APPLICATION OF REFLECTIVE ABSTRACTION TO THE PROCESS OF ARITHMETIC INVERSION

Abstract

This article aims to investigate the inversion of arithmetic operations from the perspective of reflective abstraction, based on the clinical method proposed by Jean Piaget. To this end, the test entitled "The Inversion of Arithmetic Operations," presented by Piaget (1977/1995, p. 43-58), was administered to identify the level of reflective abstraction demonstrated by the research subjects. The results revealed that, of the three participants analyzed, one was at level IB—characterized by exclusive attention to content, without articulation of forms of action, thus operating with predominantly empirical abstractions. The other two subjects reached level III, demonstrating the ability to reflect on the path taken from n to n', being able to reconstruct n through the analysis and coordination of their own actions. Thus, the comparison between performances shows that subjects in Level III develop the notion of number through reflected abstraction, especially through understanding the path, ordering, and inversion of arithmetic operations.