An Analysis of Students’ Abstraction and Use of Representations for Understanding the Operational Formal Definition of Function in Introductory Calculus

Abstract

Function is a very prominent concept in introductory calculus courses studied in mathematics education undergraduate programs. This study was conducted to investigate first year students’ construction of an understanding of the operational formal definition of function focusing on the theoretical abstraction and the use of mathematical representations in abstraction. The findings revealed that the students constructed their understanding through the process of abstraction and they used various representations in expressing their mathematical knowledge.