Pedagogia de projetos e etnomatemática: caminhos e diálogos na zona rural de Mossoró - RN

Teaching Mathematics in a contextualized and significant manner, in the world of the child and the adolescent, requires a solid theoretical and methodological basis on the part of the researcher. The present work found this foundation in two ways: teaching with projects and ethnomathematics. It is understood that these ways have points in common, such as: the real, interdisciplinarity, teaching methods, flexibility in sequencing the curriculum and interactive learning. This makes possible a theoretical cross-fertilization, which is important for the teaching/learning of Mathematics. Those points are merged in the present proposal, making possible new strategies, distinct from those of the Traditional Teaching Methodology and giving raise to an Alternative Teaching Methodology, which is to be lived in the Mathematics classrooms. This work gives a new direction to teaching, going beyond the traditional forms of education by allowing the teaching of Mathematics to become integrated with other school subjects, resulting in significant learning. In order to implement the proposal, it is necessary to form partnerships with teachers, pupils and the whole community, so that the way can be traced by continual dialogue

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

A mediação do diálogo e da reflexão na prática do supervisor pedagógico no município de Jardim de Piranhas/RN

In preparation for reviewing and reflect about the pedagogical practice of teaching supervisor, noting instances of continuing education in service, dialogue-based, reflective and shared as propelling in the construction of theoretical and practical knowledge is that we propose to undertake this research. Based in our professional practice and stimulated by the desire to contribute with the education in the city of Jardim de Piranhas-RN our intention was to highlight issues which arising from practice teaching, especially those guided in the principles of a continuing, dialogic and reflexive teachers training. In that sense we are encouraged to answer the following question. How has been developed the work of teaching supervisor in the city of Jardim de Piranhas and what kind of elements should be constituted by a continuing education in school if those elements are enhanced by a reflexive action and dialogue-based? Thus, we performed studies of theoretical foundation based in Nóvoa (1995, 2001, 2003), where he emphasizes the importance of take in account the practice itself as a source for the study in the construction of a new teaching practice process, in Alarcão (1999; 2001; 2002; 2003), Schön (1995, 2000), Tardif (2003) and Perrenoud (2002), Gomes (1998), Navarro (2005) and Oliveira (2006), among others, provided the basis to discuss the role of reflection and dialogue in the school and classroom. We still emphasize the ideas of Paulo Freire (1981; 1992; 1996; 2001; 2002), which is consistent with the proposal for a reflexive action and training. For this we adopted a methodology based in the qualitative research with field note, intending to observe the strategies which emerge in the educational supervisor practice. This practice should contribute to the training of teachers. In this process we chose three dimensions that provide structure and power in their work. So, we can describe as conceptual, strategic and changeable

Aí eu era Antônio Brasil: contribuições de situações didáticas com conhecimentos históricos para a construção da identidade pessoal da criança na educação infantil

L'objectif de cette étude est de comprendre la relation entre les situations didactiques faisant appel aux connaissances historiques et la construction de l'identité personnelle pour les enfants dans l'éducation de la petite enfance. Sa question centrale se demande si les connaissances sont offrent des contributions à la construction de l'identité personnelle par les enfants de la petite enfance. Se distingue, lui aussi, entend contribuer à élargir le débat sur l'enseignement et l'apprentissage des thèmes historiques dans l'éducation des enfants, et permettre un dialogue avec d'autres enseignants dans cette étape de l'éducation. Ont été analysés par des principes théoriques et méthodologiques de qualité et a assumé les orientations méthodologiques de la recherche collaborative. Il a été constaté que la systématisation des situations didactiques impliquant la connaissance historique dans l'éducation de la petite enfance contribue à la construction de l'identité personnelle de l'enfant. Ceci, pour prendre possession de ces connaissances, ils recueillent des renseignements qui permet le plus large éventail de relations, afin de comparer les pratiques culturelles de son temps avec des pratiques à d'autres moments. Ainsi orientée, l'enfant cherche à raconter son histoire avec le thème historique à laquelle elle a eu accès, d'organiser et de construire des réponses des explications sur leur environnement et de lui-même. Tout cela montre à la réalisation que le processus d'internalisation des connaissances historiques de l'enfant est construit comme un sujet et, par conséquent, cette connaissance peut être conçu comme un médiateur dans la formation de l'identité personnelle

