La igualdad como relación de equivalencia en contextos aritméticos: una experiencia de aula en grado sexto

Abstract

This paper reports a classroom experience based on the design, implementation and evaluation of a set of tasks, in real contexts, oriented to the recognition of the equal sign as a representation of equality, as a relation of equivalence between numerical equalities, enabling a relational look at arithmetic expressions. An instrument pilot test with numerical equalities was applied to a group of students in sixth grade from a school in Bogota, evidencing that almost al the participants considered the equal sign only as an indication to solve some mathematical operation in numerical equalities. After that, an intervention was made in the classroom, taking into account the ideas of the Realistic Mathematical Education (RME), students worked with situations of daily life that included processes of composition and decomposition of numbers, conditioned equalities, equivalence of fractions and areas. These situations were transformed into mathematical models, which allowed them to change the only operational interpretation of equalities to be considered as equivalence relations.