Students’ conceptualisations of function revealed through definitions and examples

ABSTRACT

This study aims to explore the conceptualisations of function that some students express when they are responding to fictitious students’ statements about functions. We also asked them what is meant by “function” and many voluntarily used examples in their responses. The task was developed in collaboration with teachers from two curriculum systems, England and Israel. It was given to 10 high-achieving English students from each of the years 10–13 and to 10 high-achieving Israeli students from comparable years (total of 80 students). Data analysis included identifying students’ dominant ideas for functions as expressed in their responses, and analysing the types of examples that students used to explain their responses. Differences found between the samples from the countries led to conjectures about the influence of curriculum and teaching, and in particular, about the role of word, in this case “function”, in concept image development. Whereas most students showed that they had a meaning for the word, those students whose relevant experience of earlier concepts had been organised around the word “function” generally showed stronger understanding of function as object.

KEYWORDS:

• Functions
• conceptualisations of function
• example spaces
• curriculum

Disclosure Statement

No potential conflict of interest was reported by the authors.

Notes

1. A more recent revision of the English curriculum is described in groups of years: years 7 to 9, years 10 to 11, and years 12 to 13. Content and order of relevant concepts has not changed significantly from what is described in this article.