LA CONSTRUCCIÓN Y JUSTIFICACIÓN DE IDEAS MATEMÁTICAS GENERALES POR UN NIÑO DE 5 AÑOS: EL ROL DE LAS REPRESENTACIONES MANIPULATIVAS

Abstract

Different studies have shown how early childhood students generalize mathematical relationships, a crucial aspect of early algebraic thinking. However, studies that focus on how these students justify these general ideas are scarce and this constitutes the originality and contribution of this research. Considering the predominant role of manipulative representations in the mathematical experiences in Early Childhood Education, the research question that addresses this work is: How do manipulative representations support the construction and justification of general mathematical ideas child when solving problems that have an algebraic features? To answer this question, I conducted a semi-structured individual interview with 5-years-old children, in which I posed two different problems that sought for the participant to address the relationship between a certain number of dogs and the respective number of tails / eyes. The results show that despite not using and / or referring to manipulative material to construct rules and/or general justifications, the participant finded general relationships between the variables involved in problems. Likewise, his justifications are based on the general rules that he constructed. Finally, the participant extended these general rules to the point of interacting with indeterminate quantities.