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

Conhecimento, sociabilidade e lazer em jogos online : SubTítulo: uma etnografia na "Lan House do Paulo" em São Gonçalo do Amarante-RN

In a highly dynamic society such as we live, have access to the virtual world is an increasingly common practice, is aiming to study, work or to search leisure through chat rooms, sites and games, being incorporated by the most varied groups that end up appropriating these new possibilities of interaction, shaping them in order to adapt them to their needs / wants. The specific purposes pursued through the use of tools available over the Internet can vary considerably when one takes into account specific user groups, which makes the topic quite relevant to problematization, especially when we take into account access through lan houses. This research seeks to study the networks of knowledge, sociability and leisure formed by young people who frequented the "Lan house do Paulo" in São Gonçalo do Amarante - RN based on the use of the online role-playing-game World of Warcraft, which makes possible the interaction of several users through an avatar resident in a virtual world, theoretically questioning the importance of this type of platform for the development and maintenance of social interactions among its users

Modelagem matemática para o transporte de partículas sujeitas a múltiplos mecanismos de retenção

Discrepancies between classical model predictions and experimental data for deep bed filtration have been reported by various authors. In order to understand these discrepancies, an analytic continuum model for deep bed filtration is proposed. In this model, a filter coefficient is attributed to each distinct retention mechanism (straining, diffusion, gravity interception, etc.). It was shown that these coefficients generally cannot be merged into an effective filter coefficient, as considered in the classical model. Furthermore, the derived analytic solutions for the proposed model were applied for fitting experimental data, and a very good agreement between experimental data and proposed model predictions were obtained. Comparison of the obtained results with empirical correlations allowed identifying the dominant retention mechanisms. In addition, it was shown that the larger the ratio of particle to pore sizes, the more intensive the straining mechanism and the larger the discrepancies between experimental data and classical model predictions. The classical model and proposed model were compared via statistical analysis. The obtained p values allow concluding that the proposed model should be preferred especially when straining plays an important role. In addition, deep bed filtration with finite retention capacity was studied. This work also involves the study of filtration of particles through porous media with a finite capacity of filtration. It was observed, in this case, that is necessary to consider changes in the boundary conditions through time evolution. It was obtained a solution for such a model using different functions of filtration coefficients. Besides that, it was shown how to build a solution for any filtration coefficient. It was seen that, even considering the same filtration coefficient, the classic model and the one here propposed, show different predictions for the concentration of particles retained in the porous media and for the suspended particles at the exit of the media

Terapia ocupacional em ação interdisciplinar: jogos educativo-nutricionais na prevenção da obesidade infantil

The inter-subjectivity is the answer in the search for the solution of complex problems, which concerns interfaces of knowledge, respecting their borders. This paradigm is essential in the author's work. So, the search on screen is based on this perspective, by using inter-subject groups of work conduced by professionals of Computer Science, Social Communication, Architecture and Urbanism, Pedagogy, Psicopegagogy, Nutritional Science, Endocrinology, Occupational Therapy and Nursing, it was also part of this group an 8 year old child, daughter of one of the professional who took part of the group. This thesis aims to present the course of investigation developed, analyzing the action of inter-subject Occupational Therapy and Nutrition on the promotion of learning nutritional concepts through educative-nutritional games in order to prevent child's obesity in an educative context. The research was analytic, interventionist and almost experimental. It took place in a public school in Fortaleza, Ceará, Brazil, between August and December 2004. It was selected a sample non-probabilistic, by convenience, of 200 children, born from 1994 to 1996. It was selected almost nonprobabilistically, by convenience, 200 children born between 1994 and 1996. To analyze the results it was used a triangulation, associated by quantitative and qualitative approaches. The basis collect happened through games specially manufactured to these research- video-games, board games, memory games, puzzles, scramble, searching words and iterative basics. There were semi-structured interviews, direct and structured observations and focus in-groups. It was noticed the efficiency of educativenutritional games in the learning process, which lead to a changing of attitude towards the eating choices. These games gave similar results in relation to the compared variations preferences, experience and attitudes, theses attitudes were observed through the game; and the categories to compare the possibility of learning by playing, the fantasy in the learning process, learning concepts of nutritional education and the need of help in the learning process (mediation). It was proved that educativenutritional games could be used to teach nutritional concepts, in an inter-subjective action of Occupational Therapy and Nutrition in schools. The simultaneous application of these games lead to the optimization of child s learning process. It should be emphasized the need of studies about the adaptation of tools used in a child s Nutritional Education, with the help of inter-subjective action. Because just one subject, in a fractionated way can give an answer to complex problems and help to a change of the reality with effectiveness and resolution

