Um estudo sobre a relação entre matemática e religião na obra de Blaise Pascal

The aim of the present study is to investigate the way through which the relations between Mathematics and Religion emerge in the work of Blaise Pascal. This research is justified by the need to deepen these relations, so far little explored if compared to intersection points between Mathematics and other fields of knowledge. The choice for Pascal is given by the fact that he was one of the mathematicians who elaborated best one reflection in the religious field thus provoking contradictory reactions. As a methodology, it is a bibliographical and documental research with analytical-comparative reading of referential texts, among them the Oeuvres complètes de Pascal (1954), Le fonds pascalien à Clermont-Ferrand (2001), Mathematics in a postmodern age: a cristian perspective by Howell & Bradley (2001), Mathematics and the divine: a historical study by Koetsier & Bergmans (2005), the Anais dos Seminários Nacionais de História da Matemática and the Revista Brasileira de História da Matemática. The research involving Pascal's life as a mathematician and his religious experience was made. A wider background in which the subject matter emerges was also researched. Seven categories connected to the relation between mathematics and religion were identified from the reading of texts written by mathematicians and historians of mathematics. As a conclusion, the presence of four of these seven categories was verified in Pascal's work

Espaços transversais em educação matemática :uma contribuição para a formação de professores na perspectiva etnomatemática

This PH.D. thesis is an attempt to show the beginning, evolution and unfolding of the making of a pedagogical work proposal based on culturally-built knowings in the heart of a traditional community, having as one of its starting points the knowings and doings experienced by dish-making women from Maruanum living in the city of Macapá, State of Amapá, Brazil. This proposal is strongly associated with the need we have to think about the nature of (ethnological)-mathematical knowledge generated by particular communities and about the way such knowledge can be discussed, worked out, and validated in learning environments, regardless of the level of instruction and the constraints imposed by government programs and educational institutions. Among its theoretical foundations are studies on instrumental activities that are typical of the Maruanum ceramics and investigative studies from the point of view of ethnomathematics. Methodological development took place with the application of activities, where traditional and instrumental knowledge observed in the production of ceramics had been adapted for and brought into the school environment , participative observation, as well as data collecting and organization techniques, such as interviews, statements, and audio an visual recordings. Analysis of the data collected focused on the relationship between the data-generating potential and the purpose of this study. Our aim is to make and estimate of the potential contributions from local situations and/or problems it would possibly bring to the formative learning of people involved in the educational processes of these communities, with a view to a spatial and temporal transformation of reality

A cultura da produção de farinha: um estudo da matemática nos saberes dessa tradição

This research argues about the mathematical knowledge built in the tradition of the cassava flour production, seeking to analyse these mathematical knowledge in the perspective of the categories of time and measure, built and practiced in the flour production, located in Serra do Navio and Calçoene, in Amapá - Brazil. The following work discuss the identification and the description of the mathematics during the production activities of the flour, where is presented elements related to generation and transmission of the traditional knowledge, which is the basis for maintenance of the tradition of the flour, characterizing the research as an Ethnomathematic study. The methodological procedures highlight ethnographical techniques and elements that characterize the participating observation. The results obtained showed us that the flour workers articulate some length, area and volume measure due to own and traditionally acquired systems, which is apprehended and countersigned by other kind of culturally established system; thus they relativism the measures systems and the official calendars. And it lifts as one of the main proposal that the academic mathematics and the tradition establish knowledge make conjunction of the both knowledge, that is important for a possible reflection and application in the construction of a pedagogical practice in mathematical education, trying to establish points of socio-economic and cultural mark

Globos e mapas ao alcance das mãos : ensino de matemática numa perspectiva de alfabetização funcional na EJA

The following dissertation has as its main advantage the privilege of visualizing the literacy processes through the angle of the functional perspective, which does not see the literary process as a practice solely based on the decoding of alphabetical codes, and then allows for the opening of ample spaces for the allocation of mathematical skills in the realms of the functional literacy. The main object of this study was to investigate which are the contributions that a sequence of activities and of methodologies developed for the teaching of Geometry could provide for a part of the functional literacy process in mathematics of youngsters and adults of EJA, corresponding to the acquisition or to the improvement of skills related to the orientation capacity. The focus of the analyses consisted in the practice of these activities with the young and adult students of an EJA class belonging to a municipal public school of Natal/RN. The legacies of Paulo Freire about the redimensioning of the role of the teacher, of the students, of the knowledge and of their connections within the teaching-learning process, prevailed in the actions of the methodology implemented in the classroom and, especially, in the establishing of dialogic connections with the students, which directed all the observations and analyses regarding the collected information. The results indicated that the composition of articulations between the teaching of mathematics and the exploration of maps and the earth globe enabled the creation of multidisciplinary learning environments and situations, where we could observe, gradually, the development of procedures and attitudes indicating the evolution of space-visual type skills

