Structures and generalisation in a functional approach: the inverse function by fifth graders

Resumen

Against the backdrop of functional thinking to early algebra, this paper discusses an initial study of how 24 fifth year elementary school students (10 to 11 years old) perceived the inverse function. This notion has been scarcely tackled in the context of early algebra and, particularly, within the functional thinking approach. Based on structure and generalisation notions, we analysed the responses of a group of 24 students when solving a problem, which contains questions involving the direct and inverse forms of a problem involving a linear function. Ten of the 24 students were observed to establish structures involving inverse function and five to generalise that form of the function.