Strategies, Representations, and Flexibility in Multiplicative Comparison Task Resolution

Abstract In this article we analyze, based on a theoretical framework on multiplicative comparison, Bruno's conceptual evolution, a student of the 6th grade (11 years), focusing on the adaptive and flexible articulation of concepts, strategies, numerical relations, properties of operations and representations. The way he explores the five tasks proposed in a teaching experiment indicates that the conceptual construction of Bruno's multiplicative comparison lies in the connection between the multiplicative factor and the scalar ratio. His knowledge of numbers and their relationships allows him to use different representations of rational ones in translating the strategies he implements. These vary between additive and multiplicative, and in the latter, the use of the double number line with only two points predominates. The analysis of Bruno's evolution validates and expands the theoretical conceptual framework adopted initially.