Mathematically gifted students quickly grasp new mathematical content, exhibit more complex mathematical reasoning traits, and employ more innovative and efficient problem-solving strategies than average students of the same age or grade. These students ask questions that go beyond the scope of typical mathematical tasks, think critically, and successfully establish connections and build mathematical structures. Therefore, rather than simply advancing mathematically gifted students to higher-grade courses to meet their needs, another approach is to provide them with challenging tasks that stimulate their talent. In this regard, recent research recognizes algebraic tasks as an opportunity to deepen the identification and enhancement of characteristics associated with mathematical talent, particularly through generalization, exploration, relationship representation, and justification. However, the focus on developing algebraic reasoning is not limited to supporting mathematically gifted students; its general importance at an early age is widely acknowledged within the mathematics education research community.

In this study, we compare, through a case study, the problem-solving strategies and algebraic reasoning (in terms of generalization, analytical calculation, and representation) demonstrated by a group of fifth-grade students and by a third-grade student identified as highly capable, as they solved a problem involving the study of equations.

Keywords: Algebraic reasoning, Mathematical talent, primary education.