Exploring secondary students’ conceptualization of functions in three curriculum contexts

Michal Ayalon, Karina J. Wilkie

Research output: Contribution to journalArticlepeer-review


An important goal in school mathematics is for students to develop a comprehensive and multi-faceted conceptualization of function. Yet studies have found that undergraduate students often hold limited concept images for function. This study investigated 240 middle and upper secondary (15- to 18-year-old) students’ conceptualizations of function at different year levels (Years 9 to 12) to consider their conceptualizations relative to certain prior learning, as theorized by an epistemological model for concept development in mathematics. In this article we draw on data from students and their teachers in three Western national curriculum contexts (Israeli, English, and Australian) to explore possible relationships among students’ exposure to the word ‘function’, familiarity with different examples of functions, and their conceptualizations of function. Eighty high-achieving students from each context, 20 per year level, were prompted to respond to several fictitious students’ views on what a function is, and then to provide their own definition. The students’ responses were analyzed for evidence of a dominant meaning and any contributing ideas, as well as the use of any specific examples or non-examples of function to illustrate or clarify their views. Twenty teachers also participated in the study. Analysis of curriculum content and the teachers’ perspectives on their students led to our search for possible reasons for similarities and differences found among the responses.

Original languageEnglish
Article number100718
JournalJournal of Mathematical Behavior
StatePublished - Dec 2019

Bibliographical note

Publisher Copyright:
© 2019 Elsevier Inc.


  • Curriculum
  • Function
  • Pedagogical approaches
  • Secondary mathematics
  • Students’ conceptualization of functions

ASJC Scopus subject areas

  • Education
  • Applied Mathematics
  • Mathematics (miscellaneous)


Dive into the research topics of 'Exploring secondary students’ conceptualization of functions in three curriculum contexts'. Together they form a unique fingerprint.

Cite this