Reflexões sobre a construção e evolução de conceitos geométricos nas séries intermediárias do ensino fundamental

This thesis represents a didactic research linked to the Post-graduation Programme in Education of the Universidade Federal do Rio Grande do Norte which aimed to approach the construction of the geometrical concepts of Volume of the Rectangular Parallelepiped, Area and Perimeter of the Rectangle adding a study of the Area of the Circle. The research was developed along with students from the 6th level of the Elementary School, in a public school in Natal/RN. The pedagogical intervention was made up of three moments: application of a diagnostic evaluation, instrument that enabled the creation of the teaching module by showing the level of the geometry knowledge of the students; introduction of a Teaching Module by Activities aiming to propose a reflexive didactic routing directed to the conceptual construction because we believed that such an approach would favor the consolidation of the learning process by becoming significant to the apprentice, and the accomplishment of a Final Evaluation through which we established a comparison of the results obtained before and after the teaching intervention. The data gathered were analyzed qualitatively by means of a study of understanding categories of mathematical concepts, in addition to using descriptive statistics under the quantitative aspect. Based on the theory of Richard Skemp, about categorization of mathematical knowledge, in the levels of Relational and Instrumental Understanding were achieved in contextual situations and varied proportions, thus enabling a contribution in the learning of the geometrical concepts studied along with the students who took part in the research. We believe that this work may contribute with reflections about the learning processes, a concern which remained during all the stages of the research, and also that the technical competence along with the knowledge about the constructivist theory will condition the implementation of a new dynamics to the teaching and learning processes. We hope that the present research work may add some contribution to the teaching practice in the context of the teaching of Mathematics for the intermediate levels of the Elementary School

Itinerários e marcas na formação do sujeito formador: reflexões acerca de um caminho na educação matemática

This Study inserts in Mathematical Education & Education that search to investigate the (self) formation of formers that gets graduation e pass to graduate others that get graduation and are formers in Mathematical Education. This Is a qualitative search in a perspective from search-formation.The work is formed of four topics. First topic talks about : The self-formation of formers. Second topic: at way of suppositions theorical-methodological from search. Third topic tells over: The life of a former life. Fouth topic A Station called Ubiratan D´Ambrosio created in his reverence and for build all the Knowledge´s Corpus developed by his studies and searches. It´s in sense of come and go from knowledge created at action by mankind to get finality of Transcendency and Survive. Look for to investigate aspects of academical, professional and personal life where are translated in language, thinking and practices oriented for one know-how holistical and transdiciplined in a reflexion, search and the critical it constitute to be a Professor, Teacher, Searcher and Etnomathematic that confered him the merit in 2005 the Prize Félix Klein, that declared Valente (2007), maximum distinction that can receive someone from Mathematical Education. The results point that the narratives of life´s stories are prominences to one re-direction of teach practical in formation´s courses of Mathematical teachers, opening spaces for what the teachers and particularly of Mathematical thinking and take position about your process of formation to be Formers. The Study also given possibilities to propose fourteen stoppages in Station that are beginnings with direction that emerge from studies and searches about the trajectory of life of Professor Ubiratan D´Ambrosio in perspective of re-signify the formative process in education and Mathematical Education

Simetria na dança: vestígios matemáticos na prática da dança esportiva em cadeira de rodas

To investigate in practice of the Wheelchair Dancesport (WDS), the mathematics of the characteristic isometric movements of the dance of ChaChaCha was the generating subject of this study. The subjects and the locus of the research were the athletes dancers of the Associação Baiana de Dança em Cadeira de Rodas (ABDCR). Referred him study aimed at to describe reflections concerning the athletes' practicing dancers of the technical acting Wheelchair Dancesport, using the inherent mathematical knowledge to the isometric movements executed in the ChaChaCha. For that, I stimulated in the athlete dancer the need to be investigating of his/her own practice, motivating him/it to be searching of information that they collaborate with his/her technical refinement, proposing like this roads to make possible his/her growth, while dancer and, also, promoting of their own movements. To reach my objectives I dialogued with some specialists to understand, to the light of their theories as, Espaçonumerática, Sociology of the mathematics, Etnomathematical, Dance and Symmetry, as those spaces they interact with the atmosphere of the Wheelchair Dancesport and that contributions could supply to the study. However, two authors of the Dancesport for walking , Ried e Laird, they brought contributions that aided in the creation of a prototype for the study of isometric movements in practice of the modality promoting the interface between the theory and the practice. The study showed to be possible to navigate still with the Mathematical Education in an universe little known as the one of the Wheelchair Dancesport. And it is in this adapts that propose a more attentive glance to the illustrations executed by the athlete dancer wheelchair and walking , in the dance of the ChaChaCha, verifying and proposing an analysis with focus investigate, looking for mathematical tracks concerning the symmetry that you/they characterize some of their illustrations

