Investigating Years 7 to 12 students’ knowledge of linear relationships through different contexts and representations

Karina J. Wilkie, Michal Ayalon

Research output: Contribution to journalArticlepeer-review


A foundational component of developing algebraic thinking for meaningful calculus learning is the idea of “function” that focuses on the relationship between varying quantities. Students have demonstrated widespread difficulties in learning calculus, particularly interpreting and modeling dynamic events, when they have a poor understanding of relationships between variables. Yet, there are differing views on how to develop students’ functional thinking over time. In the Australian curriculum context, linear relationships are introduced to lower secondary students with content that reflects a hybrid of traditional and reform algebra pedagogy. This article discusses an investigation into Australian secondary students’ understanding of linear functional relationships from Years 7 to 12 (approximately 12 to 18 years old; n = 215) in their approaches to three tasks (finding rate of change, pattern generalisation and interpretation of gradient) involving four different representations (table, geometric growing pattern, equation and graph). From the findings, it appears that these students’ knowledge of linear functions remains context-specific rather than becoming connected over time.

Original languageEnglish
Pages (from-to)499-523
Number of pages25
JournalMathematics Education Research Journal
Issue number4
StatePublished - 1 Dec 2018

Bibliographical note

Publisher Copyright:
© 2018, Mathematics Education Research Group of Australasia, Inc.


  • Algebra
  • Correspondence
  • Covariation
  • Functional thinking
  • Linear functions
  • Secondary mathematics

ASJC Scopus subject areas

  • General Mathematics
  • Education


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