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

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

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

Morfologia do útero de cutias nulíparas e não nulíparas

Descreveu-se a morfologia do útero de cutias nulíparas e não nulíparas por meio de ovariossalpingoisterectomia. A análise macroscópica do útero foi realizada in loco e na peça retirada. Segmentos das porções proximal, média e distal do órgão foram colhidas, fixadas e preparadas histologicamente, sendo as amostras analisadas à microscopia de luz, e realizada a histomorfometria das camadas uterinas. Topograficamente, o útero localiza-se na região sublombar, caudalmente aos rins, em continuação aos ovários e às tubas uterinas, estendendo-se até à entrada da pelve, onde se posiciona dorsalmente à bexiga. Caracteriza-se como do tipo duplo, embora culmine em apenas um óstio cervical externo. Microscopicamente, a mucosa uterina é formada por variações do epitélio, de cilíndrico a pseudoestratificado, que se apoia em tecido conjuntivo frouxo, onde se observam glândulas endometriais revestidas por epitélio cilíndrico, além da presença de vasos sanguíneos. A camada muscular subdivide-se em interna ou submucosa, média ou vascular e externa ou subserosa. A camada serosa é composta por tecido conjuntivo e mesotélio. Na histomorfometria, verificou-se que a espessura uterina total e a espessura da camada mucosa, em média, foram maiores nas fêmeas não nulíparas.

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

Influência do dimorfismo sexual sobre a morfologia da siringe de galinha d'angola (Numida meleagris)

Este estudo teve como objetivo realizar uma descrição morfológica e comparativa da siringe, órgão responsável pelo canto das aves, na espécie Numida meleagris. Para isso foram utilizados cinco machos e cinco fêmeas de galinha d'angola, a fim de verificar a sintopia (traquéia, músculos traqueais) e o dimorfismo sexual da siringe. Verificou-se que a siringe se localiza na bifurcação da traquéia e apresenta maior número de cartilagens nos machos. Nos machos, a inserção do músculo traqueal lateral bem como a origem do músculo esterno traqueal localizam-se mais caudalmente e são mais largos em relação às fêmeas. As diferenças existentes entre machos e fêmeas de galinha d'angola revelam a elevada capacidade das fêmeas em produzir sons semelhantes a tô fraco enquanto que os machos emitem arrulhos e cacarejos.

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

Parâmetros métricos da traqueia e suas correlações com o perímetro torácico, peso e comprimento corporal de cães sem raça definida (Canis familiaris, Linnaeus, 1758)

The present study aimed to analyze metric data from the trachea of dogs and to correlate them with the thoracic girth, body length and weight. We used 48 dogs of unknown breed, 19 males and 29 females. The animals were weighed and then body length, thoracic girth, length and diameter of the trachea, and the number of tracheal rings were measured. The weight of dogs ranged from 4.2 to 21.5 kg, body length from 40.6 to 81.0 cm and thoracic girth from 36.0 to 63.5 cm. The trachea exhibited a total number of tracheal rings between 32 and 43, length between 13.0 and 23.4 cm, diameter of the cervical portion between 11.0 and 23.5 mm and in the thoracic portion between 8.2 and 20.9 mm. We also evaluated the tracheal termination skeletopy, which maintained relations with the 2nd (2.0%), 3 (6.3%), 4 (20.8%) or 5 (12.5%) intercostal spaces, and with the 3rd (6.3%), 4th (35.4%) or 5th (16.7%) ribs. Strong positive correlations of tracheal length with body weight (rS = 0.756, p <0.001), body length (r = 0.808, p <0.001) and thoracic girth (r = 0.735, p <0.001) were found. Therefore, the anatomical study of the trachea provides morphological subsidies for the realization of clinical and surgical procedures in this organ, being an important tool in veterinary practice.