Objetiva(ação) da medida e contagem do tempo em práticas socioculturais e educativas

This thesis describes and analyzes various processes established and practiced by both groups about the socio-cultural objective (action) the measurement and timing, mobilized some socio-historical practices as the use of the gnômon of the sundial and reading and interpretation of movements celestial constellations in cultural contexts such as indigenous communities and fishermen in the state of Pará, Brazil. The Purpose of the study was to describe and analyze the mobilization of such practices in the socio-historical development of matrices for teaching concepts and skills related to geometric angles, similar triangles, symmetry and proportionality in the training of mathematics teachers. The record of the entire history of investigation into the socio-historical practice, the formative action was based on epistemological assumptions of education ethnomathematics proposed by Vergani (2000, 2007) and Ubiratan D'Ambrosio (1986, 1993, 1996, 2001, 2004) and Alain Bishop conceptions about mathematics enculturation. At the end of the study I present my views on the practices of contributions called socio-cultural and historical for school mathematics, to give meaning to the concept formation and teaching of students, especially the implications of Education Ethnomatematics proposed by Vergani (2000) for training of future teachers of mathematics

Utilizando processos geométricos da história da matemática para o ensino de equações do 2º grau

The present work had as principal objective to analyze the, 9th grade students understanding about the solutions of an equation of the 2° degree, using geometric processes of the History of the Mathematics. To do so, the research had as base the elaboration and application of a group of teaching activities, based on Jean Piaget's construtivism. The research consisted of a methodological intervention, that has as subjects the students of a group of 9th grade of the State School José Martins de Vasconcelos, located in the municipal district of Mossoró, Rio Grande do Norte. The intervention was divided in three stages: application of an initial evaluation; development of activities‟ module with emphasis in constructive teaching; and the application of the final evaluation. The data presented in the initial evaluation revealed a low level of the students' understanding with relationship to the calculation of areas of rectangles, resolution of equations of the 1st and 2nd degrees, and they were to subsidize the elaboration of the teaching module. The data collected in the initial evaluation were commented and presented under descriptive statistics form. The results of the final evaluation were analyzed under the qualitative point of view, based on Richard Skemp's theory on the understanding of mathematical concepts. The general results showed a qualitative increase with relationship to the students' understanding on the mathematical concepts approached in the intervention. Such results indicate that a methodology using the previous student‟s knowledge and the development of teaching activities, learning in the construtivist theory, make possible an understanding on the part of the students concerning the thematic proposal

DANÇA: linguagem do corpo na educação infantil

This production is a reflection about the practices/experiences involving the teaching of the dance developed by the teachers in the Núcleo de Educação Infantil (NEI/UFRN), with the children from 2 to 7 years old, having as objectives: describe and interpret the lived experiences with the dance focusing on the meaning of the dance and organization of the pedagogic job, identify blanks in the pedagogic practices of dance and appoint possible perspectives to the teaching of dance on the infant education. The way from the investigation has begun with the following question: Who do the teachers understand the dance and live it on the Núcleo de Educação Infantil? The research of phenomenological orientation toke as methodological reference the qualitative approach from the placed phenomenon type, this one has as beginning the interest on the phenomenon by the way as it happens on the lived experience from where comes the knowledge with we can present about the world, trying to interpret it, understand it on its essence/existence. The interviews showed that the researched subjects give to the dance different meanings and consequently present variations on the manner to organize the work around this knowledge. The most of the teachers recognizes the dance as a culture expression, being a priority on the school the job with the folkloric dances. They recognize too the dance as knowledge/content coming from the Arts and Physical Education areas and its relation with the knowledge from others areas on the pedagogic action. There were found different process on the way to conduct the job with the dance in relates from experiences done with dance at NEI and, therefore, of teach/learn this knowledge. Its perceptible that exists a systematic work with the objective of develop the dance and its various educative possibilities, starting from the research about its origins, the exploration of the movement, the contextualization until the artistic practice. Those possibilities are reinforced on the school s curricular propose. Some experiences have as a priority the free expression, the dance s vision without context or the reproduction of movements as stand manners of teaching dance, situations like those observed on the investigation as products from the blanks on the academic formation from the teachers with must be fixed. The interpretation of the experiences with dance, described by the teachers from NEI, connected with the theoretical referential from the investigation, allowed to appoint three perspectives to the work with dance in the infant education, having as main interlocutors Merleau-Ponty and Rudolf Laban: the dance as the body s language; the dance and its movement factors; imitate, improvise and play: manners of draw ways to dance. On those process are emphasized the dance on the scholar context, the elements that constitute this language and the forms of appropriate from it supported in a ludicrous, poetic and educative vision, having as focus the children s education on its peculiarities and possibilities

