Investigação histórica na formação de professores de matemática: um estudo centrado no conceito de função

In this study we analyzed the development of a teaching experience, involving students with a bachelor s degree in mathematics from UFRN, based on the history of mathematics and mathematical investigations with the aim of contributing to the improvement of the teaching-learning of mathematics. The historical investigation tasks were planned and applied in the classroom, focusing on functional thought. The results obtained during the experience were described and evaluated based on authors who support the assumption of investigation and history as an alternative to the learning of mathematics. We emphasize that the material of analysis consisted of a work diary, audio recordings, questionnaires with testimony of the students involved, and, in addition, the assessment of the teacher of that subject. With regard to the mathematical content, the study was restricted to the concept of function, forms of representation and notation. It was evident that students showed great improvement with regard to the necessary formalization of the mathematical contents which were focused on, and to the active involvement of the students at different stages of the study. We can affirm that the completed study certainly represents significant contributions to an approach in the teaching-learning of functional thought

Uma abordagem histórica para o ensino do princípio da inércia

Placed in the field of Didactic of Science, this paper proposes an approach to the introduction of the History of Science in science education, at high school level. It was designed and implemented a series of activities regarding the history of the Principle of Inertia. The aim of this approach was to give more meaning to scientific education, while opening new avenues for a better understanding of the processes of construction of scientific knowledge. The preparation of the activities involved a study of the historical development of the concept of motion, from the Aristotelian physics through physical movement concepts at medieval period, from Galileo, Gassendi, Descartes, until the first law of Newton. The strategy of teaching was applied to three classes of high school (night period) of a state public school at the city of Natal (RN). The results indicated the difficulty of overcoming alternative conceptions about movement by students. Nevertheless, we consider that the implementation of this strategy of teaching both represented gains for the learning of students, and contributed to the resizing of pedagogical practices of the teacher-researcher

Uma investigação histórica sobre os logaritmos com sugestões didáticas para a sala de aula

This study was conducted from a preliminary research to identify the conceptual and didactic approach to the logarithms given in the main textbooks adopted by the Mathematics teachers in state schools in the School of Natal, in Rio Grande do Norte. I carried out an historical investigation of the logarithms in order to reorient the math teacher to improve its educational approach this subject in the classroom. Based on the research approach I adopted a model of the log based on three concepts: the arithmetic, the geometric and algebraic-functional. The main objective of this work is to redirect the teacher for a broad and significant understanding of the content in order to overcome their difficulties in the classroom and thus realize an education that can reach the students learning. The investigative study indicated the possibility of addressing the logarithms in the classroom so transversalizante and interdisciplinary. In this regard, I point to some practical applications of this matter are fundamental in the study of natural phenomena as earthquakes, population growth, among others. These practical applications are connected, approximately, Basic Problematization Units (BPUs) to be used in the classroom. In closing, I offer some activities that helped teachers to understand and clarify the meaningful study of this topic in their teaching practice

Elaboração e aplicação de uma sequência de atividades para o ensino da trigonometria numa abordagem histórica

The present work aims to report the construction of a workbook for teaching trigonometry focusing the possible mix between the historical approach to the teaching of mathematics and the professional master´s degree. For this, considerations about the history of mathematics as a teaching methodology, the education of the math teacher who will teach trigonometry and also about the course of elaboration and experimentation of the activities in the workbook were made (using the methodological strategy of action research). Finally, the workbook for the teaching of trigonometry in a historical approach is presented as an example of the above mentioned mix between the history of mathematics, mathematical school content and the professional master´s degree

Propriedades dos sistemas de numeração: uma sequência didática em uma abordagem histórica

This paper aims to describe the construction and validation of a notebook of activities whose content is a didactic sequence that makes use of the study of ancient numbering systems as compared to the object of our decimal positional numbering system Arabic. This is on the assumption that the comparison with a system different from our own might provide a better understanding of our own numbering system, but also help in the process of arithmetic operations of addition, subtraction and multiplication, since it will force us to think in ways that are not routinely object of our attention. The systems covered in the study were the Egyptian hieroglyphic system of numbering, the numbering system Greek alphabet and Roman numbering system, always compared to our numbering system. The following teachung is presented structured in the form of our activities, so-called exercise set and common tasks around a former same numbering system. In its final stage of preparation, the sequence with the participation of 26 primary school teachers of basic education

Atividades estruturais de equações polinomiais numa abordagem histórica por meio de e-book

The present study investigates how the inter-relationship of the content of polynomial equations works with structured activities and with the history of mathematics through a sequence of activities presented in an e-book, so that the result of this research will proceed will result in a didactic and pedagogic proposal for the teaching of polynomial equations in a historical approach via the reported e-book. Therefore, we have considered in theoretical and methodological assumptions of the History of Mathematics, in structured activities and new technologies with an emphasis on e-book tool. We used as a methodological approach the qualitative research, as our research object adjusts to the objectives of this research mode. As methodological instruments, we used the e-book as a synthesis tool of the sequence of activities to be evaluated, while the questionnaires, semi-structured interviews and participant observation were designed to register and analyze the evaluation made by the research, participants in the structured activities. The processing and analysis of data collected though the questionnaires were organized, classified and quantified in summary tables to facilitate visualization, interpretation, understanding, and analysis of these data. As for participant observation was used to contribute to the qualitative analysis of the quantified data. The interviews were synthetically transcribed and qualitatively analyzed. The analysis ratified our research objectives and contributed to improve, approve and indicate the use of e-book for the teaching of polynomial equations. Thus, we consider that this educational product will bring significant contributions to the teaching of mathematical content, in Basic Education

