Geometria e arirmética numa visão multicultural: uma experiência pedagógica

This paper aims to build a notebook of activities that can help the teacher of elementary school mathematics. Topics covered are arithmetic and geometry and the activities proposed here were developed aiming print them a multicultural character. We take as a base line developed by Claudia Zaslavsky multiculturalism and reflected in his books "Games and activities worldwide" and "More games and activities worldwide." We structure our work around four themes: the symbol of the Olympic Games, the pyramids of Egypt, the Russian abacus abacus and Chinese. The first two themes allow you to explore basic concepts of geometry while the latter two themes allow us to explore numerical notation and arithmetic operations

A modelagem matemática como alternativa de ensino e aprendizagem da geometria na educação de jovens e adultos

This is work itself insert in the mathematics education field of the youth and adult education to aim to practitioners of the educational action into the mathematics area performing to with this is teaching kind, adopting to as parameter the Mathematics Molding approach. The motive of the research is to draw up a application proposal of the molding mathematics as teaching and learning geometry alternative in the youth and adult education. The research it develops in three class of the third level (series 5th and 6th) of he youth and adults education in the one school municipal from the Natal outskirts. Its have qualitative nature with participating observation approach, once performing to directly in to research environment as a mathematics teacher of those same classes. We are used questionnaires, lesson notes and analyses of the officials documents as an basis of claim instruments. The results indicates that activity used the mathematic moldings were appreciated the savoir-faire of the student in to knowledge construction process, when search develop to significant learning methods, helping to student build has mathematics connections with other knowledge areas and inside mathematics himself, so much that enlarges your understanding and assist has in your participation in the other socials place, over there propitiate to change in student and teacher posture with relation to mathematic classroom dynamics

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

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

Educação matemática, ciência e tradição: tudo no mesmo barco

Les connaissances de la tradition et position de la Science dehors pour un non-hiérarchique dialoguez qui frappe pour les distinguer mais ils sont undésavouer inséparable étant donné les compléments ils composent. Cet essai assume la possibilité de ce roi de dialogue dans un place spéciale: la classe. Sur ce qui vient au connaissance de la tradition, le centre remarquable est pour la construction de bateaux du travail manuel, una pratique culturellement déployé dans la ville d'Abaetetuba, dans le État de Pará, Brésil. En revanche, la Science est concentrée par le le contenu d'école a adopté dans l'Ensino Fundamental (École primaire). La construction du dialogue est faite en utilisant des activités de l'enseignement qui accentuez des aspects géométriques (solide, géométrique, angles et symétries) aussi bien que par information qui implique le tableau, poésie, histoire, géographie et physique - les deux inspiré dans le chiffre de bateau résumé dans un CD-ROM interactif. Les activités ont eu lieu dans D'Escola Ensino Pedro Teixeira Fondamental (Abaetetuba-Pa), avec étudiants du 6e niveau (plus spécifiquement avec un groupe de 13 étudiants) d'août à octobre2004. Ethnomathématiques et transdisciplinarité sont le support théorique sous-jacent du projet. Dans résumé, c'est possible pour dire que l'interaction entre Science et Tradition, à travers activités au-delà lesquelles vont le le contenu a restreint à mathématiques d'école, contribuées à,: identifiez le contenu a appris pas sur dans série antérieure; renouveler le rôle joué par école dans ses fonctions didactique pédagogiques; réduire le isolement entre information passée historique et les étudiants présent culturel; indiquer des obstacles à l'érudition des mathématiques intéresser aux aspects cognitifs et behavioristes; et provoquer un participation affective qui rôle principal à la qualité d'apprendre l'école contenu aussi bien que les connaissances de la tradition

Os ateliês (auto)formativos na constituição do sujeito docente da educação matemática

The object of study of this thesis is the use of (self)training workshops as a fundamental process for the constitution of the teaching subject in mathematics education. The central purposes of the study were to describe and analyze a learning process of mathematics teachers supported by the training-research methodology, which procedures have been affected with the practice of (self)training workshops as a way of collaborating to the constitution of the teaching subject in Mathematics Education. The survey was conducted with a group of teachers in the city of Nova Cruz, Rio Grande do Norte through a process of continued education realized in the training workshops having as main goal the realization of the group s (self)training sessions in order to lead participants to the extent of their autonomy in their personal and professional transformations. The results obtained in the formative processes have shown the need to develop activities of mathematics teaching as a contribution to overcome the conceptual difficulties of the teachers, apart from their (self)reflections about themselves and the educational processes in which they belong. The results raised some propositions about (self)training workshops that may be incurred in practices to be included in the curriculum frameworks or materialize as a strategy of pedagogical work in training courses for teachers of mathematics. Also, they can constitute an administrative and educational activity to be instituted in the public schools of Basic Education

