Uma análise de teoremas em ação mobilizados por estudantes do 6º ano na resolução de situações problemas do campo conceitual aditivo

Abstract

In this work, we investigate the mobilization of the operational invariant Theorem in action, in the resolution of problem situations of the additive field. As a theoretical contribution, we consider Gerard Vergnaud Theory of Conceptual Fields (1996). The investigation was carried out with students of the sixth year of elementary school in a public school in Manaus - AM. The study consists of the proposal of a questionnaire involving problem situations of the additive conceptual field, for the analyzes the fundamental ternary schemes that make up the field of additive structure proposed by Vergnaud were considered. In this way, the results show us a diversity of theorems in action that the students mobilized when solving the proposed situations, which show us difficulties in the interpretation when the terms "more than" and "unless" appear difficulties in solving addition with reservation, the order of the subtraction parcels (understanding that subtraction is not commutative) and difficulties related to place value. It is important to emphasize that the objective was not to verify if the student solved it correctly or not, but to identify the theorems in action produced in the development of the questionnaire, classifying them as Theorem in action true or false.