Relatively few students attempted t

Relatively few students attempted to present a formal definition of an inverse function in response to either I(a) or S1, despite the fact the concept had been formally defined with both Irish and Swedish students. Vinner and Dreyfus (1989) spoke of a compartmentalisation of students’ concept definitions of function and their function concept images, and it would appear that there was also a divide for the students in this study between their definitions of inverses and their inverse concept images. Vinner and Dreyfus (1989) suggested that a student does not necessarily use the definition of a mathematical concept when deciding whether a given mathematical object is an example of the concept or not. Instead, in most cases, he or she decides on the basis of a concept image and, hence, the set of mathematical objects considered by the student to be examples of the concept is not necessarily the same as the set of objects determined by the definition. Taking this perspective and acknowledging the number of stu-dents having a reflection component to their concept image, it is perhaps no longer surprising that there were so many incorrect responses to I(b).