Conceptualisations of infinity by primary pre-service teachers

Journal article


Date-Huxtable, Elizabeth, Cavanagh, Michael, Coady, Carmel and Easey, Michael. (2018). Conceptualisations of infinity by primary pre-service teachers. Mathematics Education Research Journal. 30(4), pp. 545 - 567. https://doi.org/10.1007/s13394-018-0243-9
AuthorsDate-Huxtable, Elizabeth, Cavanagh, Michael, Coady, Carmel and Easey, Michael
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.

KeywordsInfinity; Mathematical conceptualisation; Conceptual change; Inquiry-based learning
Year2018
JournalMathematics Education Research Journal
Journal citation30 (4), pp. 545 - 567
PublisherSpringer International Publishing
ISSN1033-2170
Digital Object Identifier (DOI)https://doi.org/10.1007/s13394-018-0243-9
Scopus EID2-s2.0-85056104080
Open accessOpen access
Page range545 - 567
Research GroupSchool of Education
Publisher's version
Place of publicationNetherlands
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https://acuresearchbank.acu.edu.au/item/8v48q/conceptualisations-of-infinity-by-primary-pre-service-teachers

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