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

Karina J. Wilkie, Michal Ayalon

    Research output: Contribution to journalArticleResearchpeer-review

    7 Citations (Scopus)


    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
    Publication statusPublished - Dec 2018


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

    Cite this