Conceptualisations of infinity by primary pre-service teachers

Elizabeth Date-Huxtable*, Michael Cavanagh, Carmel Coady, Michael Easey

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)

    Abstract

    As part of the Opening Real Science: Authentic Mathematics and Science Education for Australia project, an online mathematics learning module embedding conceptual thinking about infinity in science-based contexts, was designed and trialled with a cohort of 22 pre-service teachers during 1 week of intensive study. This research addressed the question: “How do pre-service teachers conceptualise infinity mathematically?” Participants argued the existence of infinity in a summative reflective task, using mathematical and empirical arguments that were coded according to five themes: definition, examples, application, philosophy and teaching; and 17 codes. Participants’ reflections were differentiated as to whether infinity was referred to as an abstract (A) or a real (R) concept or whether both (B) codes were used. Principal component analysis of the reflections, using frequency of codings, revealed that A and R codes occurred at different frequencies in three groups of reflections. Distinct methods of argument were associated with each group of reflections: mathematical numerical examples and empirical measurement comparisons characterised arguments for infinity as an abstract concept, geometric and empirical dynamic examples and belief statements characterised arguments for infinity as a real concept and empirical measurement and mathematical examples and belief statements characterised arguments for infinity as both an abstract and a real concept. An implication of the results is that connections between mathematical and empirical applications of infinity may assist pre-service teachers to contrast finite with infinite models of the world.

    Original languageEnglish
    Pages (from-to)545-567
    Number of pages23
    JournalMathematics Education Research Journal
    Volume30
    Issue number4
    DOIs
    Publication statusPublished - Dec 2018

    Keywords

    • infinity
    • mathematical conceptualisation
    • conceptual change
    • inquiry-based learning

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