Comprensión de enunciados de problemas multiplicativos: algunas dificultades semiótico-cognitivas

Abstract

In this paper, the difficulties that arise in the understanding of multiplicative problem statements are identified and described from a semiotic-cognitive perspective. For this, this work is structured in two stages. In the first stage, the representative statements of the field of statements of multiplicative problems are determined. In the second stage, a series of observations is made to the 6th grade students of the Colegio Entre Nubes School District Educational Institution of the city of Bogotá, with respect to how they understand these problem statements and how their understanding varies when making modifications to these statements. The modifications to the representative statements of the field of statements of multiplicative problems had two versions: With respect to the first version, the representative statements were modified in relation to the linguistic marks or with the intention of varying the background that can arise in the student to the Read the problem statement. With respect to the second version, figurative or iconic auxiliary representations were added to the representative statements with the objective of demonstrating the incidence of these representations in the comprehension of a multiplicative problem statement. The results of this work show that the difficulties in understanding sentences of multiplicative problems are due to the incidence that has: a) the factors of the variation of the wording of the statement, since these determine the way in which the cognitive content is explained of the multiplicative problem statements (Duval, 1999b); b) the indiscriminate use of auxiliary representations that support the multiplicative problem statement, since these representations make sense and are meaningful in the understanding of these statements if and only have been intended for teaching students; c) the interpretations made by students from the cultural background when reading a problem statement, since the interpretations they make of the statements open a gap between the meaning and content thought by the author of the statements and understood by the student; and d) the linguistic marks in the statement, given that the linguistic marks can attribute to an enunciation of mathematical problem an intention to mobilize elements of the conceptual structure (Pontoon, 2012). These results lead to affirm that the understanding of multiplicative problem statements occurs when the student achieves the capacity to understand and make any change in the representation register, that is, to be able to face the cognitive complexity of the conversion ( Duval, 2016).