Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2018.tde-26012021-201605
Document
Author
Full name
Cynthia Militão Domingos
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2018
Supervisor
Committee
Jahn, Ana Paula (President)
Costa, Nielce Meneguelo Lobo da
Monteiro, Martha Salerni
Title in Portuguese
Ensino e aprendizagem de Geometria Analítica no Ensino Médio: uma experiência com coordenadas e cálculo de distâncias no plano e no espaço
Keywords in Portuguese
Distâncias
Geogebra
Geometria Analítica
Materiais concretos
Registros de representação semiótica.
Abstract in Portuguese
Title in English
Teaching and learning of Analytical Geometry in High School: an experience with coordinates and calculation of distances in the plane and in space
Keywords in English
Analytical Geometry
Concrete materials
Coordinates
Distances
Geogebra
Registers of semiotic representation.
Abstract in English
This study addresses issues related to teaching and learning Analytical Geometry in High School. Its main objective was to present a activities for the teaching of the Cartesian coordinated topics and the calculation of distances both realized in the plane and the space, seeking understanding and not in the memorization of formulas. In order to do so, we adopted as theoretical foundation the registers of semiotic representation, a theory elaborated by Raymond Duval and the software Geogebra was used to assist the work with the graphic, algebraic and numerical registers, in particular in the conversion activities. Some research papers, as well as teaching practices, indicate that many students present difficulties in the interpretation of formulas, equations and inequalities, not assigning meanings to such algebraic expressions. An analysis in didactic books showed that, in general, the teaching of Analytical Geometry is presented through a more algebraic approach, with emphasis on the use of formulas and, in exercises, algebraic representation is the most used as a solution. We also note an absence of the approach of objects and concepts in space, but this approach can be seen as essential for the integral formation of the student in Basic Education. It was considered that the use of the 3D Geogebra Window, linked to the 2D Window of Geogebra, can support a work on coordinates and calculation of distances in space, allowing to enlarge the study of Analytical Geometry in High School in order to collaborate with the development of ability for spatial visualization by students. Aiming at a qualitative research, Design Experiment was used, which is a methodology focused on the analysis of the learning processes of specific mathematical domains. Activities were developed using Geogebra and concrete materials to introduce coordinates and distances in space. A set of tasks was applied to a group of six high school students from a public school in São Paulo. The data analysis showed the full viability of a work in space in this level of schooling, as well as the pertinence of the use of the chosen resources. With them, students were able to observe, experiment and, above all, articulate different representations of objects and geometric relations, appropriating the concepts in question.