A transformação linear no processo de ensino e aprendizagem de alunos dos curso de licenciatura em matemática e engenharia

Abstract

The study presents an investigation on the learning of students in the mathematics and engineering degree course. The main difficulties of the students regarding the concept of linear transformations were verified and a mathematical study was carried out on the theme "Linear Transformations and Associated Mathematical Objects. In view of my initial motivations and combining them with a previous literature review, I am faced with the following questions: How can elementary mathematical knowledge help in the learning process of fundamental concepts in the field of Linear Algebra? Were the students able to relate basic concepts with those seen in linear transformation? How does this relationship contribute to the teaching and learning process of the theme? The methodology adopted in this work is based on bibliographic research such as: books, documents, articles, monographs, master's dissertations, presented from the scientific perspective, as proposed by the research and its processes in the formation of algebraic concepts and their language through algebraic thinking. The study is classified in the scope of qualitative research, because it takes into account the research of the mathematics and engineering degree in the city of Teresina. In this way, this qualitative and quantitative research clarifies the results collected from the students so that the purpose of this work obtains the real difficulties and obstacles in algebraic. From the research carried out, it fosters that Linear Transformations play a central role in linear algebra and have far-reaching implications in both theoretical and applied mathematics. Their ability to preserve the structure of vector spaces while allowing for a wide range of manipulations makes them indispensable tools in many areas of study.