Construcción de nociones geométricas y desarrollo del pensamiento geométrico en estudiantes de la escuela primaria por medio de demostraciones visuales

Abstract

The purpose of this research study is to explore the construction of visual demonstrations based on geometric notions that appear in Book 1 of Euclid´s Elements by students eight to ten years old from private schools located in the city of Neiva and the municipality of Rivera, Huila. The methodology of the research is based on research as design, since each subsequent activity takes into account what happened in the previous activity in order to redesign it. Nine activities were designed which were implemented virtually with 24 students. The first activities were designed to allow students to understand and construct with ruler and compass different objects and notions posed in Euclid´s Elements Book 1, in order to identify their particularities. In the final activities, puzzles were used to build valid conjectures to be proven visually and with the support of manipulatable material. Each activity designed begins with constructions with ruler and compass supported by home-made videos that show a step by step process for each of them. Finally, in each activity problems of independent thought are posed that allow the students to develop their geometric thinking. The implementation and analysis of each of the activities and the results of the survey given to the students allowed the identification and analysis of the strategies used by students in the process of solving the different activities, and the verification that young students can effectively start activities related to proving by designing and redesigning activities that lead the student to think mathematically.