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A Popperian consilience : modelling mathematical knowledge and understanding

Nutchey, David J. (2011) A Popperian consilience : modelling mathematical knowledge and understanding. In Clark, Julie, Kissane, Barry, Mousley, Judith, Spencer, Toby, & Thornton, Steve (Eds.) Mathematics : Traditions and [New] Practices (Proceedings of the 34th annual conference of the Mathematics Education Research Group of Australasia), MERGA, Alice Springs, NT.

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Abstract

Goldin (2003) and McDonald, Yanchar, and Osguthorpe (2005) have called for mathematics learning theory that reconciles the chasm between ideologies, and which may advance mathematics teaching and learning practice. This paper discusses the theoretical underpinnings of a recently completed PhD study that draws upon Popper’s (1978) three-world model of knowledge as a lens through which to reconsider a variety of learning theories, including Piaget’s reflective abstraction. Based upon this consideration of theories, an alternative theoretical framework and complementary operational model was synthesised, the viability of which was demonstrated by its use to analyse the domain of early-number counting, addition and subtraction.

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64 since deposited on 25 Oct 2011
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ID Code: 46614
Item Type: Conference Paper
Additional URLs:
Keywords: Mathematics, Early-number, Knowledge, Modelling
Subjects: Australian and New Zealand Standard Research Classification > EDUCATION (130000) > CURRICULUM AND PEDAGOGY (130200) > Mathematics and Numeracy Curriculum and Pedagogy (130208)
Divisions: Current > Schools > School of Curriculum
Current > QUT Faculties and Divisions > Faculty of Education
Copyright Owner: Copyright 2011 [please consult the author]
Deposited On: 26 Oct 2011 08:11
Last Modified: 25 Mar 2013 23:04

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