Obstáculos superados pelos matemáticos no passado e vivenciados pelos alunos na atualidade : a polêmica multiplicação de números inteiros

In Mathematics literature some records highlight the difficulties encountered in the teaching-learning process of integers. In the past, and for a long time, many mathematicians have experienced and overcome such difficulties, which become epistemological obstacles imposed on the students and teachers nowadays. The present work comprises the results of a research conducted in the city of Natal, Brazil, in the first half of 2010, at a state school and at a federal university. It involved a total of 45 students: 20 middle high, 9 high school and 16 university students. The central aim of this study was to identify, on the one hand, which approach used for the justification of the multiplication between integers is better understood by the students and, on the other hand, the elements present in the justifications which contribute to surmount the epistemological obstacles in the processes of teaching and learning of integers. To that end, we tried to detect to which extent the epistemological obstacles faced by the students in the learning of integers get closer to the difficulties experienced by mathematicians throughout human history. Given the nature of our object of study, we have based the theoretical foundation of our research on works related to the daily life of Mathematics teaching, as well as on theorists who analyze the process of knowledge building. We conceived two research tools with the purpose of apprehending the following information about our subjects: school life; the diagnosis on the knowledge of integers and their operations, particularly the multiplication of two negative integers; the understanding of four different justifications, as elaborated by mathematicians, for the rule of signs in multiplication. Regarding the types of approach used to explain the rule of signs arithmetic, geometric, algebraic and axiomatic , we have identified in the fieldwork that, when multiplying two negative numbers, the students could better understand the arithmetic approach. Our findings indicate that the approach of the rule of signs which is considered by the majority of students to be the easiest one can be used to help understand the notion of unification of the number line, an obstacle widely known nowadays in the process of teaching-learning

A teoria de Dienes no ensino de transformação de medidas de comprimento, área e volume no curso de pedagogia

The study was aimed to test a teaching module on the Zoltan Paul Dienes theory, focusing on the content: The transformation of measurements: length, areas and volumes. The study based on constructivist theory consisted in a methodological intervention with students of the 7th period of the Course of Pedagogy, in Central Campus, Federal University of Rio Grande do Norte (UFRN). A preliminary study with 40 students called diagnostic evaluation found that students did not understand the concept of measurements transformation and its processing steps. The latter was performed only with the help of the table of measurements transformation with no understanding of the content. He applied a pretest, a set of activities and a post-test. The latter was used as a tool for evaluation of the student learning process. The answers of these ones were evaluated according to the concept of reflective abstraction of Jean Piaget, one of the authors who influenced the Dienes theory

Televisão universitária do RN (TVU): contribuição para a democratização da informação e a difusão do conhecimento científico produzido pela universidade