Práticas etnomatemáticas no Liceu do Paracuri :a propósito dos ornamentos geométricos da cerâmica

The present study analyzes the ethnomatematics practices presents in the creation of the geometric ornaments of the icoaraciense ceramic, originated and still practiced in the neighborhood of Paracuri, District of Icoaraci, belonging to Belém, capital of the State of Pará/Brasil. The object of our study was centered at the workshops supplied by the artisans master of the School of Arts and Occupations, Master Raimundo Cardoso. Referred school provides to its students, formation at fundamental level as well professional formation, through vocational workshops that help to maintain alive the practice of the icoaraciense ceramic. Our interest of researching that cultural and vocational practice appeared when we got in touch with that School, during the development of activities of a discipline of the degree course of mathematics. In order to reach our objective, we accomplished, initially, a research about the icoaraciense ceramic historic, since the first works with the clay until to the main characteristics of that ceramic. Soon afterwards, we discussed on ethnomatematics, culture, knowledge, cognition and mathematical education. At the end, we analyzed the creation of the geometric ornaments of the icoaraciense ceramic, considering the proportion concepts, symmetry and some geometry notions, that are used by the artisans when they are ornamenting the pieces of that ceramic. We verified that, in spite of the artisans, usually, do not demonstrate to possess a bit of domain on the mathematical concepts that they are working with, for instance, the ones of translaction symmetry, rotation and reflection, they demonstrate full safety in the use of those concepts, as well as the capacity to recognize them, even if in a singular specific and very peculiar way, what opens the possibility of a partnership among mathematics teachers and master-artisans of the archeological ceramic and icoaraciense workshops

Um estudo sobre a aprendizagem de alguns conceitos algébricos e geométricos

The objective of the present work was develop a study about the writing and the algebraic manipulation of symbolical expressions for perimeter and area of some convex polygons, approaching the properties of the operations and equality, extending to the obtaining of the formulas of length and area of the circle, this one starting on the formula of the perimeter and area of the regular hexagon. To do so, a module with teaching activities was elaborated based on constructive teaching. The study consisted of a methodological intervention, done by the researcher, and had as subjects students of the 8th grade of the State School Desembargador Floriano Cavalcanti, located on the city of Natal, Rio Grande do Norte. The methodological intervention was done in three stages: applying of a initial diagnostic evaluation, developing of the teaching module, and applying of the final evaluation based on the Mathematics teaching using Constructivist references. The data collected in the evaluations was presented as descriptive statistics. The results of the final diagnostic evaluation were analyzed in the qualitative point of view, using the criteria established by Richard Skemp s second theory about the comprehension of mathematical concepts. The general results about the data from the evaluations and the applying of the teaching module showed a qualitative difference in the learning of the students who participated of the intervention

A Compreensão da idéia do número racional e suas operações na EJA: uma forma de inclusão em sala de aula

The awareness of the difficulty which pupils, in general have in understanding the concept and operations with Rational numbers, it made to develop this study which searches to collaborate for such understanding. Our intuition was to do with that the pupils of the Education of Young and Adults, with difficulty in understanding the Rational numbers, feel included in the learning-teaching process of mathematics. It deals with a classroom research in a qualitative approach with analysis of the activities resolved for a group of pupils in classroom of a municipal school of Natal. For us elaborate such activities we accomplished the survey difficulties and obstacles that the pupils experience, when inserted in the learning-teaching process of the Rational numbers. The results indicate that the sequence of activities applied in classroom collaborated so that the pupils to overcome some impediments in the learning of this numbers

Investigação histórica nas aulas de matemática: avaliação de duas experiências

This study reflects on some procedural aspects about the development of mathematics learning from the experience with investigative activities concerning the resolution of second degree equation, which was tested a proposal for education, supported the use of texts in history of mathematics. The survey was conducted in two stages, taking the first-served basis for the second, which was carried out with a study group remainder of the first experiment. The intention was to investigate how the group participant, known as the study group, involved in the implementation of activities of research in mathematics, supported the use of the history of mathematics. Based on the results achieved during the study, it was possible to understand that the activities of research enable the development of students, range of learning mathematics and the development of skills and expertise for research as a vehicle for construction of their mathematical knowledge. This approach proposed research into the classroom is important, both for prospective teachers of mathematics and for students from elementary school, bringing a new phase for mathematical education that will come to schools