Pelo escuro: a poesia afro-brasileira de Oliveira Silveira

O presente estudo traz uma reflexão sobre os discursos culturais afro-brasileiros e o lugar ocupado pela poesia em meio a uma sociedade racista. A pesquisa tem como propósito fazer um estudo da poesia de Oliveira Silveira (1968, 1970, 1977, 1981, 1987). Leva-se em consideração a relação da produção poética de Oliveira com as propostas do movimento da Negritude e o diálogo lúcido que o mesmo estabelece com poetas vinculados ao referido movimento e como Silveira sugere dentro da literatura a negritude como uma forma de intersecção na poesia brasileira. A proposta aqui apresentada observa também o hibridismo na poética de Oliveira Silveira ao se enfatizar um olhar sobre uma escrita comovida pelo traço do entre-lugar do discurso. Analisa-se a caracterização de uma literatura gerada pelo tom de denúncia ao desconstruir historicamente o que há muito tempo se estabelece como democracia racial . Em cumplicidade com a poesia regional do Rio Grande do Sul, a poesia de Oliveira vem permeada pela diversidade de ritmos que traduzem o legado da cultura negra mundo afora. Essa pesquisa sustenta-se nos estudos de Eduardo de Assis Duarte (2005, 2011) e Kabengelê Munanga (2008, 2009) sobre Negritude e Identidade na literatura afro-brasileira, que se caracteriza como um movimento de consciência pela reconstrução ou mesmo revisão histórica do que foi apagado no calabouço dos navios negreiros. As leituras de Eduardo de Assis Duarte fomentam novos questionamentos, põem em dúvida a existência de uma identidade essencialista. Aponta-se nessa travessia para uma pluralidade de identidades, construídas por inúmeros grupos culturais na encruzilhada dos diversos momentos históricos. Analisam-se, portanto, a partir da crítica que Stuart Hall (2011) faz ao considerar as ideias de diásporas, as fronteiras das margens no universo da pós-colonização. Por fim, há uma encruzilhada ao se pensar a partir de Kabengelê Munanga, o discurso da negritude e da identidade negra nas relações sociais e culturais afrodescendentes

O conceito de consciência em o ser e o nada de J.-P. Sartre

This current discourse intends to prove how consciousness or Being-for-itself presents the idea that in its operation one can emphasize that it s Nothingness, transience and liberty in Jean-Paul Sartre s work O Ser e o Nada. To testify the proposed idea, the conception that Sartre gives to consciousness, representing nothingness, without any content that is connected to the possessor objects of a transphenomenal existence will be the starting point. This way, consciousness will be analyzed transcendently to the object that it s not, demonstrating its revealer-revealed condition, because it unveils a concrete world that exists against its idea, functioning as the revealer intentionality that there are beings instead of nothingness, obeying the ontological proof defended by Sartre. From this idea, every kind of consciousness will always be consciousness of something, a glance of the world, avoiding the fact that the consciousness could be considered nothing in the world. In order to live its original negation state of the world, apprehending this same world, with the purpose of a knowledge, it needs to be divided in two: the first degree consciousness or previous-reflexive cogito, that turns the proper reflexion possible, because, it s the consciousness proper transphenomenality of being different of all that connected to its existence being only its consequence; and the cogito, responsible to the positioning of the first degree consciousness, while aware of its own consciousness, that is, while being certain that knows. From this point, the way to untangle the consciousness or Being-for-itself will be developed as being Chasm, Liberty and transience. From this idea, it s intended to know how consciousness, that in Sartre s thoughts is originally nothing, could turn into Liberty that is presented in the field of transience? In other words, how these three internal structures imbricate one another to form consciousness in Sartre? First of all, it has to be considered the review of a conduct of human reality, the inquiry, that will be possible to understand how Nothingness exists as the mold of all kind of negation. After this, it will be shown, considering its way of existence, the human reality that is connected to Para-si, determined like nothingness, still is proposed like Liberty. Form this point, it will be possible to gleam how Liberty is lived deeply by Para-si in the shape of chasm, trying to how Para-si turns into nothingness, creating a chasm based on its proper liberty. Then, Liberty will be the proper mechanism used by Para-si to modificate its original chasm. The way Being-for-itself has to build to gain its goal will be projecting in transience, the building of something possible that brings one being back. However, will be demonstrated like Chasm can occupy the moment of a choice turning the decision instant an anguish stage, based on the failing of stability of the Being-for-itself, once nothingness persists in the field of the possibilities that human beings preserves in its essence while being essentially Liberty. From this idea, anguish will be studied as the proper consciousness of Liberty, being bad-faith the attempt of avoid Liberty trying to gain a shelter contradicting the fact that life is done of continual choices