Abordando o conceito de simetria através da definição de vetor

Abstract

Symmetry is one of the most fundamental concepts in modern science, dictating the basic laws of physics and defining the fundamental forces of nature. Symmetry controls physics both in the high energy regime, with relativity, and in the microscopic world with quantum mechanics. Despite its importance, this concept is not explored either in textbooks or in high school physics classes. In this work we present how structuring and fundamental concepts of physics, such as symmetry, symmetry transformations, homogeneous and isotropic universe, invariance of a physical property, among others, can be worked both conceptually and analytically through a more complete definition of vector, in which we consider the transformation relationship of its components through the rotation of the coordinate axes. Our goal is to facilitate the introduction of these fundamental concepts as soon as possible in physics classes, so that students can understand the importance of mathematics as one of the essential methodologies for the development of physics. Such concepts can also provide a justification for the way physics is treated mathematically in the classroom. Our educational product consists of a didactic sequence containing potentially significant material in a theoretical physics context. For the application of the product in the classroom, we explore the Subsumption Theory of Ausubel of meaningful learning, using the simplified concept of vector, usually worked at the basic level of education, and a simple physical system, described by a block sliding on an inclined plane, to address a more complete definition of vector and demonstrate analytically the concepts of symmetry, symmetry transformations in a homogeneous and isotropic space, and invariance of a physical property. The educational product was applied to high school students in a state school in the city of Itu, municipality of Sao Paulo, Brazil. The results, obtained from questionnaires related to the subjects of each activity, are promising for the proposed contents to be introduced in the first years of high school to be worked on and explored over it.