Strategies and representations used by early childhood education students in a functional thinking task: A case study

Abstract

This article presents a study that addressed the functional relationships that two early childhood education students (five-six years old) evidenced, as well as the representations they used when solving a functional thinking task. The proposed task involved the function f(x)=2x, with six questions on particular cases and one on generalization. The data was collected through a semi-structured interview to each of the students and a qualitative analysis of their answers was carried out in each of the questions of the task. The results suggest that the two students are capable of approaching the proposed task through different strategies, such as additive and multiplicative correspondence relationship, and covariation. Also, it was found that they use systems of varied representations, being the verbal representation to express the generalization of the functional relationship one that stands out. It is concluded that early childhood education students may be able to tackle tasks that involve algebraic notions that focus on functional thinking.