In this thesis we propose to investigate the contribution that the Universitary Television from Rio Grande do Norte state, Brazil (TVU RN), offers to democratization of information and diffusion of the scientific knowledge produced by the Federal University of Rio Grande do Norte (UFRN) from the perception of their own students. We adopt the basic assumption in wich the TVU RN needs to be connected with the scope of the current UFRN policy, since plays an important role regarding democratization and social inclusion policies in UFRN. We support the thesis that TVU UFRN offers important information for those who are part of academic culture (COULON, 1995a; 1995b, CHARLOT, 2000; BOURDIEU, 2007, 2005, 1997, 1996, 1975), as well as for society in wich it is inserted, since it contributes to the dissemination of scientific knowledge and relevant information about the university. We consider TVU RN a Public Sphere (HABERMAS, 2002; 2003a, 2003b; 2003c; 1999; 1989) conducive to discussion of issues involving higher education. Researches on Universitary Television are recent and some studies on it advanced in the way to define it and present it as a means of dissemination of scientific knowledge (ROCHA, 2006; COUTINHO, 2006; CALLIGARO, 2007; AIRES, 1999; PORCELLO, 2002; PRIOLLI, 2003, 2008, 2009; MAGALHÃES, 2002, 2008; RAMALHO, 2008; 2010; CARVALHO, 2006). For our investigation we chose the combination of quantitative and qualitative methods, both equally valid and accepted by many authors (FLICK, 2009; BAUER; GASKELL, 2002; RICHARDSON, 1999; LAVILLE; DIONNE, 1999). We developed a questionnaire initially with objective questions ending up with open questions of free text. The questionnaire was developed and hosted from a tool of Google Docs and the link to the webpage containing those questionnaires was sent by e-mail by the Permanent Commission of Vestibular of UFRN, COMPERVE, for all university students who were with their registration (status) active in the COMPERVE registers of the second half of 2010. The analysis of this material was performed using the techniques of content analysis and, within this mode was chosen thematic analysis considered appropriate for both qualitative and quantitative research (BARDIN, 2004; MINAYO, 2002). The investigation found that although most students consider that the TVU RN contributes to the democratization of information and dissemination of scientific knowledge produced in university, and moreover to arouse the interest of the academic community, still has not yet become an object of interest of the entire academy. Therefore, the research highlights the relevance and abrangency of further studies on the TVU RN due to the strategic role it plays in this new reality of public universities in the country. In addition, we suggest to the UFRN managers that they put TVU within the hall of discussions in order to receive the so much needed investment for any university organ

As relações de poder na gestão da Escola Estadual Presidente Kennedy em Natal/RN: as ações decisórias dos órgãos colegiados - o conselho de escola e o caixa escolar

The present study examined the relations of power in the management of the Escola Estadual Presidente Kennedy, including the deliberate decisions on the School Council and School Fund, which guided the organization of the school. We sought to understand the management models that influenced the school organization, promoting contradictions in the decision making process. The school management is intensely marked by management models from the business logics as in the case of managerialism of bureaucracy. The formulation of educational policies based on managerialism has proposed a school-centered management with intense accountability of the school community in planning and monitoring the public services. The influences of these models subsidize hierarchical power relations that undermine the actions of decision-making of the collegiate bodies for the democratization of school management. To develop a research on the power, the investigation was based on studies of Bourdieu and Foucault. These authors understand the power in a relational system in a double sense, both in terms of discipline and the possibility of resistance. A theoreticalmethodological matrix was developed focusing on literature review, document analysis, structured interviews with twelve representatives of the segments belonging to the School Council and School Fund, as well as observations in meetings with the production of field notes. It was found that power relations experienced in the organization and activities of the school boards are marked by changes in public management over the years, promoting the contradictions between the concepts of corporate management originated in the business logics and the perspective of democratic management subsidized by official legislative documents at the national and state levels. The observations in meetings and analysis of the records showed that representatives related to management (president and manager of the school) have a privileged position with regard to exposure of their propositions, and are more likely to take a position in the political game of the collegiate bodies of work. It was also seen that the irregularity of meetings, particularly of the School Fund meetings, limits the experience of operation of the representatives in discussions concerning the planning and monitoring the actions of school management. Reports from representatives of the School Council showed that certain segments related to the management recognize their power of decision, however others have little interfere in the decision-making process in order to expound the desires of those who are represented by them. In the School Fund, the analysis of the records and interviews showed restricted moments of the meeting of representatives, and these only being aimed at choice or approval of the implementation plan prepared by the school management. The results showed no indications of moments of reflection to study the best chance for applicability of resources. This collegiate body (School Fund) has a questionable action when planning and monitoring the applicability of the financial resources of the School. To sum up, it was found that the Escola Estadual Presidente Kennedy still lives hierarchical power relations that undermine the institutionalization of democratic management in the various representative segments may take place in the game of political decision-making processes necessary for the organization of the school

Reconceitualização das categorias de skemp de compreensão relacional e compreensão instrumental como critérios globais

