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Objectifying early-number : a visual nomenclature to express mathematical domain knowledge

Nutchey, David J. (2010) Objectifying early-number : a visual nomenclature to express mathematical domain knowledge. In First International Conference of STEM in Education, 26th - 27th November 2010 , Queensland University of Technology, Brisbane, QLD. (Unpublished)

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Abstract

To address issues of divisive ideologies in the Mathematics Education community and to subsequently advance educational practice, an alternative theoretical framework and operational model is proposed which represents a consilience of constructivist learning theories whilst acknowledging the objective but improvable nature of domain knowledge. Based upon Popper’s three-world model of knowledge, the proposed theory supports the differentiation and explicit modelling of both shared domain knowledge and idiosyncratic personal understanding using a visual nomenclature. The visual nomenclature embodies Piaget’s notion of reflective abstraction and so may support an individual’s experience-based transformation of personal understanding with regards to shared domain knowledge. Using the operational model and visual nomenclature, seminal literature regarding early-number counting and addition was analysed and described. Exemplars of the resultant visual artefacts demonstrate the proposed theory’s viability as a tool with which to characterise the reflective abstraction-based organisation of a domain’s shared knowledge. Utilising such a description of knowledge, future research needs to consider the refinement of the operational model and visual nomenclature to include the analysis, description and scaffolded transformation of personal understanding. A detailed model of knowledge and understanding may then underpin the future development of educational software tools such as computer-mediated teaching and learning environments.

Impact and interest:

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ID Code: 46610
Item Type: Conference Paper
Keywords: knowledge, modelling, early number
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 2010 David Nutchey
Deposited On: 26 Oct 2011 08:21
Last Modified: 27 Mar 2013 02:05

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