Direct and Inverse Functions in Pre-school: A Case Study with a 4 Year-Old

This paper is part of a broader research initiative examining algebraic thinking. It presents a case study involving a 4 year-old female student, examining her functional perspective through individual work. Our interest lies in early childhood functional thinking. Specifically, our research objective is to describe how the child completed two tasks involving linear functions and their respective inverse functions. We posed questions related to specific near numbers, specific far numbers, and the generalizations themselves. We gathered data from her individual written work on the two tasks and from an individual interview. We analyzed the strategies she employed to generalize, the representations and generalizations she made, and how she established relationships between variables. We observed that she used pictorial and verbal representations to complete the proposed tasks and successfully achieved generalization. As a strategy, she counted drawings; however, when verbalizing her approach, she created groups of similar elements and innately distributed them into equal groups when working with the inverse function.