Banca de DEFESA: SIMONE FERREIRA DA SILVA

ALGEBRAICAL THOUGHT, EQUAL RELATIONSHIPS AND SIMPLIFICATION OF EQUATIONS IN A TRAINING PROCESS OF EARLY YEAR TEACHERS IN THE LIGHT OF THE OBJECTIVE THEORY

 Algebraic thinking, Objectification theory, Equations and training process

This research takes a qualitative approach, emerging from the need to conduct comprehensive studies on the integration of algebra as a thematic unit in the mathematics curriculum of the early years of elementary school. This need was accentuated by the publication of the National Common Core Curriculum in 2017. The general aim of the research is to investigate algebraic thinking, equality relations and the simplification of equations in the context of a training process for primary school teachers in the light of Objectivation Theory. This theory is anchored in Hegelian, dialectical, dynamic and constitutive conceptions of subjects and cultures. According to Radford's ideas, algebraic thinking is characterized by three vectors: sense of indeterminacy, denotation and analyticity. We also adopted the methodological assumptions of Objectivation Theory in the production of the data, following the configuration proposed in the teaching-learning activities. The data was produced in four training meetings, the first three lasting 2 hours each and the last 4 hours. The participants were six teachers with initial training in pedagogy from a municipal school in Recife - PE. The training meetings were videotaped. The analysis was based on a multimodal system, using two semiotic systems: the Iconic Semiotic System and the Alphanumeric Semiotic System. Gestures, drawings, speech and written records were analyzed, revealing algebraic ways of thinking about equality relations and simplifying equations. The dialogues, images and written records indicated that the teachers understood the equal sign in a relational way, simplifying equations by generalizing algebraic rules. We also observed that elements of algebraic thinking, such as indeterminacy, denotation and analyticity, emerged and were gradually refined throughout the training activities, showing signs of algebraic thinking in the problem-solving carried out by the teachers and the researcher-trainer.