The thesis presents a systematic description about the meaning, as Skemp, relational understanding and understanding instrumental, in the context of mathematics learning, being that we had as a guide his understanding of the schema. Especially, we analyze some academic productions, in the area of Mathematics Education, who used the categories of understanding relational and instrumental understanding how evaluative instrument and we see that in most cases the analysis is punctual. Being so, whereas the inherent understanding relational schema has a network of connected ideas and non-insulated, we investigated if the global analysis, where it is the understanding of the diversity of contributory concepts for formation of the concept to be learned, is more appropriate than the punctual, where does the understanding of concepts so isolated. For this, we apply a teaching module, having as main content the Quaternos Pythagoreans using History of Mathematics and the work of Bahier (1916). With the data we obtained the teaching module to use the global analysis and the punctual analysis, using research methodology the Case Study, and consequently we conduct our inferences about the levels of understanding of the subject which has made it possible for us to investigate the ownership of global analysis at the expense of punctual analysis. On the opportunity, we prove the thesis that we espouse in the course of the study and, in addition, we highlight as a contribution of our research evidence of need for a teaching of mathematics that entices the relational understanding and that evaluation should be global, being necessary to consider the notion of schema and therefore know the schematic diagram of the concept that will be evaluated

Formação da habilidade de interpretar gráficos cartesianos em licenciandos em química segundo a teoria de P. Ya. Galperin

It has been remarkable among the Science Teaching debates the necessity that students do not learn only theories, laws and concepts, but also develop skills which allows them to act towards a critical citizenship. Therefore, some of the skills for the natural sciences learning must be taught consciously, intentionally and in a planned way, as component of a basic competence. Studies of the last twenty years have shown that students and teachers have plenty of difficulties about skills development and, among several, the skill of interpreting Cartesian graphics, essential for the comprehension of Natural Science. In that sense, the development of that type of professional knowledge during the initial education of future Chemistry teachers has become strategic, not only because they need to know how to use it, but also because they need to know how to teach it. This research has as its general objective the organization, development and study of a process of formation of the skill of interpreting Cartesian graphics as part of the teachers professional knowledge. It has been accomplished through a formative experience with six undergraduate students of the Teaching Degree Course of Chemistry of Universidade Federal do Rio Grande do Norte (UFRN Federal University of Rio Grande do Norte), in Brazil. In order to develop that skill, we have used as reference P. Ya. Galperin s Theory of the Stepwise Formation of Mental Actions and Concepts and its following qualitative indicators: action form, degree of generalization, degree of consciousness, degree of independence and degree of solidness. The research, in a qualitative approach, has prioritized as instruments of data collecting the registering of the activities of the undergraduate students, the observation, the questionnaire and the diagnosis tests. At the first moment, a teaching framework has been planned for the development of the skill of interpreting Cartesian graphics based on the presupposed conceptions and steps of Galperin s Theory. At the second moment, the referred framework has been applied and the process of the skill formation has been studied. The results have shown the possibility of develop the skill conscious about the invariant operation system, with a high degree of generalization and internalized the operational invariant in the mental plane. The students have attested the contributions at that type of formative experience. The research reveals the importance of going deeper about the teaching comprehension of the individualities tied to the process of internalization, according to Galperin s Theory, when the update of abilities as part of the teaching professional knowledge is the issue

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

A Formação docente no fazer e refazer da prática pedagógica

This work dealt with formative actions that were developed by Educational Practice in Movement (GEPEM) at Universidade Federal do Rio Grande do Norte (UFRN). This group aims to transform the way education is carried out. This is done either through intervention or in research considering that school has an explicit objective, to change action, and this presupposes an educator formation process. The methodology used is a reflection on educational practice, aiming to built knowledge that can be generalized to other realities. The analysis of the group s prior work was done considering what has been used as a parameter for decision making, the regularity in the process itself, all of which allowed the identification of their principles, once these were always mentioned in the documents that were analyzed. Some principles for formative actions of the GEPEM were identified: the subject as a social historical being is part of a given community; knowledge is built through social relations and local reality is a content generator; dialogically, collective construction and awareness process. The research also pointed out four characterized organizers, parameters and action criteria that make articulation with practice possible. Thus, these are used in order to analyze two initial formation proposals (secondary and higher education) of rural settlement educators