A discussion about the semantic congruence of a translation: an opportunity to promote algebraic thinking at elementary school

Abstract

In this study, we analyze how 9-10 years old students represent and refer to indeterminate quantities when posing equations associated with arithmetic word problems. The analysis focuses on the semantic congruence of the expressions proposed by them and on the dialogue they held during the translation process. The results show that arithmetic word problems allow the indeterminate to become an object of thought for students, who represent it in multiple ways and refer to it when proposing equations that represent the structure of each problem. Another finding highlights that reflection on the interpretation of the equations favors the identification of two meanings associated with indeterminate quantities, namely, unknown and variable.