumas de suas propriedades

In this TCC the deal with a underlying but essential topic of Mathematics, namely: Functions. Many students start their course in the University asking: Why do we need functions? With that in mind we try to antecipate to this question and we try to show that functions come up so naturally that a name was needed to express that association which exists between the elements of two sets. After this definition was established, we present and formalize some other concepts that functions might have, as: an interview of ascendence/descendence, 1-1, etc.

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.