Resumo

AVILA, Alicia  e  GARCIA, Silvia. Ratios of area to perimeter: from initial intuition to operative deduction. A study in children with high academic performance. Perfiles educativos [online]. 2020, vol.42, n.167, pp.31-52.  Epub 30-Abr-2020. ISSN 0185-2698.  https://doi.org/10.22201/iisue.24486167e.2019.167.58890.

This article is the product of an investigation which sought to analyze the initial intuitions of children ages 9 to 12 regarding ratios of area to perimeter and the process whereby they abandon such intuitions. The study was conducted with 12 children with high scholastic performance in mathematics, who, at the time of the investigation, were in the fourth, fifth, and sixth years of elementary school. We analyze their initial intuitions on area-perimeter ratios and their evolution toward operative deduction based on solving six problems involving them and discussion of the solutions reached. With the aid of critical questioning rooted in psychogenetic theory, we also identify the mathematical resources the children used in that process. The study concludes that working on these ratios with a geometric approach has great potential to develop mathematical thinking in children.

Palavras-chave : Area-perimeter ratios; Children; High performance; Intuition; Mathematical thinking; Operative deduction.