Corpo e gestualidade :o jogo da capoeira e os jogos do conhecimento

In the direction of questing a sociology that considers the flesh dimension of the existence, that favors to think the body while place of the production of the knowledge, our itinerary of research is characterized for the reflection on the gesture of the body as power of life and production of knowledge, recognizing the precision of the gesture as a privileged breach of comment of the collective life, of the projection and registration of the culture, of the symbolic, of the sensitivity. Our problematic can be meet in the possibility to enhance an open and sensible rationality, tattooed in the body and accessible for the gestures, that its materialized in the relations of the human being with the other and the world, in singular and collective relations. Therefore, the gesture, constructed in the intention the experience of the body, can tell us about the human being, the society and the culture, therefore the sensed of the gestures is constructed from the established and recognized mutual actions for the citizens. It is in this field of production of the knowledge, of knowing of the meat that we direct our perception, in the challenge to immerge into the intention of the gesture in the capoeira game. Of the methodological point of view, for the analysis of the gestures of the capoeira, therefore, of the body as knowledge power, we consider registers of images as well as narratives registers of the universe of the capoeira, as well as my experience of more than seven years in the group of capoeira cordão de ouro1. A epistemological exercise has as support a qualitative research where parts of the quantity of images of the investigated group, as well as interviews, daily registers in of field and over all my experience of life next to the group and to the capoeira, in intention to recognize symbols tattooed in the body and for it produced in the inter subjectivists relations. We search therefore, to evidence sensible and meanings drawn for the gesture and evidenced by the look of the researcher. We presents as objectives of this inquiry to nuance ribbings around of the social and cultural elements in the production of the knowledge of the body, of the gesture, weaveeed for the sensible rationality

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

Professores em contexto formativo: um estudo do processo de mudanças de concepções sobre o ensino da matemática

El objetivo en esta tesis consistió en estudiar el proceso de los cambios de los conceptos de profesores de la educación infantil y de los años iníciales de la educación básica referente a la enseñanza de la matemática. La investigación se desenvolvió en la escuela Presidente Kennedy, en la ciudad de Natal, en Rio Grande do Norte, teniendo como participante 05 (cinco) profesores del curso normal superior a través de la educación superior del instituto relacionado. El trabajo asocia el programa a él Programa de Pós-Graduação em Educação da Universidade Federal do Rio Grande do Norte, en la base de pesquisa Formação e Profissionalização Docente coordinada de los doctores Betânia Leite Ramalho e Isauro Beltran Núñez. El referencial teórico-metodológico en quien si apoya el trabajo se inserta en la señal conceptual usada por Giordan y de Vecchi (1996), de Carrillo y Contreras (1994), Ramalho; Núñez y Gauthier (2003), Ponte (1998), Guimarães (1988), Ernest (1989). En esta investigación, los conceptos de los profesores habían sido estudiados en el contexto educativo de la formación del nivel superior, usándola reflexiva crítico práctico como estrategia formativa. Estos conceptos se entienden como estructuras subyacentes al pensamiento del profesor. Dado la naturaleza del objeto del estudio, la información, para las intenciones de esta investigación, habían sido cosechados a través de los instrumentos siguientes: cuestionario, plan de la lección, entrevista diaria y del campo. El cuestionario fue constituido de preguntas abiertas y de las entrevistas de la mitad-structuralized. La organización de los datos permitió a La inferencia de los conceptos, usando la técnica de la triangulación de datos. La investigación divulgó que los conceptos de los profesores, a través del proceso formativo, se habían desarrollado de una plataforma para otra, yéndose puesto que los modelos didácticos tradicionales para otros modelos dirigidos a una tendencia didáctica de espontaneísta/investigativa. La reflexión crítica era considerada como elemento catalítico de los cambios de los conceptos de los profesores en la educación de las matemáticas, sin embargo déjenos verifican que estos cambios son difíciles de ocurrir para la naturaleza compleja de estos conceptos. Como facilitadores de los factores de estos cambios, encontramos y el investigativo el trabajo, la dinámica y la naturaleza de las actividades se convirtió en el colaborativo de proceso formativo, entre otros. Como obstáculos a los cambios, identificamos el contexto del trabajo de los profesores, de la cultura de los individualistas prácticos de sus profesores de los colegas, del concepto linear, estático y de los mecánicos de los procesos para enseñar, el conocimiento profesional construído durante la formación inicial, alineación con los modelos didácticos de sus viejos profesores, entre otros

