In the last years, the development of algebraic thinking from the earliest levels of schooling has garnered wide consensus within the mathematics education research community. In particular, various research studies have highlighted the importance of working on the structural properties of arithmetic operations and the relationships of equivalence and order as a way to develop algebraic thinking in the early educational stages. This paper analyzes the responses of fifth-grade primary education students (ages 10-11) to two activities in which students had to, on the one hand, recognize the validity of algebraic identities, and on the other hand, decide whether the relationship between two given algebraic expressions was of equality or of order. Most students did not experience difficulty in solving the first task and justifying their answers. In contrast, slightly more than half successfully solved the second activity, showing more difficulties in detecting equality relations than order relations. It is concluded that there is a need to include this type of activity as a means to develop flexible algebraic thinking.

Keywords: Early algebra, generalized arithmetic, algebraic equalities, algebraic inequalities, primary education.