Os jogos com regras na perspectiva do desenho universal: contribuições à educação matemática inclusiva

To think about a school that is for everyone has been a challenge for many people connected to education worldwide demanding from researchers of each level of knowledge an association to such effort. The study presented on this paper unites itself to the voices, movements and researches of these scholars, seeking to contribute on building possibilities on which mathematics can be thought and worked on schools in order for every student to learn, whether they have some sort of deficiency, disorders, syndromes or not. This essay has the goal to investigate the possibilities of inclusive pedagogical practices mediated by math games with rules, developed and used throughout the Universal Design perspective; a qualitative research took place with a collaborative methodology that involved managers, teachers and students from a public school situated on the city of Natal/Brazil. On the investigation math games with rules were developed and made according to the Universal Design concept, starting from initial studies which articulated theoretical groundings to the reality of school and the teacher s conceptions. After that, classes using these tools were planned collectively which oriented inclusive pedagogical practices of classes from the 1st to the 4th year of elementary school. Throughout the process many instruments such as: tape recording, video footages, notes from the researcher; the teachers and the students were used for constant work evaluation and also to record the research data. In the end, the data indicated effective contributions of the mediated pedagogical practices by games with rules under the perspective of Universal Design for Inclusive Mathematics Education

Os jogos com regras na educação matemática inclusiva

This present study aimed to examine the use of games with rules in working with math education in regular classes included in Elementary School, in the municipal education schools of Natal/RN, observing the learning process and development of all students, especially those with disabilities. The theoretical references used are based on Vygotsky's works and other authors from the historical-cultural perspective, as well as researchers in the field of Inclusive Education and Mathematics Education. The investigation was based on the qualitative research guidelines, with the application of semi-structured interviews with educational coordinators and teachers from the schools involved as well as classroom observations, looking for, in the speeches of those involved and in their teaching practices, elements to reflect on the Mathematics Inclusive Education, the use of games with rules -starting from its goals, the participation of disabled students, the pedagogical mediations, up to its accessibility - and from the learning of disabled students. The analysis results showed that the concepts underlying the development of inclusive teaching practices still refer to the clinical-medical paradigm, understanding the student with disabilities from their deficiencies; which teachers use, in their majority, the mathematical games with rules in their classes, but which the teaching mediation, during these activities, still needs to be qualified so that they can, effectively, contribute to the learning and development of all students; students with disabilities do not always participate in games with others colleagues; games with rules are rarely accessible; and that the Universal Design principles are not adopted in the selected classrooms for this study. Thus, it is clear that much remains to be done so that Mathematics Education can contribute to the learning and development of all students, and among those actions the teacher continuing education is recommended

A matemática sob a ótica do Tarô: Uma experiência com a educação de jovens e adultos

La recherche de la formation des citoyens critiques et participatifs, dans le travail pédagogique avec les jeunes et les adultes, a besoin d un entraînement pédagogique qui va au delà de l attitude traditionnelle d'apprendre avec des méthodes mécaniques et arbitraires qui, en insistant excessivement sur l image du professeur, donnent priorité à l'enseignement, au détriment de l apprentissage. Dans ce sens, la présente étude, cherchant la possibilité de réalisation d'un travail alternatif pour l'enseignement des Mathématiques, dans une perspective transdisciplinaire, dans le sens de développer l apprentissage significatif des étudiants jeunes et adultes du Projet Croire, présente les résultats d'une recherche-intervention qui a utilisé les lettres du tarot comme ressource didactique en salle de classe. On prétend, avec cela, montrer cet instrument comme facilité d apprentissage de contenus des Mathématiques comme systèmes de numération, nombres entiers et géométrie, en amenant les Mathématiques dans une perspective historique et culturelle et donnant un traitement global à l'acte complexe d'apprendre. Dans ce travail, le jeune étudiant et l étudiant adulte est pris comme individu concret, prenant en considération les aspects cognitifs et les aspects d attitude de son apprentissage, ce qui est favorisé par la nature des lettres du tarot et par la compréhension adoptée, des mathématiques comme système symbolique

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

Princípio da Indução Matemática no Ensino Médio

We developed this dissertation aiming its in the process of teaching and learning of the Principle of Mathematical Induction and we set our efforts so that the students of the first year of the high school can assimilate the content having the knowledge seen in the basic education as foreknowledge. With this, we seek to awake in the student the interest on proofs, showing how much it s needed in examples that involve contents that he is already seen

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.

