Abstract:

The growing interest in making the development of algebraic reasoning a reality from the early years of schooling keeps research on early algebra an ongoing concern in mathematics education. Several authors argue that the development of early algebraic thinking should focus on articulating arithmetic and algebra as a meta-discipline that seeks a unifying language between the two. They emphasize the importance of working on the structures of arithmetic operations and on relations of equivalence and order in the early educational stages.

These researchers acknowledge the role of conjecture and justification in the development of algebraic reasoning, particularly of relational thinking, highlighting the importance of verbalization in fostering students’ ability to reflect on their own algebraic practices. Studies that have specifically analyzed the role of justification in the development of early algebraic reasoning show its potential to identify how primary school students progress, think, and express themselves when addressing tasks involving generalized arithmetic or equations, as well as their relational or analytical thinking.

In our research, we conducted an experience with sixth-grade primary students (ages 11–12) with no prior instruction in early algebra. The students were asked to justify the truth of arithmetic identities, decide when identities involving literal symbols (as unknowns or generalized numbers) are true, and to invent algebraic identities with different ranges of validity (never, sometimes, always).

The results show the students’ ability to justify the truth of both arithmetic and algebraic identities and highlight the importance of using examples in their reasoning practices. Greater difficulty was observed in creating identities compared to justifying previously given statements.

Keywords:

Algebraic reasoning, conjecture, justification, primary education.