The Encounter With the Concept Of Function

Abstract

The concept of function as commonly known through the Bourbaki definition (a correspondence between two sets which assigns every one of the elements in the first set to an element in the second set), plays a central and unifying role in mathematics. However most students do not generally associate function with this formal definition. Their images of the concept (e.g. Vinner, 1983) are varied and numerous. Most of the studies that examine these images do so in an Analysis / Calculus context (e.g. Dubinsky & Harel, 1992); in the Episodes that follow the focus is cross-topical and the students’ encounter with the concept is seen in a variety of contexts from Analysis, Linear Algebra and Group Theory.