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

Um estudo sobre a concepção de paradoxo segundo o pensamento de Augustus de Morgan

This work aims to analyze the concept of "paradox" posed in the work of The Budget Paradox (1872) of mathematical and logical English Augustus De Morgan (1806-1871). Here it is important to note that a large part of this book consists of re-prints of a series of writings by the author in journal Athenaeum, where its performance as auditor of literature. The tests refer to some scientific work produced between the years 1489 and 1866 and the rules of selection for the composition of the work is, basically, the methodological aspects used in the completion or disclosed by such scholars. The concept of paradox is presented in two distinct moments. At first, we found a study of definitions for the term in a philosophical approach, characterizing it as something that requires further investigation; which was complemented with the classic examples of a scientific context. In the second, we present a concept advocated by De Morgan and, under this perspective, that he conceptualized the "paradox" is directly related to the non-usual methods employed in the formulation of new scientific theories. In this study some of these scientific concepts are detailed, where, through the redemption history, engaging in issues of our study Mathematics, Physics, of Logic, among others. Possession of the preliminary analysis and comparison with the design of De Morgan, it became possible to diagnose some limitations in the conceptualization suggested by the author. Further, evidenced, in front of the cases, the nonlinearity of the process of production of knowledge and hence the progress of science