Geometrias não-eucludianas como anomalias: implicações para o ensino de geometria e medidas

This present research the aim to show to the reader the Geometry non-Euclidean while anomaly indicating the pedagogical implications and then propose a sequence of activities, divided into three blocks which show the relationship of Euclidean geometry with non-Euclidean, taking the Euclidean with respect to analysis of the anomaly in non-Euclidean. PPGECNM is tied to the line of research of History, Philosophy and Sociology of Science in the Teaching of Natural Sciences and Mathematics. Treat so on Euclid of Alexandria, his most famous work The Elements and moreover, emphasize the Fifth Postulate of Euclid, particularly the difficulties (which lasted several centuries) that mathematicians have to understand him. Until the eighteenth century, three mathematicians: Lobachevsky (1793 - 1856), Bolyai (1775 - 1856) and Gauss (1777-1855) was convinced that this axiom was correct and that there was another geometry (anomalous) as consistent as the Euclid, but that did not adapt into their parameters. It is attributed to the emergence of these three non-Euclidean geometry. For the course methodology we started with some bibliographical definitions about anomalies, after we ve featured so that our definition are better understood by the readers and then only deal geometries non-Euclidean (Hyperbolic Geometry, Spherical Geometry and Taxicab Geometry) confronting them with the Euclidean to analyze the anomalies existing in non-Euclidean geometries and observe its importance to the teaching. After this characterization follows the empirical part of the proposal which consisted the application of three blocks of activities in search of pedagogical implications of anomaly. The first on parallel lines, the second on study of triangles and the third on the shortest distance between two points. These blocks offer a work with basic elements of geometry from a historical and investigative study of geometries non-Euclidean while anomaly so the concept is understood along with it s properties without necessarily be linked to the image of the geometric elements and thus expanding or adapting to other references. For example, the block applied on the second day of activities that provides extend the result of the sum of the internal angles of any triangle, to realize that is not always 180° (only when Euclid is a reference that this conclusion can be drawn)

Atores sociais e política ambiental urbana do Município de Mossoró/RN pelo prisma das cartografias sociais analíticas

It starts with the understanding that the relationship between society / nature is largely problematic in a context of socio-environmental crisis. In this context, we use the principle of hope to plan and work out new ways of understanding social reality, the relationship between science and alternative knowledge. The research is to investigate how the actors influence the social construction of urban environmental policy of the city of Mossoró / RN with reference to the processes of implementing the Master Plan and Agenda 21 of the municipality. The hypothesis of this research is that the Environmental Policy in Mossley has a normative character that is expressed primarily in the creation of an institutional political framework to manage environmental issues involving so incidental and or functional society participation mossoroense. Thus questioned who are the actors that build environmental policy Mossoró / RN. The specific objectives of this research are: Identify the environmental dimension of the Master Plan Agenda 21 articulated Mossoró / RN mapping information from the managers, engineers and members of the Municipal Environment and Municipal Council of Cities on the operation of urban environmental policy mossoroense and how it is performed by the Manager of Environmental Management in conjunction with the Department of Environment and Territorial Development (SEDETMA) and Executive Management of Urban Development. As a methodology, we used the method of the sociology of absences and emergencies in conjunction with the ecology of knowledge and productivity. It is a qualitative research and documentary, which was used as the Master Plan documents Mossoró / RN, minutes of meetings of boards and complementarity were carried out 12 semi-structured interviews with managers and directors of the Urban Environmental Policy of the Municipality of Mossoró / RN. They used also the social analytical or thematic maps for the translation of the dialogue among social partners, managers and directors who make the Environmental Policy Council. We conclude that these dialogues and experiences point to the construction of an environmental policy more participatory and effective, committed to individual and collective transformation of society mossoroense