O ensino de matemática no Rio Grande do Norte: trajetória de uma Modernização (1950-1980)

This work aims to describe and analyze the process of the mathematics teacher modernizing in Rio Grande do Norte, in the period from 1950 to 1980. For that, we use as theoretical foundation assumptions of Cultural History and memories of the researchers Maurice Halbwach, Ecléa Bosi and Paul Thompson. As methodological tools, we used bibliographical resources and semi-structured interviews, in order to do a historical reconstruct of the mathematics educational scene of institutions and people who taught mathematics in Rio Grande do Norte, or those who participated in the modernization of the teaching of this subject, recovering their training and its practices in teaching. For the analysis of the bibliographical resources, initially we organized in a systematic way the transcripts of the interviews and documents, which were accumulated during the research, so long our thoughts, returning to the theoretical basis of this research, through questioning of knowledge acquired and that guided the problem of our study. The analysis showed that, important moments to modernize the teaching of mathematics in Rio Grande do Norte happened such: (1) Training Course of Lay Teachers in Rio Grande do Norte, in 1965, (2) Course for Teachers in Normal Schools, in 1971 (3) Satelite Project on Interdisciplinary Advanced Communications (SPIAC) in 1973; (4) Lectures of the teacher Malba Tahan, at Natal, from the end of the 50 s, that could be analyzed through the lessons notes of the teacher Maria Nalva Xavier de Albuquerque and the narrative of teacher Evaldo Rodrigues de Carvalho and (5) Courses of the Campaign for Improvement of Secondary Education and Broadcasting (CISEB). Thereby, the modernization of the school s mathematics teaching in Rio Grande do Norte, in the period from 1950 to 1980, was given mainly by disclosure of the Discovery Method and by the Set Theory contents in Teacher Training Courses

Pedagogia etnomatemática : ações e reflexões em matemática do Ensino Fundamental com um grupo sócio cultural específico

mongst the trends in Mathematics Education, which have as their object a more significant and criticallearning, is the Ethnomathematics. This field of knowledge, still very recent amongst us, besides analyzing an externalist history of the sciences in a search for a relationship between the development of the scientific disciplines and the socio-cultural context, goes beyond this externalism, for it also approaches the intimate relationships betwe_n cognition and culture. In fact, the Ethnomathematics proposes an alternative epistemological approach associated with a wider historiography. It struggles to understand the reality and come to the pedagogical action by means of a cognitive approach with strong cultural basis. But the difficulty of inserting the Ethnomathematics into the educational context is met by resistance from some mathematics educators who seem indifferent to the influence of the culture on the understanding of the mathematics ideas. It was with such concerns in mind that I started this paper that had as object to develop a curricular reorientation pedagogical proposal in mathematics education, at the levei of the 5th grade of the Ensino Fundamental (Elementary School), built from the mathematical knowledge of a vegetable farmers community, 30 km away from the center of Natal/RN, but in accordance with the teaching dimensions of mathematics of the 1 st and 2nd cycles proposed by the Parâmetros Curriculares Nacionais - PCN: Numbers and Operations, Space and Form, Units and Measures, and Information Treatment. To achieve that, I developed pedagogical activities from the mathematical concepts of the vegetable farmers of that community, explained in my dissertation research in the period 2000 through 2002. The pedagogical process was developed from August through Oecember 2007 with 24 students of the 5th Grade of the Ensino Fundamental (Elementary School) of the school of that community. The qualitative analysis of the data was conducted taking into account three categories of students: one made up of students that helped their parents in the work with vegetables. Another one by students whose parents and relatives worked with vegetables, though they did not participate directly of this working process and one third category of students that never worked with vegetables, not to mention their parents, but lived adjacent to that community. From the analyses and results of the data gathered by these three distinct categories of students, I concluded that those students that assisted their parents with the daily work with vegetables solved the problem-situations with understanding, and, sometimes, with enriching contributions to the proposed problems. The other categories of students, in spite of the various field researches to the gardens of that community, before and during the pedagogical activities, did not show the same results as those students/vegetable farmers, but showed interest and motivation in ali activities of the pedagogical process in that period