Um estudo sobre as origens da Lógica Matemáitca

The present study has as objective to explaining about the origins of the mathematical logic. This has its beginning attributed to the autodidactic English mathematician George Boole (1815-1864), especially because his books The Mathematical Analysis of Logic (1847) and An Investigation of the Laws of Thought (1854) are recognized as the inaugural works of the referred branch. However, surprisingly, in the same time another mathematician called Augutus of Morgan (1806-1871) it also published a book, entitled Formal Logic (1847), in defense of the mathematic logic. Even so, times later on this same century, another work named Elements of Logic (1875) it appeared evidencing the Aristotelian logic with Richard Whately (1787-1863), considered the better Aristotelian logical of that time. This way, our research, permeated by the history of the mathematics, it intends to study the logic produced by these submerged personages in the golden age of the mathematics (19th century) to we compare the valid systems in referred period and we clarify the origins of the mathematical logic. For that we looked for to delineate the panorama historical wrapper of this study. We described, shortly, biographical considerations about these three representatives of the logic of the 19th century formed an alliance with the exhibition of their point of view as for the logic to the light of the works mentioned above. In this sense, we aspirated to present considerations about what effective Aristotelian´s logic existed in the period of Boole and De Morgan comparing it with the new emerging logic (the mathematical logic). Besides of this, before the textual analysis of the works mentioned above, we still looked for to confront the systems of Boole and De Morgan for we arrive to the reason because the Boole´s system was considered better and more efficient. Separate of this preponderance we longed to study the flaws verified in the logical system of Boole front to their contemporaries' production, verifying, for example, if they repeated or not. We concluded that the origins of the mathematical logic is in the works of logic of George Boole, because, in them, has the presentation of a new logic, matematizada for the laws of the thought similar to the one of the arithmetic, while De Morgan, in your work, expand the Aristotelian logic, but it was still arrested to her

Olhares sobre a formação do professor de matemática. Imagem da profissão e escrita de si

The main focus of this thesis is the formation of a mathematical teacher at a college institution. The general aim is to describe and to analyze the formation process of a mathematical teacher which is an undergraduate student in Mathematics at the Instituto de Educação Superior Presidente Kennedy IFESP, in Natal-RN. It is based on a qualitative ethnographic approach, and has its theoretical anchorage in the (auto)biographical narratives, the social representative theories, and the mathematical education. The number of participants in this investigation was 12 undergraduate students, which corresponds to 25% of the total number of students. The corpus utilized in our analysis included 48 (auto)biographical essays, 12 (auto)biographies (formation's memories), and 12 contextualization files, besides the research's diary. The sources were obtained from the whole program of studies, i.e. from November 2003 to December 2006. The analysis revealed that the reminiscences of the 12 students' academic trajectory influenced their professional formation, since their images of a mathematical teacher were intrinsically related to the one they had before. These representations were being either demolished or constructed in a network along the assertive image of their profession, changing afterwards the mathematical representation and the teaching way of this discipline. Our study also shows that the beginning of their teacher career was marked by mechanical practices influenced by their old teachers. The (trans)formation of themselves and their teaching practices happened in a smooth way as soon as they increased their knowledgements in Mathematics, and it reflected upon the way they learned mathematics. The writing of their (auto)biographies helped the set up of new knowledgements, leaving to a self-consciousness as well as a self-formation, and contributed for the construction of a new way to see and to live the profession. Therefore, a mathematical teacher, for the undergraduate students of the IFESP involved in this work, is made at the interface of the familiar, academic, and professional context, besides the reflexive writings about the formation path, the way of life and the relationships among them

Geometrizando no segundo ciclo :relato de uma intervenção pedagógica voltada à construção de conceitos geométricos no ensino fundamental

This work has proposed to relate the experience product of a pedagogical intervention, performed in a public institution of teaching situated in this capital. It had as objective to validade the applying of a teaching module of geometry, more specifically about the conceptions of perimeter and área in the second cycle of fundamental teaching. This dissertation has presented the problematic which involves the teaching of geometry in different contexts. It has adopted the broach of the radical constructivism while methodological theoretical referencial through which it has tried to explain the phenomena that involves the teaching and the apprenticeship. It appropriates Jean s Piaget contributions related to the development stages, while referencial that will dialogue in the search by sense and comprehension of the geometric apprenticeship process and it runs over Richard s Skemp (1980) theory in order to explicit the student s apprenticeship according to the levels of instrumental comprehesion and relacional comprehension . The research has presented datum related to initial diagnosis evaluantion, the pedagogical intervention and analysis of the activities and students perfomance displaying still the results of the final evaluation. According to the results got, we could check the students group growth front to the acquisition of the concepts of perimeter and área in comparison with the previous knowledges presented in the initial diagnosis evoluation of the students participants of the research. We have concluded evaluating the objectives of the research, connecting the strategies and reasoning employed by the students in order to resolve the questions and then to reach the objectives proposed by the teaching module. We have presented still the main obstacles to the apprenticeship of such concepts