The definition of function: operationalize to articulate and articulate to understand

Abstract

To understand a mathematical concept it is needed to knowing to articulate the multiple representations of these concept. Articulate the representations of the concept of function it is not just about knowing how to identify if a table, diagram or graphics represents a function, imply to building a semantic knowledge of the concept. We believe that the articulation between various representations could be managed by the definition of function that learners would adopt. Not any definition, but one that be used and reach all representations, what we call operationalization of the definition of function. In this paper, our aim is to reflect about how to favoring the operationalization of the definition of function by learners. For this, we made a bibliographical survey focusing on the analysis of the historical-epistemological development of the concept of function, and a discussion on the multiple representations of this concept. We conclude by presenting three categories that we believe would favor the operationalization of the definition of function and that could be object of study in future projects.