A etnomatemática dos trabalhadores das cerâmicas de Russas-Ce e o contexto escolar: delineando recomendações pedagógicas a partir de uma experiência educacional

It is still common among contemporary educational proposals an overemphasis abstraction, to the formalism and symbolism of mathematical knowledge at the expense of the sociocultural aspects of Mathematics. Coming up by questioning some academic mathematical tenets and valuing knowledge developed in different sociocultural contexts within Mathematical Education, the Ethnomatematics is consolidating itself as a research field. Despite its contributions to the educational context, because its philosophical character and the paucity of debates about the subject, the implementation of educational proposals for basic education are scarce. Given this situation, this dissertation comes up with a view to develop an educational intervention in the light of Ethnomathematics in a class of 6th grade of an elementary school from a red ceramic industries workers community, located in a countryside from Russas-CE and from this intervention, to develop a set of pedagogical recommendations aiming basic education teachers. Adopting a perspective of qualitative research, particularly guided by action research, this study used observation, field diary, interviews and activities with students as tools for data collection. It was found that the use of field research as part of teaching and learning favored the placement of students as critical subjects of their own reality . Furthermore, the educational experience culminated in the development of a method of teaching based on a relationship between protocooperational Ethnomatematics and the Resolution of Problems. It is necessary to broaden the debate about the ways in which the Ethnomatematics can contribute to the school context, bringing proposals closer to the reality of basic education teachers in order to help the promotion of an education which values cultural diversity without taking away the students from the access of the academic knowledge

Dificuldades na construção de gráficos de funções

This study describes about graduation s students difficulties of to draw functions graph. Specifically, we intend to observe their abilities evolution, as well as their difficulties during Calculus I subject in engineering course. For that, we show them publications about the elaboration of graphs and its difficulties in obstacle terms and some researches witch contain this subject and that it was done during postgraduate studies in mathematical education. It shows by research methodology aspects related to French didatic s mathematic and some theories of cognitive psychology considering the high value between theoretical-methodological relation that was evidenced in both theoretical conceptions about ways to understand and teach mathematic. This methodology is based on didactic engineering purpose, that consist in preliminaries analysis, conception and didactic sequence analysis prior, trials by application followed analysis up and conclusion. We had also used pedagogicals actions and analysis of results achieved, to classify types of errors made by the 2005 s students during second semester, from conceptions related to the episthemologic and didactics obstacles

Um ensaio sobre as concepções de professores de Matemática: possibilidades metodológicas e um exercício de pesquisa

Este artigo tem como tema principal as concepções dos professores de Matemática. Considerando o termo concepção a partir do pragmatismo de Peirce, elabora-se um conjunto de parâmetros metodológicos - chamado de método indireto - a ser aplicado no estudo das concepções de professores de Matemática. Trata-se, em síntese, de investigar as concepções dos professores interpelando-os não sobre suas crenças, mas sobre suas práticas. Fundamentando essa abordagem indireta e explicitando-a em sua natureza qualitativa, o artigo segue apresentando, como exemplo, um exercício desse método indireto: um estudo sobre os critérios que os professores utilizam quando escolhem livros-texto para sua sala de aula, abordando, conseqüentemente, quais concepções de Matemática e de seu ensino e aprendizagem tais critérios desvendam. Partindo de depoimentos de professores de Matemática, o estudo indica que os professores agem com certa independência quando escolhem os materiais utilizados em suas atividades docentes. Buscam, ao mesmo tempo, apoio em uma vasta gama de livros didáticos, desconsiderando as particularidades de cada obra e as abordagens e perspectivas defendidas por seus autores. Embora submetam-se ao livro didático - considerado uma referência legítima e segura -, os professores o subvertem, buscando adequá-lo ao que consideram correto. Dessa constatação, algumas das concepções dos professores podem ser realçadas: o aluno, via de regra, é avaliado e classificado pelas lacunas que apresenta em relação aos conteúdos. Dessa postura, segue a valorização da precedência lógica dos conteúdos, de sua apresentação linear, e a defesa de pré-requisitos que viabilizariam o ensino e, conseqüentemente, implicam a legitimidade de aulas predominantemente expositivas.

Um Ensaio Sobre História Oral e Educação Matemática: pontuando princípios e procedimentos

Recently, we can perceive an intensification of assignments developed into Mathematical Education with the use of oral history as a research methodology. In this article, facing the living experiences during the preparation of our Phd tasks and later, when we had the role of advisors of scientific papers and of Postgraduate students in their researches also using the same methodology, we discussed the implication of ethics, mathematical education and oral history. Furthermore, we enunciated possibilities of the posture of the researcher before interviews, texts and iconography - photos and several images-provided by collaborators of our projects on Oral history and Mathematical Education.