Geometria de Moulton x geometria euclidiana: trilhas de aprofundamento para o ensino médio
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2023-03-24
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Universidade Federal de Goiás
Resumo
With the advent of the approval of the National Common Curriculum Base for Secondary Education - BNCC, which brings learning based on Skills and Competences, and made the content no longer the protagonist of the teaching-learning process, this is what the present work addresses . For this, we present a little of the trajectory of this BNCC homologation process, its main paths and resolutions. We present how this Base was structured, enunciating the expected Skills and Competences, as well as proposing an educational product in the form of a Deepening Track in Mathematics, for the student's formation.
The purpose of the deepening trail proposed here is to present the model of geometry proposed by Moulton, as a way of provoking a comparison with the geometry proposed by Euclid, evidencing the existence of other geometries, the so-called non-Euclidean geometries that, in most cases , are not introduced to students until the end of high school. Thus, through skills already acquired in Elementary School in relation to the study of Plane Geometry, lead the student to review already known concepts and propose challenges, so that through scientific research, he can further develop his skills and competences that lead them to propose solutions and conjecture new ideas about the proposed subject.
We begin with a presentation of primitive concepts and postulates of the Euclidean model, and then we present primitive concepts of the model proposed by Moulton. We show how its structure was defined for the plane, the behavior of straight lines and their equations, how to calculate the distances between two points and also how to determine the measure of angles between straight lines. For this, we make use of Cartesian Geometry, structured by René Descartes, as a link in the comparison between these two models.
The concepts to be worked on are already well known in Euclidean Geometry and, from this other model, we are going to show some of the transformations and modifications undergone by these classic figures of Plane Geometry, namely: parallel and perpendicular lines, the triangle and its notable elements , circle, ellipse, parabola and hyperbola.
With the intention of making a broad initial exploration of the transformations and modifications undergone by these figures, we will also present the step-by-step of a constructive process of some conics, using dynamic geometry software, in this case, Geogebra, in order to also develop computational and programming skills, which are expected in the new National Base.
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BORGES, C. M. Geometria de Moulton x geometria euclidiana: trilhas de aprofundamento para o ensino médio. 2023. 129 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2023.