Ensino por investigação para a aprendizagem de operações com matrizes à luz da teoria dos registros de representação semiótica

Abstract

This work has Raymond Duval's Theory of Registers of Semiotic Representation as a theoretical framework. This theory presents a cognitive approach that analyzes the difficulties presented in the learning of mathematics. One argument for these difficulties to occur is that mathematical knowledge is only transformed into knowledge when students spontaneously mobilize different semiotic registers of the same mathematical object. In this sense, this theory addresses the importance of using different semiotic registers when developing a mathematical activity, since the use of different registers associated with the same mathematical object and coordination between them evidences the possibility for the student to understand the mathematical object as a whole. Based on these considerations, we outlined the objective of this work: To show signs of student learning based on the Theory of Semiotic Representation Registers on operations with matrices in tasks developed from the perspective of Teaching by Investigation. From the research objective, it is intended to analyze the students' cognitive learning, residing in the ability to recognize the mathematical object of each proposed task, in the correspondence of the units of meaning in the conversions and congruences, and finally in the coordination of records presented by the students. To develop the research, we relied on the didactic approach of Teaching by Investigation, taking into account that in this didactic approach the teacher encourages the student to search for solutions and understand a new perspective of what is being studied, awakening a scientific, logical reasoning and objective and at the same time creative, and in the development of exploration and investigation tasks, tasks that have the potential to develop different semiotic registers. In order to seek evidence on the research question, data collection took place with a group of students in the 1st year of New High School, in a public school in the city of Londrina with the content operations with matrices, this content was chosen because it is proposed in the curriculum matrix to be developed in the 1st trimester, when data collection took place. The research is qualitative with an interpretative nature, the collected data are analyzed from the semiotic registers that emerge from each proposed task, through the transformation that occurs between them: treatment, conversion and coordination. Based on the analyzes carried out, we evidenced evidence of student learning through the different semiotic registers developed and their transformations, as well as identifying that the analyzed groups understood the relationship between the different representation registers associated with the mathematical object of each proposed task, the that demonstrates understanding in mathematics. As a result of this research, we elaborated the Educational Product entitled “Teaching by Investigation for the understanding of operations with matrices through semiotic registers: Guidelines for the Teacher”, composed of six tasks involving operations with matrices, each task has development guidelines in the approach didactics of Teaching by Investigation.