Vad är en funktion?

Abstract

The concept of function represents a major part of mathematics and becomes more significant in school during high school. Throughout history, it has been a difficult concept to define and may create challenges for contemporary students. This literature study aims to identify students' difficulties with the concept of function, as well as to account for how the definition of a function has evolved historically. The literature study has been conducted through database searches in ERIC, Education Research Complete and MathSciNet via EBSCOhost, as well as through chain searching. The study results in identifying that students' difficulties with the concept of function primarily include the graphical and algebraic forms of representation. The identified difficulties can be categorized according to conceptual understanding, students' mental images, graphical representation and specific mathematical difficulties related to constant functions, split domain and one-valuedness. One reason for the difficulties is discussed to be that calculation processes dominates over concept learning in the classroom. A consequence is that students lose interest in the subject. The results of this study are partly evaluated through the formulation of questions the studies are based on, aiming to promote students' competence, and partly through reliability when multiple sources reinforce each other. The historical development of the concept of function has, over several thousand years, resulted in a general and standardized definition, where historical milestones such as variable relation and differential calculus have been significant discoveries. It can be confirmed that the concept of function is abstract and can present various types of difficulties for students in their mathematical understanding. This can be related to the definition of function from a historical perspective, as the concept has been difficult to define throughout history.