Banca de DEFESA: LUDMILA WANDERLEY MARTINS

THE EQUAL SIGN AND INITIAL NOTIONS OF EQUATION IN THE FIRST SEGMENT OF YOUTH AND ADULT EDUCATION: a didactic experience in the light of the Theory of Objectification

Algebraic thinking; Youth and Adult Education; Initial notions of equation; Equal sign; Objectification Theory.

This qualitative research arises from the emergence of studies on algebra teaching-learning processes and the development of algebraic thinking in the Early Years of Primary School in the Brazilian cultural context. The general aim of the study is to analyze the signs of algebraic thinking that emerge as four students from the First Segment of Youth and Adult Education collectively explore teaching-learning activities that address equations and the equal sign in their relational character. Our theoretical framework is the Objectification Theory, a cultural-historical educational theory developed by Luis Radford, inspired by Hegel's dialectical materialism, Freire's concept of education and Vygotski's school of thought. According to this theory, algebraic knowledge is already culturally instituted, it is not something purely internal to the student, but a potential historical knowledge that can be achieved through the joint and interactive work of the subjects, known as joint labor. According to this theory, three conditions characterize algebraic thinking: (1) the indeterminacy of quantities, (2) denotation and (3) analyticity. It is also on the methodological assumptions of the Objectivation Theory that we base the production of the data, following the configuration proposed for teaching-learning activities. Our activity was designed on the basis of the following pedagogical principles:  (1) the indeterminacy of quantities, (2) denotation and (3) analyticity.It is also on the methodological assumptions of Objectivation Theory that we base the production of the data, following the configuration proposed for teaching-learning activities.Our activity was designed based on the following pedagogical principles: (1) the creation of a social space for interaction to solve equations, through the formation of a small group; (2) the design of tasks and visual semiotic systems that promoted awareness of the concepts needed to solve equations.With regard to data analysis, because I believe that algebraic thinking can be revealed through language that is not exclusively symbolic, but also through natural, gestural and pictorial language during the objectification process, the method used to analyze the data is multisemiotic.The data produced showed that, in the process of introducing algebra, the students followed a process in which algebraic ways of thinking about equations emerged progressively in the joint activity with the teacher.Our analysis also highlighted the important role of signs, artifacts, language and gestures in the development of algebraic thinking.