Enseñanza del sistema de representación de puntos en el plano cartesiano a partir del estudio de los desplazamientos en el espacio

Abstract

This document presents the design, experimentation, and analysis of a teaching proposal for the representation system of points on the Cartesian plane. The proposal is based on the planning of activities according to Brousseau's Theory of Didactic Situations (1986), and aims to develop students' spatial knowledge until they understand the Cartesian coordinates of a point as displacements on the plane from the origin of the system. This proposal is based on the document "Spatial Orientation: A Teaching and Learning Path Centered on Locations and Trajectories" by Zapateiro, Poloche, and Camargo (2018). It includes some of the ideas proposed there and makes important modifications, particularly with regard to the potential of technology to promote adaptive learning. A sequence of nine situations was designed involving the planning and execution of robot movements (initially within a maze, then within a coordinate system), using the tools offered by three.js and DGPad-Colombia. The goal is for students to leverage their spatial knowledge and develop it to take into account references to their own body, the bodies of others, and the cardinal points, and then assimilate them to the coordinate axes and the ordered pairs that represent points on the Cartesian plane. For the implementation and analysis of this proposal, the research methodology of educational engineering was adopted, including experimentation with activities with two pairs of fourth- and sixth-grade students. In conclusion, this work seeks to contribute to the development of spatial thinking and an understanding of the Cartesian coordinate system through a teaching approach based on the potential of information technology to promote adaptive learning.