Students’ conceptualisations of function revealed through definitions and examples

Michal Ayalon, Anne Watson, Steve Lerman

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalResearch in Mathematics Education
Issue number1
StatePublished - 2 Jan 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017 British Society for Research into Learning Mathematics.


  • Functions
  • conceptualisations of function
  • curriculum
  • example spaces

ASJC Scopus subject areas

  • Education
  • General Mathematics


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