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

Uma reavaliação do pensamento lógico de George Boole à luz da história da matemática

The aim of the present study is to reevaluate the logical thought of the English mathematician George Boole (1815 - 1864). Thus, our research centers on the mathematical analysis of logic in the context of the history of mathematics. In order to do so, we present various biographical considerations about Boole in the light of events that happened in the 19th century and their consequences for mathematical production. We briefly describe Boole's innovations in the areas of differential equations and invariant theory and undertake an analysis of Boole's logic, especially as formulated in the book The Mathematical Analysis of Logic, comparing it not only with the traditional Aristotelian logic, but also with modern symbolic logic. We conclude that Boole, as he intended, expanded logic both in terms of its content and also in terms of its methods and formal elaboration. We further conclude that his purpose was the mathematical modeling of deductive reasoning, which led him to present an innovative formalism for logic and, because the different ways it can be interpreted, a new conception of mathematics

Ensino de matemática, história da matemática e artefatos: Possibilidade de interligar saberes em cursos de formação de professores da Educação Infantil e anos iniciais do Ensino Fundamental.

This work is located at the shield of research that defends the use of Mathematics History, based on the utilization of historical artifacts at teaching activities, at Mathematics classrooms, and at graduation courses for teachers of Elementary School and of the first grades of High School. The general objective is to examine the possibility of the use of historical artifacts, at teaching activities, at graduation courses for teachers of Elementary School and of the first grades of High School. Artifact, at this work, is comprehended as objects, documents, monuments, images and other kinds of materials that make sense to the Human actions at the past and that represent what have been said and done at the Human history. At the construction of the theoretical-methodological way of the research we have based ourselves upon the ideas of the authors that are engaged at the teachers formation; at researchers adherents to the use of Mathematics History (MH) as a methodological resource, and at studies accomplished that elucidate the role of the artifacts at the history and as a mediatory element of learning. We defend the thesis that the utilization of historical artifacts at teaching activities enables the increasing of the knowledge, the development of competencies and essential abilities to the teacher acting, as well as interact at different areas of the knowledge, that provides a conception of formation where the teacher improves his learning, learning-doing and learning-being. We have adopted a qualitative research approach with a theoretical and pratic study disposition about the elements that contribute to the teachers works at the classroom, emphasizing the role of the Mathematics history at the teacher s formation and as a pedagogical resource at the mathematics classroom; the knowledge, the competencies and abilities of the historical artifacts as an integrative link between the different areas of the knowledge. As result, we emphasize that the proposition of using the MH, through learning activities, at the course of teacher graduation is relevant, because it allows the investigation of ideas that originate the knowledge generated at every social context, considering the contribution of the social and cultural, political and economical aspects at this construction, making easy the dialog among the areas and inside of each one The historical artifact represents a research source that can be deciphered, comprehended, questioned, extracting from it information about knowledge of the past, trace and vestiges of the culture when it was created, consisting of a testimony of a period. These aspects grant to it consideration to be explored as a mediatory element of the learning. The artifacts incorporated at teaching activities of the graduation courses for teachers promote changes on the view about the Mathematics teaching, in view of to privilege the active participation of the student at the construction of his knowledge, at the reflection about the action that has been accomplished, promoting stimulus so the teachers can create their own artifacts, and offer, either, traces linking the Mathematics with others knowledge areas.

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