Revealing the structure of argumentation: a case of gifted students’ proof on circle’s area

This study investigates how gifted students construct arguments while proving the formula for the area of a circle, using Toulmin’s Argumentation Model as its analytical framework. Participants were 12 gifted fifth-grade students at a Science and Arts Center. Classroom interactions were analyzed in terms of claims, data, warrants, backings, and rebuttals to understand how students reasoned, dealt with misconceptions, and drew on creative strategies. The results show that the students were particularly skilled at connecting abstract ideas with concrete representations, relying heavily on visualization and analogies. Backings and rebuttals, however, appeared less often in their arguments, suggesting a need for more explicit instruction in these areas. A common misconception, confusing circumference with area, was resolved through guided questioning and peer discussion, underlining the importance of teacher scaffolding. The study recommends argumentation-based activities, targeted scaffolding, and interdisciplinary approaches in teaching proof to gifted learners. Future research could examine their long-term effects.