Por que o seno de 30° é ½? : uma proposta de investigação para uso em sala de aula

Abstract

This work presents a pedagogical, investigative and multisemiotic possibility, created with the objective of contributing to the teaching and learning of trigonometric ratios, in elementary school, final years and in high school (in the stage in which this content is addressed). The starting point is the understanding that sine of 30º is always ½, regardless of the measures of the sides of a right triangle. This occurs due to the existing proportionality between the homologous sides of the infinitely similar right triangles, determined by this angle. Aiming to promote such a contribution, a set of activities was developed in this dissertation. This study was born out of the researcher's concern with the recurrent difficulties of students in relation to the subject, and also from her interest in contributing to the literature to overcome this difficulty. This development had two moments as a methodology: the first consisted of the elaboration of a literature review, in which the fundamental theoretical references for the creation of the set of activities were presented, with the support of concrete low-cost materials, which aims to instigate curiosity of the student and allow a mathematically grounded path for learning the topic in focus. We sought here to raise studies that dealt with curiosity and investigation, both with a solid mathematical theoretical foundation for the theme. The second moment consisted of creating, based on this review, each of the activities that make up the pedagogical path. During development, such a set is discussed, based on the literature surveyed. As a result, a set of 6 activities is presented, two in Step 1 (preparatory activities) and four in Step 2 (activities for the production of specific knowledge). This set is available for printing at the end of this work, facilitating access to teachers who wish to experience it in their classes.