BASIC FUNCTION IDEAS:

evolution and pedagogical implications

Abstract

This study is an excerpt of a work from a master's thesis, which was carried out, at the time, from investigations that supported the theme Function.  The problem that sustains it is linked to the understanding of this concept (Function) by elementary school students. We thought it pertinent, at the time, to investigate how the student deals with activities that contain the basic ideas of Function, so that the possibility of carrying out a project that favors the construction of his concept is verified. Currently, we follow-up on this topic in our PhD research, and now we are narrowing our interest in relation to the idea of generalization. It seems convenient, therefore, to present our notes from the past, since we resort to these ideas frequently. We use these points in our current research, now more focused on the aspects of regularity and generalization. Thus, the objective of this work was to perform a historical study about the basic ideas that make up the concept of Function. We also deal with the appropriate pedagogical implications that involve teaching and learning of this concept. For this, we made a bibliographic review from files available in the scientific literature. The analysis shows, in addition to the results of some researches dealing with the theme, that the evolution of the concept of Function was slow and that its records go back from Antiquity to the 20th century.