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

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

Possibilidades de exploração da história da ciência na formação do professor de matemática: mobilizando saberes a partir da obra de Nicolau Copérnico de revolutionibus orbium coelestium

This study aims to analyze the implications that the knowledge of an important work for the History of Science, De revolutionibus orbium coelestium , by Nicholas Copernicus, can bring for the formation of Mathematics professors. The study focuses on Book I of Copernicus s work, where, in the final part, is found the Table of the Subtense Straight Lines in a Circle, a true sine table constructed by the author. The study considers two theoretical references, the History of Science and of Mathematics, in the professor s formation searched amongst others in Miguel and Miorm, Brito, Neves and Martins, and Radford, and the necessary teaching knowledge professors mst have, on the basis of Gauthier, Schulman and Imbernón amongst others, through which it is established a net of knowledge grouped in dimensions such as mathematical, psycho pedagogical, cultural and practical diversity, that guide the study analysis. In the search for more necessary elements to enrich the analysis, beyond the theoretical research in Book I, it is carried through, with under graduation pupils, future Math professors, the construction of a sine table following the project used in De revolutionibus . The study still makes a description of the life and work of Nicholas Copernicus, detaching the historical context where the author lived and the conceptions about the Universe existing at that time. The research reveals that the studied work is an important source of culture, able to provide to the Mathematics professor in formation, beyond the conceptual and procedural mathematical knowledge, a cultural knowledge that allows him to be opened to the knowledge of other areas that not his specific area, and so to acquire knowledge about the world history, the development of sciences and of the society

Círculo de ação-reflexão-ação: uma possibilidade praxiológica para a prática pedagógica da formação problematizadora de professores

Considering the dialogue as a gnosiological act and teachers as a researchers of their own practice, this thesis deals with the contribution of Paulo Freire thoughts to teacher s formation process. The study was made over an intervention carried out at a regular Pedagogy Course, however directed to teachers on duty inside a program called PROFOMAÇÃO (Special program for professional formation on Basic Education) promoted by Universidade do Estado do Rio Grande do Norte (UERN). From Freire s ideas of problematizing education, action and reflection dialectics, conscientization and from the analysis of the course itself, I support the idea that the dynamics of collective construction of knowledge- three pedagogical moments (ANGOTTI, DELIZOICOV e PERNAMBUCO) when intermediated by individual reflection, provided by written register, permits the development of three important dimensions of knowledge about pedagogical practice; observation and selfobservation; understanding the theories witch grounds the action; and theorization. By these means, initial and permanent teacher s formation could materialize its political commitment in a concrete action of collective and participative act of conscientization and transformation of the reality of pedagogical practice at school ground, developing itself as a truly circle of action and reflection

Como se fora brincadeira de roda: a ciranda da ludopoiese para uma educação musical humanescente

The present work concerns an auto-ethnographic study based on life experiences and reflections of an educator at Escola Viva Preschool and Elementary-Middle School, located in the city center of Natal, Rio Grande do Norte. As a cognitive model of operation, we use the metaphor of the Circle Dance. The objective of this study is to identify, interpret and describe the ludopoetics that are achieved through a Musical Education program, which we denominate, Humanescent. The data of this investigation was derived from the music making by Preschool and Elementary-Middle School students at Escola Viva during 2007, 2008 and 2009, from which 20 learners were selected to form the corpus, along with the description and interpretation of photos of their experiences and sand tray scenes. We justify the methodological systemization of the research based on our own pedagogical practice, which supports Musical Education in the schools based on the principals of Embodiment, Autopoesis and Flow. The methodological systemization was developed through an Action Research model and on the concepts of Systemic Development, with the goal of re-reading the context investigated through the structuring of categories of Ludopoesis: Self-esteem, Self-territory, Self-connectivity, Self-realization and Selfworth. We used an observant-participant research approach with regard to the perception of emergent knowledge, the surroundings, the experience lived and the contextual and vibration of the circumstances. Besides this, we used projection to interpret the experiences lived, in the form of drawings, short poems, letters or sand tray scenes as symbolic interpretations of experience. In the unfolding of the Ludopoetic Process (Selfesteem, Self-territory, Self-connectivity, Self-realization and Selfworth) we draw conclusions about the relevance of the ludic musical experience, which foments the formation of the self based on music learning, and which is demonstrated in the Embodiment of the learners. In the auto-formative process (of learners and educators) we observe the importance of pedagogical work based on Musical Humanescent Education that gives value to the music making path to the construction of music and performance in play, creativity, and sensibility. The experience of making music in a playful way allows for organization of the self and its autonomous production in the joy of living within a ludopoetic process. These findings highlight the educator as in a permanent state of selfformation, which generates moments of flow. However, in Musical Humanescent Education, music is learned collectively, doing a circle dance, experiencing love, fostering an expansion of the creative spirit, and giving recognition to playfulness as a necessary condition for education and to the value of music made with the true nature and sensibilities of the educators

Um estudo sobre a aprendizagem de alguns conceitos algébricos e geométricos

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