Desenvolvimento de conceitos algébricos por professores dos anos iniciais do ensino fundamental

Abstract

It has been shown in many researches that activities connected to the algebraic thought in the initial years has been the only way to obtain meaning and develop concepts such as the equation, the unknown quantity and the equivalence. However, there’s still a lack of investigation regarding how teachers from these respective grades are capable of thinking about these concepts and add them up to their pedagogical practice. Researches about the concepts’ development by teachers from the initial grades in Elementary School have been very few explored in books, especially in Brazil. This research’s objective was to investigate the development of algebraic concepts by Elementary School initial grades’ teachers by using manipulative activities and digital resources. The study was performed with teachers from a State School in Fortaleza through two stages. Initially, 11 teachers took part in a workshop exploring the concepts equations, inequations, relations among unknown quantities, equivalence, relational thought and the use of unknown quantities in activities directed at Elementary School’s initial grades. After the workshop, one of the teachers was chosen to plan and use the activities in her practice. The study data was made of the activities’ observations and records during the workshop, classes’ interviews and observations and activities’ records with the participant teacher of this second stage. The data was analyzed based on the categories of algebraic knowledge pointed out in literature. The results during the workshop pointed out the teachers’ initial difficulty in understanding the basic notions of the algebraic thought as how to solve 1st degree equations and explain the differences between arithmetic and algebraic activities. These difficulties were partially overcome throughout the project. On the second stage, the planning and use of the activities in the classroom point out to a greater comprehension by the teacher about the meaning of equations, the development on the concept of equality, working with unknown quantities and the relations between numeric and symbolic expressions. The data allows us to conclude that the used activities aided in the development of concepts connected to the teachers’ algebraic thought, both in the workshop and in the use of the mentioned activities inside the classroom. This project also points out the importance of investing in continuing education so that teachers can reflect upon the educational practice, developing arithmetic concepts together with algebraic concepts.