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Mathematics Education Research Journal

, Volume 30, Issue 4, pp 545–567 | Cite as

Conceptualisations of infinity by primary pre-service teachers

  • Elizabeth Date-Huxtable
  • Michael Cavanagh
  • Carmel Coady
  • Michael Easey
Original Article
First Online:

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.

Keywords

Infinity Mathematical conceptualisation Conceptual change Inquiry-based learning 
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Notes

Acknowledgements

Support for this project has been provided by the Australian Government Department of Education and Training for Opening Real Science: Authentic Mathematics and Science Education for Australia (ORS), part of Enhancing the Training of Mathematics and Science Teachers (ETMST) (2013–2017). The views expressed in this publication do not necessarily reflect the views of the Australian Government Department of Education and Training. This paper was improved by the pedagogical advice of Katherine Stewart, statistical advice of Russell Thompson, and editorial advice of Leanne Rylands, Joanne Mulligan, and anonymous reviewers.

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Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2018

Authors and Affiliations

  1. 1.School of Computing, Engineering and MathematicsWestern Sydney UniversitySydneyAustralia
  2. 2.CardiffAustralia
  3. 3.Department of Educational StudiesMacquarie UniversitySydneyAustralia
  4. 4.School of EducationAustralian Catholic UniversityBrisbaneAustralia

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