Uma sequência didática para o Teorema de Tales

Abstract

The purpose of this research was to elaborate, apply and evaluate a didactic sequence with tasks related to the Tales’ Theorem, and directed to the ninth year of elementary school, in which the gradual use of concepts, dialogue between studentes and teamwork facilitate the acquisition of learning about the theme. It focused on the following research question: "A sequence of tasks created for gradual appropriation of contents in which the student has access to different resources to solve the questions that are proposed provides the learning of the Tales’ Theorem?" The didactic sequence was implemented in a class with 30 students of the 9th grade of elementary school from a school in the municipality of Curiúva, Paraná, from August to September of 2017. It used Didactic Engineering as a Research Methodology and the tasks were elaborated based on Guy Brousseau's Theory of Didatical Situations (TSD). As data collection instruments were used: the resolutions of the tasks performed by the students and their manifestations, annotated in a field diary by the teacher-researcher in the course of the research. The analysis of the students' responses indicated that the proposed didactic sequence contributed to their differentiation between the concepts of straight, semirect, straight line, parallel and transverse lines, as well as the concept of reason and proportion, which culminated in the learning of the Tales’ Theorem, proved by the evaluation they performed at the end of the implementation. It also indicated greater motivation and involvement in the accomplishment of tasks, perception about the importance of Mathematics and its presence in daily life. Difficulties in doing work in pairs, in justifying their answers using natural language and mobilizing prior knowledge as the concepts of reason and proportion were minimized throughout the implementation of the tasks in the classroom. Reformulations in the didactic sequence were carried out from this experimentation and composed an educational product called "Tasks to revise prerequisites and to study the Tales’ Theorem" (appendix of this dissertation). In the final considerations, and particularly in the educational product, recommendations are made to teachers who want to use this material, such as adjusting their tasks to their needs and care in the approach to mathematical concepts.