Números racionais: fatores que influenciam as conversões entre figuras geométricas planas e frações impróprias

This research aimed to understand the influence of semantic non-congruence and the double counting procedure on conversions between the representation register of plane geometric figures with more than one integer and that of fractions. It has a qualitative approach, based on the Theory of Semiotic Representations Registers. The protocols of different studies that complement each other and involved the analysis of semantic non-congruence between these registers were analyzed. It was concluded that even at different school and academic levels, the double counting procedure is used in conversions between the studied registers, disregarding the Reference Unit, when unifying the integers initially represented. And, in cases where the improper fraction was instituted, a strategy was identified that generates intermediate representations and minimizes semantic non-congruence, maintaining semantic correspondence with the double counting, which may lead to the misunderstanding of the reference Unit of improper fractions.